This headline probability - the only thing most people care about - is fine. Whether Democrats are favorites or underdogs with two months left isn't worth quibbling over. The problem with their forecast is the same one Nate Silver and the Silver-copycats had: indefensibly wide “CYA” tails.

Whether or not it's technically mathematically possible for Democrats to get to 58 seats (D+16 in this chart) …also not worth the quibble. Here's the beginning of the problem:

As a reader of mine, I know I don't have to reiterate it too much, but I need to for my own sanity - do you understand how large of a probability 1.64% is? It is, roughly, 1/60.

It gets worse. If you sum “Dems 58 seats, Dems 57 seats…Dems 55 seats” (that is, Dems hold 55-58 seats) the DDHQ probability of this is greater than 10%.

Exactly 55 seats is given a 1/20 chance, and more than 55 seats also a 1/20 chance - for a combined probability of 10%, or 1/10. Then, on the other end of the bell curve, Republicans are given about a 1/12 chance of doing the same.

What this means in terms of “real seats”

For Democrats to get to 55 seats, they would need to hold all seats they're defending, and flip North Carolina, Alaska, Iowa, Maine, Ohio and Texas

…And, presumably, Kansas and Missouri? Maybe some other state?

For Republicans to do the same would require them to overcome extreme unpopularity nationwide, and would probably require they knock out some highly popular candidates (e.g. Cooper in NC, Ossoff in GA). Unlikely.

But again, I'll be clear: the probability of this is not zero. 2% and 10% are both very fairly called “unlikely” but in my world - and proper math - those are different universes.

Probability in elections is not like probability in coinflips: states are independent in name only. Voting patterns are very highly connected, such that if something unlikely happens (e.g. Dems flip Missouri) the probability of them also having flipped Ohio goes from “toss up” to “extremely high.”

And I'm not ashamed to admit, was a major contributor to my improved modeling of this phenomenon.

It is NOT understanding the relatively basic fact that states are correlated that caused and others to infamously give Clinton indefensibly high win probabilities in 2016.

Oh god, it gets worse again

If you sum all the probabilities of each specific outcome in the DDHQ forecast…

You get 95%.

That means that their forecast says that there's a 1/20 chance that the actual outcome is not even pictured!

Republicans flip Virginia, Colorado, New Jersey? Sure!

Democrats flip Arkansas, Kentucky, Louisiana? That is also possible!

And not like…decimal percentages, either

To be fair, they don't really “hide” their full forecast, and I suspect I know what's going on here. Most political forecasts are built on junk science, and all forecasts require making some assumptions. But what I suspect doesn't matter - what matters is what their forecast shows, and not all assumptions are created equal. When they give these extreme-outlier events such high probabilities, resulting in the astrapia tails, they are necessarily underconfident in more likely outcomes.

Let me explain why that's a problem, with a simpler example:

Assume you will flip a fair coin 20 times. Calculate the range of possible outcomes.

Let's just say myself and DDHQ are tasked with this. We might agree, for example, that heads and tails have an equal probability of “winning.” But that's trivial. If I say there's about a 95% chance there will be between 6-14 heads, and they say there's a 95% chance there will be between 3-17, the “win probability” is not the only relevant question to what makes a good forecast.

The calculation for the probability of “exactly 10 heads” being accurate depends on the probability of “exactly 5 heads…exactly 2 heads…and so on…” being correct.

In other words, if I overestimate the probability of flipping heads exactly 5 times, that necessarily leads me to overestimating 4 times, 3 times - which leads to drastically underestimating the probability of far more likely outcomes.

What Makes A Good Forecast?

In statistics, there are different ways to measure forecast quality. The two best in my experience are calibration (relatively basic) and Brier score (more comprehensive). Both have strengths and weaknesses, but for a testable measure of “good forecast” either function just fine.

• Calibration: given a sufficient sample size, how often do the model's estimated probabilities happen?

  • If you have 100 events with probability ~90%, if they happened about 90/100 times, your model is well-calibrated. If they happen much more (say, 99%) or much less (say, 75%) it is not.

  • Note that for a forecast to be well-calibrated, it must - about 10% of the time - assign a probability of 90% to an event that doesn't happen.

• Brier Score: a mathematical formula that punishes overconfidence and underconfidence. Saying an event is 99% to happen - if it doesn't - gets a far worse score than one that says it was only 95%.

Both of these formulas require a large sample size to “play out”…and political forecasts are simply too rare, and too highly correlated, to ever get any reasonable sample size. Knowing this, combined with how forecasters are judged by how accurate their “calls” are - even though there is literally no such thing - there's a huge incentive to be risk averse: even if you're 99% certain, there's a 1% chance you're wrong. Call it 95%, or 92%, and the average consumer knows no different.

This isn't just a hypothesis. FiveThirtyEight’s own calibration scores - which they promoted because they think they're good, I guess - show extreme underconfidence on the edges.

A similar phenomenon exists in prediction markets.

That many political models use these “astrapia” tails, CYA tails, or whatever you want to call them, is not a new discovery. Though it turns out Silver's model almost certainly uses a “fudge factor” as I discovered when I found his data erroneously stated Hillary Clinton lost Maine by 3 (implying his calculation of 2016’s poll error there was 9 points) when she actually won Maine by 3 (thus it was only 3 points).

This article goes into more depth on his (and other) models.

Serious analysts are risk averse, while unserious analysts are risk-seeking, usually for attention. People like - who had no “model” but made very confident guesses for clicks - seems to have accomplished his goal of being loudly wrong but gaining followers who liked the confirmation bias.

And that's the state of the forecasting world today.

The average consumer is incapable of distinguishing between genuine, measured uncertainty (which every honest analyst has) and hedging via wide tails, and indefensible confidence like Wang and Bouzy had. Add in the confirmation bias - we tend to favor forecasters who say things we want to be true - and it's an unhealthy ecosystem.

As a scientist - and fighter of misinformation - the problem is even bigger than that. Imagine a world where the appropriate probability is 50/50, but one of these attention-seekers makes a guarantee, and they're right. There's a ton of value in that - whether you have something to sell, or just like the attention. Your work gets promoted more, and next election you get promoted again for “getting it right.” Now imagine it happens twice in a row. Or, as it happens for me, 14 times in a row. If someone is not a serious analyst - e.g. are more closer to “influencer” than “statistician” the downside of being indefensibly certain is much lower: you laugh it off, or simply block people who dare bring it up.

If you found this article insightful, helpful, or want to read more, check out this older post on a similar subject, with more detail.

And yes, my forecasts are coming soon too.

This problem is not new.

The “up by” or “spread” form of analysis stems from the fact that people in this field believe - literally - that “if polls are accurate” the margin from the poll will equal the margin from the election. And that's wrong. Not just “wrong” in the technical, semantic sense (as if that wouldn't be worth correcting)…but wrong in the absolute, logical and scientific sense.

Polls are not predictions.

Because I also wrote a book - and I know how much effort, criticism, and revision goes into it - I'm not particularly inclined to forgive commentary like this from as harmless or inconsequential.

Nor am I willing to grant that he understands polls are not predictions while…well you can read.

Here's the simplest - though perfectly real - example I can offer as to why this is wrong, and why it matters. Given a poll (or poll average) of

• Candidate A: 46%

• Candidate B: 44%

• Undecided 10%

And an election result of:

• Candidate A: 49%

• Candidate B: 51%

The consensus of experts and analysts around the world would agree: POLLS WERE WRONG.

Polls said “up by 2” but they “lost by 2” so there was a FOUR POINT ERROR.

Is that right?

Even assuming that no one changed their mind from Candidate A to Candidate B (you'd be shocked how often this happens: and it happens much more often in primaries) let's look at the sometimes larger factor: undecideds.

10% isn't exceptionally high or low for polls taken close to the election. But notice what major assumption the “four point error” claim encodes:

It assumes they split evenly.

Probability nerds like me could ramble about conditional versus unconditional probability, bore you with covariance calculations, but it's kind of funny - the basic of this problem is much simpler than that.

• “We don't know how undecideds voted”

And

• “We can assume they split 50/50”

Are not the same. The first is correct; the second is a guess.

It's quite easy to teach, at the most fundamental level:

Is it possible that undecideds don't split evenly?

If the answer is yes, then you agree with me: calculations that operationalize the “50/50 split” assumption are - AT BEST - imprecise.

Now, let's assume that we do some research after the election, and discover that 2/3 of undecideds went to Candidate B. That might feel like a lot…but it happens all the time. Sometimes predictably, sometimes unpredictably. But to quote myself:

Looking back at the 46-44 poll, with 10% undecided, if two-thirds of undecideds opted for Candidate B (6.67%), then suddenly…

That election result almost perfectly matches the poll.

Now consider what has happened:

A pollster who perfectly measured the population at the time they took the poll is derided as WRONG because Undecideds resolved in a way analysts assumed they wouldn't. Sound problematic?

It gets worse.

Now assume - due to bias, luck, or random chance - that some pollster or poll aggregator had reported:

• Candidate A: 44%

• Candidate B: 46%

Despite having some error regarding the pre-election population they were trying to measure - much more than the other - the Analyst Undecided Assumption (though wrong) made this poll seem very accurate.

The consensus of experts in the field would say that this pollster is better (or, at minimum, their poll had less error) - even if we have data to show they were less accurate. Wild, huh?

Without getting into the second and third order impacts of this (e.g. pollsters fudging data in the hopes of getting the “spread” right) - the fundamental problem is this:

If we reward polls for predicting the election rather than measuring the pre-election population, we create a system where being wrong in the right direction can be indistinguishable from being right.

Now consider that otherwise reputable forecasters give pollsters “additional weight” by this exact logic!

It's ironic, really, that ALMOST every expert I've spoken with claims to understand that “polls are not predictions…polls are snapshots” and then turn right around and do math that literally assumes that polls, if accurate, will predict the election outcome.

One such recent interaction: this person expressed both disbelief and disdain that I would assert experts don't understand something as “simple” as “polls are not predictions” and then…in the very next sentence…did a calculation that makes that exact mistake!

A Slightly Technical Version

Undecided voters are not a random subset of “all voters” nor is that an acceptable assumption. Even if it were an acceptable assumption (being very generous now) it still violates dicto simpliciter to say “this is true in general, therefore this will hold true in every case” - which is how poll error is currently calculated.

On a very introductory level, consider how the following might be different:

• Elections including well-known, multi-term incumbents

• Elections with a very high (or very low) percentage of undecided voters

• Elections with viable third-party candidates

• Midterms vs General vs Others

• Elections in states with very high percentages of R or D voters, vs others

• Primaries (where ideologies are similar) vs. Others (less so)

• Statewide vs District

• And much more

All of these variables can…vary…from election to election. Remember, the 50/50 undecided assumption is not based on any established data or scientific basis. It is, literally, a tradition - as evidenced by the fact that different countries make different assumptions.

(While “spread” analysts assume undecideds split evenly, “proportion” analysts assume they split proportionally to decided ones. Read this next if you want to learn more.)

What This Means For “Average Joe”

It means:

We can't make hasty, unverified assumptions that translate how much someone is “up by” into how likely they are to win.

It's silly, but I've researched this topic for years, and while “Polls Are Not Predictions” is accurate…what that means is sometimes lost. That sentence is probably the best single sentence I can offer. Put another way:

We cannot attempt to translate how much someone is “up by” into how likely they are to win - or how much they'll win by - because it encodes many hidden assumptions that are not derived from poll data - or any data.

A list of common, wrong interpretations

• “This person is ahead, therefore if the poll(s) is accurate, they will win.”

No.

• “This person is ahead, therefore they are favored.”

Also no.

• “If the polls are accurate this is what the map would look like.”

Dear Jesus take me now. That's the absolute worst.

I know it's frustrating, given the real-world impact of all these events, to not be able to know with some level of certainty what will happen. And I'm sorry. But your options are either to let respectable analysts honestly give you a probability, which requires uncertainty - or live in a black-and-white world where probability isn't real, undecideds always split 50/50, and giving someone a 68% chance to win is the same as saying they will win.

I don't begrudge people for favoring a world that is simpler, less stressful, with more hopium. I just encourage people who want to and are capable to understand what is and isn't scientific.

A Recent Example

At the risk of alienating my anti-MAGA friends, this one sticks with me, because it's from my home state of Ohio, and features a name you might recognize.

Then a lowly Senate candidate, JD Vance wasn't even that popular in the Ohio Republican Primary - securing less than one-third of the vote.

His Democratic opponent, Tim Ryan, was far better known and had enough crossover appeal to make Ohio competitive in a state Trump had won 53-45 just two years earlier.

Polls well into September - totally not to draw any comparisons to upcoming midterms - showed Ryan ahead!

You'll note that this is far from cherry-picked: Ryan was “ahead by” even more in August!

But whether he was “up by” 6 or 1.7, any hasty translation of that real position to “he's favored” misses some very important data.

Again, those polled as undecided are not necessarily (ever) random subsets of the voting population, nor are they total unknowns. We have demographics, we have party registration, we have past voting behavior - and sometimes more!

Does that mean we know how they'll vote? No. We don't even know if they'll vote! The same can be said of people who declare support for one candidate, the other, or a third party.

But it does allow savvy analysts - those who do proper science - to say “it's unlikely they split evenly” for example - and calculate a range of plausible and likely outcomes.

For Ohio in 2022, my forecast and other decent ones agreed that Vance was favored. Not just towards the end, after he took a “lead” in the polls - long before, including August and September. How could that be? Ryan was ahead!

Well, because of the state’s partisanship, plus the demographics of the people who were undecided, the most likely outcome was that many of them “come home” and vote Republican. That's…almost exactly what happened.

It is this logic - polls showed Ryan “up by 2” in September, but then he “lost by 6” that causes analysts like to say things like “polls overestimate Democrats early.”

This, again, imposes the unscientific and disproven assumption that undecideds split evenly.

A Rule of Thumb, If You Insist

In elections with high two-party dominance (the top two candidates are likely to combine for nearly 100% of the vote):

Poll averages that show a candidate consistently over, at, or near 50% are far better indicators of their strength than a larger “lead” far from 50%. Yes, 49-46 is better than 46-40. I checked.

There are no electoral bonuses for winning by 10 (which 46-40 is more likely to do, even though they are less likely to win overall). This is the disconnect between what the data means, and what it feels like it means. This is a very good article on why that “sports” mindset of “lead” is misapplied.

Undecideds add uncertainty. Elections with lots of candidates, especially primaries and non-US elections where candidates overlap in their beliefs, have higher uncertainty. Because the field’s de facto standard has poisoned our minds, people find the idea that undecideds may split 80-20 to be implausible, or that people can defect from one candidate to another very close to the election - despite the fact that it happens quite often. There are even very well-understood mathematical phenomena to explain why: the smaller the subgroup, the greater the sampling variance. And undecided voters may share characteristics that make their eventual decisions correlated with one another. Their uncertainty may not be independent or randomly distributed: the covariance structure among people who identify as undecided may be quite different from -and potentially much stronger than - the covariance structure of the electorate as a whole.

In other words:

A poll that shows a relatively close race on the top line (say, 46-44) may have a bunch of disgruntled Democrats - or Republicans - hiding out in “undecided” because they don't like (or have never heard of) the candidate. Others may hint at their preference by declaring support for a left or right-leaning third-party - i.e. if they change their mind, they're not equally likely to vote D or R.

But a disgruntled/uninformed Democrat or Republican is (probably) far more likely to vote for the candidate they more closely align with - or not vote - than they are to vote for the opposition. This is one big reason why the 50-50 split is rarely defensible. These simple, testable facts violate how pre-election polls are currently analyzed for accuracy: either these statements are wrong, or the present standards are.

I'll leave you with this chart from the British Election Study, done in the aftermath of two highly contentious elections (2015 General, and Brexit) where polls were derided as wrong.

Does this look like no one changed their mind close to the election?

Does this look like undecideds split evenly, proportionally, or according to any set rule that will apply in the next election, or forever?

Or - perhaps - should we use data to inform our analysis of poll accuracy, instead of our assumptions?

Support my work and my sanity - and maybe even learn something - by buying my book, or just sharing this post.

I'm happily available for guest speaking, podcasts, presentations, etc.

So here's a very short, accurate explanation.

With Prediction Markets, there are exactly two possibilities:

1) The markets provide very accurate win probabilities such that winning or losing money is basically chance - pure gambling.

2) The markets are (at least) sometimes inefficient such that it is possible for savvy bettors to make money.

It should be clear, but both cannot logically be true.

• If prediction markets cannot be beaten in the long run (i.e. those who participate are just gambling) then they must provide extremely accurate probabilities.

• If prediction markets sometimes offer inaccurate probabilities, then it is possible for savvy bettors to make money in the long run.

That is it. There are no other options. So what's the problem?

Many people assert simultaneously that the markets are just another vehicle for degenerate gamblers (1) and also highlight times they believe that markets have had very poor prices (2). This requires both cherry-picking, and a poor understanding of probability.

Markets said she had a 96% chance of winning and then she lost! Markets was wrong!

As I said regarding the accuracy of pre-election polls:

Lesson 1: Uncertainty

All probabilities resolve to 0% or 100%: they either happen or they don't. But with real-world events, such as sporting events and political outcomes, it is impossible to know the outcome in advance unless you cheat.

What that means is, given all the data available - and models that incorporate any number of assumptions, inferences, and data - you will only ever arrive at a probability, you will never know the answer in advance. The more assumptions you have to make, the larger margin of error your model has.

For example, if you try to assign a probability to me making a free throw, your model’s margin of error (if it's any good) would be much wider than if you attempted to do the same for Steph Curry: there is simply much more data for him, fewer assumptions needed. Whether you “make a bet” on a given free throw outcome - mine or his - depends on:

• Your personal risk tolerance

• How you quantify entertainment value with your wager

• Your confidence in your calculated probability, and most importantly

• Your perceived edge, if any

And herein lies the major factors in prediction markets: information gap, risk tolerance, entertainment vs. profit-seeking, and model quality. Everyone has the same access to Steph Curry’s data, not mine. The only people who would bet meaningful sums of money are people who have some combination of sufficient information, risk tolerance, and belief the market is mispriced: it's an equilibrium problem.

The same can be said of political outcomes.

You might scoff at the prospect of betting on some random guy making a free throw, or who wins some political primary - fair. But as I noted in the beginning, I'm not talking about ethics or risk tolerance frameworks; I'm proposing an analogy to understand how accurate prediction markets are, and if it is possible to make money (without cheating/insider trading).

Whether you're considering the outcome of a coin flip, whether Steph Curry makes his next free throw, a player hits a home run, or who will win a given election - it is all just probability.

And in probability, how do we determine if a calculation or model is accurate?

1. If the probability is high, but the outcome doesn't happen, it was wrong.

2. Given a sufficient sample size of similar events (e.g. sports outcomes or political outcomes) find how often do the events at the time of resolution resolve to a given outcome, compared to the probability of that outcome in the markets at some time before the event.

Of course, our brains are wired for 1, that's how markets are often discussed - that's another layer to the problem. But the answer is 2.

The Answer

Find the probability of victory given by the prediction market x time before election day.

Compare that probability to other similar probabilities with some tolerance (say, +/- 2.5%).

How often do events of given a 2.5-7.5% probability resolve to “yes”? 47.5-52.5%? And so on. If the answer is “about as often as the markets say” then they are well-calibrated; if the answer is “not close” then they are not. The problem people have with this - which a very concise but accurate explanation of how probability works in science - is that events with a 5% probability, as a mental shortcut, are rounded to “almost impossible.” In reality, in accurate markets, these events will happen about 1/20 times - which given the number of elections, is quite often.

Here's what that might look like given weather forecasts:

My research with prediction markets is limited to 2024-present: before they were mostly legal, publicly available, and fee/limit structures made respectable, there were too many other variables to account for. As such, there is not yet nearly sufficient sample size to say with certainty that they're “pretty good” at calculating probability - but all available data points that way. There is too much money to be made (in relatively short periods of time) for them to move significantly and sustain that price on the whims of degenerate gamblers, or organized political influencers.

Political Markets are sometimes inefficient - but (usually) not for long.

The Nuance

Political outcomes are highly correlated within an election cycle. That is, if Democrats or Republicans outperform expectations in one state or district, they've likely done so in several nationwide. This covariance makes “calibration” scores from individual election cycles highly inappropriate: just because we have thousands of elections each cycle does not mean they can be scored independently. It’s not like sports, where teams combine to play hundreds or thousands of games in a season; in politics, candidates are on ballots at the same time, being voted on by the same people. For that reason, you can see outcomes in the “tossup” range in politics being far off “perfectly calibrated” - elections in the 40%-60% win probability are far more likely to be decided by just a few points, and a few points in the same direction across the country results in a win percentage very far from 50%. This is a statistical phenomenon created by the very narrow sample size, not a calibration issue.

That being said, to reiterate the point made in the beginning: this is testable. If over the next few election cycles the calibration doesn’t trend closer to efficient, there’s a case to be made that political markets are the exception to the prediction market rule. I don’t think there’s a strong case for this, though - my own research shows that political markets with higher volume (i.e. more incentive for winners) are already more calibrated than the cited data above suggests.

This is not to say we can or should expect them to be as highly efficient as weather, finance, or sports markets: those are very high sample size, high data, low assumption fields. Politics are, by their nature, very low sample size, and many election cycles produce unique problems - I believe that’s what attracts folks like myself. It’s a challenge that, if modeled well, has the potential to return a good amount of money.

Closing Thoughts

If you give me 10/1 odds that a verifiably fair coin flip will be heads, I’d happily wager a very large amount on it. I think most people would - even if our definitions of “large amount” differs. If you give me 2/1 odds, I’d also wager - but an edge of this size might not be sufficient to convince more risk averse people to bet. And none of these calculations of “edge” means the outcome will be favorable, there is only a 50% chance; it is, technically, gambling. But given enough opportunities with comparable advantages, it will be profitable in the long run.

What might be called “gambling” by some, more shrewd bettors view as “investing.” Gambling to investing is a wide spectrum. I doubt most people would consider an arbitrarily diverse portfolio of stocks and bonds to be gambling - though it technically fits, given risk of losses. Disciplined bettors view their bets - whether stocks, sports, crypto, gold, or political prediction markets - as a portfolio: a mix of calculated risks and safer moves, with the goal of long-term profits.

Whether such disciplined bettors comprise 0.001% or 1% of prediction markets, I don’t know for sure - though I’d guess the lower end, and be shocked if it were higher, given the numbers. But remember: prediction market odds are determined by money volume, not the number of unique bettors on each side. If “the public” or someone just betting for fun bets enough on one side to meaningfully move the odds, it only takes one “sharp” to come correct it.

Do some people use prediction markets strictly as a vehicle for entertainment, and/or pure gambling? Absolutely. But this is a commentary on human behavior, not the utility or accuracy of prediction markets.

There are plenty of legal, ethical, societal arguments to be made for and against prediction markets. But don’t conflate those valid beliefs with utility or accuracy.

My research - and book - on political data was driven out of a desire to educate, in a field that needs educators.

It’s been a few years. But I think I just made another breakthrough.

The Background

One of the biggest disconnects between what is true, and what people believe, is the relevance of how much someone is “up by” in a poll. It seems intuitive that being “ahead” by a larger number in a poll is better than being ahead by a smaller number.

Statistics give us the ability to test things we think are obviously true, and science demands that we test them. Recent history alone includes the Monty Hall Problem and Moneyball as counterintuitive problems about which the field's experts were wrong, and among my favorite historical examples is the Ptolemic Model of the Universe.

Put simply, I'm a firm believer in requiring evidence for our most fundamental assumptions. And it turns out, contrary to the field's accepted approach, bigger leads are not always better, and leads of the same size can yield drastically different win probabilities.

The short version is that it's better - as it relates to win probability - to have support at or near 50%, than a larger lead farther from it.

I'll also note, that this chart only includes highly polled statewide races. Spoiler alert - if you conduct the same research on House races (where undecideds are much higher) or on Primaries (where voters are far more likely to switch preferences) - the relationship is even more shocking.

Now, whether or not you already knew that, think it kind of makes sense, or would even go so far as declaring this phenomenon that as far as I know had never been submitted for peer review or formally considered until my book was published is “obvious” - I'm not going to press.

All that matters is that the data shows it. This is a hypothesis tested, and it is empirically, overwhelmingly true.

But the ability to revise one's beliefs in the face of data is notoriously rare. And if I just keep showing people what is true, without meeting them where they are and figuring out why it’s not enough for them to understand, I’m lecturing - not teaching.

The MARGIN!

I have long been aware that language influences how people think about science. The term “theory” having a scientific meaning different from its colloquial usage is famously frustrating for educators.

The margin of error - a statistical measure of sampling uncertainty - sounds like it's highly related to the margin. But margin is just a term that means “difference between two options.” We could just as easily use “difference” - or my preferred term - “spread” and avoid unnecessarily introducing one potential source of misunderstanding.

It happens that whatever term being used to describe the difference between the two candidates is more misleading than it is informative. Here's what I mean:

Candidate A 46%

Candidate B 39%

Undecided 15%

Margin of Error +/- 3%

In most cases, this poll is simplified to “up by 7.”

The lead is said to be outside the margin of error because the “margin” between the candidates is more than double the margin of error. That is, if it “overestimates” Candidate A by 3, and “underestimates” Candidate B by 3…A is still ahead. Outside the margin of error.

This is imprecise in itself, but becomes misinformation because of the existing malpractice of treating polls as predictions.

It is outside the margin of error relative to a Simultaneous Census - the appropriate target parameter for the poll data - not the election result, as is erroneously assumed.

To illustrate:

In an example like below where Candidate A very narrowly wins - or especially if they lose - commentators and otherwise legitimate analysts would declare that the polls missed or failed. When it’s entirely possible the poll wasn’t just within the margin of error - it was perfectly accurate.

Here, Candidate A was “up by 7” in the poll, but only won by 2, so the poll is said to have had a 5-point error. In reality, it is shown that two-thirds of undecideds favored Candidate B, which is extremely common in electoral history - yet polls are derided as wrong for not predicting the margin - despite in this case perfectly measuring the population at the time the poll was taken.

Bonafide, published researchers have used this exact, flawed logic to conclude many polls were “outside the margin of error.”

One more famous researcher - who frequently contradicts himself on pretty fundamental stuff - recently published this, in which he compares polls to elections to make non sequitur declarations about the Margin of Error, which is, I'll reiterate, only a measure of sampling error.

The Slightly Technical Version of Why It's Wrong:

A poll’s margin of error (MOE) is only one source of uncertainty. Even if we disregard or (for the sake of example) assume other sources of uncertainty like nonresponse are zero, we still have not isolated the uncertainty to a single source.

When you compare polls to elections, you are introducing more uncertainty that the MOE does not capture: people can switch from one candidate to another (or not vote), and undecideds will always resolve to 0 - either by not voting or by choosing a candidate. Assuming you know how undecideds will resolve is statistical agnorance; the blanket assumption that they will always split evenly to the two major candidates is even worse. Putting all of that uncertainty into a pile and claiming it's all the “poll's margin of error” is plainly unscientific - it misrepresents what the MOE is.

If you're interested in a variable-isolated experiment showing how uncertainty works when we control for the margin of error, I recommend this.

The Straightforward Version of Why It's Wrong

The margin of error relates to the poll at the time it was taken, for all of the options given. Not a future result.

Given the same data and MOE of +/- 3%, it is accurate enough for intro levels to say that for the time the poll was taken (a simultaneous census):

Candidate A ~43-49%

Candidate B ~36-42%

Undecided ~12-18%

Just because Candidate B - given the MOE - is almost certainly not “ahead” at that moment does not resolve the undecideds. Assuming undecideds will split evenly “or else the poll was not accurate” is just incorrect. And yet -

This common numerical content masquerading as analysis is not unique to “media.” It is utilized by otherwise reputable individuals and organizations. It’s the same logic used when an analyst calculates the percentage of races that a poll “called correctly.”

Consider, to illustrate the magnitude of this misrepresentation, if the poll reported as

Candidate A 46%

Candidate B 39%

Undecided 15%

Had a small error with regard to the major candidates. The population at the time the poll was taken was actually

Candidate A 45%

Candidate B 40%

Undecided 15%

Most reasonable people would chuckle at the prospect of calling that poll inaccurate. A tiny error, right? We're all in agreement, I hope.

Well, here's what the same 2/3 undecided resolution looks like given that environment.

A candidate which poll(s) said had a 7-point lead actually only had a 5-point lead - a tiny error no matter how you quantify it. In other words, a very accurate poll. Yet the unexpected undecided resolution causes the surprising result, and magnifies the objectively incorrect assertion that the poll was not just inaccurate, but “outside the MOE.”

You can also find the probability of the initial state of Candidate A 44%, Candidate B 41% - both also firmly and easily within the poll’s margin of error - and the potential impact of unexpected undecided resolution.

Same Margin, Different Meaning

While the above is mostly related to what the margin of error means and how it’s misunderstood - the problem is even larger when you layer on the fact that polls are misused as predictions.

Consider the following two polls with the same spread:

Poll 1

Candidate A 53%

Candidate B 46%

Undecided 1%

Poll 2

Candidate A 46%

Candidate B 39%

Undecided 15%

Both share a spread of “+7” but how this translates to what the data means for the population of interest and the separate step of forecasting the election result is also poorly understood - with real ramifications for data analysis. Here’s a powerful visual:

In the interest of transparency, I’ll note this chart is a slight simplification - the reported MOE is not a hard boundary as pictured, the probability distribution is more likely to be closer to the center than the edge, and is not uniform across all reported values (e.g. the reported 53% poll value does not have the same exact MOE as the reported 15% value).

Nevertheless, representing the margin of error as a symmetric interval provides an acceptable introductory conceptualization of what the poll data says and means about the population at the time it was conducted. And the “guaranteed victory” callout is neither conceptual nor an estimate: it’s a mathematical fact. In a field loaded with uncertainty and difficult-to-quantify variables, it is extremely helpful to have an objective anchor related to the target metric of interest.

Sports!

It’s ironic that in attempting to translate someone’s “lead” to their chances of winning, political analysts have effectively adopted a sports mindset within which these probabilities can be generalized, while my own background in modeling sports data is what helped me identify why this approach is flawed.

In most sport environments (with rare exceptions like the Elam Ending) the “margin” alone - given the game state - is a sufficient statistic to calculate win probability. Though factors like run-scoring environment (baseball) and pace of play (basketball) might not be quite negligible, a 3-run lead entering the 9th inning (whether 4-1 or 7-4) yields effectively the same generalized win probability of 97-98%. Likewise for an NBA game where a team enters the final 30 seconds of a game up by 3 (90-96%, depending on possession): whether that 3-point lead is 87-84 or 117-114 is extremely insignificant.

And this fact, I believe, is where a great deal of the confusion comes from

In most sports contexts, there is no number of points you can score to literally guarantee victory. This is not true in politics; if you get 50% of the vote in an election, you win, game over. For a candidate whose poll/poll average is 53%, the margin of error calculation quite directly means - at the time the poll was conducted - a majority of that population almost certainly supports that candidate.

In the interest of completeness, I’ll reiterate for clarity that even this even this even this even this even this even this (repeated for emphasis) does not mean “if the poll is accurate, they’ll win” because there does exist some probability that people who supported that Candidate change their mind between poll(s) and the election or do not vote. But this is the closest possible relationship between poll data and “if this is accurate, then this is what the result will be” and it is plainly not how it’s currently understood. The current understanding is literally as simple as: ahead in poll(s) = win, or else inaccurate. And if you can’t tell by my tone, I find this conflation of measurement and prediction frustrating in a field that is supposed to be scientific.

My fundamental recommendation is to think about each candidate’s poll number as an approximate base of support - not to reduce a multidimensional space into a single number and ignore the possible projection flaws.

Ignoring for the moment that my published work shows this relationship between poll spread and win probability is far more nuanced than the sport-spread mindset, many otherwise reputable analysts dismiss it with no data to support it. For example, in this article by he states “51-48 is not that much more likely to ultimately win…(compared to) 47-44.”

Cut from this quote - the very next sentence, in fact - is possibly the most indicative of the problem I’m describing. Ruffini says that the “Margin of error applies about equally to both cases, whether or not one hits the “magic” 50 percent number.”

This is, as illustrated above, true.

The problem is when we use that as support for the claim that the candidate at 51 is “not that much more likely to win.” That disregards the irrefutable fact that hitting the magic number means - with 100% probability - you win.

Meet Them Where They Are

Among my earliest work on political data - which generalized political races of interest into both “poll lead” and “poll number” I found this:

Given the fact that elections in any given year are - unlike sporting events - both highly correlated and very low sample size, I would never say that this chart is anything close to authoritative. I will also add that because of the highly correlated nature of same-year election trends (i.e. if Democrats overperform poll expectations in one state, they have likely done so in most states) and the fact that elections are only every 2-4 years, you would need a sample of data that goes back to roughly the founding of the United States - with pollsters utilizing similar techniques for the duration - to achieve a sample size close to decisive.

What the chart does show, however, is a point directly derivable from the underlying mathematics, one I want to teach instead of lecture: spread is not a sufficient statistic. I believe that this can be taught and grasped by new learners, but only if the spread-to-win probability models (also proposed by more decorated statisticians) are understood as flawed.

Scroll back up to the first chart in this article, which I’m required to state is from my book, and note the proportion of black (win) to gray (loss) for the poll leader given a lead of - say - 3%. As the leader’s poll number approaches 50%, their chances of winning are dramatically higher.

Based on the win probability chart in this section, a candidate with a poll average of 51-48 (for which we need to extrapolate a bit) can be reasonably postulated as around 95%. Compared to 47-44, closer to 80%.

Mathematically - if we input the poll average and sampling MOE into a simple forecast model, and allow for a given Standard Deviation of Undecided Resolution (even granting the near-uniquely American assumption that the median of undecided resolution is 50-50 to each candidate, which I don’t think is a given) the output is directionally similar, if less dramatic: 83% versus 77%.

As far as I know, the disconnect between why - at least in this millennium - candidates closer to 50% in a poll average perform far better than mathematically expected should be a topic of substantial interest. But relationships that are not understood to exist cannot be researched.

A Better Sports Example

The Snapshot Analogy, coming through again!

Very close to the finish line of a race, would you rather be ahead of your opponent by 2 meters, or 3 meters?

That’s not a trick question. Of course, all else equal, up by more is better. But “all else equal” is doing a hell of hidden work here. I’ll remind you that measurement uncertainty - as explained above with regards to the margin of error - is an inherent, unavoidable property of political polls that does not exist in snapshots of footraces. And even with that:

Temporal uncertainty - how much time between the observation and event of interest - is a factor present in both elections and footraces.

For an election, is it the

• Day before the election

• Week before

• Month before

• Three months before?

Most people can intuitively recognize the difference: more time means more opportunity for things to change.

In sports, are the runners:

• One meter before the finish line

• Five meters before

• Ten meters before

• Fifty meters?

Of course, whether the race is a sprint event or endurance event makes a meaningful difference too. (I’ll resist layering another analogy here, but veterans of electoral data may find one). Ahead by x meters, with y meters remaining, is not something we would expect to yield equal win probabilities across different race types. But even if we limit it to the same race type - “very close to the finish line” is subjective - as evidenced by the fact that different analysts use different cutoffs for what “close” means in election data: one week, two weeks, several weeks (even “after Labor Day” i.e. two months) are all used.

For a footrace, “close to the finish line” can mean 1 meter or 5 meters; both are “close” in any context. But “ahead by 3 meters” intuitively carries different meaning with regards to win probability, depending on whether there’s 1 meter left in the race, or 5, or 15.

Now, would you rather be ahead by 2 meters when you're 1 meter from the finish line, or ahead by 3 meters when you're 5 meters from it? A larger lead, here, regardless of probabilistic or mathematical prowess, is understood as insufficient information. Our interpretation (and a valid calculation) of win probability requires this context; it is not unconditional.

50%, in electoral terms, is the Finish Line.

Undecided voters, then, create a minimum unresolved uncertainty. Even the day before an election, if undecided voters remain - even just a few percentage points - the fact that someone is “ahead by 3 the day before the election” does not yield unconditionally similar or even comparable win probabilities to elections with close to zero undecideds, or 50% undecided.

Undecided voters represent a visible wall among the competitors and how close they can possibly be to the finish line, regardless of the number of days or weeks until the election.

By considering “days to the election” as the only meaningful source of uncertainty, we are dismissing one of the most important variables - what do we not know about how close this race is to the finish line?

That uncertainty around how undecided voters will resolve - in addition to uncertainty regarding the present state of the race given poll data and its margin of error - means that we must be very careful in declaring “if the polls are accurate” even if “the race were held today” as is commonly stipulated

The race being held today does not remove the uncertainty of undecided resolution.

And even this relatively nuanced explanation exists primarily for two-candidate races, where one candidate must receive 50%. In races with many viable candidates - as is far more common outside the US - the finish line also is in an uncertain location, because some percentage of votes less than 50% guarantees victory.

A Favor

There will be A TON of analysts (some for clicks, some for genuine mathematical reasons) who make posts of the genre “if the polls are accurate…if the election were held today…” followed by some map or projected result. This is true every election season. This is a major cause of misunderstanding and misinformation around electoral outcomes, and statistics. Share this article on that post, with a simple caption like “this is wrong” - and tag me.

As California counts votes, MAGA predictably gets angry: the person they wanted to win looked like they had a chance, but then they lost! Fraud!

So many people, my past self included, are eager to point out the logistics of vote counting. Whether California this year, or Michigan in 2020 - as mail-in votes were counted, we saw what we already knew: a highly disproportionate number of Democrats vote by mail.

If you spend months in a bubble telling you that your candidate is ahead, that your movement represents "real America," that the polls are fake, and that everyone you know agrees with you, then a loss requires an explanation.

Then there are only a few possibilities:

1. Your candidate lost.

2. Your understanding of public opinion was wrong.

3. The election was rigged.

The first two possibilities require updating your beliefs. The third allows you to keep every prior belief intact.

That's why claims of fraud are so resilient. They are not primarily about evidence. They are about preserving a worldview.

And as I pointed out in this article, what someone says they believe - and what they actually believe - are not always the same.

The claim - in this case, rigged elections - is not the belief. It is an excuse. The excuse is designed to make you spend time and effort explaining to them why their “rigged” claim is false - so they don't have to present their real belief: any election where their preferred candidate doesn't win shouldn't count.

Because if they can trick you into remaining focused on the mechanics and side-arguments, they never have to defend their premise.

The premise is not "I have evidence this election was rigged."

The premise is "an election that produces this outcome is difficult for me to accept as legitimate."

Those are very different claims.

One is an empirical claim that can be tested with evidence. The other is a value judgment about which outcomes feel acceptable.

This is why factual rebuttals are simply ineffective. You can dismantle one argument, only to watch another appear immediately in its place.

The vote machines were compromised.

No? Then the ballots were fake.

No? Then the counting was manipulated.

No? Then the courts were corrupt.

No? Then the media is complicit.

The claim changes, but the conclusion remains fixed.

The purpose of the argument is not to reach the conclusion. The conclusion already exists. The argument's purpose is to defend it.

It's designed to make you point out the hypocrisy of accepting the many House and Senate seats that Republicans won were legitimate, but the same election was rigged for the Presidential race. Anything to shift the burden of proof away from their claim.

This video, was sent to me by a follower, and it's right on. I stole this from it.

And once you see it, you can't unsee it.

Once you see that the words they say are chosen not because they believe them, but to distract from what they truly believe - it all starts to make sense.

And once you learn how to push back, they crumble.

1. “Prove it.”

2. “If I prove you wrong, will you admit you're wrong?”

It included this graphic, perhaps the most often shared on gerrymandering, and I'm told it's even used in classrooms:

One big problem with that: it's misinformation. It looks and feels educational, it seems intended to be educational, but it unquestionably promotes the same myth about “how gerrymandering works” that partisan liars use to claim things like “New England is extremely gerrymandered.” I'll explain.

What Gerrymandering Is

Gerrymandering is defined as the drawing of political territories - usually House Districts - in a way that favors a particular political party.1

What Gerrymandering Is Not

A certain percentage of votes not yielding a similar percentage of Representatives for a given state or region.

The most common posts circulated on the subject treat gerrymandering as above - an “expected value” calculation.

That is: given 5 Representatives in a state that votes 40% Republican, how many seats should Republicans receive (implicitly, in a fair state that does not gerrymander)?

40% of 5 seats is 2; therefore, a “fair” calculation is considered 2. Whether gerrymandering is explained this way is not my opinion. This so-called best explanation of gerrymandering literally called this perfect representation.

To be perfectly clear, this is not just an oversimplification - it is wrong. Explaining gerrymandering this way would be analogous to “explaining” the Electoral College by invoking the National Popular Vote: your opinion of what is “fair” is irrelevant to how the system works.

The United States does not proportionally allocate House seats based on statewide votes, nor does it allocate Electors based on National Popular Vote. Stating what would be “fair” in a system we do not have is not an explanation of anything. It is a strawman. And in the context of “explaining gerrymandering” it is misinformation.

The public is confused, and I'm once again pissed off about misinformation coming from sources that should know better.

It is the exact same reasoning used by right wing purveyors of misinformation, when they share graphics like this:

According to this meme, given 36% of the vote, 0 seats in a state like Massachusetts with NINE representatives must be gerrymandering (or, at minimum, “is unfair”).

It's just this:

And that has nothing to do with what gerrymandering is, isn't, or how it works.

The Gerrymandering Test

Assuming you know what gerrymandering is: drawing lines to favor a particular political party, and what it is not - deviation from proportional statewide representation - how can we explain or teach to the public what is and isn't gerrymandering?

This is a calculation that can be done for every state. I'll show you how.

Here is the rationale:

Without considering political or demographic data at all (i.e. the complete absence of any possibility of gerrymandering) how many seats would a party be expected to win?

The findings will be called the expectation.

To illustrate how it works, first consider the following map. It may look familiar.

There are two rules that all districts must follow:

1. Contiguous (all districts touch another part of the district)

2. All districts are the same size

Given those two rules, there are a few thousand possible configurations (4,006, I think). There are only so many shapes you can make when each district contains just 5 equidistant units, but here are a few examples of what a valid map might look like:

Remember, each of these maps were drawn with zero consideration to political affiliation. The proportion of red to blue in any district is purely chance - none of them can possibly be “gerrymandered” by any definition. More on this map in a moment. But first, note:

There's exactly one map that results in blue controlling all 5 districts: it's pretty easy to see in this layout.

Myth debunked:

“Gerrymandering is when funny lines”

It's approximately impossible that this map would be selected by chance. The absence of weird shapes does not mean the map isn't gerrymandered. In real life, communities of interest don't always reside within neat shapes. Weird shapes are a red flag, not a checkered flag: suspicious, not conclusive.

Whether or not the above 5-0 map is “fair” simply isn't relevant to the topic of gerrymandering. The question of gerrymandering requires asking: was it map drawn neutral of political consideration? With a probability of 4,005/4,006 (~99.98%) - no.

A brief exploration of this map teaches a few important lessons.

Map # 1: Clustered

Given this exact “clustered” configuration of red and blue, in the total absence of any possible gerrymandering, here is the range and probability of possible outcomes:

Blue probably gets 3 seats. Maybe 4. Simple enough. That's exactly what you would have thought! Where's the misinformation, Carl?!

Well first, remember, the old “explanation” described maps as fair or unfair based on the outcome, not whether the maps were gerrymandered. Also, there's about a 1/4 chance that maps that are drawn with zero political bias result in blue not having 3 seats.

At the risk of this turning into a lesson on probability (you can bookmark this as your next read, if you like), it's perfectly fine to say:

For this map, blue has an expectation of 3 seats.

Foreshadowing, “60% Blue and 40% Red” isn't the only relevant variable. It's not even the most important one!

Map #2: Dispersed

Surprise! Count the dots if you want - it's still 60% Blue and 40% Red. And yet, in this scenario, it is very hard for blue not to have a majority in at least four out of five districts!

Here's the percentage of non-gerrymandered outcomes:

Maps 1 and 2 have the same exact percentage of red and blue: the only thing that has changed is where they live. With that alone, the expectation has gone from 3/5 seats to 4/5 seats. Not just that, but Blue’s chances of controlling 5/5 districts is higher in the “dispersed” configuration than it was of controlling 4/5 districts in the “clustered” configuration!

Map #3: Dispersed Threshold

At 60% of the vote, the expectation for Blue (where red is dispersed) is about 4/5 seats.

At 64%, that expectation becomes 5/5. And it's not particularly close.

The reason for the unintuitive threshold is this:

In a winner-take-all system, every district has a winner and a loser. A loser may receive 49% of the votes, but they don’t get 49% of a seat - they get 0. This nonlinear relationship between votes-to-seats doesn’t cease to exist simply by zooming out to the state level.

And that’s where the misunderstanding comes from.

The calculation of “fairness” in (for lack of a better descriptor) non-Carl graphics assumes a linear relationship of statewide votes to seats: 50% of the vote yielding 50% of the seats, 60% of the vote yielding 60% of the seats, and so on. That is simply not correct. This is not my opinion, this is the provable mathematical reality.

Without considering how “spread out” voters are, seat percentage to statewide popular vote percentage will follow a sigmoid shape, like this:

Going from, say, 55% (z =1) to 60% (z=2) of the popular vote in a given state has a highly disproportionate impact on seat expectations because there become far fewer permutations of districts within which the majority party doesn't get at least 50%. This is represented by the steep middle of the chart.

Going from 65% to 85% (z= 3 to z = 7) would be much smaller, if not negligible, despite a larger gross change - illustrated where the curve becomes asymptotic/flat. If that explanation is too many words, don't sweat it, there are more charts to illustrate.

Map #4: Dispersed Dominance

If you ask someone how many seats is “fair” for a party that receives 28% of votes statewide, given 5 seats, the answer will probably be “one.”

But that outcome is impossible to achieve except with gerrymandering.

I'll repeat:

For the map above, the only way for Red to get even one seat is to consider partisan affiliation and then draw the maps specially to ensure it: reverse gerrymandering.

Not what you expected? Blue winning 5/5 seats isn't just the expectation anymore. Anything else would require special treatment for Red.

Real World Application: “Blue States”

1. The percentage of voters who support a party statewide matters somewhat for expected seats per state. But when it comes to how many districts are won under the rules in the United States (Single Member, most-votes-wins), how those voters are dispersed matters at least as much, if not more! This is because of the concept I illustrated above called “spatial nonlinearity.”

   In the Northeast, where Democrats hold a comfortable majority in most states, rural voters are extremely dispersed and make up a smaller percentage of the population than, for example, in the Midwest.

2. Even without spatial nonlinearity (clustered vs. dispersed) - which is a huge variable - the relationship between votes to seats is also not linear.

Put these two facts together, and you can understand why “60% of the votes → 60% of the seats = fair” makes no sense: it has nothing to do with the system we actually have, nor anything to do with “gerrymandering.”

If someone wants to argue about what type of system we should have, great. You can talk about proportionality or multi-member districts or even look at my article on Uruguay’s neat system if you want. If you're really itching to learn more about the difference between US-style and the many other European systems, and how we forecast probabilities within them, check out this article from .

But you don't get to draw a map that shows your opinion of what a fair map would look like, and claim any deviation from it is “gerrymandering.”

Now that we’ve disproven the “New England gerrymandered!” lie, let’s look at how where people live impacts red states.

Map #5: Blue Minority, Clustered

This 60-40 Red scenario is designed to look like a state that is relatively Red statewide, but has Blue “big cities.” That is, a nonrandom geographical cluster that mirrors reality.

Look at the expectation for Red in this scenario:

And compare that to the 60% Blue map presented earlier in which Red is dispersed - as is the case in most “Blue” states:

Well I'll be damned. These are the same percentages, only in a different configuration!

This difference is entirely attributable to spatial nonlinearity where people freaking live.

Now, to be clear, this is not to say blue states don't gerrymander or red states don't gerrymander - I'll get to that.

This is to say in the total absence of any possibility of gerrymandering, where people live (clustered versus dispersed) makes this much difference. This has nothing to do with “fairness.” It only has to do with math. Quote me.

Map #6: Red Dominant Clustered

If you're anything like the people I've presented this to, your mind is probably already kind of blown by how different the expectations are for those 60-40 maps. I'm not finished yet.

Earlier, I defined “dominance” as 72%. While shrinking states down to 25 dots loses some nuance, it is certainly not an oversimplification to illustrate the impact of geography on the chances of reaching a majority in a district.

And here’s the punchline:

Even at 72% dominance, the expectation for Red is barely four seats. Compare that to:

That collective gasp you heard was the people who created the “fair” graphics acknowledging that those graphics have nothing to do with gerrymandering.

Do I need to say it again? Distribution matters.

One final map before I give an overview of how gerrymandering works and what it looks like.

Map #7 : Red WTF clustered

This Reagan 1984-looking map features an extreme version of what actually exists in the deepest-red states: a Blue-majority city packed densely within a sea of Red.

It would be quite easy, if Red gets to draw the map, to deny Blue any representation. But it would be done explicitly for that purpose. That transitions nicely into what “Representatives” are for, and how gerrymandering is actually done.

Why the House of Representatives exists

Without getting into the “shoulds” and “fairs” of the matter, Congress was designed to balance possibly competing interests: “big states” and “small states” - and perhaps big cities vs rural areas.

Since all states - regardless of population - receive two Senators, there's a highly disproportionate impact of voting power-to-population in the Senate. California gets two senators - a maximum of two votes in the Senate - as do states with less than a fiftieth of their population, like Wyoming.

As a trade-off, Representatives are allocated based on population. As the population grows but the number of Representatives stays the same, that ratio changes. In any case, the trade-off is that Representatives represent districts within states, not states as a whole. As such, invoking a state’s voting preference in discussions of Representatives is again a red herring: we already have elected officials for that office. It's called the Senate.

How Gerrymandering Works:

There are two simple concepts that are required to understand gerrymandering, that are required to be present in any real gerrymandering:

1. Packing

2. Cracking

“Packing” is intentionally putting likely supporters of a political party into a single district.

“Cracking” is intentionally splitting likely supporters of a political party in close geographic proximity into multiple districts.

Notably, packing is done almost exclusively to put a party at a disadvantage statewide. Cracking, on the other hand, can be done to give your party an advantage or to put another party at a disadvantage.

To borrow a chart from the Gerrymandering Project, a great visual:

On the left, Purple is packed mostly into one district, giving Green a big advantage. On the right, purple strategically “cracked” their own cluster of voters, spreading them into several districts.

The math behind both strategies is simple:

In a winner-take-all district, winning 60% of the vote (a pretty comfortable margin in itself) yields exactly as many seats as winning 99% of the vote in that district would. Strategically, every vote beyond what is already a comfortable margin of victory can be described as wasted votes. A good gerrymanderer wants to:

1. Waste as few votes as possible

2. Make your opponent waste as many as possible

Now, you might describe any votes beyond the 50.01% to guarantee victory as “wasted” and that's kind of true, but only with the benefit of hindsight. The best (honest) predictive modelers will only get you to +/- 5% for the next election - and maps are supposed to be in effect for several elections. Without getting into the weeds - maybe another article - it’s probability and risk tolerance.

Given just 25 units and only a few valid shapes (compared to real life where any shapes are possible) it's harder to illustrate packing and cracking - but it can be done. Consider the following:

And here's the corresponding range of outcomes:

In the absence of gerrymandering, there's still a 1/3 chance that Red holds a majority of seats, despite not receiving a majority of the vote.

But look at the entirely plausible maps that could be drawn if Blue or Red were in power:

What's important to understand, is that with advanced models that are now sensitive down to the street level (seriously), aggressive gerrymanderers can choose their voters. This scenario above isn't an exception, it's the norm.

“Gerrymandering is when politicians choose their voters, instead of voters choosing their politicians”

- (unknown source)

Almost no one likes gerrymandering - except when it benefits their side. Even then, it feels dirty. How could we eliminate gerrymandering, in the event we get bipartisan agreement? Well, getting bipartisan agreement will probably require a mutual understanding of what gerrymandering is. Republicans demanding a reverse-gerrymander of states like Massachusetts in the name of “fairness” seems problematic.

In the event there is an agreement to end gerrymandering, “how” is a big unanswered question. I'm skeptical of elected or unelected commissions because it's an inherently political job where those ideas of “fairness” and bias tend to interfere. Though, don't get me wrong - far better than the free-for-all we currently have.

I have some ideas (though you probably won't like it). But no matter what - remember:

In order to get rid of gerrymandering, we first have to properly define it. Misleading people into believing that any deviation from our opinion about what is fair is “gerrymandering” won't get us closer to that goal…and it also happens to be bad for education, which isn't cool.

Best Explanation Ever?

If you liked this article, please share it. You are welcome to use it or any portion in a classroom setting - a comment or tag on social media would be appreciated (@RealCarlAllen). I am also available for speaking engagements.

If you found this article accessible and insightful, consider buying my book The Polls Weren't Wrong, which irrefutably debunks the pervasively accepted myth that polls “underestimated” Trump in 2016, that polls “missed” regarding Brexit, among other interesting topics. It offers readers of all backgrounds the ability to understand poll data for what it means - not be misled by analysts who assert how much someone is “up by” is the primary (or only) variable of relevance.

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As you probably know, in addition to teaching people how polls work (and don't work) I am pretty passionate about fighting misinformation in science and statistics.

Recently, I've done some posts on anti-vaxxers, gun homicides, and fructose for some reason.

What you may not know, is my weird ascent as an expert in the field of political polling exists because of my well-calibrated bullshit detector.

Most people who are elite performers in scientific fields are very smart, they can elaborate with great detail all the supporting evidence for their field's findings, and they do not trouble themselves with the simpletons who debate what they have proven.

While experts can identify misinformation and misuse of statistics, they rarely understand how to combat it. This leaves an enormous (and growing) expert-to-public gap that is increasingly filled by ideologues who weaponize oversimplifications to push political, social, cultural, and/or financial agendas.

The result is a public discourse where truth is often overshadowed by confidence and confirmation bias - and expert knowledge never reaches who needs it most.

This article will directly address how to combat misinformation.

Pseudoscience

To be brief (because we all want to know what I think about what Elon thinks about what makes a Real Woman): pseudoscience throughout all of history follows a surprisingly predictable pattern.

It starts with a hypothesis, usually one that just makes sense (Flat Earth, Stationary Earth, Creationism, Heavy Objects Fall Faster) or has supporting data that could feasibly fool a nonexpert (Anti-Vax, Climate Change denial, Accurate Polls should Predict Election Margin)…

As someone who does science, I'll remind you that, scientifically, there is nothing wrong with any of the above hypotheses. The first step of the scientific method is brilliantly summarized by Feynman: “first, we guess it.”

But when evidence is presented to contradict or outright falsify those beliefs, that's when science versus pseudoscience is revealed. In pseudoscience, the hypothesis is not revised. Instead, the standards for evidence are shifted, and reasons for accepting the belief modified. Apologetics are invoked (what they really meant was..) and auxillary assumptions added - known as ad hoc reasoning - to protect the initial hypothesis.

Which leads me to…

Is Sex Binary?

This is a hot “debate” right now. Not because of any scientific breakthrough or unresolved problem…but because some people need someone to hate for no reason* and transgender people are easy targets right now.

*to distract from far more important and consequential issues

Of course, transgender is a social and psychological construct, not really relevant to the biological definition of sex, but you wouldn't confuse most of these people with intellectuals - or logicians.

For most, “biology” is just a useful excuse to hate someone for being different. Indeed, similar arguments were used against homosexuals and interracial marriage not long ago.

Whether or not sex is binary has nothing to do with transgender rights, participation in sports, and so on. It's a deflection to offer external support for the core belief: “I think it's okay to discriminate against transgender people.”

The question of a sex binary is incredibly complex - more complex than anyone who hasn't studied the topic can comprehend.

Anyone who claims the answer is simple or easily proven is...simply…wrong. Any educated person who does it is doing so because they have something to sell (and a certain crowd is happy to buy), or has an agenda they believe is advanced by saying it.

There are still things we don't know about sexual development, and almost everything we learn uncovers more things we don't.

The right answer to the question is: probably not. But it almost certainly depends on how “sex” is defined. Yes, seriously.

Here, I will honestly represent the best argument in favor of the sex binary:

“There are two gametes: sperm and ova. Sex refers specifically to sexual reproduction, therefore there are only two sexes.”

That creates a few awkward logical problems. There's a bit of motte-and-bailey going on which I'll touch on momentarily, but there's a more glaring issue:

It defines sex by an outcome (gamete production) that many individuals - children, post-menopausal adults, infertile people - do not and may never realize. The category is treated as fundamental, but the criterion is conditional, incomplete, and developmentally contingent.

Very quickly, this definition is shown to be insufficient. You may be able to classify most people by it, but there are lots of people who probably are objectively “male” or “female” not covered by the definition.

In case you think I'm being disingenuous about the position of those who argue in the affirmative for a sex binary, below is a debate I had with one of the field's influencers, who regularly publishes on the topic.

I asked him for evidence that sex is binary, he responded as follows:

Citing a source the way he did (“world's leading experts”) is a common poisoning the well tactic, with a touch of appeal to authority - rarely accepted in rational discourse - rarely needed in scientific discourse.

Nonetheless, I gave him a big benefit of the doubt, and opted to focus on the content of the definition rather than his framing.

You'll note that the definitions were not “should” or “would” or “could” produce certain gametes…but are given in relation to what gametes someone produces.

Testable, falsifiable, definitions that are easily shown as incomplete.

So I asked a simple follow up:

According to these definitions, what is the sex of a person that produces no gametes?

After a nearly instant back-and-forth leading to the above comment, citation, and my question he stopped responding.

For over a year.

Then, a few months ago, he cited my tweet and said this:

See the change?

No longer is world-leading-expert definition sufficient, apparently. He never answered my question regarding a person who produces no gametes, he simply revised the definition to shift the standard of evidence.

Now, people who don't produce gametes can fit. Post-menopausal women: obviously female. And so on.

But now, he's invoking something much harder to test, something subjective: what their anatomy is “organized around.”

That gets into the highly complex nature of sex, requires a lot of criteria that go down to the molecular level, and raises even more questions: is it a “majority rules” situation…can it be represented on a flow chart? The answer is no, not without begging the question.

It gives adherents to the belief, who have gone through the discomfort of having their “produce egg = female, produce sperm = male” proposal disproven, something to cling to - without changing their beliefs. Something that SOUNDS scientific, but provides goalposts slippery enough to: “organized around”

That's because pseudoscience doesn't thrive under honest complexity; it requires dishonest simplification. It reminds me of my teenage years when I pressed creationists on their definition of the word “kind” and they couldn't define it, they just gave examples. It means whatever they want it to mean. Objectively defining it would subject it to unwanted scrutiny.

It's specific enough to sound scientific, and too vague to be disproven by science. The pseudoscience sweet spot.

Normally, someone less experienced at dealing with these types of people (and myself, when younger) would argue against the new “organized around” definition being subjective, unfalsifiable, or simply point out that it changed.

Then the new topic is how the definition isn't subjective (even if it is) how it isn't unfalsifiable (even if it is) and so on. The topic changed, they are no longer accountable for their original definition, ego protected.

But I've learned some things over the years.

The first step here is to “close” the original debate, not acquiesce to a new one.

Make them admit their previous definition - which was clearly different than this one - was insufficient to classify all males and females, and that it changed.

It doesn't mean conceding their new definition is wrong, or even that the old one was, it just shows a shred of intellectual honesty, integrity, and respect for rational discourse. A respectable scientist would have no problem doing this. And conveniently, it's a very quick way to determine who is worth your time and who isn't.

To be blunt, most people aren't.

Debates of fact, and science, imply adherence to the rules of reason, but as I explained and illustrated here, this deception is intentional. Do not assume someone is willing to adhere to scientific standards merely because they claim a scientific position. You do not need to grant the benefit of the doubt on a fundamentally pivotal - and simple - question, and is it not overly intrusive or rude to confirm it. Though I promise you, very many will act offended as an escape (and coping) mechanism to avoid being pinned down. Pseudoscientists need to feign scientific adherence, but they cannot (intellectually) survive being forced to adhere to scientific standards. The easiest way to determine whether someone is “worth the time” is to ask a question like:

• Is there anything that could change your mind?

• If I prove you wrong, will you admit you're wrong?

Rule Number One (two, and three)

If rule number one is “establish what their position is”

Rule number two goes one of two ways.

2. “Prove it” - if they make the claim they accept the burden of proof.

• 2a - “If I prove you wrong, will you admit you're wrong?”

This is an important step because it will save you a ton of wasted time trying to change the minds of people who are, by definition, irrational. Anyone who doesn't follow “2” or “2a” is conceding that they are not rational. Both of those responses require a direct response - they won't want to give one. Don't let them change the subject.

It doesn't mean they're a bad person, just not suited for rational discourse.

Occasionally, very occasionally, a person will revise their original statement when presented with the possibility that someone could prove it wrong. Sometimes it's a genuine explanation, others a dishonest deflection. In either case, if you insist on engaging with people in matters of fact, follow rule three:

3. Before a new topic is introduced or debated, the previous one must be resolved, closed, or conceded. That means no topic changing, no “what I meant was” - if the original claim is incomplete or insufficient, it must be conceded (that is, they admit it was wrong, incomplete, or insufficient) before a new topic is allowed to be discussed.

This standard allows you to know if the person you're dealing with is engaging honestly. If they're not willing to admit that statement was wrong, it follows that if this one is, they won't admit that either.

I'm working on a more concise flow chart of my own, but this one is very good:

Here, a curious account responded to my post seemingly requesting directly to have a livestreamed debate.

I simply stated the terms under which I would have the debate.

They refused.

When I asked if they would agree to the terms, they went from a direct, inquisitive challenge to…well…

Notice how quickly they went from a confident challenge to angrily name-calling, just by being asked to agree to very simple terms. This is standard in the post-Kirk “debate” era.

Don't get me wrong, debate has long included sophists and eristics - and the practice been rightly criticized as not being a truth-seeking activity.

My approach to exclude people from “debate” who are not seeking truth is very intentional, and a lesson I'm proud to have learned. I'm less proud to have learned that this excludes most people.

In the social media era, where platform size is more important than substance - and vibes more important than valid logic - it's easy to get disheartened by this lack of intellectual curiosity.

Looking at the history of pseudoscience - I've constructed a very helpful visual. Two pyramids, almost identical:

Note the bottom of the pyramid is the same on either side.

On the side of science, there are the truth-seekers: people who will change their minds if evidence justifies it.

On the ideology side, there are “influencers” who give their followers the lines and “sources” to regurgitate as if they are meaningful or profound. Importantly, debunking any of those sources does nothing to change the underlying belief - making it inherently unscientific and irrational.

Musk says Womb = Woman

There are few examples that could possibly be clearer than vibes and “virtue signals” being more important to an ideologue than fact.

Authority is not exclusive to ideologues, science has this problem to an extent. But if Albert Einstein himself proclaimed the Sun revolved around the Earth, that claim survives or fails on its merits, not who said it.

The comment - clearly an effort to establish some objective basis for “sex” - fails on so many levels. The most basic of which is that some women receive hysterectomies, and Musk's position awkwardly asserts that this procedure changes someone's sex.

But remember, Elon has positioned himself at the top of the ideologue pyramid. And it is not permissible in the pseudoscientist ideology to question authority. So the apologetics began:

What he meant was…

And other comments took the form of:

“If you have a womb you are a woman! What's so controversial about that?”

(While conveniently ignoring the very strong qualifier: “otherwise you are not.”)

Apologetics are very common among those trying to preserve unscientific beliefs.

Remember, if you choose to engage with these types of people, that the terms of rational discussion are explicitly stated and agreed to. Anything else will be a massive waste of time, unless you're a sicko like me who does it for batting practice, to prepare to take on actual scientists.

Almost without exception, people like this simply want a platform to state their beliefs - Elon paid billions for that privilege. Ideologues do not genuinely want to gain knowledge or have their understanding challenged, they want to position their opinion as on the same level of your facts.

But this one, for whatever reason, attracts a particular interest among a large group of people - both sports bettors and outsiders - confidently wrong.

There's nothing wrong with being wrong, even confidently so - been there more than once. But when you're corrected (politely or otherwise, for the record) and refuse to acknowledge as such, it becomes willful ignorance.

As it happens, the reasoning underlying the “equal action” belief is perfectly plausible on the surface - like most misconceptions. But the error in reasoning crosses domains: it's not “just” a sports betting problem.

Interestingly, there has been very little published on the topic, so my post will aim to both fill that void and debunk the myth once and for all.

The Reasoning

If sportsbooks get equal action on both sides of a bet, they will make money. This is basically true!

The disconnect - where the myth comes from - is that since this “guaranteed profit” scenario is ideal…

The Hypothesis

Sportsbooks can (and/or do) set lines with the goal or intent of attracting equal action.

There are many avenues to prove this wrong - in theory, practice, and reality. First, a few terms. Then the math.

Important Terms

The most common “juice” or “vig” on a bet is -110 (in American terms). That means you must risk $110 to make a $100 profit on a winning wager. Wagers can be any amount, but the simplest example is: “Risk $110 to win $210.”

A line is a number a bettor can bet either side of: most commonly a point-spread or over/under (aka total). For example, if the spread is “Team A -3” bettors may wager on Team A -3, OR Team B +3.

The final score is adjusted by this handicap to determine the winner: if Team A wins by more than 3, those bettors win. Ties are possible, in which case bets are refunded.

The process for “over/under” bets is similar. The teams’ combined points, goals, etc. determines the result.

A sportsbook (or “book”) is a place that allows people to place wagers. Oddsmakers are the people who decide what line the books will offer.

In simple terms, if two people risk $110 on each side of a bet with -110 odds (assuming it's not a push) the Sportsbook has collected $220, pays out $210, and pockets that sweet $10. Of course, sportsbooks deal with many more zeroes, but the concept holds. The mathematically astute may note that the number doesn't have to be literally equal for the sportsbook to profit, but it needs to be pretty close.

The Math

Sportsbooks are in the business of making money. They built resorts in the desert with that money. As you can imagine, oddsmakers deal in probability, and are tasked with things like “exposure” and “risk management.”

The first and perhaps most important concept that I've found helps people make sense of the “guaranteed profit” myth, is this: sports betting is a portfolio. Each game makes up a percentage of that portfolio.

Similar to a casino, where a game like roulette has a clearly defined “house edge” - the casino doesn't set up the game to attract “equal action” on black and red. Or odd and even.

That would, of course, be the “ideal” scenario but it's simply not possible to enforce.

Sportsbooks, like casinos - because they're in the business of making money - are more concerned with long term good exposure than a “guaranteed profit” in every event: they accept some risk of loss with every spin, every card, every bounce - as long as there's a greater chance of winning.

And this roulette analogy works quite well for the basic “math” section:

If I stumble up to an empty roulette wheel and place a $1,000 wager on “black” do you think they'll announce to their patrons they're offering a better payout on “red” to entice more action? Or turn me away because they don't have anyone else on “red”?

Of course not. There's about a 48% chance I double my money, and a 52% chance I lose. They're perfectly content with that exposure.

For this spin, the casino may lose money. This specific roulette wheel may “lose them money” for hours, days, even weeks. But “this specific roulette wheel” does not make a casino. Because the odds are in their favor, even if only slightly, they will make money in the long run - at this wheel, and across the casino.

Now consider a sportsbook with perfect balance on a game: $10,000 on both sides. A second before the game starts, I try to get my stumbly $1,000 bet on whichever team wears black jerseys, because black is hot, baby. Do they take it? If the goal is balanced books, they could simply turn me away. But they never do. Almost.

Moving Lines!

In sports betting, unlike roulette and other casino games, there's a unique mechanism sportsbooks have at their disposal: they can change the line.

A game that starts at “Team A -3” may move to “Team A -4.” Now, the additional point may inspire more action on Team B +4. Theoretically, this may “balance the books” but this move is also not without risk. If Team A wins by exactly 4 - a probability that can be calculated - they pay out the “-3” bettors, and the “+4” bettors get refunded.

Alternatively, instead of moving the line, sportsbooks may modify the juice on the wager. Instead of Team A -3 at -110, they may change the line to -3 at -120. The corresponding change would allow bettors to take Team B +3 at +100.

Within tight bounds, these moves don't necessarily create bad exposure.

However…

Huge Exposure

What's a sportsbook supposed to do when they take six figures of action on one side?

And the action keeps coming in on that side?

Then they move the line…

And it keeps coming in on that side? Millions of dollars profit or loss riding on the outcome.

It turns out, people who bet for fun (we'll call them casual bettors) make up almost all of the money wagered on any given game. You can't “control” which side they bet on, any more than you can control whether they bet red or black in roulette.

But! Mythholders insist - you can PREDICT it!

That's kind of true, actually. Casual bettors disproportionately bet favorites, and “overs.” And coinflip bettors disproportionately prefer heads.

(Though rarely so drastically).

So the next step of the hypothesis requires asking…how much do you need to move the line in order to attract “equal action” on both sides?

And this is where it breaks down. All because of the dreaded Sharps.

Sharp Bettors

While casual bettors bet for fun, sharp bettors bet because they believe they have an edge. They tend to have deep pockets, discipline, advanced models, and lots of “outs” (places to make bets). Sharps don't just try to identify wagers with edges, they act quickly to compare odds across books, get the best odds, and aggressively wager: lines may “correct” in seconds or minutes. Getting an extra half-point on a spread, or -105 juice instead of -110 makes a remarkable difference in a sharp’s long term profitability.

And here is the main reason the “even money” hypothesis breaks down:

Sharps act as a “check” on bad lines, even if a particular line would have otherwise attracted even money from casual bettors.

Sharps don’t wager on a given game or side just because it's a big game, or they're bored… their wagers are dependent on the line.

Other fields have names for this error of thinking:

Economists have the Lucas Critique: models that treat behavior as fixed break down when in reality people adjust. Setting a line intended to respond to bettor behavior changes bettor behavior.

Goodhart’s Law applies in that if sportsbooks targeted balanced action instead of accurate pricing, the line becomes exploitable - because sharp bettors respond to mispricing, not balance.

The larger, more universal flaw in reasoning is called endogeneity. It means a variable is jointly determined inside the system (dependent), not independently set from the outside.

The mistake:

Treating something that responds to your decision as if it were independent of your decision.

Simply put, the only way to ensure long term profitability is for oddsmakers to set lines with the result in mind. For events with odds around -110, their line needs to result in each side winning close to 50% of the time.

I think I have successfully simplified this:

50-50 Myth Flow Chart

A Fine Hypothesis You Have There

Like all good hypotheses, we have to honestly answer questions like:

• What would we expect to observe if the hypothesis is accurate?

• What would serve as evidence against it?

It follows that if sportsbooks are trying to get 50-50 action, they should (at least) often or usually get it. Likewise, if they're setting lines with regard to outcome, favorites should win around 50% of the time, as should overs.

Some years or decades ago, before sports betting was as easy as a few clicks in an app - it was quite hard to know how much exposure sportsbooks had unless you were an insider. Which is to say, it was kind of forgivable to say that even though my reasoning makes sense, I couldn't really “prove” it.

After all, are sportsbooks really taking six, seven, or even eight figure risks in individual games?!

Yes.

It is literally public information now.

And even people who make the odds aren't shy to talk about “needing a side”

The reality is that they almost never get 50-50 action, or close to it! 75-25 splits are more common.

But guess what they DO achieve?

With regard to the actual result, their lines yield outcomes very close to 50-50.

For any given game - like any spin of the roulette wheel - they may lose money. They may lose a lot. For days, weeks, even months on occasion. But as long as their exposure is good exposure, they know that in the long run they'll make money. Here's a random baseball game today.

The fact is - if sportsbooks are setting lines to “try and get the most action on both sides…”

They will lose money.

If their models don't pick the winner, someone's model will.

From The Makers’ Mouths

If you're not sufficiently convinced by everything I shared above - from the math to the logic to the actual numbers - you don't deserve to keep reading this article. But since it's the only good source I've found that deeply addresses the 50-50 myth, I should share:

From the article:

There is a popular belief that sportsbooks take an equal amount of money on both sides of a game to guarantee a profit.

Is it fact or fiction?

“That’s a fallacy,” former William Hill and Caesars Sportsbook director Nick Bogdanovich said. “It never happens that way. The books always have decisions. That’s the bottom line. And some are bigger than others.”

Red Rock Resort sportsbook director Chuck Esposito:

“It’s somewhat of a myth to be able to divide action equally on every game,” he said. “We’re going to have a vested interest in every game in every sport.”

Westgate SuperBook Vice President Jay Kornegay:

“an urban legend.”

South Point sportsbook director Chris Andrews:

“There’s almost always more money on one side than the other, either naturally or by design.”

Sharps vs Books

Your friendly author with some explanation here - by design? Why would sportsbooks want more money on one side by design?

Well, if their goal was to balance their books - they wouldn't. But you understand now that it's a myth. Still, it's weird to think about sportsbooks effectively gambling on a side. But that often happens.

MGM Resorts director of trading Jeff Stoneback said:

“when professionals get involved, we want to make sure we’re on their side.”

The answer to the question most people have: “why would sportsbooks let someone they know is ‘sharp’ bet with them? Aren't they afraid to lose money?”

Starts to fall into place now.

Andrews, who refers to sharps as “wiseguys” says:

“If I have the wiseguys on one side and the public on the other, I’ll do my best to go in needing the wiseguy’s side to win.”

One of the most commonly cited facts among the mythholders is that lines and odds move, which they conclude supports their “equal action” hypothesis.

Setting aside the fact that lines can change due to player injury reports, weather, and lots of extraneous factors, we can strip all of that away and again follow the direction of line movement according to the money wagered.

If the goal were even money, the line should change to benefit the team or side that has received less money. But that isn't how it works.

Kornegay says:

“A regular house player can bet six figures, and there’s a chance we might not move the line. But there are times a very sharp player bets 10 dimes on something, and we could move it off of their $10,000 bet.

In fact, there are many examples of teams getting a lot of money bet on them, and their line gets worse anyways. It happens so often, there's a name for it: Reverse Line Movement.

For example, if Team A is -3, and has received 80% of bets, the “even money hypothesis” says the line should be moved to -3.5, -4, or higher, to get more action on Team B.

So why does the line sometimes move to -2.5 despite that?

Wiseguys.

This can only make sense if line accuracy > bet distribution

It's not about even action. It's about good exposure and volume. There's a life lesson in there somewhere, probably.

Relating To My Other Work

Traditionally held beliefs are hard to overcome, especially if they're in the majority. Whether it's Nate Silver pushing polls-as-predictions into mainstream prominence, or whatever pseudoscience is popping right now, being able to overcome that bias - changing your mind when presented with correct information - that's how science is done.

In other words:

All models have assumptions. There’s no such thing as a “purely data-driven” model - only models whose assumptions are obvious, and models whose assumptions are hidden or intentionally obfuscated or ignored.

The difference between a good model and a bad one isn’t whether assumptions exist. It’s whether those assumptions are valid, explicit, and aligned with the real-world process being modeled.

The best models don’t pretend to eliminate assumptions - they interrogate them. They ask:

• What must be true for this input to have meaning?

• What mechanism links this variable to the outcome?

• What happens if that mechanism doesn’t hold?

Weak models do the opposite. They inherit assumptions - often unconsciously - because they are standard, convenient, or historically accepted. They optimize for the recent past (so they can say it backtests well) without asking whether the inputs actually measure what they claim to measure.

And in domains with limited, noisy data - like presidential elections - that distinction becomes everything.

Because when the data is sparse, assumptions don’t just support the model…

They are the model.

In most cases, "what happened last time/game/season" is the most basic model. And it's not always the worst. But it does have a ton of assumptions - such that it is NOT always the best model. Sometimes it's not even the best starting point.

Nate Silver's political models did exactly this.

My predictive models for player performance noted the reasoning flaw used by Silver:

And in political applications, Silver’s models were honestly even worse than that.

Silver's Early Models

In 2008, his first public models, he noted that his older versions had “heretofore” assigned undecideds 50:50. (Back to that in a moment)

But he then says he doesn't want a neutral assumption, he wants a predictive one. A nice sentiment, if you can keep it.

In his efforts to be "more predictive" he looks at primary data, how much Obama "overperformed" in each state (by comparing the margin of the poll to the margin of the election)…and uses that to inform his general election undecided allocation.

There is so much wrong with this approach.

The two things most wrong are:

1. It assumes primaries & general elections are similar enough to use in a predictive model

In primaries, it's D vs D. In general elections, it's not.

A voter switching their polled preference from Biden to Obama before the primary (thus causing a poll "overperformance") is far more common and likely than switching from McCain to Obama during the general.

This is a problem I've effectively solved, but apparently still stumps the field's experts, like when they asked “perhaps it is harder to predict the margin when more candidates are
running?”

2. The assumption that this poll “spread” vs election “spread” is a measure of "overperformance."

At some point (I think 2012, certainly by 2016) He realized this "model" was garbage.

Not because he noticed an error in his process, mind you - but because he realized this allocation wasn't predictive.

He reverted to the 50:50 assumption, adding error bars with varying size and tails.

This process highlights a central, and frankly, elementary modeling problem.

The Predictive Modeling Problem

There's a huge correlation-causation problem when it comes to "predictiveness" such that construct validity is absolutely ESSENTIAL to a model's viability.

Modern forecasters copy Silver's approach to using how well polls “predict” some result because they can't fathom of a better approach.

The problem is that metric can appear highly predictive purely by chance, especially in small samples or noisy systems. Because Presidential Elections are four years apart, it feels like going back to, say, 1996 is a long time. The reality is that the sample size from that is eight. Literally eight.

Some (like Silver) believe this can be improved by going back farther…but now you're including far fewer polls with very different methodologies from a far less polarized populace…to get your sample size to, what? Twenty?

There is no fixing the sample size problem in Presidential Elections. And critically: these are not independent, identically distributed (i.i.d.) observations.

Even if you weight by recency, you're just back to the sample size problem. It's circular.

So when analysts say things like:

“Over the last 4 elections, pollsters have had an average error of X”

What they are implicitly assuming is:

• Those 4 elections are comparable

• The underlying error distribution is stable

• The causes of past error will persist in the same way

None of those assumptions are reliably true, some are provably false.

This creates the central problem of “predictive” models:

A poor predictive metric can have a high predictive correlation if your only concern is "does it get the right answer?"

This is PROBABILISTIC reasoning vs DETERMINISTIC reasoning. (Put this in a new tab to read next. This concept is not as intuitive as it seems.)

For example, the alphabetical first name of the Vice Presidential Candidate has successfully predicted the last 14 elections. 14/14. Insane. Does it get the right answer? Better than any system ever.

Doesn't mean it's a valid metric.

That is a more obvious example (probably 0 correlation despite high predictive accuracy) than the relationship of poll leads to election margin of victory: a metric that does have some correlation - but not nearly as high as experts seem to think. And it's still internally invalid.

Analysts around the world are always looking for an undiscovered or underutilized metric that has explanatory value for some outcome.

But laymen like Shane (who have far more in common with the field's experts than you would believe) think "a single realized event" can meaningfully measure "accuracy."

If I say there's a 67% chance that Iowa St. beats Kentucky in the March Madness game tomorrow…

And someone else says 50%…

The game's outcome is irrelevant to the accuracy of each model!

When we talk about uncertain future events with probabilities that are absolutely unknowable, it seems rational to use "closer to result" as a substitute for "true value"

But this is hindsight bias.

If you ask me the odds of rolling a 3, 4, 5, or 6 on a single die, the answer is 4/6 or 2/3

We can call it 67%

Someone who says "nah, either it happens or it doesn't, 50/50" is not validated when the roll happens to be 1 or 2.

Based on this "single realized event" they were "closer to the result" - but this is meaningless.

But there's no way smart experts would do things like this...right?

Welcome To My Hell

Based on a sample size of one election, Silver (and a consensus of experts on poll data around the world)

Believe that, yes, we can say with a remarkable level of precision who the most accurate pollster was based on one election.

Silver and others use this assumption in their models to give more weight to "more accurate" pollsters in future elections 🙃

And, if you could believe it…it's worse than that.

Leading up to the 2012 election, Silver noted that there was “not a single instance in the database where a candidate lost a state when he held a lead of more than 3.5 points in the polling average (in highly polled states) at this point in time.

A 2.4-point lead in the polls, Silver calculated then, amounts to roughly an 80% win probability.

By 2023, they claimed a lead of this size is “little better than tossup”

The reason these calculations continuously fail, is because they're assuming a strong correlation where there is only a small one. All of their calculations, every single one of them - no dispute, no argument, no debate - they all assume that undecideds split 50-50 in every case.

The thing Silver said in 2008 wasn't a good assumption, but then abandoned because he couldn't figure out how primaries and general elections have different underlying variables…

That assumption underpins every single calculation made for poll accuracy. Every single one.

And they use a sample size of "one election" to justify this.

It all starts from the same untested axiom that he (and the rest of the field) has always used: comparing margin of the poll to the margin of the election. The field simply cannot fathom the assumption that "accurate polls will predict the winner and margin of victory" being invalid - despite it being a trivial proof.

Their bias + tradition does not allow them to question the core assumption. A pattern that often repeats itself in scientific history.

To wrap this up with Silver's more recent models:

Yes, his more recent models are "better" in that they model a range of outcomes with appropriate uncertainty.

But I found a hidden variable in his models thanks to a very simple input error that proves he STILL uses this "most recent election" logic to inform that uncertainty calculation.

In 2020, Silver said Trump had a 10% chance to win Maine

This was absolutely baffling, considering Biden had a 53-40 advantage in the poll average. My model (and others) put Biden’s chances in Maine at 99% or higher (thus Trump's at or below 1%).

So why the discrepancy?

2016.

In 2016, it's often claimed Trump drastically "overperformed" his polls. He didn't, really: he won a majority of undecideds and a big chunk of people who said they were going to vote third-party but changed their mind. This doesn't mean the polls had “zero error” - sure - but there's no question much or most of the ascribed error as calculated by poll vs election margin was contributed by this factor that has nothing to do with the poll's accuracy.

This claim of "overperformance" was a case study in what happens if a field's consensus doesn't understand what a confounding variable is.

Nonetheless, due to this "overperformance" resetting every model's priors about how "off" polls could be, Silver's model was EXTRA careful.

But that's not all...

He didn't use a uniform "uncertainty" procedure.

He used the "poll margin vs election margin" logic FROM EACH STATE to inform his model's range of possible outcomes.

States that had a larger "error" by this 2016 calculation were more likely to have a larger error in 2020, in his model.

In Maine specifically, their model had a sign error!

From my book:

(FiveThirtyEight's analysis) said Hillary was "+6.9 in Maine polls" and "LOST by 3"

A 9.9-point "error" by this metric

THAT'S NOT RIGHT!

Clinton won Maine by 3, which (by his math) is a 3.9-point "error"

Given Biden's "+13" position in Silver's reductionist model, a 9.9-point error being within the range of plausibility is the ONLY way you can conclude a 10% chance of losing.

Copycats

I have come to the highly evidenced conclusion that the only reason my political models ever differ from others is because the other models copy Silver's.

They use the exact same "margin" logic, they use the exact same "well, I have data from like 8 recent elections, that's CERTAINLY a large enough sample size to derive meaning from this invalid polls-as-predictions metric"

When I started, I was either too conceited or lazy to try and copy Silver. I used poll data as a starting point, not a prediction of the result.

That led to some remarkable discoveries.

You can read about them here or here or this interesting article, elsewhere on my Substack, ask me about them, or for a really deep dive, my book.

I'm a math nerd, and a stickler for statistical literacy, so if I told you my tips would make you win your bracket pool, I'd be lying.

The truth is, following these tips will double or triple your chances - depending on how good your competitors are.

Bracket math

If there are 10 people in your pool, you have about a 1/10 chance to win.

If there are 100 people in your pool, you have about a 1/100 chance to win.

And so on.

Yes, that is to say that even math doesn't guarantee you'll win.

But anything you can do to increase your win probability is good.

That all starts with the champion.

Champ Picks

In order to win your bracket pool (assuming your pool is larger than like five people) you will almost certainly need to pick the right champion.

For that reason, you're not competing against everyone in your pool: you're competing against everyone who picks the same champion.

If you are the only person in your pool to pick that champion, your probability of winning your pool is almost exactly equal to that team's probability of winning the championship.

For that reason, we can calculate that the bracket with the best probability of winning a pool is the most unique bracket that has the best chance of truly happening.

In other words: calculated risk. Calculated being a very appropriate term here.

Here's my math for the championship:

A Little Lingo

Small pool = 100 or fewer people

Large pool = 500 or more

Green = good pick (with a few qualifiers)

Red = bad pick (with no qualifiers)

Because you need to pick the right champion to have the best bracket, it's best not to go too crazy here, unless you're in a very large pool. There's nearly a 60% chance that one of Duke, Michigan, or Arizona wins the championship. I will refer to these as “Top 3.”

If you choose one of them as your champion, it's recommended that you choose a few small and/or medium upsets depending on your pool size. Recommendations below.

Upsets Math

Because you want a unique bracket with only calculated risks, my biggest recommendation for anyone not in a very large pool is to not pick too many upsets.

Upsets happen every year. They will happen this year, too. But predicting which ones will happen ahead of time is a mathematically impossible task - literally. Even the most well-informed stats nerd can only get you to a ONE-IN-TWO TRILLION CHANCE at a perfect bracket.

For perspective, it's far more likely that a 16-seed wins the championship.

One of the biggest advantages you can have in your bracket pool is to pick a mostly boring bracket with only a few of the most valuable upsets. Valuable meaning “likely to make your bracket unique without being implausible.” I'll give my recommendations for each region.

“Upset” definition:

I assign “upset points” to various selections to guide which, and how many, upsets you should choose to maximize your chances.

If an upset fits multiple categories below, DO NOT double-count upset points, take only the largest value one time.

Catch all (+x upset points):

• The sum of the seeds in your Final 4 minus 6 (if 6 or less, 0 upset points).

Wise Champion Pick (-1 upset points)

• Duke, Arizona, or Michigan to win the championship. Highly recommended for small pools.

Not an upset (+0 upset points):

• 9 over 8 in the first round.

• A better seed (e.g. 4 over 13) winning.

Small upset (+1 upset point)

• Team with a seed EXACTLY ONE LOWER than their opponent (e.g. 5 over 4) EXCEPT 2 over 1.

• Florida to win the Championship.

Medium upset (+3 upset points)

• Any double-digit seed winning a game in any round (this adds for each victory)

• A team with a seed TWO TO SIX higher than their opponent winning (e.g 6 over 3) OR 2 over 1.

• Any #2 Seed winning the Championship

• Round one only: a team with a seed SEVEN TO NINE higher than their opponent winning (e.g. 12 over 5)

Large Upset (+5 upset points)

• A team with a seed SEVEN TO NINE higher than their opponent winning in any round EXCEPT round one (e.g. 10 over 2)

• A 3 or 4 seed in the Final 4

Huge Upset (+7 upset points)

• A 3 or 4 seed winning the Championship

• A team with a seed TEN OR MORE higher than their opponent winning in any round.

Enormous Upset (+10 upset points)

• Any seed higher than 4 in the Final 4

• Any other champion

Enormous upsets should be reserved for people in enormous pools: 1000 or more.

Small pools (under 100 people): Choose 3-6 upset points

Large pools (over 500 people): Choose 7-14 upset points but no enormous upsets

Enormous pools (over 1000 people): Choose 14-24 upset points, with at least two large or huge first round upsets.

Final 4 Selections

Left Side

On the left side of the bracket, Connecticut, Houston, or Illinois (+3 upset points) are good picks. If you do not choose Duke as your champion, Connecticut over Duke is a good upset choice for large or small pools.

Nebraska or Vanderbilt (+5 upset points) are good choices for large pools.

Louisville or UCLA are good values because almost no one picks them to go far and they have a small chance to do so. But remember: they would likely need multiple upsets BEFORE the Final Four, which makes an “eggs in basket” problem. Enormous pools only.

Right side

Iowa State is a good Final Four choice for large or small pools, as is Purdue (+3 upset points).

Tennessee is a strong 6 seed, and would probably be my favorite pick to make an Elite 8 (large pools) or Final Four (enormous pools) as long as the rest of my bracket was relatively tame.

Round 1

Going quickly because you only have a couple hours to get the brackets in!

Midwest

West

East

South

Good luck!

That doesn't mean people won't try to lie to you.

I'll also remind you, many arguments people make (with statistics or otherwise) have little to do with genuine reasoning. They are simply choosing what they perceive as the “most reasonable” argument to support their desired conclusion.

This meme is especially popular among the right, even cited by the Vice President as proof of gerrymandering “in New England.”

Here's a simple question to test your knowledge on Gerrymandering - and a question I highly recommend you ask anyone before engaging in a discussion on the subject:

Do you think gerrymandering is when a party doesn't receive a number of representatives proportional to their statewide vote percentage?

For example, since Connecticut votes 36% Republican statewide and received 5 Representatives, do you think the fact that they don't have 1 or 2 Representatives from Connecticut is proof of gerrymandering?

Now, this is where it is very important to understand the purpose of this question.

The meme obviously implies that this is the case (despite ignoring some important facts like that Vermont literally has one representative elected statewide).

But when you're “debating” or “arguing” or “discussing” what is true with someone, it is implied that facts and truth are the goal of the conversation. I hate to break it to you, but that's not usually the case.

Do not allow this to remain implied, or their position to remain implied: make them state it explicitly. This is not too much to ask, though they will pretend it is (because it doesn't allow them to engage in performative debate where they can pretend opinion and feelings are substitutes for facts, data, or science).

Anyone who is willing to engage honestly about “gerrymandering” will have no problem defining “gerrymandering” - or more directly - answering a simple yes/no about what gerrymandering is or isn't.

Disingenuous people THRIVE on their arguments not being pinned down, because it gives them escape routes. By pinning them down to a definition immediately, you eliminate their comfort zone.

It happens that debates of fact are systematically biased in favor of those who have facts on their side. My approach is simply a shortcut to the finish line.

This graphic, which I've seen shared by the left and right alike, is a much more subtle piece of misinformation - because it's a nice looking graphic instead of a meme - but it follows the exact same reasoning as the graphic above.

It assumes that “fair” representation is when parties receive a number of representatives Proportional to their statewide percentage.

Districts are winner-take-all. You don't get a tenth of a representative for 10% of the vote. You get 0.

That's exactly how many you get for 40% of the vote.

According to this graphic, that's "unfair.”

There is nothing unfair about “2” in this graphic. The fact that red gets zero reps despite 40% of the population has nothing to do with fairness, everything to do with population distribution and our electoral system. Womp womp.

Districts provide representation to geographical areas, not a state. If lines are not drawn with the explicit purpose of gaining a political advantage, it's not Gerrymandering. 2 is about the fairest map possible.

Does the Northeast Gerrymander?

This section is for people who don't care to debate, and just want to understand facts. I cannot impress upon you enough the importance of NOT skipping here with someone who asserts this to be so. Follow the instructions above.

That being said.

No.

The Northeast has relatively small states that vote more Democratic than average in rural areas, and the large cities (which are even more blue) have to be split to ensure all districts have an equal population.

Massachusetts, for example, receives 9 Representives statewide, and voted about 36% Republican in 2024.

People who don't understand statistics (willfully or otherwise) might be led to believe that ZERO Republican seats can only mean “gerrymandering.”

But fair districts are not drawn to give proportional representation. They are drawn to give geographical representation.

To win any district, a candidate must win the most votes in the district - that percentage of votes is usually at or near 50%.

Here is how Massachusetts districts are drawn:

And here is how those areas voted:

This map shows that even the counties Trump won were not by the margins you see in rural areas of other states. Any accusation of gerrymandering would logically require splitting (unfairly or otherwise) the red areas to prevent them from getting to 50%. Without looking at the population of the counties (an important variable) the accusation of gerrymandering only even looks possible in Districts 1 and 2, and maybe 4 and 9.

District 1: Democrats won with 62.5%

District 2: Democrats won with 68.6%

Those districts can't be shifted in any way where Democrats don't win by 20+.

District 4: Uncontested

District 9: Democrats won with 56.4% - the closest district by far.

The fact is this:

Not only is there no gerrymandering in Massachusetts or other northeastern states…

There's literally no way to draw maps in Massachusetts that would guarantee Republicans even ONE district.

That's correct.

Even if you tried to pack the red areas into a district to get Republicans at least one Representative - a kind of reverse gerrymander - you still wouldn't be able to, because the population of those red areas are too small to qualify as a district!

The best possible reverse-gerrymander for Republicans would MAYBE get them ONE seat. That is, a chance at 1/9 (11.1%) in a state that is about 37% Republican. If you don't understand math, or our electoral system, that might seem “unfair.” And remember, it would require drawing maps with the sole purpose of favoring Republicans as much as possible just to achieve that.

A fun math fact:

When it comes to gerrymandering, the distribution of the population is more important than the overall percentage.

In Massachusetts, Republican votes are scattered.

On the other hand, a state like Missouri (with 8 Representatives) is almost as Republican-leaning statewide as Massachusetts is Democrat-leaning.

However, by nature of Democratic voters being concentrated in major cities - and districts having a set population size - it's impossible to draw maps where Democrats don't get some seats in Missouri.

I'll let you infer which district(s) elected Democrats in 2024.

I also wrote about the anti-democratic practice that is gerrymandering, what's happening in Virginia, and what the paradox of tolerance has to do with this.

If you found this article enlightening or interesting, use your knowledge for good.

Subscribe to get important and insightful updates ahead of midterms (plus some surprises) and scroll my Substack for more analysis.

Likewise, the House of Representatives being artificially capped, though less impactful, also plays a role.

The most aggressive gerrymandering was by Republicans in the 2010 redistricting cycle. The strategy, called REDMAP - which I prefer to call “ratfucking” - disregarded norms and seeked to maximize political gain.

My home district looked like this:

Contrary to popular belief, districts that are “weird shapes” are not inherently unfair or biased.

Moreover, removing myself from the pesky “fairness” mindset - as a strategist - this is exactly what should happen for a party seeking to maximize power. This article isn't to convince you of the ethical problems with gerrymandering. If you'd like to read a short summary of the history and implications, this is a good start.

Unilateral Disarmament

Unilateral disarmament is problematic both strategically and ethically, somewhat akin to the “paradox of tolerance.”

When your opponent exploits loopholes and bends the rules when given the chance, you not doing so in return gives them a disproportionate advantage. For many years, Democrats believed that in order to achieve their eventual goal of abolishing gerrymandering, they needed to maintain a moral consistency of sorts by not gerrymandering. Though not the case across the board, there was a clear lean.

The net result was that the states with the most support for Democrats were mostly “fair” to Republicans, while Republican legislatures largely attempted to maximally disadvantage Democrats.

As Democrats begin to fight back, there's a new map taking shape:

Gerrymandering may be shifting to be a net benefit to Democrats.

This recently passed and approved California map will likely cost Republicans a few seats.

This Virginia map still needs to pass the VA Supreme Court - which is a major hurdle - but would likely net Dems a few more seats.

All-in-all, Democrats have started to fight back…and realized that when they play by the same rules, they may be even better at the game.

Human nature biases us in favor of things that benefit “us” - and against things that don't. We rationalize with excuses (which we call “reasoning”) as to why that system is better….when the real reason is “it benefits me.”

I wrote an article explaining why this happens.

Predictably, Republicans are suddenly concerned with the “disenfranchisement” caused by gerrymandering…how it's “unfair.”

And as Democrats benefit from it, they start to support it, then have no strategic advantage to abolishing it.

In order to abolish gerrymandering, one side will have to sacrifice their own advantage. And the probability one side is willing to abolish it correlates directly with how much benefit the other side has…thus making them unlikely to want to.

Everyone says they want fair maps. Almost no one is willing to accept a process that might disadvantage them next cycle with no one to blame.

If we ever reach that day, the problem is only half-solved. How can we draw maps that are truly fair?

It's Harder Than You Think

For one, let's say some bill was passed to abolish gerrymandering. What does that look like? Bipartisan commissions deciding what a fair map is? A state Supreme Court? That's a larger hurdle than it seems - because of the partisan bias that remains.

Beyond that, some proposals for multi-member districts are theoretically appealing, because it would more closely achieve “representativeness.” Those risk creating a new type of mandering where single-member districts have disproportionate power.

Other proposals that seem fair (like drawing maps according to racial or political boundaries to ensure proportional representativeness) still requires humans to distinguish partisan and/or racial affiliation, and then draw the lines based on this data. Who gets to define what is “fair” creates a new problem.

A truly “representative” map - by my definition - requires all states to agree on a framework, such that no side has an inherent advantage or disadvantage.

Do I think that will happen? No.

But if it did happen - and the states came together and said “we all want to get rid of gerrymandering, we will agree to any system that doesn't guarantee a partisan benefit to either side”

I believe the solution should be to work within the existing system: single-member districts, redrawn every 10 years.

Here's my solution:

Draw Districts At Random

Random does not always equal fair. The point is that it is the fairest approach. It is the only serious answer that can solve the larger problem: it eliminates the systematic bias inherent in the current process.

Here are the constraints I would propose:

• Each district has the same population, plus-or-minus some % tolerance

• Contiguous districts

  Here's what that looks like in practice:

  • Precinct chosen at random by code

  • Continue to continguous precincts at random until the population threshold is reached

Repeat

The only inputs needed to the program are population size by precinct and their respective geography.

Yes, this will often result in “weirdly-shaped” districts, and other aesthetically displeasing things. I'm not sure this is a major issue.

I also understand the resistance to allowing computers to draw maps…this is the most common contention. But I have some news:

Computers already draw the maps. They have for decades.

As of now, the inputs are to maximize partisan advantage. My proposal is to remove all possibility of that.

“But who makes the code?!”

Is also not a substantive rebuttal. Random and contiguous are simple and transparent parameters, not riggable ones.

Why this is fairer than anything else:

• No guaranteed partisan outcome

• Some random maps will favor Democrats. Some will favor Republicans. Across states and cycles, those advantages cancel out.

• Outcomes reflect voters, not partisan bias.

• You can’t rig a randomized procedure.

You can argue about whether a particular outcome is “fair,” but you can’t argue that it was designed to help someone.

No, I don't think this will be adopted.

I created it in response to someone challenging me to create a system such that even if everyone agreed to abolish gerrymandering, it wouldn't still contain strategic partisan loopholes.

I don't think the system of letting partisans draw maps to maximize partisan advantage then relying on partisan and/or biased courts to determine whether said map is technically illegal or not…is a superior option or sustainable.

If you want to propose improvements or argue against this procedure, you're welcome to do so.

I only request that you do better than - who was too cowardly to respond directly to me, and too ignorant to provide any argument of substance.

As with other better-known fallacies like “moving the goalposts,” “appeal to authority,” and the plain old “strawman,” identifying the flawed reasoning is the first step necessary to overcome it.

One of the reasons the “most reasonable excuse” (or “self-strawman”) has not been previously named, I believe, is because it overlaps with several well-known fallacies - but does not neatly fit any individual one. As a result, it escapes classification, even though it represents a distinct and recurring pattern of logical inconsistency and disingenuous argumentation.

First, The Definition

The “most reasonable excuse” or “Self-Strawman Fallacy” is defined as:

Defending an unstated belief by adopting a separate position (the excuse) chosen because the user views it as most effective at defeating an opponent and/or shielding the belief from criticism. Notably, even a successful refutation of the excuse does nothing to overturn or challenge the underlying belief.

Perhaps somewhat impossible to prove - though no less real - some users of this fallacy seem to invoke it on a subconscious level. I'll provide evidence and examples below.

The Rationale/Theory

Whether conscious or unconscious, certain beliefs are deeply held and resistant to change. When these beliefs are threatened, people experience cognitive dissonance - the psychological discomfort that arises from holding conflicting thoughts or from evidence that challenges their core convictions.

While most people simply ignore or rationalize the dissonance in their mind (thus never exposing it to criticism), the increasing prevalence of social media and high visibility, polarizing events has led to more people making statements. Whether those statements reflect their true beliefs or are simply excuses adopted to defend them is central to this fallacy.

The most reasonable excuse fallacy arises as a strategy to manage that dissonance while maintaining the appearance of rationality. I believe this fallacy is most often used when the user knows (again, consciously or subconsciously) the unstated belief is irrational, or perhaps even unethical. I would welcome formal research on this subject.

If my hypothesis is correct, the most common belief that someone who uses this fallacy holds is: “nothing would change my mind.”

Of course, that statement is unscientific (and irrational, by definition) so anyone who wishes to present themselves as a competent, serious person - a prerequisite to engaging in argumentation - could never admit that.

The excuse is selected based on its ease of defense without exposing the true belief, not a particular conviction. There also appears to be Gish Gallop-like element to this tactic, forcing the opponent to combat various positions only indirectly related to the topic - creating a win-win-win for the user:

• If the opponent gives up, or fails to effectively combat the excuse, the user can claim victory

• If the opponent refutes the excuse, but engages in side arguments or the user forces them to become mired in technicalities, the central topic can still be avoided

• Even if the excuse is defeated, the user hasn't lost, because their true position is untouched. More excuses (layers) provide distance between stated contention and true belief

As the excuses are defeated - or ignored until terms are explicitly agreed upon (e.g. “if I defeat this argument will you admit it fails and commit to never using it again?”) - users seem more desperate to escape the argument without meaningful engagement.

For that reason I believe that the layers - the distance between the excuse and the true belief - correlates very highly with the willingness of the user to engage earnestly (or feign earnestness).

While it may seem obvious, it must be mentioned: an individual unwilling to state their position clearly and honestly, and stop using it if disproven, is engaging in performance, not attempting to discover truth. This deception would make it the single largest contributor to ineffective* discourse.

*Ineffective in this context mean failing to resolve conflict in accordance with any scientific validity - a waste of time.

Some people believe that stating an opinion is itself an argument, that this opinion merits as much respect as any scientific fact (framed as your opinion), and take any disagreement as a personal attack.

Before explaining how to combat this without openly asserting bad faith, a few examples to provide some context.

A Few, Short Examples

My first serious contention with this fallacy was one of the most glaring: debates regarding Greta Thunberg.

In her rise to notoriety, Thunberg was a teenager speaking in favor of policies to urgently combat human-driven Climate Change. As a response to her activism, social media and mainstream commentators pointed out:

• “She's just a kid”

• “She's not a scientist”

• “She's not an expert on climate”

Taken at face value, those seem like perfectly rational reasons to reject or even ignore her case. If you don't accept the realities of climate change - or simply dislike her activism - cognitive dissonance demands that the challenge be neutralized.

Remember, since the vast majority of people are not subjecting their beliefs to criticism, any of these rationalizations is accepted by the brain as a resolution to the dissonance.

But as previously discussed, private reasoning leeches into mainstream discourse, and these excuses form the first “line of defense” for users.

How can I say with certainty they are excuses?

Because if an adult, scientist, expert said the same things Thunberg did (defeating all listed excuses) - the users would not accept or consider the same arguments valid. They would introduce some other reason (or excuse) to reject it.

It follows, then, that those “reasons” were not reasons for disbelief - but excuses to dismiss the undesired conclusions.

And that was my first insight into why the fallacy is so prevalent, and how it's used. My first attempt to define this fallacy informally called it the Thunberg/Nye Fallacy.

Why Bill Nye?

As one of the most popular modern commentators on everything science, Bill Nye “The Science Guy” talks about issues that cross over many different fields.

But as anyone who has the unfortunate experience of engaging with anti-science activists, you'll note:

“He doesn't even have a degree in science! He's an engineer! Not a scientist!”

Now, most educated readers understand that engineering requires a lot of science courses - and in any case lack of degree in a specialized discipline does not equal lack of competence in it - and I'd wager in a discussion or debate you'd be tempted to point this out. Most people do.

And that's exactly why anti-science people say it.

I direct you to bullet number two from my win-win-win presentation:

“Engages in side arguments…mired in technicalities.”

The user has successfully deflected from whatever fact or argument was presented by Nye, shifting the debate to his personal credentials.

In both above cases, the “most reasonable excuse” seems reasonable to the user. Their argument takes the form of: I shouldn't be expected to change my scientific beliefs just because a high school student asked me to - or an adult non-scientist made a show about how sex is a spectrum. Why should I?

As with Thunberg, this ad hominem fits neatly into the larger category of “fallacy of relevance.” Once addressed, users move the goalposts.

For that reason, it seems clear that this “most reasonable excuse” fallacy should fit into the same taxonomy. In fact, both arguments above are basically just ad hominems to begin with, followed by moving the goalposts, so it seems like - so far - it shouldn't need a new name.

But the use of excuses does not always use ad hominems, nor does it always fit under the already broad umbrella of “fallacies of relevance,” nor is the excuse always fallacious at all!

Why It Needs A Name

The distinction between this fallacy and others is that what the argument is doesn't always describe how it's being used.

In other words, some use ad hominem sincerely, because they believe it is a valid argument. However, others do it strategically, understanding that the argument is flawed on some level, but do so in an effort to keep layers between their belief.

In the latter case, the fallacy is not the error - it is the instrument. A means to an end. The argument is selected not because it is believed, but because it is perceived as effective. If challenged, even defeated, the user has succeeded at forcing the opponent to expend time and effort to overcome it. Since the argument was not made sincerely, it can be discarded without meaningful concession or dissonance by the user, and the next-most reasonable excuse introduced.

Indeed, much of my experience and research on the subject results in the opponent concluding that the user of various forms of this argumentation is not serious…trolling…or generally just keeps moving the goalposts. All of which may be true.

But because the opponent has engaged in the argument from the beginning (e.g. she's just a kid!) they have implicitly accepted that the person is worth debating. If they later conclude the person is no longer worth debating, even if justified, the user feels as though their (unstated) belief has been successfully defended.

Another person rightly responded that this fallacy also overlaps with the Motte-and-Bailey (itself one of my favorites). But again, I don't think it's quite an accurate characterization:

In the Motte-and-Bailey, the user states a bold “bailey,” position, defends the similar but much less bold “motte(s),” and claims to have defended the bailey.

In the "most reasonable excuse" the PURPOSE of the Motte is to PRETEND the Bailey doesn't exist.

The “self strawman” may be any combination of motivated reasoning + moving the goalposts + bad faith argumentation + more…I'm not sure it can be as neatly classified as I'd like, but I do think it merits a new classification, if not further research.

For what it's worth, lots of existing fallacies also overlap with earlier-named ones, but are better explained with the new version. For example:

Gish Gallop is a deliberate pattern of many Red Herrings - but the intent and style give it a separate classification.

Nirvana fallacy is effectively just a false dichotomy, but when used in a specific way, it is better described by the Nirvana fallacy.

The purpose of naming fallacies is to recognize a pattern (and counter it, if necessary).

Other Examples of “Self-Strawman”

A prominent, recent example relates to the COVID vaccine. It is likely the best illustration of this “most reasonable excuse” fallacy in practice, and why I also refer to it as the “Self-Strawman.”

Because the debate relates to a matter of scientific fact that invokes polarizing opinions, people who wish to be perceived as “competent, serious” understand that their opinion is not “reasonable.” So excuses are offered.

When the vaccine first came out, many people who fit the mold of “anti-vaxxer” said things like:

• “I don't want to be first!”

Despite trials being done, this position seemed reasonable enough. Indeed, many people who are not stereotypical anti-vaxxers claimed it. So it follows that after a few weeks or months of proven safety for tens of millions, they'd get it, right?

No. The next-most reasonable excuse is offered.

• “It’s only emergency authorized! Not FDA approved!”

Right. So once it's fully FDA approved you'll get it?

“Nope. Don't trust the data. Seems rushed.”

And so on, until all of these excuses are defeated, and the person finally offers an excuse like:

• “Just to get booster injection jab next year?!”

I'm paraphrasing.

Ultimately, it reaches the point of:

• “It shouldn't be (or have been) mandatory.”

A very common sentiment, though not quite relevant to the safety/efficacy argument, but the user feels it validates their skepticism towards the vaccine(s). Nothing more than a goalpost move.

This is why I call it a Self-Strawman. The regular strawman is when someone creates a weakened version of your position to argue against it. But with the Self-Strawman, they are creating a stronger version of their own position, forcing you to engage with beliefs they don't actually hold!

While “stronger” is relative, remember that for many people, the belief is:

“Nothing will change my mind.”

And even a weak excuse is stronger than that. But because you're spending time and effort to argue against the excuse, and not overturning their unstated belief, once the interaction is over the user feels as though they've successfully defended the belief.

Most people aren't introspective enough to realize that they are not defending their core belief, and those that are won't admit it. So out of the need to defeat dissonance while maintaining the self-image (or public image) of rationality, they invoke whatever excuse seems most reasonable.

Every scientific field with its anti-science counterparts has a list of regurgitated excuses invoked by those who have reached an immovable conclusion, seeking to defend it under the guise of reason.

“It's just a theory.” May be the most common. Feel free to share your favorites in the comments.

P.S. if you think you're immune to this fallacy - probably not. Consider any conversation you've had with a salesman or…dare I guess…a family member whose function you don't want to attend. It's not exclusively applicable to debate, just the most pertinent application.

RIP Alex Pretti

The atrocities in Minneapolis and nationwide at the hands of ICE are unforgivable. I am only writing about this because it is - unfortunately - the most desperate invocation of the “most reasonable excuse” fallacy I've ever seen. Any doubt I may have had about it being a real phenomenon - which was close to zero - is now zero. The mask is metaphorically coming off.

By definition, users want to keep as many layers as possible between their true belief and the excuse. The more layers, and the more reasonable the excuse, the better.

Well…

“But he had a gun.”

That's their best excuse. That's their best excuse? That's their best excuse?

And it appears to be their only excuse.

“No guns at protests!”

Yep. Seriously.

Above all other issues, nothing defines what it means to be MAGA, Conservative, Republican, than the right to own and carry a gun.

Again, you can fall into their trap and argue about the fact that Pretti legally owned the weapon, never had it or even reached for it (side arguments…technicalities) but that's a short one.

And where does the user go from there? There are no more layers. No more excuses.

This is why it's such a troublesome topic, and illustrates the mindset involved.

Rather than make an apparently uncomfortable admission like:

“That ICE agent messed up”

Which is an admission that this case was very bad, but preserves the right to claim there is not a systemic problem…

They can't even do THAT!

By proving that they would rather make an excuse that requires abandoning their most sacred principles than admit a guy they don't like was wrongly killed, they're showing that nothing - literally nothing - that would change their minds.

Who it happened to, not how or why it happened, motivates their reasoning.

It's not hard to deduce, but I fear the unspoken position is “when it happens to someone we don't like, we don't care.”

And that's a very dangerous belief, spoken or not.

How To Combat The Self-Strawman

Preemptively, but not presumptuously.

The easiest rule of thumb to identify a user of this fallacy is that they post “easily disproven nonsense.”

Folks who are more advanced in this arena (the ones at the top of the misinformation pyramid…the influencers who often even have decent credentials) make the nonsense harder to detect and disprove - usually dressed in academic-sounding language, or requiring a level of expertise in the field to refute.

In any case, they want you to engage, and let them dictate both the terms and direction of the discussion.

1. They thrive on keeping distance between their core belief and stated arguments.

2. They discard arguments (with opponents) after they have been defeated, but recycle them when engaging on the same topic with others.

The second argument requires some research and mostly applies to those with a more substantial presence. Unless you're taking part in a more formal debate, it's not worth the effort to research. Though I'll note - it is remarkably effective to keep receipts like this in your back pocket if you find yourself in such a situation.

But in any case, the most effective tool, by far, is to preemptively combat it.

In debates of fact, it is implied that the goal is to discover who is right. Who is right - in rational discourse - is determined by the weight of facts and evidence.

Do not let this goal be implied. Make them state it explicitly, and do not engage with any claims or reasoning until a clear, affirmative response is given.

Here's how you do it:

“If I prove you wrong, will you admit you're wrong?”

This reframes the discussion. It takes them out of their comfort zone, which is tossing excuses for you to spend time and effort to combat, and forces them to answer what should be - for anyone engaging in rational discourse - a very easy answer.

An unqualified “yes” is the only acceptable response. A soft deflection like, “I'd love to see you prove me wrong” is not.

It is striking how effective the question is. It distinguishes rational debate from rhetorical performance. It is not accusatory, nor is it a loaded question. It is the baseline, fundamental question that is left unspoken in debates of fact - and allows disingenuous people to thrive.

So don't let them.

The vast majority of the time - far more than I would have ever expected - the excuse-user gives up the whole game at this one question. They present themselves as a rational, intelligent person originally - confidently making their case - but instantly resort to inflammatory language (intentionally, to try and force you to let them deflect) and any number of odd responses when asked the question.

They are stunned that their usual tactics won't work, and become deeply uncomfortable - and retreat. You've saved yourself lots time and energy, congrats!

“Sorry, I'm not interested in a debate of fact with someone who can't commit to letting facts guide conclusions.”

Or

“The refusal to answer is the answer. I'm establishing whether this is a debate of facts, and you've opted out.”

Do not concede that the excuse is worth engaging with, that the person is worth engaging with, until they can agree to the bare minimum term.

But I'm here to tell you, it's not that simple. And after giving it some thought, I've concluded it's not true at all.

Statistics cannot "lie" any more than long division can. They can only be misunderstood or logically invalid.

The problem starts with the fact that statistics and probability - overlapping but unique fields - are not that complex on their face, especially at the introductory levels. Most individuals who have conquered calculus, differential equations, or astrophysics find it offensive that you would question their comprehension of something so basic as the margin of error formula, for example. Because the calculations seem so simple, users mistake computation and familiarity for understanding.

Indeed, there are a lot of publications by “experts” whose own words prove they do not understand what the margin of error in a given calculation means…and apparently no one bothers to correct them.

Statistics do not lie, but people who do not understand statistics are easily misled.

Lesson 1: What the Data Mean is More Important than What the Data Say

I have read Feynman, Box, Sagan, Asimov, and many other influential scientific educators. I have no doubt, however, that I have read only a miniscule fraction of what exists and stimulates scientific thought.

That being said, I contend that there is no idea more profound, important, and influential in this field - perhaps all of science - than this one. I'm not sure there can be an idea more important, because it strikes at the core of why statistics are used, how they can be misused, and what it means to think critically.

Of course, with my primary topic of research being poll data, this applies directly, and I'll build on it. But make no mistake: this axiom applies to sports data, medical research, population statistics, finance…anywhere statistics are involved.

In introductory stats classes, students are often provided a problem, an equation, and expected to calculate the correct answer. The exercise trains them to follow procedures, plug in numbers, and arrive at a solution. I suppose at the introductory level this is necessary. But this approach rarely teaches them the more important lesson: understanding what the result actually means, and why the formula exists in the first place.

Here's how I think of the problem - and how I propose it be taught:

1. What problem do I want to solve?

2. What data or facts do I need to solve it?

This is perfectly acceptable for an introductory level. It moves beyond selecting a formula and plugging in numbers, and teaches that even if you can't personally solve the problem, you know what information is needed to solve it.

This applies just as well whether the “problem” is finding the area of a rectangle or the efficacy of vaccines.

By understanding the data needed to solve a problem (and perhaps what information seems relevant but isn’t) when a charlatan or purveyor of pseudoscience confidently presents some data, you are not so easily fooled.

In other words, the process emphasizes understanding the meaning of the data over mechanically producing an answer - or even producing an answer at all. Students learn to distinguish between knowing a procedure and understanding a problem.

This is statistical literacy in its purest form.

Richard Feynman, in his lecture on how to test competing theories that both seem to produce valid outputs, lamented that scientists often followed procedures that took the form of:

“Never mind the philosophy…just guess the equations, the problem is only to compute the answers so they agree with experiment.”

Again, finding a formula that works to solve some problem - wonderful, and important. But explaining why it works, and why it might fail - understanding the implicit assumptions - that's a higher level of thinking than “got the right answer who cares bro.”

And identifying in advance such “got the right answer” type thinkers offers the ability for more sophisticated minds to improve on methods by identifying the conditions in which the calculations “got the right answer” and those where they might - or will - eventually fail.

This pattern is evident throughout history. Whether it's something hard to test like the orbit of planets, easy to test like the Monty Hall Problem, or counterintuitive like the mass of an object versus how quickly it falls…

Note how long the world's smartest people believed something that is very incorrect because of how obvious it was.

What seems obvious isn't always obvious, that's why the scientific method exists in the first place; in fact, if you ever have a serious discussion with someone, and you ask them to explain something - and they contend that it's “obvious” - you have likely discovered a gap in their understanding. Stating it's “obvious” is both a deflection and a subtle ad hominem that implies you not fully understanding something reflects on your intelligence, to distract from the fact that they feel like they know it…but can't explain it.

The problem has been explained more in depth recently, and it's called the illusion of knowing.

In short, familiarity produces comfort and fluency, not understanding. Analysts might know all of the terms in the margin of error formula, use it often, and mistake this regular use (or their years of experience in the field) as proof of understanding.

But the reality is, finding the right answer often requires questioning and testing the simplest assumptions - even those that seem obvious - and realizing that reality doesn't particularly care about “years of experience.”

In the case of Ptolemaic Astronomy, they “got the right answer” almost all of the time. As such, it seemed foolish to question the most basic assumptions about whether the Earth was stationary. The world's most brilliant statisticians (including those at MIT) failed to solve a problem a few years ago that many high school students can solve today.

Indeed, one of the most brilliant people in history apparently didn't bother to test the rate with which objects fell because the answer seemed…obvious.

Likewise, Literary Digest’s poll - though unscientific - “accurately predicted” the result of four consecutive elections. As such, it was considered the gold standard…until it wasn't. Getting “the right answer,” not valid processes or even logic is all the field cares about. And not much has changed.

The problem with all of this, I believe, is that otherwise brilliant people believe these are lessons of the past - not the present or future. They believe the solution to the Monty Hall Problem is “obvious” and that if they had been presented the problem in the 1990s - when the credentialed experts were almost universally wrong - they would have obviously been able to solve it and overcome the consensus.

They are born on the shoulders of giants but believe they have climbed there.

Established procedures and accepted assumptions shouldn't be questioned just because you think they might be wrong; they should be questioned because you think they aren't.

Lesson 2: Logic is more important than math

Statistics: what the data says. It is a branch of math

Probability: what the data means. It is a branch of logic

This is not to diminish the importance of statistics. It is to say that without asking what problem needs to be solved, numbers alone cannot guide reasoning. Logic provides the framework for interpreting results, determining what information is relevant, and connecting observations to conclusions. In short, mathematics tells us how to calculate; logic tells us what it means.

Probability itself is a remarkably new field, given the age of relatively more complicated fields like physics and calculus. But probability isn't purely math: probability is the logic of uncertainty.

Uncertainty can be quantified, but as evidenced by the responses to political forecasts that conclude a forecast is “wrong” when someone given “about a 67% chance to win” doesn't eventually win…thinking you understand what something means, and truly understanding it, are quite far apart.

Seemingly simple statistical statements are often very poorly understood.

Indeed, this exact logic holds true at the highest level of political data:

They conclude that a candidate being “ahead” in a poll or poll average - if they don't eventually win - is evidence (or proof) that “polls were wrong/missed/failed.”

When I politely present some simple data - a poll average of 46-43 with 10% undecided, for example - there are a lot of very big assumptions being made if you conclude the person at “46” must eventually win (and win by about 3) or else polls were wrong.

It's simple arithmetic, in fact, to show that undecideds favoring the candidate at “43” can - by itself - cause them to win, even if the poll were perfectly accurate for the population at the time it was taken.

This is a trivial mathematical proof (forgive me for violating my rule on calling things obvious) - but the problem isn't the math. They understand the math.

The problem is the logic.

Because of the 100 years of implicit bias in the field - that undecided behavior can be assumed to follow some rule (splitting evenly or proportionally to decided voters…incompatible and conflicting statistical conventions that literally depend on which country you were born in) the possibility that they could overwhelmingly favor the candidate BEHIND in the data is considered so objectionable that they pretend it can't happen.

Even when presented with irrefutable data that it can and has it's dismissed as a rare exception.

Back to that thing questioning established procedures.

But perhaps most telling about the flaw in reasoning, is that “in the long run” it is implicitly accepted that undecided voters will converge on some split (usually 50-50) - which is the rationale given for pollster grades that assume a 50-50 undecided split. Even if the grades are inaccurate for any given election, “in the long run” the 50-50 assumption will make for accurate grades.

Ahem

Taps microphone

Prove it.

To quote myself:

Of course, the idea that polls are predictions - which is the indisputable (incorrect) consensus within the field - is flawed at its core. But even if I were to grant the grading procedure as worthwhile, it still lacks validity.

Why is a long run 50-50 split for undecided voters accepted as true? Why not 75-25 against the incumbent, and 60-40 against the party of the incumbent when there is no actual incumbent?

Why do we use the same rules for Senate races as House races as midterms as Presidential Elections?

The reasoning, I suspect, is obvious.

The field seems to be so concerned with finding a formula that provides the right answer that they disregard the philosophy behind it.

That's without getting into the discomforting mathematical reality that it would take multiple human lifetimes of data to have a sufficient sample size.

In any case, my work at its fundamental level is simply challenging the field's consensus - the historical assumptions - that undecided behavior can be modeled unconditionally.

Historically, it's as though they're claiming heavy objects fall faster, and I'm climbing a tall building to drop two objects of disparate weight to test it. Instead of anxiously or even passively following what is very easy to test, they demean or understate the value of the findings.

As with “so they fall at the same rate, so what?” - the implications of the understanding that polls aren't predictions are far greater than the headline.

One of them is this:

While polls are not predictions, they are our best tool for informing them. And understanding that polls are not predictions teaches us - as Panagakis also noted - that “rules of analysis are necessary.”

My research shows that a small lead with a poll average close to 50% is far preferable to a larger leads far from it. Indeed, I believe that this is a conclusion that follows directly from an understanding of how polls work: they are an approximate base of support, not a prediction of an outcome. And this understanding is only possible if you allow yourself to escape the trap of polls as predictions that currently forms the field's consensus.

And when published the following in 2012, he concluded that leads of “2 or 3 points” in highly polled states were very strong leads.

He's observing an output with no valid underlying philosophy.

Of course, Panagakis addressed this decades earlier…and there's nothing wrong with not reading everything every person has ever written on the subject.

But the lack of intellectual curiosity in challenging your most fundamental assumptions - that “obviously” how much a candidate is ahead by in a poll average is a meaningful proxy for their win probability - violates the most basic principles of scientific reasoning. The question is not whether the number can be calculated, but whether it answers the question being asked: how likely is this candidate to win this election?

Treating a margin as a probability substitutes familiarity for logic, and convention for understanding. It confuses what the data say with what they are being assumed to mean.

Lesson 3: A Thought Experiment (and Actual Experiment)

I have a database of 10,000 responses to the following question:

Of the following, which is your favorite color?

• Red

• Blue

• Green

The order of the options were randomized in the survey.

Your assignment is to estimate the percentage of respondents who said which color was their favorite.

1. Just guess. Make your best guess.

   *Answers are turned in and reported*

2. As a class, here is the average of what everyone guessed. Based on this information, would you like to update your guess?

   *Answers are turned in*

3. I took a random sample of 600 from my database. It yielded:

   • Blue: 48%

   • Green: 29%

   • Red: 23%

Based on this, would you like to update your guesses?

This step, of course, provides far better information than an individual guess, or wisdom of the crowds. While some students will cling to their original guess like Monty Hall contestants, most understand why this data far supercedes its predecessors. “Why” is a good question here.

Depending on the class, you can even discuss the margin of error.

Now, the first super hard, obvious question:

4. Given that poll data, what does it mean?

Challenging learners to explain what feels obvious is one key difference between teaching and lecturing.

Any answer that takes the form of:

“The 10,000 responses in your database are probably close to those percentages” is fine.

Take a few more polls with the same sample size, to illustrate the variability of these ideal polls.

Blue, at 48%, would probably return some results over 50% and some under 45% given a few random samples.

The lesson “fluctuation is normal and expected” is good here.

Having established that the students understand what the data means - not just what it says - drop the Monty Hall, Literary Digest, Nate Silver-sized piece of variable change on them:

A few days after the earlier survey, I asked the same 10,000 people:

Of the following, which is your favorite color?

• Red

• Blue

5. Estimate the percentage of respondents who said each color was their favorite. Your grade on this assignment requires providing a correct answer. Extra credit for confidence intervals.

Discuss in the comments!

Do you think it's a waste of time? Maybe I can convince you otherwise.

Do you find yourself doing it? This article will teach you how to be better at it - by wasting less time - and maybe give you a sliver of respect for Jake Paul.

You can argue it's not productive to engage with trolls - and you're mostly right - but in my field, understanding how people think, why they think it, and how to effectively combat that level of thinking is very useful. Both for teaching, and for overcoming misinformation.

You may or may not be surprised to learn it, but people at the very top of the fields I work in often employ the exact same tactics as Internet trolls - simply with more followers and (sometimes) better vocabulary.

To use a sports analogy:

I debate internet nobodies for the same reason professional baseball players take batting practice. It's not because soft-tossing a ball to a professional hitter mimics elite competition - but because the form can be refined such that when facing a rare, qualified opponent, performance becomes muscle memory.

Debating Internet Nobodies

I don't use the term “Internet nobodies” demeaningly. It spans a very wide spectrum of literal trolls to educated professionals. Occasionally, though very occasionally, people in this broad category will present something I find useful. The batting practice equivalent of finding a hole in my swing, so to speak. A good hitter can (and arguably, must) respect it and refine their approach.

But more often than not, people who attempt to engage in a debate of fact (but will lose the debate if “winner” and “loser” is judged purely on merit) follow a predictable pattern:

1. Make a claim

2. Refuse to support that claim

   2a. Refuse to admit they're wrong if proven wrong

Of course, the burden of proof in rational debate is on the person who makes the claim.

But in particularly easy cases like above, I'm happy to prove them wrong. Under one condition:

“If I prove you wrong, will you admit you're wrong?”

It's 2026, and this approach is still undefeated.

And still undefeated.

It's the boxing equivalent of putting your opponent in the corner. People who can't win a debate on merit don't like being cornered: their continued performance relies on not being cornered.

The most common techniques in avoidance of defending “2” are:

3. Change the subject (if they don't let you corner them, they can't lose!)

   • Move the goalposts

   • Self-strawman

   • Ad hominem

   • Easily refuted nonsense

You can see Mark try to move the goalposts above, while '“prof” weakly lobs an ad-hominem. There's also

4. Invent a strawman of your position, propose a motte-and-bailey, or outright lie.

My claim on the post below was that an above average male would not defeat an elite female in tennis:

Robolivermd says, but aha! Not “the average medium level male college tennis player” though.

A mouthful of qualifications make it perfectly clear he's changing the subject.

So I bring him back to the original point:

How close are those “average male college tennis player” (his strawman reference point) to “average male?”

He didn't answer. And in an attempt to avoid being held accountable, he simply makes a wild, indefensible claim:

“If they're not a professional, they (are) part of the range of average.”

It would've been easy to dunk on him (another sports reference, whoa!) with a chart like this:

But I've taken enough BP to know what's going on here. I only provided this chart for your entertainment. Hope you love it.

What is happening is that he's offering an argument unrelated to his original claim in an attempt to change the subject - and avoid defending his original claim.

I call it “easily refuted nonsense.”

Robolivermd dangled this easily refuted nonsense in an attempt to again change the subject, to avoid defending his original claim…which also changed the subject. See the pattern?

The more separation an unqualified debate combatant can keep between making a claim and being accountable for it, mentally and tactically, the more comfortable they are engaging.

His claim is so easily refuted that you think you can simply prove them wrong and return to the original point. No. That's the purpose of easily refuted nonsense: (metaphorical) breathing room.

If allowed, he would simply move the goalposts ad infinitum. “No I meant average men IN THE SPORT, not THE POPULATION!” an innocuous misunderstanding! Others accompany such retorts with childish insults like “learn to read” with an optional “moron” (or synonym).

You conclude they're not debating in good faith, they contend they were, and their tactics worked: they never had to concede anything.

Veteran debaters may recognize this “easily refuted nonsense” in the form of:

• “Just a theory”

• Mercury!

• “Abortion is the same as killing babies”

• “Climate has always changed”

• “Mysterious ways”

• Guns don't kill people!

And so on.

While you, veteran debater, most often conclude that people who use these arguments are simply ignorant, and that if only someone could explain it to them clearly, using strong citations and persuasive language, they'd stop making that argument.

I regret to inform you that this is almost never the case.

That is what they want you to think. They often know the point they're making is wrong, and they don't care: that's the point.

It's easily refuted nonsense that keeps distance between their true belief(s), and what you're arguing about.

These arguments commit the fallacy of self-strawman: they misrepresent THEIR OWN beliefs, so their core belief can't be attacked.

The Self-Strawman (and Easily Refuted Nonsense)

Definition:

The act of deliberately presenting a weaker or fabricated version of one’s own belief for debate, so the central topic and user’s actual position (usually irrational and/or unfalsifiable) remains untouched and protected.

It works on three levels:

1. The speaker can “lose” arguments without risking the belief they actually care about,

2. It attempts to force opponents to exert time and energy against something mostly unimportant to either person, keeping distance from the central topic or true belief, and

3. It gives the user an illusion of rationality: that they are subjecting their beliefs to critical debate, and yet they continue to sustain.

Other Tactics

Less academic folks, when cornered, lash out with name-calling and personal attacks. Same subset of argument, same function: deflection. It's an attempt to make you let them change the subject.

Below, a recent example of someone who (believe it or not) portrayed themselves as engaging genuinely, making calm claims and statements of fact. Until cornered…

They use increasingly inflammatory language when cornered (r*tarded is a current favorite, though there are many others) because once you call them on their language you have let them escape the corner of debate.

You might believe you're rightly calling out an important point about respectability or decorum, but that's the thing: they want you to not respect them. In their mind, if you react, you’re the snowflake who “can’t handle it.” And at that point, consciously and subconsciously, that’s why the debate ends. Not because they were wrong, but because you don't like the words they used.

More educated folks rarely sink this low; they stick to more sophisticated insults like “not nearly as smart as you think you are” - but for the same reason. It's an ad hominem designed to try and escape accountability…but won't cost them their job.

Do you see what I mean about batting practice?

I asked a direct question relevant to his claim. He feigned emotional outrage.

I ignored it and asked a direct, relevant question. The corner is uncomfortable! Must escape. Personal attack. Waste of time. Cope.

For bonus points, the claim “you're arguing semantics” is a sophisticated form of easily refuted nonsense! Brilliant gambit, sir!

In fact, his 5 sentences take the form of: Irrelevant. Ad hominem. Easily refuted nonsense. Ad hominem (circumstantial). Ad hominem.

It’s quite impressively done!

You might think it's weird, and it's probably bad that I'm so desensitized to it, but when the trolls resort to a variation of “beta cuck r*tarded soyboy bitch” it hits me the exact same way as Tom's “not nearly as smart as you think you are” string of deflections. They're the same thing! It's adult children screaming about their ego being hurt in an arena where the debate is “what is true?” And/or “who is right?”

Yes, yes, let it all out now. You're a big, smart, alpha boy, aren't you? You sure are.

It's reactive, performative, and consciously or subconsciously only something someone would resort to if they realize they can't win the discussion on any merit. Even if you spend time and effort disproving the easily disproven claim (which they will counter and deflect from) they don't actually hold that belief. It's a misdirect.

That's why the reaction is so emotional, and truly visceral, when you focus your attack discussion on the actual position or claim and don't let them change the topic at will.

“If I prove you wrong, will you admit you're wrong?” Is an inescapable corner.

Quoting their exact, original words to them after they ramble for multiple posts trying to get you to let them out of the corner is quite triggering for some reason.

In any case:

“Is there any collection of fact(s), data, or information that would change your mind?” (and then making them state it) is also undefeated.

Unlike Jake Paul.

Respect For Jake Paul

I don't follow his social media antics much, and I'm sure there are plenty of reasons not to like (or respect) Jake Paul.

But credit where it's due: most of the time when unqualified nobodies talk a big game, they don't stick around to back it up.

They enter the debate “ring” with clearly defined rules, get cornered, then take their gloves off and say something like, “betcha can't beat me at MMA!”

If you keep them on topic:

“Guy, we were just boxing”

They say:

YEAH, SEE, YOU'RE AFRAID TO TAKE ME IN MMA.

And this pattern will continue no matter how many times they are cornered. That's why it's important to give them zero benefit of the doubt:

“Okay, so you're conceding that you lost the boxing match, and now want to change the topic to MMA, is that right?”

They don't like being held accountable. You're being so rude by…establishing accountability.

The other technique - resorting to name-calling - is the equivalent of running out of the ring after getting cornered. The debate - in the ring - had defined rules. They exit the ring shouting obscenities, pretending they never agreed to any such rules.

“I will still fight you! What, you're afraid to chase me over here to this different topic? Bring it beta soyboy!”

They assert that since they challenged you to chase them outside of the ring, even though it's something other than what you originally agreed to, they haven't actually forefited anything.

Same mindset.

In debates of facts - like a combat sport - it doesn't matter what anyone thinks…it matters what you can prove.

When someone steps into the ring - boxing or debate - they're asserting "I think I can beat you"

That's okay. Maybe you can. Only one way to find out.

So, Jake Paul. Respect.

He talked his shit, didn't run away, got his jaw broken…and it was settled.

By Popular Demand

I'm working on my own version of this flow chart, but it's extremely useful.

Use it wisely.

I want to explain this phenomenon from a psychological, statistical, and social perspective. It will get way too deep into topics of misogyny and population statistics, so if you keep reading, you've been warned.

Recently retired Correction - recently recovered from injury, professional tennis player Nick Kyrgios comfortably defeated (6-3, 6-3) the world's top-ranked woman, Aryna Sabalenka. Like past iterations of the event, the rules were slightly modified to favor the female player.

Certain groups of people believe this is proof that females are simply unable to compete with males, and use this to solidify their pre-existing belief in the superiority of men…but totally only in sports. 😅

The fact that people who are most passionate about the topic of male superiority in sports tend to hold negative views of women who exercise power in conventionally male-dominated fields like business and politics is not a coincidence.

Not toxic: males and females competing against each other in sports.

Toxic: using these examples as proof of anything other than what they are: elite male athletes are generally better than ULTRA elite female athletes.

I'll share some statistics on this later. First, the psychology.

The Psychology of Toxicity

It's no secret that a lot of men value stereotypically masculine things: physical strength, athletic superiority, financial status, and even intellectual or technical mastery (thanks, Renaissance).

There is nothing fundamentally wrong with any of this. Competition challenges us to get better, gives many of us purpose, and I would argue that people finding things they value is generally healthy. Sure, coding these things as “masculine” is problematic, but that's a separate topic.

But there's a fine line between valuing something and identifying with it.

Chances are, you've witnessed a female beat a male at something athletics-related, and can attest to the reactions. In most cases, it's light-hearted and most people (men included) take it well. But to borrow a misused saying that's more appropriate here: “not all men.”

Being good at sports is very man. If a girl is better than you, what of your precious status? This is where things go wrong - and where toxic masculinity comes into play.

The fact that some men would disproportionately concern themselves with the athletic superiority of other men can only make sense through the lens of toxic masculinity.

Most of the men who comment on the fact that, in a given sport, the worst professional male is better than the best professional female are not motivated by an interest in any physiological or scientific mindset.

They are doing so because of their own insecurity, and they psychologically identify as "one of the males" to borrow status from elite male performers to maintain an illusion of superiority to females.

This phenomenon is not new or even particularly controversial.

Humans constantly compare themselves with others for the sake of status or identity.

The Physiology of Masculinity

If you've studied biomechanics, physiology, and other related concepts, you understand that it is...not at all surprising that elite men would outperform elite women in many sports. A few factors in performance in most sports:

1. Higher Absolute and Relative Muscle Mass

   • Higher Max and Submax Strength and Power

2. Higher Testosterone Exposure

   • Muscle Hypertrophy

   • Bone Density

   • Tendon Stiffness

   • Motor Unit Recruitment

   • More

3. Greater Hemoglobin Mass & Oxygen-Carrying Capacity

4. Skeletal and Anthropometric Differences (mechanical advantage)

   • Longer limbs

   • Narrower pelvis

5. Essential Bodily Functions

   • Men typically reach peak athletic performance with body fat percentage in the single digits. Women can seldom remain healthy below the teens. Smaller frames + greater non-contractile mass generally reduces athletic performance.

All of these well-known facts (of which there are more) is my way of illustrating that I'm not some ideologue who believes that if only females had more opportunities, they could compete with elite men.

By nature of dealing with a nonrandom selection of “elite athletes,” we are by definition dealing with both genetic and physiological outliers. In order to quantify performance on the same scale, we can define the “elite” male as x standard deviations above average and the elite female as x+y standard deviations above average.

In general, most male versus female athletic performance can be summarized as something like this:

Given objective standards (like Special Ops Forces) we should expect to see far more men than women above a certain physical threshold.

But notice: there are many men who qualify as “elite” who would not outperform very elite females.

And the above is a generalized chart. Other areas show greater disparity:

And other areas less disparity:

We see a similar pattern in high levels of Olympic and Professional Sports.

It's not really a coincidence that these charts closely mirror sex differences in height.

You'll note that the majority of the NBA is not even represented on this chart, with a median height of about 6’7. Stats nerds will note median height for males (about 5’10) is less thick than that of females, which means greater variance.

With greater variance, that right tail (very tall people, on this chart) is exponentially different. The number of males who are, say, 6’6 is roughly 99.9-percentile for males (about 1/1000) compared to one in several million for females. As a result, the number of males to be selected from this category is in the tens of thousands. The number of females is in the dozens.

Competitive sports nonrandomly select outliers.

And with all that being said:

The gap between professional female and professional male is still FAR SMALLER than the gap between average male and professional female. I summarize this simple fact as:

Caitlin Clark is closer to Steph Curry than you are to Caitlin Clark

(H/T Brian Scalabrine)

This statement triggers all the right people because it punctures the fragile psychological shortcuts they take. Bringing “you” into the discussion - which can be taken many different ways but can be generally interpreted as “the average” is what causes the puncture.

Many men derive vicarious comfort from their identity as “man” - which is quickly conflated with “good at sports” …which then mutates into “better than women at sports” … and this discomfort is evident in the (ironic) emotional recoil.

If I had a nickel for every time an insecure man said BUT US WOMEN'S SOCCER VERSUS HIGH SCHOOL BOYS I'd be in Forbes. The fact that the match was a scrimmage is not considered relevant - because the result confirms the pre-existing belief. The fact that the teenage boys were a select team, many of whom are currently professional or Division 1 Athletes - details.

Ask the men who cite that select U15 boys team if they could outperform the US Women's Soccer Players…or the U15 boys…and the borrowed status bubble is popped.

The need for facts is secondary for the need to support the feeling. This story is regularly, wrongly cited as they lost to “pre-teen boys,” and that they lost to “a high school team” on social media, which is a strong indicator that the feeling informs the facts and not the other way around.

The fact that (retired) US Women recently lost to (retired) Wrexham players was also recently cited to support the claim about… teenage athletes being better than elite women. A well-informed group, to be sure.

The move is emotional, not scientific. Mediocre men invoke elite male athletes (even teenage ones) as if they’re on the same team in any meaningful sense, using group identity as a crutch to convert someone else’s excellence into their own imagined superiority. For some, it’s less about proving male superiority than asserting female excellence can never be enough.

“They might be better than me, but not my (imagined) team” is a textbook cope.

And that discomfort is precisely why the conversation keeps getting rerouted to elite men, away from themselves, because borrowed status feels safer.

The Statistical and Social Whatever

The gap in ability is far from equal across sports, and this is without yet getting into the highly relevant fact that girls were practically forbidden from participating in sports until very recently, and the mediocre compensation for elite females disincentivizes athletes (therefore coaches, therefore trainers, therefore…domino effect) from pursuing or investing in it.

When the male league-minimum is higher than the top-paid female, there is a clear incentive structure. Even in more equitable sports like golf, the median PGA pay is roughly 700% larger than the median LPGA salary.

Note, I'm not making any moral or even economic claim here about what pay “should” be: it's a simple incentive structure, with some social scaffolding. Which leads me to…

The Math

Wherever there is a larger pool of participants (which is true of male sports), we should expect the number of those selected for being elite to be greater, and those who are elite (but not selected) to be greater!

Reducing the discussion/debate - or far more often, diatribe - to “athletic superiority” illustrates a reductionist flaw commonly present in unscientific arguments.

Ignoring the performance differences for the moment, assume two equally talented populations: one with a population of 1,000,000 compared to another with a population of 100,000. Here's what that distribution looks like:

Elite athletics don't deal in percentiles, they deal in absolute maximums: the best of the best. You can probably field every team's starting lineup (if not a whole league) just in that tiny area between maximums given the population sizes. Bench players from one population would be better than stars from the other.

And remember: this only due to population size - BEFORE controlling for performance differences!

The consequence is that if we segregate the two leagues of different population sizes (we can use US Basketball versus France Basketball, as a timely and non-sex related example) we will get an occasional outlier - Victor Wembanyama may soon have a case as one of the best players of all time - while the next best players are the likes of Tony Parker, Boris Diaw, Evan Fournier, and many other very talented players…who were never the best players on their NBA team. Not far down the list, you get players who would not even make an NBA roster.

This is not a statement on the country's relative athletic prowess, it should be understood as an inevitable result from the fact that the US has more people, basketball is far more popular here, and we invest far more money into developing our (basketball) athletes - with a much larger financial incentive to be elite.

Some may be able to draw the analogy between intra-country comparisons and intra-sex comparisons. While there is indisputably a physiological factor in the latter, it doesn't exist across borders. And yet, US natives indisputably comprise almost all of the all-time top-100 basketball players (shoutout to Hakeem, Dirk, Nash, and Jokic) - but none of this has anything to do with a country’s physiological superiority! It's population statistics.

Indeed, if you go down a tier or two in France, you would get professional teams that would struggle against top US high school teams.

Even still, the number of elite basketball players from outside the US has accelerated drastically in recent years - and it's not a coincidence. That acceleration coincides very closely globalization of basketball infrastructure: expanded youth academies, international scouting, analytics-driven talent identification, and - critically - the rise of the NBA as a credible, lucrative incentive for non-U.S. athletes.

As barriers to entry fell and the expected payoff rose, the effective global participant pool expanded. What started as a trickle with a few foreign players making solid NBA contributions, quickly rose into a flood of competitive participants. The result was not a gradual shift, but a nonlinear jump in right-tail outcomes: Petrovic and Kukoc became Ginóbili and Gasols which evolved into Nowitzki, Jokic, Giannis, Doncic, Embiid, Wembanyama, and so on. This is exactly what selection theory predicts when a large, previously under-sampled population becomes more integrated into a high-incentive system.

It's not a difficult hypothetical to conclude that if the international infrastructure hadn't grown, and basketball were not as popular globally, those elite players would not be in the NBA today, and their predecessors wouldn't have been either…largely because their predecessors weren't. The current performance does not exist independently of the past, just because the players are different.

The Infrastructure

In case you still mistake me for an America-supremacist because I'm talking about American sports, I'll be honest:

We suck at sports like Rugby and Cricket. Despite our enormous population, the huge crossover in skill sets between American Football and Baseball, why doesn't America also dominate them? Wouldn't it make sense for players who fail to make it professionally in their preferred sport to just convert?

Well, that infrastructure simply doesn't exist, because we (generally speaking) don't play them. Other countries, even those with tiny populations, even those with holy shit less than a million people, dominate because it's their favorite sport. It sounds boring, but it's (in large part) a math problem: their best athletes are training in this sport from a young age, so they invest in it, and have a larger population of elite athletes to select from in that sport. America doesn't.

Given the size of a country like New Zealand or Fiji, and even a much larger one like South Africa, their dominance in Rugby can't be explained solely by population statistics or even financial ones, though. And certainly not physiology. There must also be a social factor driving competition: a social concentration of athletic talent. A similar phenomenon happens with professional baseball.

This means comparing male to female athletic prowess is not as straightforward of a problem as people think.

There is, no question, a physiological difference between men and women. But stating “better because physiology” is proven to be insufficient when the same physiology systematically produces inferior outcomes due solely to environmental and social pressures.

The gap between elite U.S. basketball players and elite players from low-participation countries is often larger than the gap attributed to sex differences alone. Outcomes at the extreme right tail are driven by who enters the funnel, how competitive it is, and how much pressure exists to reach the maximum.

Physiology sets limits and bounds, it does not determine results.

The Funnel

The “sports funnel” starts from a young age, where kids of all skill levels participate. By their teens, there is a strong selection effect against below-average performers. Put simply, the more people forced through the funnel, and the more capital pumped into it (capital referring to either literal money, labor of coaches and others, or social status) the farther you can force the maxima to the right.

This is not speculative, it is a direct implication of selection theory. Larger, more competitive, better-resourced funnels do not merely produce more elite athletes - they produce better ones, because the surviving set is drawn from a deeper and more intensely filtered pool.

To illustrate how the funnel works, here is a clip of back-to-back plays from the New York Knickerbockers game in 1950. These are elite male basketball players.

To be fair, this isn't a fully representative sample of the game - there were some nice plays. The kind of plays you might call “nice” in a modern High School JV game, anyways. You can watch a condensed version of the game here, if you want to cringe.

No serious observer would compare the performance from that game - two teams that finished in the middle of the league standings - and conclude that today's WNBA players wouldn't overwhelmingly dominate this level of competition. Physiology and all.

Before the very modern NBA era, being large and mobile was more than sufficient to land an NBA job. Now, guys who are even larger and more mobile are also elite shooters and ball handlers…and even that doesn't guarantee you're good enough to play. Al Horford is a better 3-point shooter than Larry Bird was - a fact determined by both three-point percentage and volume - and Bird was indisputably one of the best shooters of his era, Horford isn't close. Selection pressures have aggressively raised the bar for playing in the NBA.

As such, we can easily see that League-wide improvements in performance is measured in years and decades, not generations. This trend is seen across all sports.

The elite male athletes from the 80s and 90s were motivated by the elite male athletes of the 60s and 70s. Though earlier generations were largely less skilled, the funnel filled, and pressure drove progress. That pressure increased as sports rose in popularity and compensation.

And to bring this all together, the above clip is from 1950, while the WNBA wasn't founded until 1996. That raises an obvious question: who was motivating female athletes to be elite before that point? How many existed in the funnel, and what pressures were forcing them to improve?

For most of the 20th century, the answer is: very few, and almost none. While millions of girls were probably interested in basketball and other sports if only because they watched the boys play, there was no professional league for them to dream about, no stable developmental pipeline, limited youth participation, minimal coaching infrastructure, and little social or financial incentive to pursue elite performance. The right tail simply wasn’t being populated.

The Head Start

The modern Olympics were established in 1896, but women weren't allowed to compete in the marathon until 1984. Katherine Switzer was violently assaulted by the Director of the Boston Marathon for the unthinkable act of Woman Participating - but finished the race with her friends protecting her. This is not ancient history; she still runs!

And yet this structural, misogynistic disadvantage is ignored when discussing performance disparities because it makes people uncomfortable. Observers who lack historical context or statistical literacy assume that athletes exist in a vacuum, as if people are born independently of the systems, incentives, and barriers surrounding them. The result is a persistent misattribution: outcomes are treated as innate, rather than the product of decades-long social, institutional, and developmental funnels.

This phenomenon is not unique to sports or even the general public: it is a form of hindsight bias seen in science as well. From the next article on your reading list:

Fortunately, there are lots of good scientists who put their personal biases aside to perform valuable research.

This study illustrates empirically the concept I've discussed in this article, with record time progression over the decades in males and females. They nicely summarize “policies that explicitly forbade females” as “social factors.”

Men in the 70’s compared their scores in the 70’s to women's and called the enormous gap laughable. By the 80’s, it narrowed substantially. Into the 90’s, the 12% performance gap, though small, remained as proof of male physiological superiority. What they must not understand (or more likely, ignore due to cognitive dissonance) is that women in that same decade would have outperformed men from just a few decades earlier. Physiology alone cannot explain that - and this is for a sport where physical ability dominates rather than a mix of technical skills.

While that performance gap has sustained among the very elite, it's important to be very clear: no above-average male in 2026 who decides to train can simply outperform elite females because Male. Not in marathon running or any well-developed sport. That was not the case in 1970. What changed, and will continue to change more rapidly as women are allowed to participate in sports and they grow in popularity, is the right tail pressure.

What we are seeing in the 2020s is plausibly only the first or second true wave of fully professionalized female basketball: athletes who grew up knowing a league existed, who trained year-round, who faced dense competition from childhood, and who were pushed by real incentives to reach the extreme right tail.

Physiology explains performance ceilings, clearly illustrated in the chart above, but it does not and cannot explain how quickly those ceilings are approached, how many people get near them, or why performance accelerates when systems mature. Claiming otherwise isn’t biological or scientific - it requires both historical and statistical ignorance.

Elite male athletes did not emerge in a vacuum. The right tail of the NBA pulls the right tail of college sports which pulls the right tail of high school sports. Each level raises the incentive and selection pressure on the one below it, progressively densifying the extreme right tail.

Stating that there are some high school males who can or do outperform some professional females isn't proof that the entire sex enjoys physiological superiority, though many men desire that conclusion. There is a distribution overlap influenced by asymmetric selection. The selection pressures make the right tail more dense for males, raising the bar for what qualifies as “elite male,” in the first place.

They were produced by decades of early access, dense competition, cultural reinforcement, professional pathways, and sustained capital investment. To attribute the resulting gap entirely to biology is to ignore the very mechanisms that created elite male sports.

Because of this century-plus head start, plus the real physiological factors that exist - which are not independent - I don't expect a female athlete to supplant a male at the highest level of any sport, though some overlap would not be shocking. I do expect, however, that with continued development and investment, the right tail of female sports and will grow and widen significantly. Just as elite male athletes have separated themselves from their past generations (and the population averages) elite females will too.

I made this chart for angry male commenters who disliked the conclusions I made from literal data, and I'm adding it here so I don't lose it:

Minutes are reflected by a decimal, which in hindsight, would've been much easier to reflect as minutes & seconds, but the point holds.

“Top 1%” is approximate derived from Army Physical Fitness test and a few other sources - mile and 5k times among self-selected competitors who train - then corrected to determine an approximate number of people who don't jog or run (90%) correcting upward for people who are generally somewhat active but don't run then a little more for people who used to run, then setting lower bounds above a brisk walking pace.

https://www.elon.edu/assets/docs/rotc/APFT%20standards.pdf

https://www.mdpi.com/1660-4601/20/19/6872