Does Moving Up in Tiers Affect Injury Rate

As a quick reminder, building on the concept of the Joi - essentially the men who would reasonably expect to face a Yokozuna in the tournament - I created further tiers to extend beyond just the top wrestlers. Absolute rank simply represents the order of the Banzuke so Yokozuna 1 East is 1, Yokozuna 1 West is 2 using 2026 tournaments where there are 2 Yokozuna and then Ozeki 1 East would be 3 and so on. I included a representative range meant to approximate what those ranks would be as an added column.

The question I wanted to test was: does moving up a tier make you more likely to be injured. The underlying thesis is that facing more skilled and likely physically imposing wrestlers leads to more injury. It’s reasonable enough, but part of the purpose of this blog is to use statistics to see if this folk wisdom is indeed valid. The rates are below and please note that I filtered all of it dependent on the wrestler having no injury losses the prior tournament.

Looking at the stats that is in fact not borne out. I actually initially misread this and thought it was proving that thesis true, but no: based on the data it looks like moving up a tier actually leads to lower injury rates. This is surprising to me and will require greater scrutiny to investigate why it’s possible, but I have a few ideas. A wrestler moving up a tier did well the previous tournament (or else they would have moved down rather than up). That means that this is almost certainly a healthier group of wrestlers. Additionally, the higher up the ranks you are, the more money you earn creating an incentive to keep competing even if you have a minor injury. Finally, and I’m repeating myself a bit here but you can see that there are far more possible bouts where a wrestler did not move up a tier vs ones where they did. As we mentioned, the group moving up is likely healthier and has more momentum which similarly implies the group that didn’t move up a tier is less healthy and less likely to have confidence from recent positive performance. Even with these explanations in hand I think this merits further investigation.

Does Wrestling Style Affect Injury Rate

We previously classified wrestlers into 3 archetypes based on the Kimarite (technique used to win the match) they use. As a refresher here is the table showing the average rates and please note that while there are labels like Pusher-Thruster, Belt Grappler, and Balanced, those are labels I applied after creating these three archetypes so they might not fit the stereotype we think of when hearing those names perfectly.

The next test was whether or not these different archetypes had different injury rates. Using these clusters I simply looked at all bouts by wrestler type and then how often they were injured.

I’ll be the first to admit: I’m not an expert on all the intricacies of the physical aspects of Sumo but rather a guy who enjoys the sport and is alright at working with data. Do these results make sense? I’m honestly not sure and I think that there’s probably further experimentation that can be done. For instance, instead of looking at wrestlers by archetype, try to see if we can establish a link between injury rate and kimarite employed directly. Maybe if wrestlers do Sotogake they more frequently get injured in the near future.

That said, trying to make sense of the data I do have a hypothesis of sorts on what explains it. With Pusher-Thrusters being injured the least and Belt Grapplers being injured the most, I do think it’s possible that when you’re not going (more or less) straight forwards or backwards as Pusher-Thrusters do, you open yourself up to greater injury potential. Your knee might twist easier, being on the belt and trying to throw could pull a muscle, and so on and so forth.

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Does Time of Year Affect Injury Rates

As we know there are 6 tournaments a year with a comforting lack of change to the calendar. Is there a certain tournament wrestlers are more likely to get injured in?

Looking at the data it appears possible with lower rates for March and November. However, we can do better than just simply eyeballing it; enter hypothesis testing. If that sounds familiar, we did something like that last year. To give a short summary though, we begin with the assumption that two phenomena are not different (the null hypothesis) and then use a threshold (traditionally 95%) certainty for whether or not there is statistical significance. In this case, we’re starting with the assumption there is no difference (at that 95% certainty level) between these tournaments and if we reject it, that means we do think it’s possible that one (or more) of these tournaments have statistically significant higher injury rates. Don’t worry too much about it; the thing to keep in mind is that if the p-value is under .05 then the results (might be) meaningful.

As you can see, the p-value for the Calendar Test is above .05 and so it’s likely that this is just random noise. Doing the same for style and moving up a tier gives the following:

So we do think that differences in style lead to meaningful differences in injury rates, which is quite different from what we can conclude on moving up in rank. Similar to the calendar test, it appears that moving up a rank leading to fewer injuries does not clear the bar for statistical significance.

Conclusion

We are still just scraping the surface of the kind of analysis we can perform. In the future I think it would be worthwhile to filter further for Yokozuna and Ozeki as they have higher injury rates and different incentives from the rest of the wrestlers. I also earlier referred to getting more granular in analyzing kimarite directly rather than the amalgamation of kimarite into wrestler archetypes.

That said, I think we learned a valuable lesson today on styles meaningfully affecting injury rates. I look forwards to continuing this kind of analysis at Ozeki Analytics. Thanks for reading. Cheers!

Because of this, there’s a phrase: the best ability is availability. Today I’m going to begin digging into injuries in Sumo and work towards mining insight from the data. Luckily, the reporting is fairly clear on the Banzuke with injury losses broken out into their own separate column. For instance in May 2026, Onosato withdrew completely from the tournament but the reporting has him at 0-0-15 aka 0 wins, 0 losses, and 15 injury losses. I took this data for the modern period (1988-2025 in this case) and made some graphs to show trends over time. After that I’ll do some light analysis, explain auto-correlation, and lay out how I think this research could go even further and become more useful.

To refresh, Sekitori are wrestlers in the top two divisions of Makuuchi and Juryo. I excluded Yokozuna because once a wrestler reaches Yokozuna they cannot be demoted. As a result they have greater latitude to withdraw from tournaments when injured without risking their rank and as a result, money. Ozekis do not have the same degree of protection, but unlike the wrestlers below them, a bad tournament cannot result in them losing their rank (of Ozeki). In fact, even if they have Makekoshi (8+ losses) two tournaments in a row the following tournament they’ll be Sekiwake but eligible for immediate Ozeki reinstatement with 10+ wins. The top two ranks of Ozeki and Yokozuna as a result tend to have higher injury rates hence me bracketing them out. In fact, I have a chart that illustrates this well.

Please note that Sanyaku above in this chart refers to Komosubi and Sekiwake only. Normally it refers to all wrestlers Komosubi and above. Next let’s look at the injury rate by age buckets.

Now looking at injury rate we can see the results are about as expected. for wrestlers older than 36 their lower injury rate is more reflective of the fact that the only men still wrestling at that age are much healthier and skilled in general. There aren’t many men able to compete in the top divisions at that age. To analogize to another sport, I’d imagine in American Football, players in those same age brackets have lower injury rates too. It’s likely largely Quarterbacks, Kickers and Punters or in other words, special cases1. This geriatric Sumo wrestler phenomenon might be worth a deeper dive in the future but for now let’s move on.

This chart is hardly surprising; the longer you wrestle the more injuries you suffer! Still, calibrating and confirming things like these are helpful.

Auto Correlation

When we’re taught about probability, the first example we encounter is that of a coin flip. 50% of the time it will land on heads and the other half on tails. If I land heads 10 times in a row, the next flip should still have an only 50% chance of landing tails despite feeling that tails is “due.” Coin flips are what we call independent; one event does not affect another.

However, many events are not independent and in fact rely on the previous event. In the case of our coin flipping, if they were not independent, then the last flip of the coin does affect the current one. This is autocorrelation. This is present in many cases like finance. There’s a whole branch of trading called trend following based on the fact that stocks going up tend to go up more and when securities fall, they tend to fall further.

Sumo injuries seem like a prime example where autocorrelation is worth testing. If you’re so injured in a tournament you have to pull out or suffer injury losses, you’ll likely still be feeling effects the following tournament. Testing that out, this is indeed the case.

The Lag-1 correlation means that ~25% of the time a wrestler has injuries in one Basho, the following they’ll have further ones. But we can look at this in a different way. Below we’re looking rather at injuries between Bashos.

As we can see ~94% of the time health means health the following tournament. When injured 7/10 times the following tournament is injury free but the other 3/10 are injured the following Basho.

These numbers obviously aren’t the same as what they’re measuring differs slightly but in key ways. A good way of thinking about it is that the transition matrix asks "are you injured?" while autocorrelation asks "how injured are you?" A wrestler who misses one bout and a wrestler who misses all fifteen are both simply classified as "injured" in the transition matrix. Autocorrelation, however, recognizes the difference. The transition matrix therefore captures the persistence of injury status, while autocorrelation captures the persistence of injury severity. A rikishi can remain injured across consecutive tournaments while seeing the seriousness of that injury improve or worsen, causing the two statistics to tell slightly different stories.

Future Analysis

One upside of tilling the relatively virgin soil of Sumo data analysis is that my research can be fairly basic but still (hopefully) provide value at least in terms of novelty. However, I realize that the frontier can and should be pushed forwards. In baseball, analytics is able to help players make better pitching or swing decisions and directly improve their abilities. Analyzing opponent’s tendencies can allow defenses to better position themselves. I’m humble enough to realize that unlocking such valuable insights in Sumo that can directly improve on-the-dohyo outcomes remains far away. However, I do think a notable exception is in injuries. The level of data to improve health outcomes for wrestlers might not be easily available for public analysts, but I do believe that data could exist and could better the lives of hundreds if not thousands of rikishi some day in the future.

Here are some ways I think that injury analysis in Sumo could be advanced; some are testable hypotheses, others models.

• Analysis of reaction times. Through a consistent placement of high definition cameras and frame-by-frame analysis I think we could make advances on getting reaction times at match start. Could slower reactions be an indicator for higher injury risk? This could also be helpful for concussion diagnosis.

• I’ve talked about Elo (commonly used in chess to assign “skill ratings” which can then be leveraged to get implied probabilities of who would win in any given match) in Sumo before. I need to update my model and data, but I do believe that this would be a key measure for diagnosing injuries or injury likelihood earlier. For instance, if a wrestler is doing significantly worse than expected, it could be an indicator that they’re wrestling with an injury and are at a higher risk of future injury. There would be a lot of moving variables here, but I do think this is a realistic hypothesis that could be tested and could lead to better health outcomes for wrestlers.

• In the future I’ll look at wrestling style which we discussed recently and if certain styles are more correlated with injuries whether its their occurrence or severity.

• While we do have available data on wrestlers’ heights and weights, unfortunately it appears a bit spotty. If there was more consistent data, figuring out if optimal combinations of weight and height existed would be worthwhile.

With that all out there I’ll end this post but please look forwards to more on this topic. Cheers!

This isn’t a philosophy blog, but I think that paragraph helps set the stage for today’s post. Every Banzuke is unique. Even when it’s Hakuho going 15-0 at the peak of his powers, there’s always further intrigue across the Banzuke. Maybe it’s 2 Ozeki chasing Yokozuna promotion. There’s new debutants. There’s a veteran trying to halt his slide out the top division. There are different storylines every tournament. It’s similar to the flow of water and the passage of time ensuring that even if you are at the same location, you’re stepping into a different river.

Despite that, I wanted to try and find what the “average” Banzuke might look like. Just as there are many answers to who the first Western philosopher was, I’ll provide a few different answers to this question.

As usual I am doing since the start of 1988 right after Futahaguro’s retirement. For this exercise I’m just sticking to pure rankings and will be charting this out in a few different ways. Additionally, at the end I’ll show the most appearances by general tiers of the Joi, the mid-Maegashira, and lower Maegashira. If you’re interested how I calculated those tiers I have a piece explaining it here.

Starting off I ran the numbers for what I call Absolute Rank. The top ranked wrestler is almost always Yokozuna 1 East, but in theory if there were no Yokozuna then it could be an Ozeki 1 East. I started off by not looking at the rank’s name, but rather the numerical position on the Banzuke. So whoever is on top of the Banzuke is Absolute Rank 1 and so on. Here is the top 42 (the current Makuuchi top division total) from every Banzuke 1988-2025.

No surprises with Hakuho up top. I also have a table showing the various ties for this ranking which puts respect on Kisenosato having the joint most appearances at number 3 on the Banzuke.

Next I looked at the most common rank across Banzuke based on their numerical position in the Banzuke. In other words most of the time the top rank in the Banzuke is Yokozuna 1 East, then Yokozuna 1 West. After a 42 rank top Banzuke is assembled, I found the wrestler to appear at each of those positions (i.e. Y1e not 1) the most. In other words, what were the most common ranks in a Banzuke, and who occupied them the most?

As you can see, from 1988 to 2025 Juryo 1 East and West were more common than Maegashira ranks in slots 41 and 42. Part of that is that 42 top division wrestlers only came about in 2005. Fun fact: at the beginning of our period in the 80’s there were only 38 wrestlers in the Makuuchi. Here are the ties.

I felt that the most relevant measure was unique wrestlers (no repeats) but if I didn’t use that rule Hakuho was the most common Yokozuna 1 East and West. Whenever you research sumo statistics Hakuho is probably at the top of it if it’s a positive stat.

I also checked who the most common wrestlers were at Maegashira 17 East and West instead of Juryo ranks.

Finally, I applied my tier-system (methodology found here) of the Joi, Mid-Maegashira, and Lower-Maegashira and just took most appearances in each of those categories. As you’ll see the Joi becomes much more top-heavy. As mentioned earlier in that article I linked to I calculated the Joi to be 1-17, Mid-Maegashira to be 18-35 and the Lower-Maegashira; you can see the methodology there. In a sense, if you turned on the TV to watch sumo, these are the men you’d be most likely to see towards the top, middle, and bottom of the Banzuke.

Hakuho and Kaio up at the top are incredible. Again each appearance represents one tournament so a good way to think about it is that both those men have spent over 4 years more at the top of Makuuchi than any other wrestler in the modern era.

The Joi section really is incredibly impressive with the only man there not a Yokozuna or an Ozeki being Akinoshima.

One thing I enjoy about sumo is that each tournament every wrestler fights an odd number of matches meaning you either have to have a winning or losing record; no ties. However, that means unless you are a Yokozuna or an Ozeki where your position is more constrained, it’s difficult to have a steady rank once you’re below Komosubi.

With the Mid and Lower Maegashira it’s not surprising there are fewer appearances given that you can either win or lose your way out of those tiers. In the Joi if you keep getting Kachi-koshi (8 or more wins) you’ll stay there indefinitely. Furthermore, with the Lower Maegashira it makes sense that the appearances are lower as it’s a smaller tier and if anything even smaller than it looks given 42 rank Makuuchi only came about about halfway through this time period.

When looking at the men who have wrestled in the top division it frequently strikes me how few there have been. But reframing it we can see that actually there are relatively few opportunities to reach Makuuchi. Men in the Joi can occupy it for a decade or more. Takanosho is a top division mainstay who can snag a Jun-Yusho if he’s mid or lower Maegashira. He’s 31 and likely has a couple years more at the top and is already at nearly 7 years in the top division. He’s actually split time between the Joi and Mid-Maegashira fairly evenly so he won’t end up on either career appearances lists but the “average" Banzuke likely features a few guys like him. By the time you’ve accounted for all the top guys and mid-level men the pickings are slim for Juryo hopefuls.

Looking at the top rankings where we began by using Absolute Rank (1st position, 2nd, so on) and then looking at the most common title for each Absolute Rank (Y1E for 1) we can see that beyond the tippy-top Banzuke are relatively fluid. Being in the same position or rank is uncommon. That makes sense, but it’s nice to have numbers to confirm it.

Going into appearances by tier, the numbers show that despite the brutality of this sport, there are wrestlers who are able to find their level and maintain it for years, sometimes even more than a decade. From that I gained a much deeper appreciation of those iron-men and can now quantify it in a way I couldn’t have before. This was a fun exercise and I got to look into some more classic wrestlers (been a fan since ~2019 so getting an idea of the 90’s and 2000’s beyond Yokozuna is always nice). Hopefully you found a name or two to look into also!

Heraclitus told us that we can not step into the same river twice. Similarly there are so many ways to look at an “average” Banzuke that I could spend years charting nothing but different permutations of that. Sure, Hakuho and Kaio will likely feature, but our modern day top division features 40 more men and their stories matter too and make sure that there’s intrigue and a different look every 2 months.

We’re using statistics to create archetypes of sumo wrestlers! Every match of sumo there is a Kimarite - or winning technique - that is used. If you watch enough you’ll start to get familiar with the more common ones such as Oshidashi and Yorikiri (frontal push out and frontal force out involving belt respectively) but in total it’s over 80 different techniques. Using K-means clustering (will explain in next section) we’ll look at ~2000 wrestlers and their kimarite to try and create archetypes of sumo wrestlers.

I alluded to before there are some general archetypes out there - pusher-thruster, belt grappler, etc. - but not based on repeatable processes and hard data rather experience and intuition. I’ll be clear that I think those are quite valuable too, but as the author of a sumo statistics blog I think there’s merit in using data to build on that.

As usual I’ll begin by explaining the data used, the overall process, and any considerations or decisions I had to make along the way. If you just want the data on the archetypes and how they differ in types of kimarite they win by that can be found at the bottom. I also include a table showing the 42 wrestlers in the Makuuchi for January ‘26 and how they’re classified. Finally there’s a table of Yokozuna in the dataset and which archetypes they fall under.

Data Used and Techniques Explained

As usual I am using wrestlers from 1988 to present. 1988 is right after Yokozuna Futahaguro stepped down and provides a clean, convenient marker for the modern era. Within the subset of wrestlers from 1988-present, I then looked at every wrestler who had at least 100 matches with defined kimarite. In all that left 1,940 wrestlers. With the kimarite you can actually find which kimarite the wrestlers lost to as well. For instance, Examplenofuji won 20 matches via Yorikiri and lost 10 via Yorikiri. Let me show you what the data looks like:

As a note I ended up looking only at wins. I tried going through this process with Wins and Losses but it performed worse than using Wins alone. I do think there could be some value in knowing how wrestlers lose, but at least for this exercise and implementation I’m unsure how to improve results with that information.

Next, I converted these to percentages. It’s important to compare what percentage of matches wrestlers won with a given kimarite vs how many matches they used the kimarite in. It makes comparison across wrestlers apples to apples.

Next we apply K Means Clustering to the data. I could try and go into the mathematical explanation but I think it would be easier to illustrate by analogy. A Voronoi Diagram is a diagram that takes a bunch of given points, and then splits it into various regions based on which point they’re closest to. This illustration from Wikipedia ought to help.

The K Means Clustering is so named because we provide k number of clusters (I tested k=3,4,5, and 6 but 3 was best1) around each average. So when I run the algorithm for k=3 it’ll calculate 3 averages and then classify every wrestler based on which of those 3 it’s closest to. The same idea applies when I set k=4 and so on.

Results

Here’s the fun part! As stated before there are 80+ kimarite, but for visualization purposes, those 80+ dimensions (each representing a different kimarite) are collapsed down to two dimensions2. The clustering itself was done in the full 80+ dimensional space; the 2D plot uses Principal Component Analysis (or PCA - as noted in the footnote beyond the scope of this post) purely for visualization. Using 3 different groups, it looks like this:

As you can see, there isn’t really a sharp dividing line for these classifications. I also have a kimarite comparison table to help elucidate the differences between the archetypes. The names of the archetypes and the graph make clear that it’s more of a spectrum with Pusher-Thrusters and Belt Grapplers on opposite ends with Balanced in the middle.

Next is the highest exemplar of each of these archetypes. In other words, who most fits the Pusher-Thruster classification would be the guy ranked number 1 below and the same for Belt Grapplers and Balanced wrestlers.

Next up we have our Makuuchi - I applied the framework to the 42 top division wrestlers in January ‘26 and these are the results. Typicality_Score goes from 0-100 with 100 being the most typical of that archetype.

Finally I have the Yokozuna from the dates covered and their styles. Interesting that none of them are classified as Pusher-Thrusters.

With that I’ll conclude the article. That said, I think you can expect further work on this in the future. Cheers!

Appendix

I said earlier that I ran the code with 4, 5, and 6 clusters vs the above k=3. From my perspective it doesn’t look like it adds a ton of value. The dots are all in the same places, and with them all being in a large cluster, the bounds can feel even more arbitrary. If someone who knows more about kimarite and has ideas on how to classify wrestlers via those kimarite reached out though I’m all ears.

While the two men had different paths there, they found themselves both at the pinnacle of the sport and a reasonable observer might conclude that the odds were 50/50 who would win. But the records showed something different: Hoshoryu had won 6 of their 7 previous matches1. Did he have Onosato’s number? That is to ask if Hoshoryu had some durable advantage over his fellow Yokozuna.

In fact, this is a question we can ask and answer using statistics and at least if we assume that it was a true 50/50, despite the lopsided record we could not assume that Hoshoryu had definitively figured Onosato out. And the results bore this out with the Mongolian (Hoshoryu) taking the first match to force the playoff only to falter and fail to win the Yusho in the second match. The Yokozuna split the day’s matches with each man winning and losing one apiece.

Today we’ll go over the basics of this common statistical test, try to put in “Plain English” and in a first, I wrote a basic script so you can test it from the comfort of your home at the link here. That’s right: think of any two wrestlers and you can test there if one of them figured the other out.

All you have to do is plug in the number of wins, total matches contested, and then what you think the split should be. Plug all those in and hit Run Test and it’ll tell you whether it seems that one wrestler figured out the other or not.

Now if you’d actually like to understand the thinking behind it then continue on to the next section, if not, the link is below again:

https://ozekianalytics.github.io/BinomialSite/

Binomial Test Explanation

Here’s the equation that’s happening under the hood:

Looks easy, right? I’m kidding of course. Let’s unpack this.

On the left side we have P(k wins) which is the probability that we have k number of wins, k being 6 here.

Next we go to the more complex side of the equation. Please note that ! in math is factorial - which is just the product of all numbers up to n or k or whatever you put in front of the !. So 2! would be 1*2=2. 3! is 1*2*3=6 and so on.

Let’s take them one at a time. The first term is meant to calculate how many different ways we could get that outcome. Using our example if there were 7 matches of which Hoshoryu won 6, then there are 7 different ways that could have occurred. Onosato could have won their first match and then lost the next 6. He could’ve lost the first match, won the second, then lost the next 5 and so on. Visualized alternatively here’s how their wins and losses could have gone:

Scenario 1: LWWWWWW

Scenario 2: WLWWWWW

and so on. This is easier because we know there’s only 7 different ways it could’ve worked out, but here’s the math.

7!=5040

6!=720

5040 will be divided by 720*(7-6)! and 1! is going to be 1 (1*1=1) so 5040/720 which is indeed equal to 7.

The next term is p raised to the k. That’s actually straightforwardly the odds of anything happening for a given probability. Using our assumed 50% odds of Onosato winning against Hoshoryu, the odds of him winning a given match is 50%. To calculate the odds of him winning two in a row that’s 50% * 50% which equals 25%.

With our example the probability is 50% and the number of wins is 6 so it’ll be .5^6=.015625

In English now we’ve calculated how many different ways we could’ve gotten this exact outcome. We then calculated the probability of the exact outcome. Let’s unpack the final terms and wrap this up.

Looks worse than it is. We know that p is our probability aka 50% (or whatever you want to use). N is the number of matches and k is the number of wins. Hopefully reading that helped crystallize it for you but it’s close to the flipside of the prior term. We calculated how likely it was to get exactly 6 wins, and now we calculate how likely it is to get 1 loss. That’s all. By the way, (1-.5)^(7-6) =.5^1=.5

So after going through we can see that we basically looked to see how many different ways we could get 6 wins and 1 loss, and then multiplied it by the probability of getting 6 wins multiplied by the probability of getting 1 loss. That’s all there is to a binomial hypothesis test.

So our final equation is:

7*.015625*.5=.0546875 or 5.4% for 6 wins exactly which is just above our p threshold of .05 or 5%.

Technically speaking our question is odds that Hoshoryu would have won this many matches or more. That’s a little confusing why we’re doing a cumulative probability function rather than just the specific probability of 6 wins. Think of it with coin flips: if we got heads 60 times in 100 flips, testing how likely you are to get heads 60 times is pretty meaningless on its own; you’re unlikely to get heads exactly 50 times on its own too rather we want to know the probability that heads that many times or more in that many coin flips is evidence of a biased coin. Testing the exact number on its own is just unlikely to tell us much.

For the record the same equation for 7 wins no losses is .0078125 so if you run it with the default values on the site that’s why you’ll see .0625.

Hopefully that makes sense, but if that feels a bit arbitrary or using .05 for the P value then you’re not alone and actually a lot of recent stats history is hand wringing and self reflection of how much of stats is founded on round nice numbers like that .05 but here at Ozeki Analytics we’ll leave overturning decades of statistical conventions for after we have better mathematical models for predicting matches. Cheers!

Yokozuna Preview

Kotozakura went 9-5-1 last time out so it’s a blank slate for him. As always the bar for Yokozuna is 26 wins over two tournaments which he’s absolutely capable of, but the path to success is only getting narrower as more top prospects ascend the ranks. He did look better last tournament around in my opinion so with good health and luck maybe he can get a rope run started.

Ozeki Preview

There’s really only two guys worth discussing in my opinion this tournament for Ozeki since most of the top of the Banzuke is guys recently promoted or that had bad records last time around.

Aonishiki, Sekiwake - Last Tournament 11-4, Komosubi; 2 Tournaments Prior 11-4 Maegashira 1 (22 Wins over 2 Tournaments)

33 wins in 3 tournaments from the top of the Banzuke is the general bar for Ozeki. It almost feels inconsequential if he gets it this tournament or not because Aonishiki has made his astonishingly quick rise to the top of the sumo world feel so inevitable every step of the way. He looks like he belongs as a Sekiwake already if not an Ozeki. Still 21 until March of 2026 it really feels like the sky is the limit for him and I’m already hoping he can develop some great rivalries with the other men at the top of the Sumo World.

I looked around online at some sumo blogs and the news and I couldn’t find if there’s any official stance from the Sumo Association officials commenting on how many wins he’d need for a promotion. My opinion is that they might actually like balancing the Banzuke and given it seems unlikely he’d prove an incompetent Ozeki and make them look foolish which means he could even get in with 32 wins. That’s probably a hot take. If he goes 12-3 with a Jun-Yusho (runner-up finish) that would force their hands and that feels surprisingly possible despite how few pro tournaments he has under his belt. We’re in an era of wrestlers reaching the top faster than ever before with the influx of polished college wrestlers like Onosato. The fact Aonishiki is already nearly caught up is incredible. I’m really appreciating the run he’s on.

Oho, Sekiwake - Last Tournament 10-5

Despite having been a Makuuchi mainstay the past ~4 years since the beginning of 2022, he’s still only 25. This grandson of Yokozuna legend Taiho, since sticking in the top division has mostly just grinded his way towards the top with the few outlier results along the way. He seems clearly up to the skill of the Joi (upper ranks) in 2025 so maybe he’s still improving and can eventually reach Ozeki. He has a solid base to continue a run from with 10 wins last time around.

Interesting Prospects

I tried to get rikishi in each division from Juryo-Jonidan and these are all guys who have had good 2025's. I’m also trying to include a little bit on kimarite (winning technique) too now. It might be wrong but I do tend to be more impressed with guys who win with many different techniques and throws and trips in particular. I actually did a little Judo so I’m biased but this definitely merits a look; does using many different techniques correlate with success, higher ranks, etc.? That’s for another time, but here are some prospects I’m keeping an eye on this tournament.

Himukamaru - Juryo 13E, 21 Years Old

Coming in at 5’8 (173 cm) this is more a pick for how he might be Takakeisho reincarnated (don’t worry, he’s actually still around and looking great!). He wins with Oshidashi (push out) 48% of the time with the average being 26%. Takakeisho’s rate? 46%. He’s made his way up the Banzuke pretty quickly since coming in at ~18 years old but doesn’t quite compare to how quickly Takakeisho did. Takakeisho was an Ozeki at 22 years old. Man I miss Takakeisho but luckily his highlights are still there.

Noda Tenga - Makushita 10W, 19 Years Old (20 on November 27)

If anyone knows why sumoDB has him entering Jonokuchi at 185 cm but later being 182 cm which is what he’s listed on the official sumo site at, I’d love to hear that story. Besides that if he does well this tournament he’ll be slated to join Juryo before his 20th birthday which would be impressive. With good size he mostly wins with yorikiri at 54% of the time vs 25% for the average wrestler.

Yumenofuji Yudai - Sandanme 7E, 17 Years Old

Still 17 in Hatsu (first) Basho of ‘26, he already has 16 tournaments under his belt. After ending 2024 with a missed tournament, he had a strong 2025 and is at the upper Sandanme. Clocking in at 6’2 (183 cm) he could get bigger and fill out his frame. This is more of a long term pick, so facing off against upper Sandanme for the first time if he can go Kachikoshi 4-3 or even 3-4 I would be impressed. He actually has some pretty diverse kimarite including uwatehineri which I’ve never heard of because it’s won with in .11% of all matches. Here’s a video of it (according to Youtube).

Ryuho Kazuma - Jonidan 45W, 18 Years Old

Not much to add here; this one is a lotto pick. I find it interesting that as I look through the lower divisions for guys doing well, so many of the best performers are college wrestlers (went to university rather than joining pro sumo at ~18 or younger). We’ve explored before that the percentage of college wrestlers has risen quite rapidly even if they’re still only ~15-20 percent now. But just looking at the guys making their way up the ranks quickest it certainly feels most of them went to university.

Hikarumusashi Update

It’s not good folks. Jokes aside he went 2-5 at Sandanme 51 last time around but luckily stayed in the Sandanme. The only American in sumo, I think the opportunity to face off against mid-upper Sandanme talent if he does well this tournament is good for his development. He just turned 20 years old but is still relatively new to sumo so hopefully he sticks with it and can improve. I think it’d be really neat and big for the sport if an American succeeded in this day and age. Maybe I’m overly optimistic but I think it could be a genuine cultural phenomenon or at least a meme if an American made Makuuchi. Will it be Hikarumusashi? I mean it’s pretty unlikely right now but he does have good size so as long as he keeps at it I’ll include these updates.

I think it’s an interesting problem that I can’t really find anything similar online in English at least. So I’ll go over the methodology and then show the results. Furthermore, we’ll have more work on this so if it interests you then please subscribe!

A Framework For Judging Individual Wrestler Success (skippable)

Across sumo wrestling there are 6 divisions and approximately 500-700 wrestlers. As stated above we’d like to have the relevant metric be applicable for shorter terms and ideally for all those rikishi; I’ve highlighted prospects as young as 15 and in the bottom divisions of Jonokuchi and Jonidan where they might not reasonably reach the upper divisions for 3-5 years if that.

So looking to craft a metric that could account for the above I came up with the idea of looking at simply whether wrestlers were higher or lower on the Banzuke (the rankings of all wrestlers) on a rolling basis for various amounts of tournaments. In other words, what % of wrestlers were at a higher rank after 3 tournaments, or 6, or 9 and so on (I’ll show the numbers below). Furthermore, I tried a few different groupings and settled on just doing by career high division rank except for the Sanyaku (in Makuuchi) where I split out Komosubi, Sekiwake, Ozeki and Yokozuna. We then look at how those various groups did across divisions; so how did future Yokozuna do in Sandanme vs guys whose career high rank came in Makushita (only one division higher). I think it gives us a start for quantifying prospect success on a shorter term, and again I’m incredibly proud that we’re some of the first folks to do this. That said, we also hope that our work here inspires others to improve on the building blocks we’re laying out today.

A few final notes on data selection: I’m only looking at the careers up to their peak and then an additional 9 tournaments. The idea is that we want to capture when a wrestler reaches their best (and directly after) without having metrics depressed by their career decline; this is for prospects who should be on the upswing. If a wrestler only reaches Juryo, then languishes in Makushita and below then their data will be cut off 9 tournaments after their Juryo debut.1 Finally for the wrestler selection I used my typical “modern start date” of 19882 and 2020 as the end date to avoid wrestlers whose careers are still on an upward trajectory. Any wrestler who appeared on a Banzuke in that time period is included.

Results

To explain the above it’s saying that Yokozuna when in Makuuchi after 5 tournaments are at a higher rank 70.4% of the time. For those same Yokozuna in Juryo it’s 92.3% of the time. Career high Ozeki are at a higher rank (further up towards the top of the Banzuke) 70.2% of the time in Makuuchi. The higher rank can be any higher rank so even moving from Juryo 14 West to Juryo 14 East would represent a rank increase3.

I don’t think any of the above is too surprising, but the conclusion itself is fairly clean: if after 5 tournaments at any given rank you’re not higher up the Banzuke, then ~1/2-3/4 the time you’re topping out in that division. This looks very useful for Juryo in particular.

Under Additional Data I talk a little on how I ended up using 5, but to give a simple explanation please see the below for 3 tournaments ahead and how the relationship isn’t quite as clean.

The guys who are topping out in the current division are a little worse off, but so are guys topping out at higher divisions too. I think the relationship is less clean and clear as compared to five tournaments. This is one of the perennial problem with applied statistics that more data gives us more confidence, but we often want to be able to study this data so we can apply it to situations in which there are few data to work with!

Additional Data

Statistics can often be as much of an art as it is a science. We often have to make decisions based on what seemingly works or “feels” correct. I won’t go into it today, but there’s a big controversy in the stats community if we should retain .05 as the P value cutoff for various tests - long story short the P value is important and we used a nice round number because it looks and feels nice and does work relatively well but we’ll talk about P values further another time.

This aside is to say that I ended up using 5 tournaments ahead because it seemed to best balance stability of results while also being relatively short term (less than a calendar year). I landed on that based on looking at how much the pct_improved changed. Seeing it will explain things:

As you can see 62.4% of the time after 2 tournaments Yokozuna had a better record in Makuuchi. After 3 tournaments it goes to 67.2% or a 4.8% difference. Now that you understand the above, you’ll hopefully have a fighting chance with the below pivot table showing the aggregated Average Percent Improvement and Standard Deviation for it across 2-9 tournaments ahead:

So you can see that the average and standard deviation look solid for 5 tournaments out. 6 might be slightly better where there’s a slightly higher average but much lower standard deviation but like I said, it’s an art like it also is a science.

Conclusion

I think that we reached a fairly clean conclusion through the data which is that: if after 5 tournaments at any given rank you’re not higher up the Banzuke, then 1/2-3/4 the time you’re topping out in that division.

I think this is a nice yardstick to judge wrestlers by and going forwards I’ll look to incorporate this to my analysis.

I began by saying this is one way we can judge prospects. Next time around we’ll look to see how we can use wrestlers’ age to determine their future potential. Once we have that then we’ll be in a good spot to apply two criteria (or possibly more if we combine them or I think up any others4) to my past prospect picks and see if I actually have any idea what I’m doing. Hopefully you enjoyed this. Cheers!

Really quickly the criteria for reaching Yokozuna is generally 26 wins over two consecutive tournaments and at least 1 Yusho (tournament win). For Ozeki it’s simply winning 33 matches over three consecutive tournaments while being towards the top of the Banzuke (the ranking of wrestlers from top to bottom). As for prospects, things have gotten weird particularly the past few years as we’re seeing a much higher percentage of wrestlers having wrestled in college whereas they previously they usually entered straight out of high school, if not sooner. We’ve even done a piece on there being more college-background rikishi (wrestlers) and the numbers confirmed this.

I embedded videos on some of the wrestlers so if you see a link over a wrestler’s name and it has a link then please click it and enjoy the highlights.

Finally for the intro, I want to apologize for my work being more inconsistent this year. I can’t announce why that has been the case yet, but I believe there should be a big announcement (or two) that will show the exciting work I’ve been focused on in the absence of sumo writing. One of those announcements in particular readers of this blog will surely be pleased with and I anticipate to have that announcement in the next few months. I hope that when that news drops it makes some amends for my absence this year and that the passion behind that project shines through.

Real Time Update on Yokozuna and Ozeki Promotion Criteria (Skippable)

When doing research projects for sumo, I’ll often use data from the beginning of 1988 to present. I consider that the “modern era” of sumo because that marks when former Yokozuna Futahaguro was notoriously forced into retirement. We’re skipping that story for now, but the fallout from it resulted in greater scrutiny for promotions to Yokozuna.

The point is - and our research has shown this - there isn’t a strict criteria per se for these promotions be it Yokozuna or Ozeki. Rather there are general guidelines and various circumstances will affect how closely they are followed. When I look at the Banzuke right now, I believe that will be to the detriment of any future would-be Yokozuna. Yokozuna is for life, and while Onosato has looked good in his first tournament at the pinnacle of sumo, Hoshoryu has looked decidedly less superior. Furthermore, he’s still just 26 while Onosato is 25. With all that in mind, I think it will lead to stricter criteria for promotion. As a result, look for them to hew closer to the 26 wins minimum over two tournaments. Additionally part of the promotion guidelines say over those two tournaments the wrestler should have the Yusho equivalent. Sometimes that’s loosely interpreted as a Jun-Yusho (runner up) or even a strong showing that resulted in no Yusho or Jun-Yusho. I also think that will be adhered to more closely.

As for the Ozeki we actually find ourselves in the exact opposite situation. The Banzuke is unbalanced because Kotozakura is our only current Ozeki and just look at this screenshot from sumoDB:

It doesn’t look clean with Kotozakura all by his lonely! I’m being a bit cheeky, but the balancing of the Banzuke genuinely is a consideration. That means until that second Ozeki slot gets filled, you might actually be able to get away with 32 or maybe even 31 wins securing promotion to Ozeki. The Ozeki promotion also considers the ranks at which you won all those matches. The Georgian legend Tochinoshin had part of his Ozeki run come from Maegashira 3 (he won that tournament) and I think that’s about as low as part of the run can come from. That’s unfortunate news for Aonishiki who won 11 at Maegashira 9. I’m not including that in his current run and I feel fairly confident because he’s not even a Sekiwake and no modern Ozeki has been promoted from any rank other than Sekiwake.

Again, these are guidelines rather than strict rules, but my research gives me good confidence that any deviations from the above should be a decent surprise.

Potential Yokozuna Preview

Kotozakura O1E - 8-7 Last Tournament

Having won 8 matches in July, even a Zensho Yusho - 15 wins, no losses - would be insufficient for promotion to Yokozuna. For things to go well and him to be on track to go up even higher he’ll need 13 wins which is more or less saying he’ll have to be competing for the championship in the final days. There’s honestly not too much to say about Kotozakura. He finds himself in a similar position to Hoshoryu before his rope run to the top; firmly ensconced at the Ozeki position and just needing to put it together two tournaments in a row. Why Kotozakura seems to have trouble finding that consistency despite his terrific stature and solid all around game is the million dollar question. As I was writing this I couldn’t help but think of the “Potential Man” meme and so I made a version for Kotozakura. It’s meant to be more of a joke so don’t take it too seriously and hopefully in a year or two we can look back with a smile at how he finally put things together.

Potential Ozeki Preview

Here’s where there’s more intrigue over potential promotions.

Wakatakakage Sekiwake 1 East - Last Tournament: 10-5, Two Tournaments Ago: 12-3 (Two Tournament Total: 22 Wins)

In 2022 Wakatakakage nearly ended up an Ozeki. He began the year 9-6, 12-3, 9-6 leaving him at 31 wins and a Yusho. Unfortunately injuries sunk him back down to Makushita and now recovered he has an even better shot. As stated above, with only one Ozeki, I think he could probably get promoted with 10 wins, but 11 wins all but guarantees it. Best of luck to him and glad that wrestlers recovering from injuries and reaching the top again (if not new heights) is becoming more common.

Kirishima Sekiwake 1 West - Last Tournament: 8-7, Two Tournaments Ago: 11-4 (Two Tournament Total: 19 Wins)

Unfortunately the only scenario in which he’s viable to return to Ozeki involve him winning the tournament overall which seems rather unlikely. Still, he seems to be back closer to his form that got him to Ozeki rather than got him demoted. He still is in the prime age for sumo albeit on the back half of it and I’ll be rooting for him. 14 wins is a probable lock and 13 wins might suffice if Wakatakakage doesn’t get the job done.

Takayasu Komosubi 1 East - Last Tournament: 10-5, Two Tournaments Ago: 6-9

Takayasu has the more enviable position of the former Ozeki. 10 wins is a solid base for a run and if he can secure double digit wins again he’ll be in a strong spot to get the job done in November. It’s probably not super likely, but I also wouldn’t have guessed he’d be here after some of his tournaments over the past couple years.

Aonishiki Komosubi 1 West - Last Tournament: 11-4, Two Tournaments Ago: 11-4 from Maegashira 9

I mentioned that the first 11-4 is from Maegashira 9 because they won’t count that for an Ozeki run. That and the fact that he’s still just a Komosubi means that he will not get promoted unless they break a lot of rules and traditions. The big thing for him is doing well enough to get a Sekiwake slot in November and with that and a solid win total he could be an Ozeki come 2026.

Tamawashi Maegashira 1 East - Last Tournament: 11-4

Writing this about sumo’s Ironman who is in his 40’s is just incredible. One of these days I should do a “Best Run By Older Rikishi” because Tamawashi deserves his flowers for this. I hope he keeps at it, and even though I don’t expect this to realistically result in him reaching Ozeki, I’m always open to surprises and by still being in the Makuuchi at this age he’s shown he’s full of them.

Interesting Prospects (Skippable Intro)

When thinking about prospects, one of the biggest questions is: how quickly should you update your thoughts on the wrestlers? Let me explain; Aonishiki has not been a professional sumo wrestler very long. Furthermore, he started all the way at the bottom of the Banzuke. He went 7-0 and 6-1 from Jonokuchi to Jonidan to Sandanme to Makushita before finally reaching Juryo 6 tournaments into his career. He then had 22 wins over two tournaments to reach Makuuchi and is in the Sanyaku after just 3 tournaments in the top division. Given he is still just 21 years old, I think it can be said he’s at least a prospect for Ozeki if not Yokozuna.

But when should we have reached that conclusion he’ll be one of the top 3-5 wrestlers on the planet? When should we have concluded he’s a future Makuuchi wrestler? I don’t have an answer here, but I would like to point out that sumo Greatest of All Time, Hakuho actually had a 3-4 Makekoshi in his first tournament in Jonokuchi. He had another in Sandanme. With wrestlers still developing and at younger ages and with fewer matches below Juryo (7 vs 15 for top 2 divisions) there are inherent difficulties.

My approach is to find guys that are young for their division and are coming off a good tournament. If they do well again then (in my mind) it confirms that prospect status, but if they don’t do well, then they’re young enough that we shouldn’t have to ask any larger questions over their potential. That’s where my approach comes from here.

Fukuzaki Maaru Makuushita 6 - Age: 18

A beneficiary of starting in Makushita, he’s proven he belongs there. Last tournament he went 5-2 from Makushita 15 proving to me he has decent odds of ending up in Juryo next tournament. Making Sekitori (top 2 divisions) before your 19th birthday would be incredibly impressive.

Kobayashi Arashi Makuushita 25 - Age: 21

Coming off winning the Sandanme Yusho this marks a career high and Makushita debut. This comes off an extended injury layoff where he looks much stronger than before at least record-wise. This pick is more speculative than others. I just want to see how he’ll do facing competition unlike any he’s faced before.

Tenrosei Kenichi Makuushita 57 - Age: 18, Shusshin: Mongolia, Ulaanbaatar

From the same stable as Abi, the Mongolian has encountered little resistance thus far in his young career. Makushita is where I think you can really see the true talents separate themselves so like Kobayashi I think we’ll learn a lot based on how they fare in their first time facing this talent level.

Hikarumusashi Eru Sandanme 51 - Age: 19, Shusshin: USA, Hawaii

As an American it warms my heart seeing a compatriot in pro sumo. Even better, I had my concerns that he went 4-3 in Jonidan, but his second go around and from higher in Jonidan he went 6-1. He’s still young, and I believe he’s newer to sumo so as long as he keeps at it, and keeps making his way up the Banzuke he should have a bright future. At least this is what I tell myself hoping he can usher in a new age of American rikishi. The name might sound familiar because

Yamanobe Chikara Jonidan 60 - Age: 15(!)

The way to end up here is to be young for the division you’re in. Well 15 years old will do it! He went 5-2 in Jonokuchi last time around so there is some merit here, but this is as much about having a name filed away because wouldn’t it be fun if we see him in Makuuchi ~5 years from now?

Japan is alone as far as I am aware in being a liberal democracy with free and open elections, and despite that having more or less one party rule for the past 60-70 years. This is a simplification of course with two brief periods in the early 90’s and late 2000’s of an opposition led government before quickly reverting back to the Liberal Democratic Party (LDP). Furthermore, these have not been solely LDP governments with the more recent coalitions featuring Komeito. Nevertheless, the July Upper House elections in 2025 might very well mark the end of an era for Japan.

That over the past 4 decades the LDP has held power for about 35 of those years might come as a surprise given that it coincides with the popping of the Japanese economic bubble and subsequent “Lost Decades” of essentially nonexistent growth. Part of the pitch of liberal democracy is that when things aren’t working - and the economy and rising living standards are most paramount things in voters minds - it possesses the dynamism to change things up and course correct with a new political regime.

But perhaps there is a pragmatism to the Japanese voter. In those 3-4 decades of economic stagnation a multitude of different measures have been tried and all failed to effect the meaningful jolt to GDP growth they were designed to. Stimulative low rates failed to spur growth. Just about every form of fiscal stimulus has been tried at some point or another. Business culture has shifted towards less loyalty to employees to their chagrin without compensating for that greater risk borne by employees leading to large scale gains. Richard Koo’s explanation of the “balance sheet recession” - that companies themselves took a long time to recover from their debt binges in the Go Go years of the 80’s thus neutralizing aforementioned stimulus packages - is analytically useful. Yet unless those companies stayed in that balance sheet recession since the bubble burst, then it still fails to fully explain sluggish economic figures.

There’s an old joke that there are four types of countries: developed, non-developed, Japan and Argentina. The joke is that economists can explain the developed and non-developed but Japan and Argentina are just inscrutable. I studied economics in college myself but I tend to think of it as a rather useless (and more ideological than scientific) field in part because of the failure of any economist to be able to “solve” Japan1. The point I’m making is that the LDP seems hard to blame for Japan’s continued economic stagnation when there’s little reason to think anyone else would have been able to solve this problem. In that light, their continued electoral dominance is easier to explain.

Even with this story in hand, Japan stands apart from the rest of the world in the LDP’s continuity. As I survey the global landscape, democracies and autocracies alike face problems they seem unable to solve and suffer at the ballot box or in public opinion respectively as a result.

I could easily go in on the impotence of the UK Labour party and how quickly they shifted from winning large majorities (albeit due to a splintering of the right thus flattering their “success” at the ballot box) to feeling like a doomed government merely waiting for the far right to take power. But European impotence as a whole is easy to characterize with the Ukraine War. It was supposed to be the sort of wakeup call to arouse the sleeping giant of European defense spending. And while there have been marginal shifts, as a whole the strategic European autonomy that French leaders have dreamed of (with them in charge of course) and subsequently done little to actually effect since the end of World War 2 remains an ever distant dream. Even with Trump in office again - who has not only downplayed the idea of NATO as a whole, threatened fellow NATO member Denmark, and is perceived as more pro Russian based on his rhetoric than his continued weapon transfers to Ukraine show in practice - there is little appetite for taking the European project beyond its economic remit. This can be easily explained by many of these European leaders facing domestic challenges as they face a resurgent far right spurred by an inability to satisfactorily deal with immigration, youth unemployment, and dim economic prospects.

This inability to satisfy domestic audiences is hardly a uniquely European issue. I confess Africa is an unfortunate blind spot in my knowledge of the world, and yet in that meager familiarity I’m unaware of any countries where citizenry is not only happy with their government but that same government feels in charge of their future. If we take our survey to Latin America the story is hardly different with a couple of exceptions that I’ll address later on. Gustavo Petro is a useful example. Colombia a few years back under most definitions elected for the first time in its history a left wing president in Petro. That this would finally happen is evidence in part of the inability of governments to satisfy constituents leading to such a radical break with history. Petro’s subsequent floundering in power can be chalked up to marginal competence, but in this case points to the larger structural impotence of global leaders across the political spectrum to deal with today’s challenges.

Back to Asia we can see two countries with some of the highest state capacity in the world in South Korea and Japan who have failed to increase their birth rates even as they approach levels that some might call existential. This is hardly a rigorous scientific paper, but hopefully I have shown that there seems to be a theme of leadership worldwide not only unable to enact change in the way they seek, but furthermore a failure to manage the expectations of the everyday people as they deal with those shortcomings.

So where might we see the the counter-examples? Modi of India has managed to retain his popularity by delivering well enough on the economic front while simultaneously taking advantage of the BJP’s organizational prowess and raising the salience of Hindu nationalism. The latter part (albeit just nationalism, not Hindu) has been characteristic of many upstarts trying to regain a sense of national control. Is the organization the secret sauce? China with its massive CCP apparatus and membership alongside the United Front might suggest so. But even in both these examples, the popularity is there and yet India still faces questions why they can’t grow like China and China deals with youth unemployment and their own failure to combat low fertility.

With that I end on two further possible countries we could plausibly say are “in the driver seat of their own country” and also popular. El Salvador is a rather easy one to dispense with. Nayib Bukele comes across as swaggering, and by putting large swathes of the country’s male population in concentration camps, crime has abated for now officially. However, given much of this is built on backroom deals with the very gangs he’s “combatting” it hardly feels appropriate to see him as a man of destiny. In fact, his erosion of civil society and legal bounds in many ways feels like him getting ahead of the backlash as the memory of the crime wave fades in the distance but fundamental problems remain unaddressed.

This leaves me with just Mexico. In many ways Mexico stands out for appearing how we actually would expect politics to work. After multiple corrupt neoliberal regimes, Andres Manuel Lopez Obrador finally attained his long sought prize of the presidency. He moved quickly and decisively to curtail apparatchiks paid more for their resumes and social class than for actual results in the bureaucracy. Simultaneously he enacted reforms that rapidly increased the economic standing of those worst off in society. They have consequently richly rewarded his Morena coalition at the ballot box leading to his successor Claudia Sheinbaum winning the presidency with margins few but dictators could dream of.

I think that’s a good stopping point for our global survey. Mexico is a terrific example because even as I recount their domestic successes, it’s hardly as if they don’t face challenges in the near abroad with Trump threatening tariffs. And yet, and it is early days still, Sheinbaum and Morena do feel as if they are authors of their own destiny in spite of that. They continue to push through large scale reforms, and broadly those reforms seem supported by the average citizen. Looking across the globe they seem unique in that way that they identify problems and seem able to address them and please constituents in doing that2.

A little while ago we discussed the inability of Japan to get economic growth going despite a myriad of different approaches. That impotence in the face of such large scale challenges is in my opinion hardly unique as recounted above. But what was unique was that in spite of those challenges the LDP was able to hold on to power. Perhaps the LDP being unable to win at the ballot box anymore is the politics catching up to the economy and perhaps in that way Japan is becoming less unique and more like the rest of the world.

Addendum

This is a sumo and statistics blog but I do have the idea for a blog focused on East Asia in particular. I actually studied China as much as statistics in college (and more successfully) and Chinese the language much more than stats. The goal would be to rotate between China, Japan, Koreas, and Taiwan and try draw out and impart larger picture observation and information as opposed to being a pure link dump and news recap. Hopefully discussing how this election could signal a shift in Japanese politics is a teaser of deeper insights. I speak Chinese pretty well, Japanese less well and Korean essentially barely at all. As such, this project is likely 2 years off as I think being able to engage with local reportage and netizens is important3.

Further Addendum

I alluded to it earlier, but China does indeed face many problems. I think in many ways, it’s more interesting analyzing where Xi Jinping (or the Chinese state as a whole) is constrained vs where they are able to implement their will; the financial structure of the state and the tax and revenue of the Central Government vs Provinces and their genuine Green Revolution respectively. I’m a terrible pedant so I tend to think everyone more bullish on China than I is a wide eyed optimist and depending on their politics, naive and everyone more bearish on China than I a sufferer of motivated reasoning on why NATO needn’t fear Chinese hegemony and possibly a Sinophobe4. I have been banking some China related book reviews and some writing on it and Japan too so look forwards to it. I’m excited to share these thoughts.

Hakuho is the greatest sumo wrestler ever. When you have the greatest ever in a sport, you want to keep them around, even if they’re not perfect. Michael Jordan owns part of an NBA team. Wayne Gretzky is the same. Neither of those men is without their warts, but if you asked the commissioners and owners of their respective leagues, there would be no hesitation that it’s best to keep your GOATs (Greatest of All Time) inside the sport.

Hakuho seemed set for a similar trajectory. He had tensions with the Japan Sumo Association (JSA) as an active wrestler, but was able to obtain the elder stock necessary to have his own sumo stable post retirement. Top prospects came to his stable with the idea of training with the greatest ever. Furthermore, his eponymous youth tournament, the Hakuho Cup, was another achievement among his many. Not only did it grow over time, it attracted international attention and delegations; that is no mean feat for a sport than can often be insular.

Unfortunately, one of his wrestlers - Hokuseiho - was found to have been physically abusive towards stablemates, and the JSA determined that Hakuho’s supervisory actions were insufficient. As a result Hakuho was punished by essentially having his stable folded into another indefinitely with no clear criteria on when or even if it would ever be allowed to be independent again. That all came to a head after the 2025 Natsu Basho when Hakuho announced his resignation.

Abuse in sumo stables is an all too common problem in the sport, and I do applaud the association for coming to take it increasingly serious. Part of that will involve stern punishment for those that make sumo a less welcoming place. It must be addressed.

In no way do I wish to excuse Hakuho’s neglect as a stablemaster. Being put in charge of these young men is an incredibly weighty duty, and it is his job to serve as a role model for them. In fact, I think the association did the right thing when it would have been easier to sweep it under the rug as has been all too common in the sports past.

But this is not to say that the JSA acted in an optimal way. If they believe that Hakuho has proven unworthy of running a stable again, so be it. I think the chief sin is the utter lack of any guidance provided. Perhaps Hakuho or someone else will come out and share how and when he could’ve had his stable restored, but everything I’ve read leads me to believe that has not happened. Furthermore, if you have followed the sport, it’s hardly a secret that the JSA can be arbitrary, secretive, and there are certainly things one could point to if you felt they were less accommodative towards foreigners in the sport. I can hardly blame Hakuho from wanting to walk away from a sport, or rather an association, to whom he has given so so much and that has failed to reciprocate a fraction of that. That’s more or less all I have to say about that, and I rather dislike having to open this with the necessary background by recounting the fallibility of the GOAT of one of my favorite sports and the poor management of it by the powers that be.

A Sumo Rival?

There are reports that Hakuho is far from leaving sumo as a whole and rather looking to set up a potential rival organization. It’s still early days, but this gives us an incredibly rare opportunity to consider in a semi-realistic sense what a better sumo looks like. I won’t pretend that I have any insights into what they are looking to do but as I’ve said before I watch a lot of sports and think about sumo a lot so here’s a list of ideas I think we could improve on sumo with and can be considered my job application if Hakuho, or someone reading this connected to him, wants an idea guy.

Please note that this is simply a list of potential tweaks and some of them might be mutually incompatible. Again, it’s early days with few details and even more importantly: I’m an anonymous guy writing an English language stats blog of suggestions for a Mongolian sumo wrestlers who is collaborating with Japanese companies on this project. This is meant to be fun and hopefully even spark discussion on how the sport we love might be improved.

This week’s piece will be focused more on rules and regulations, and the next piece will be more focused on potential marketing. That said there might be some overlap between the two.

The Matches Themselves

Two wrestlers putting their hands in the dirt, launching into each other, and then the match ending when one of their body parts touches the ground or outside the ring is pretty much perfect as is. I do not think sumo fans should take this for granted!

Another of Japan’s top sports, baseball, I doubt people want to leave as unchanged. The introduction of the pitch clock was met with near unanimous approval. I imagine when the challenge system - allowing batters to challenge balls or strikes - is introduced to the MLB in the next couple years that will receive similar praise. The NBA has “how to improve the game” as a near constant topic of conversation. Even in boxing you’ll occasionally see people float rule changes to improve the sport. Sumo is not in that situation; I can’t even think of any proposals to improve the action itself and as a result I think Hakuho and his venture should retain all the rules as they are.

Actually, I do think there is a proposal that might not necessarily improve the sumo action, but I think simultaneously might not necessarily make it worse either. In this case it would be primarily for safety, having the wrestlers start from a two point or standing stance like the below photo so that the initial collision is less violent.

I will fully admit that I cannot tell you with any certainty what would be the result of this in terms of the action. Would it make belt techniques more effective? Would it make pusher thrusters less effective? I’m guessing for the latter yes as they generate less initial force, but again the proposal here is more about the safety as opposed to the action.

The Dohyo

I’ll keep this short: the Dohyo should be lower in this sumo venture. It’s another safety feature. A lower Dohyo will lead to fewer injuries and trauma in the course of matches. It’s a no-brainer and they should have already done this years ago for the health of the wrestlers.

Officiating

As a soccer fan who has seen the VAR (Video Assistant Referee) addition play out, I think a point that can’t be understated is: having perfect officiating is impossible, and there are tradeoffs between accuracy and timeliness of decisions.

So I’ll keep it brief and vague here: an on the ground official should make the initial decision, and a video replay assistant should check to see if they agree. Perhaps a challenge should be allowed to the wrestlers. That said, the inherent difficulty that we’ve seen play out is that the referee on the ground and the video referee will mutually abdicate responsibility to each other. The referee on the ground will ref knowing he has the video as a safety net but the video assistant will be hesitant to overturn the ref for various reasons. This inherent tension is unresolved in every sport I follow.

The only other point I’ll add is that I think that the Gyoji (sumo refs) do a good job explaining their decisions generally regardless of how accurate you think they are. I’m a massive fan of how in rugby the referees give detailed explanations, and furthermore the respect that players must show them. Other sports could learn a thing or two from that, in my opinion.

The Tournaments

I also think that the general tournament structure is good, but in this case I do think there are improvements that are possible.

To start: I think that having wrestlers compete in an odd number of matches is terrific. You either finish with more wins than losses or vice versa. It really heightens the tension for the final match when both guys are on the bubble.

However the tournament length in days is where I think we might get to our first big tweak. I’m getting a bit ahead of myself by bringing this up, but I imagine tickets to the tournaments will form a non-insignificant portion of revenue for what this venture ends up being. Furthermore, the amount of wrestlers will almost assuredly be fewer than the several hundred in current sumo. As a result, I do think that multiple matches in a day would be better for multiple reasons.

First off though is that this is a feasible proposal. We’ll often hear about on the Jungyo tour (where wrestlers go around Japan in between tournaments) that guys will perform numerous matches on the same day. They’re not going full effort, but having proof-of-concept is important and perhaps the extra time between tournaments would make this on the whole even safer1. For the justification, I believe that to compensate for fans seeing fewer unique wrestlers and to prevent oversaturation of the product - how many cities could fill even a small arena for 7-15 straight days of an upstart sumo league? - that multiple matches for wrestlers on the same day is prudent.

The second suggestion: I believe that not only should there be individual tournaments, but that there should also be a larger over-arching “season”. This would mean that if Onosato won the most matches and or perhaps the most tournaments in a calendar year for instance that there should be some sort of additional prize. I actually have some exciting ideas related to this for the next piece on commercialization.

The third suggestion, which I’m actually less hot on but I believe should be raised regardless: a playoff structure. There’s a bunch of different ways this could be implemented but the basic idea would be to have 9, 15, however many initial matches, and then a certain number of competitors who did well enough are then entered into a tournament structure. It might look like the below:

Again, I do not favor this tournament structure unless the entire tournament is structured like this. In short, if you introduce something like this at the end of the “normal matches” then the effect will be to make it less likely that underdogs can win. Lately we probably have had a few too many underdog Yusho winners in my opinion, but the current structure forces Yokozuna and Ozeki to be on their A level game days 1-15. If they have a playoff at the end then they only need to ensure that they make the playoffs and then they have a clean slate and having dropped a day 3 match suddenly no longer matters.

The Ranking and Banzuke Making

One of the few details that has emerged so far is that Hakuho has referred to other countries having their own Yokozuna. I’ll get to the international component under the Competitors section but I do think having relatively equivalent titles for whatever this new venture ends up being would be ideal. My partner works in IP law and I have played many Ace Attorney games so I do believe the fact that the title Yokozuna being centuries old means that upstart competitors would be able to use that title (and others similarly old) but to be clear this is not me applying to be Hakuho’s legal counsel nor is this legal advice.

Jokes aside, I do think that the naming conventions when feasible should be retained.

If we do retain Yokozuna and Ozeki, I do think it would be good if they put out guidelines for what wrestlers have to do to attain those ranks. The guidelines need not be super strict, but just saying that 26 wins over two tournaments is the general starting point for Yokozuna consideration would be helpful. In particular a clarification of the “Yusho-equivalent” would be much appreciated. I think we have a good understanding of that, but I’d also like to hear officially how the powers that be conceive of that.

As for the Banzuke, I have two suggestions. First and most importantly: I think we should have more insight into that process. My second is that I think they should move to a more formulaic process.

Guess the Banzuke is a fun game for us sumo fans, but I also think that there is something to be said for having a more rational process. It tends not to come up as the big financial difference is between the Makushita and Juryo (third and second divisions) which are less focused on but it quite frankly does not sit right with me that these men sacrifice so much for our entertainment and yet their pay can be greatly affected by the inscrutable decisions of men behind closed doors that we have little insight into.

Now a more formulaic process doesn’t mean that we would have an algorithm we plug a bunch of numbers into and it spits out the rankings/Banzuke necessarily - although if you want that, I have done work to do exactly that previously. Rather, I think it would make sense to have something akin to the ranking system in college football. We can have a panel of experts who provide their rankings/Banzuke (publicly!) and then just combine them all to get the final product. In fact we could even combine that with a more algorithmic ranking so we get both a more subjective judgment from experts alongside a more objective one from a disinterested computer looking at strength of schedule.

I would say that the principle here is that the venture absolutely can retain flexibility for these rankings and the Banzuke, but that greater transparency also represents an opportunity to not only help fans, but to also help folks feel that everything is above board and in line with stated practices.

The Matchmaking

Here is where I think the major disagreements begin. Currently in sumo the way it works is that Yokozuna will begin by facing their weakest opponents in the first week: guys in the upper Maegashira, lower Sanyaku (Komosubi and Sekiwake) and then the final day if there are two Yokozuna they’ll fight each other.

Two Yokozuna facing off on the final match of the final day sounds great in theory, and often is in practice, but all too often injuries result in that match not materializing.

Unfortunately I don’t have a slam dunk idea on how to exactly fix this, but I do think that this venture should look to have some of those highly anticipated matches earlier.

This will tie into the marketing aspect, but I think that this new league should heavily encourage the formation of rivalries. This means that you might have guys matching up who in the current format wouldn’t typically meet in a tournament. I think as long as the organization is transparent about this, and also meaningfully responds to fan feedback that this could represent an improvement over the current matchmaking.

The Competitors

This is the rule I’m most passionate about: unlimited registration of wrestlers from any and all countries!

If you are unfamiliar, in the 90’s, threatened by the influx of Hawaiians in particular, the JSA banned foreigners from sumo. The rule was subsequently relaxed to allow one foreigner per stable. This is an explicitly discriminatory rule.

I will say I think that some restrictions are understandable given sumo’s unique place in Japanese culture and society, but I think as the rule currently exists it is too tight2.

However, as Hakuho’s new venture will not have the same heritage and history inherently I think that there is no need for such restrictions.

Luckily as we alluded to above, Hakuho already sees Yokozuna across other countries - whoever and whatever those are - as the basis of the talent for this.

An additional point about the competitors: in sumo there are currently restrictions where you can only enter professional sumo between the ages of 16 and 25.

I think we should also relax this on the upper end but tighten it up on the lower end. So maybe 18-30, or perhaps no upper age limit. The talent level will assuredly be lower than Japanese sumo, so I think that one way to both drum up interest and to increase the pool of fans, looking to get ex pro athletes from other sports would be a good idea. Guys that couldn’t make it in the NFL or hockey or professional fighting might have a final chance to regain glory here. I’ll expand on this in the next piece for the marketing aspect.

The Stables

This is the final topic I’m discussing for a potential rule change and it also is a a good opportunity to transition to the piece next time which will focus more on how to market this new venture to ensure it’s a success. Stables should not just be stables: sumo stables should be teams.

One of the cool things about sumo is that in theory any Japanese male between the age of 16-25 can walk off the street and work their way up to the top. Most won’t, and some stables cater towards guys that will never see higher than Makushita if not Sandanme (3rd and 4th division respectively). I don’t think that should change with “traditional sumo” but for Hakuho’s new venture there almost certainly will not be the financial wherewithal to carry guys that don’t have the potential if not ability to be top tier competitors.

This means that if properly structured there can be apples to apples comparisons between various stables or “teams.”

Conclusion

It’s incredibly early days. It’s been less than a month since Hakuho left the JSA and something like this will likely require months if not years to get off the ground in any meaningful way. However, we so rarely have the opportunity to think of sumo being different and there being a real chance of that change being implemented I think as fans we’d be remiss not to fantasize a bit. I can’t wait to hear what other people think and am incredibly excited for part 2 where we go over the potential commercialization.

Onosato has been a healthy wrestler thus far, and I see no reason for that to stop anytime soon, but we all know that sumo is a contact intensive sport and like any athletic competition, injury is an unfortunate ever present possibility. Luckily it’s a small probability but our previous models feel lacking for not at least including that in a more explicit way. In fact, ideally we would lay out the various probabilities such as how long he wrestles for, how likely he is to win any given tournament within that timespan, and how (hopefully) unlikely he is to suffer an injury. Then we could run that model 100’s or even 1000’s of times and get a look at the various ways his career could play out. Even better would be if this model were flexible to allow us to tweak those various probabilities, so if you think my projections were overly optimistic (or pessimistic) you could run it with your numbers and get results.

The good news is that’s exactly what we’re doing today with a Monte Carlo model! I will include the python code at the bottom so that you can run it yourself too. I’ll walk through the various inputs we want, justify the initial assumptions we use, and then we can actually do the Monte Carlo part which consists of using those assumptions and running the model many times to show us what Onosato’s career Yusho total might look like.

Feel free to skip to the end if you only want to see the results and get the code to run it yourself. Otherwise I’ll walk through how we built up to those results.

Career Longevity

Last week we found that Yokozuna with 10+ Yusho retired on average at 32 almost 33 years old. The standard deviation is a little over 2 years. Don’t worry too much about standard deviation - it’s essentially “add or subtract this to the average and it should cover most cases” - not a perfect definition but good for a layperson’s understanding.

So we’ll use 33 as the “average” retirement assumption for Onosato and have a standard deviation of 2. That means that in our model on average he will compete till he’s 33 and careers where he ended up retiring somewhere between 31 (33-2) and 35 (33+2) should cover the majority of cases - about 2/3 in fact.

Tournaments Won

In large part a good model is based on the following: is the structure of the model good, and are the assumptions good?

Starting with the structure, I don’t think our previous version where we simply chose “how many tournaments will Onosato win in his age 25 year” and so on was bad. But I also think we can improve. So for this model, what we’ll do is have individual tournaments as our unit of prediction; i.e. the next tournament, Onosato has a 50% chance of winning. That introduces more chance into it, which is how reality tends to work, and also let’s us get more granular in terms of our predictions.

Injury Probabilities

Like I said before, this unfortunate chance does exist. If we could donate our health to our favorite wrestlers then Terunofuji’s knees would be a lot better, and we wouldn’t have to entertain this thought, but alas we do. So for injury probabilities I think we should actually have 2 separate figures used. One probability is just the probability in any given tournament Onosato picks up a minor knack. He will be able to continue fine in the next tournament, but he’ll be out of the Yusho race for the current one. The other one is catastrophic injury which results in the end of his career. It hurt typing that out but again, we want to have a good model and we do have to consider such things.

Putting It All Together

Let’s just get our general process out there.

First, we’ll estimate at which age Onosato will retire - likely between ~31-~35. That will give us a number of tournaments or Yusho opportunities.

Next, we will go through all those tournaments, however many there are, and use the probability he wins that tournament subtracting out the minor injury probability.

Finally, we’ll apply the catastrophic injury probability and if he’s fine (he will be!) then we continue to the next tournament.

I’ll talk about the implementation and the odds I used for the tournament wins in the next section, but real quickly, I put this in a mathematical equation.

Don’t worry - this looks intimidating to me too, but it’s nothing new here. First we begin with his retirement age, simple enough. Then the T is just figuring out how many tournaments he’ll participate in which is his retirement age, minus 25 (his age as of next tournament) multiplied by 6 to account for 6 tournaments a year.

We still haven’t proposed the probabilities to use yet- that’s in the next step - but we do know that we’ll need them and so can define them. Then we end up with a loop where we go through each tournament, check for the injury probabilities and see if he won.

That leaves us with the Bernoulli, which I think Wikipedia does a solid job summing up: “In probability theory and statistics, the Bernoulli distribution, named after Swiss mathematician Jacob Bernoulli, is the discrete probability distribution of a random variable which takes the value 1 with probability p and the value 0 with probability q=1−p”

In English we use a Bernoulli distribution when we’re modeling something which can be only one of two values. Well in this case we’re modeling if Onosato will win or lose a tournament, so we use the Bernoulli.

The Expected Total Yusho equation at the bottom is just putting it all together. It looks a bit confusing, but we hopefully all can understand the general process. As someone who has struggled through many a statistics textbook, I wish they built up to those abstract equations via examples like this, so hopefully I’m being the change I want to see in this world and you can follow.

Filling In the Blanks - How to Handle Tournament Win Probabilities

For simplicities sake, I’ll just have the injury probabilities flat over time. Obviously it would be better to have them start relatively low as he’s young now and get higher over time, but no need to make this too complex. There can also be virtue in keeping your models simple not only to reduce the number of chances to make a mistake implementing the model, but also in terms of understanding the model itself.

So I’ll use 7% for the minor injury probability and then .5% for catastrophic injury probability.

That leaves us only the probability that he wins any given tournament. Here I will actually do a more complicated implementation instead of one flat percentage for his entire career.

In this case I’ll use 4 different numbers consisting of:

Yokozuna Peak/Current: 60%

Yokozuna - Rivals Emerge: 50%

Yokozuna - Decline Phase: 30%

Yokozuna - Final Hurrahs: 15%

I’ll structure the model so that each of these phases is given equal length. In this case that means for 25% of his remaining tournaments he’ll have a 60% chance to win the Yusho, followed by 50% and so on. That said, I will provide the code so if you think there should be 2 phases, or 10 phases or even one for each individual tournament, you’re free to mess around with those inputs.

Results!

Mean Yūshō: 19.42
Median Yūshō: 19.0
Chance of 10+ Yūshō: 94.4%

Just as a note - this is not numerically stable. That is to say, if you run everything with the exact same variables you will get a different result. Still, it shouldn’t be hugely different.

Conclusions

A model is only as good as its assumptions. Looking at my assumptions they seem reasonable but then again I wrote them so of course I’d say that. Still, assumptions aside I think that we put together a compelling structure that allows for quickly testing how many Yusho Onosato will when with a variety of different inputs. Even if you aren’t a programmer, I would encourage you to give this a shot if you think different numbers should be used. The inputs are all up top before the “Simulation Function” bit. If you want to change the number of career phases then you can simply add or reduce the size of the list so [.50, .20] or [0.60, 0.50, 0.30, 0.15, .05] and note that they are percentage form so if you do 50 instead of .5 that’ll cause issues. Replit can be signed up for and should be able to run this code for free.

Here’s the final table comparing the various numbers I arrived at with varying methods; funny that I started with 18 Yusho as my guess and ended up with my most in-depth model yielding a single more Yusho than my shot in the dark. Cheers!

Extra Credit: as usual I try to balance between readability and simplicity vs accuracy. In this case, I would like to note that a lot of the assumptions here are based on the idea that these outcomes are normally distributed.

Code:

import numpy as np

import matplotlib.pyplot as plt

import seaborn as sns

# --- Model Parameters ---

# Career assumptions

mean_retire_age = 33

std_retire_age = 2

start_age = 25

tournaments_per_year = 6

# Injury probabilities

p_minor_injury = 0.07

p_catastrophic_injury = 0.005

# Career phases and win probabilities

win_probs = [0.60, 0.50, 0.30, 0.15]

# Peak, Rivals, Decline, Final

phases = 4

# Number of phases to divide career into

# Simulations

n_simulations = 1000

# --- Simulation Function ---

def simulate_yusho_total():

# Sample retirement age (cap to stay in a reasonable range)

retire_age = np.clip(np.random.normal(mean_retire_age, std_retire_age), 28, 40)

total_tournaments = int((retire_age - start_age) * tournaments_per_year)

# Handle edge case

if total_tournaments <= 0:

return 0

# Phase lengths (evenly split)

phase_len = total_tournaments // phases

win_schedule = []

for i in range(phases):

win_schedule += [win_probs[i]] * phase_len

# Fill remainder with last phase probability

win_schedule += [win_probs[-1]] * (total_tournaments - len(win_schedule))

yusho_count = 0

for prob in win_schedule:

if np.random.rand() < p_catastrophic_injury:

break # Career-ending injury

if np.random.rand() < p_minor_injury:

continue # No chance to win this basho

if np.random.rand() < prob:

yusho_count += 1 # Wins Yusho

return yusho_count

# --- Run Simulations ---

yusho_results = [simulate_yusho_total() + 4 for _ in range(n_simulations)]

# --- Plot Results ---

sns.set(style="whitegrid")

plt.figure(figsize=(12, 6))

sns.histplot(yusho_results, bins=range(0, max(yusho_results) + 2), kde=False, color="darkred", edgecolor="black")

plt.title("Monte Carlo Simulation of Onosato's Career Yūshō Total (1000 runs)", fontsize=14)

plt.xlabel("Total Yūshōs Won")

plt.ylabel("Number of Simulated Careers")

plt.xticks(range(0, max(yusho_results) + 2))

plt.tight_layout()

plt.show()

# --- Summary Stats ---

mean_yusho = np.mean(yusho_results)

median_yusho = np.median(yusho_results)

percent_10plus = np.mean(np.array(yusho_results) >= 10) * 100

print(f"Mean Yūshō: {mean_yusho:.2f}")

print(f"Median Yūshō: {median_yusho}")

print(f"Chance of 10+ Yūshō: {percent_10plus:.1f}%")

Mine using solely his age, his 4 current Yusho and having looked at most career championships above courtesy of Wikipedia I’m guessing 18. Remember yours and you can compare at the end with various assumptions and even use the models provided here.

Model 1 - Naive Assumptions - Build Up

Simply start with 5 (or a more reasonable number like 10) and ask yourself: do you think there is a 50%+ chance he gets that many Yusho in his career? So 5 is really easy - he’s almost guaranteed that many. 4 is 100% because he already has that many but I used a hypothetical of my thinking to show what it might look like continued.

In a sense this approach is thinking like a sports bookmaker. If you’re familiar with the spread, this is basically a simplified version of what they do1. If you’re not, imagine a really good basketball team like Team USA playing a team like Japan, then obviously the US will be favored and probably by double digits. So what the oddsmaker will do is essentially “spot” the Japanese team 15 or 20 points or however many they have to to make it 50/50 that Team USA can beat Japan by 15 points. That’s what the spread is and if the USA beat Japan by 16 then that’d be beating the spread.

I call this naive in the meaning that I make no assumptions. I just ask myself sequentially: is it 50% or more likely he reaches this career Yusho number. Sometimes thinking in a more structured way like this can be helpful.

Model 2 - Basic Assumptions and No Data

For Onosato this question is likely less about his skill and more about the number of opportunities he has to win a Yusho. He has yet to miss a match and he can hopefully keep up his sterling record on that front. But everyone gets old eventually, so we can essentially break down our problem into two sub-questions: how many Yusho wins will he get while active and when will he retire.

The retirement will affect how long he’s active so let’s start with that. Again no need to do a data deep dive yet so knowing he’s almost 25 and having some basic knowledge of wrestlers’ ages I think we can set some solid ranges: I’ll say that he retires somewhere between age 32/33 and 36/37 or he has ~8 more years to 12 more years left wrestling. I’d love if he went even longer like Tamawashi, but let’s split the difference and say he has 10 years left of top level sumo. Now we can move on to the “how many Yusho wins he will get while active” since we’ve given ourselves the number of opportunities to win he’ll have.

This is still the simple model so I’ll just look at his various ages and assign a number of tournament wins for each year, but you can see how by structuring our data and model in a more formal way, suddenly it not only gets easier to play with assumptions, but also we have a better idea what kind of data we should be looking for to make sure that our assumptions are good. It seems simple but this is basically a low level of what the world leading hedge funds, AI researchers, and so on are doing. Anyways, below is my model but I’d encourage you to try your hand at it too!

You can leverage my framework or the principles here but next we have the final model where we’ll use more in depth data. I’ll say that going from 18 to 32 is almost double and makes me think I went too high for this one and probably too low for the initial one.

Model 3 - Robust Assumptions and (some) Data

In finance one common way to value companies is to use “comps” or comparisons. Company X trades at $100 a share which is 2 times its annual earnings of $50 a share. That’s called Price to Earnings or PE and I’d use that number to compare it to Company Y. If I think X is fairly valued and I see company Y trading at a PE of 1.5 I might buy it as I think in the future the market will appreciate X and Y are similar and so the price should be bid up till Y’s PE is 2. Conversely if the PE is 2.5 I might go short (bet it goes down) till it’s at the reasonable PE of 2.

Unfortunately in sumo wrestling, and particularly for top tier Yokozuna like we anticipate Onosato to be, there just aren’t many comparables. Sumo has only had its 6 tournament a year calendar since the late 50’s. Since then there have been approximately ~30 Yokozuna depending on who you count. So already our universe is pretty small. Then you narrow it down to guys who won 10 or more Yusho and suddenly there are only 13 men comparable to Onosato. So I used those men to compare Onosato to on what age they retired and when they won their Yusho age wise.

A quick and important note: statistics is a lot of math and algorithms which can be pretty tough, but sometimes even tougher is applying good judgement. What data is relevant to the problem you’re approaching? How might it be biased? What should be included and dropped? I think that using “modern Yokozuna” since 1957 is the proper universe to compare Onosato to, but there might be a better group. Maybe I shouldn’t have included all these guys; maybe I should have included more. Questions like these are in large part what practicing statistics consists of. With that in mind, here are those 13 Yokozuna:

Funny enough if you take the average retirement age of these great Yokozuna and add the standard deviation that gets us to right about 35 so intuition wise from Model 2 we did pretty decently2. I will defend putting him on the upper end of the spectrum simply because Onosato has had fewer professional tournaments. That actually sounds like a good future research project: do college wrestlers have longer careers all else equal? I’d guess so, but as far as I know we’ll be the first ones researching this.

Next I looked at how many tournaments each of these men won at each age. It’s not perfect but I think it approximates an aging curve at a high level.

It’s nice getting our earlier work on sumo wrestlers’ primes confirmed to be around 27 or so with a drop-off at 30 and they can hang until around 32 when the final drop-off occurs. Again it’s important to note the small sample size here, but when your data aligns with your expectations or general wisdom that can often be a good thing.

So I used this data and also a little bit of my “prospect knowledge” to adjust the second model. When I say prospect knowledge I mean knowing the up-and-comers like Hakuoho, Aonishiki, Takerufuji, Atamifuji and more who are younger or less established that I think might not necessarily rival Onosato but could grab tournaments from him. In fact, there’s a good chance that whoever ends up his greatest rival isn’t in the Makuuchi yet and may still be in college or the lower ranks right now. Even still, it’s hard not to feel confident about Onosato’s future prospects and so my adjustments mostly ended up looking the same but giving him that weird age 27 blip from above.

Conclusion and Numbers Comparison

Looking at these various numbers above and comparing models I have adjusted my initial pick. 32 feels a bit rich for me as much as I’d love him to tie Taiho so I’ll give my final optimistic take and put it at 26 and he beats Asashoryu for career Yusho. That gives us the following table and please comment with your predictions! Did you significantly change from your initial guess to your final?

For the pessimists out there I promise there’ll be a part 2 where we look to model this in terms of a tournament by tournament basis and then run a Monte Carlo simulation. This will allow us to have many different runs including some where we handle the unfortunate but real probability of injury.

In fact, a great deal of the work on here is normally descriptive. That is what it sounds like; the statistics describe who ends up Yokozuna. Conversely many of these measures I propose here could (potentially) be prescriptive or normative - meaning it’s actionable advice; it’s what you should do. To give a preview, I think that knowing how quickly a given wrestler comes out of the tachiai (where they touch both hands to the ground) could be incredibly useful for wrestlers. For instance if I knew one wrestler can get out of their stance quickly, but also often has slow starts then as a coach it’d give me normative data to work with; the data is giving direct recommendations.

Some of these are doable if you had videos of all the matches and some dedication. Others are probably a bit more infeasible or would require the kinds of changes to the sport (having wrestlers wear devices for tracking for instance) that probably won’t come about from a humble blogger’s suggestions. But if for some reason a heya is reading a niche English sumo blog and has access to historic sumo videos please reach out at OzekiAnalytics@gmail.com. In fact if you’re curious about why I included PFF in the title, it’s because Pro Football Focus (PFF) is a company that pioneered a similar statistics based approach to football themselves.

There is no particular order for the various stats, but for each one is included the following measures: basic description, how it could be obtained, and potential use. If I think of more I’ll potentially do another round of this.

New Sumo Stat 1 - Wingspan

Wingspan is what it sounds like; spread your arms flat from the shoulders and measure tip to tip from one hand to the other.

I’m actually quite surprised this isn’t a more standard measurement. In combat sports like boxing and MMA, it’s very commonly included along with other various key stats like height and weight when introducing the fighters. You would probably need the sport as a whole to get behind it and release the number or otherwise each heya (sumo stable) would keep the data to itself.

Wingspan is obviously important for a sport like sumo wrestling where you’re trying to push your opponent with your arms. Imagine a match-up between two rikishi of similar rank and size, but one has a 3-inch reach advantage. If he tends to win matches with tsuppari-style pushing, that wingspan suddenly becomes a more predictive feature. It usually is correlated with height, but you’ll also have the occasional guy with disproportionately long arms which only benefits them (Floyd Mayweather had long arms). Conversely, some wrestlers on the taller end might have shorter arms than it seems.

That said, I do wonder if it’s a bit like Judo. I’m an amateur (retired) practitioner but from my recollection and knowledge of the sport, I do believe there’s a bit of ambivalence about arm length. Some throws are easier for the longer limbed, while others are much harder to execute unless you have short arms. For this alone I’d love the wingspan data and ideally going back into history to ascertain if there is indeed ideal arm length for sumo wrestlers. Finally, it would be helpful to figure out how wrestlers should focus their development - your arm length can’t be changed, but you can change your style to maximize your effectiveness with your physical gifts.

New Sumo Stat 2 - Grip and Arm Placement Frequency

Another relatively straightforward one, this could probably be done with simple video review1. We often hear commentators discuss one wrestler getting his preferred grip on the Mawashi (belt) or an under arm grip for instance. By looking at all of a wrestlers given matches you could begin to classify not only how well they do when they get certain grips on their opponents, but also how well they do when their opponents have them in certain grips.

This would be valuable data for qualifying what kind of skills wrestlers need to practice most. If only rikishi at Ozeki and above can get a grip on me/get to my belt then focusing on grappling like that might be a potential misallocation of practice time and resources. Conversely, if a wrestler has particular trouble dealing with their opponent having a certain grip on them, it would be quite valuable to practice handling that situation. They likely have some idea on this already, but having a stat allows you to directly quantify those weaknesses and strengths.

New Sumo Stat 3 - Tachiai Reaction Time

The tachiai’s Japanese characters can be more or less directly translated as “Stand Meet.” It’s when both wrestlers have touched their hands to the ground and then explode to meet each other. I would love to know how quickly they explode out and which wrestler is quicker.

This stat would actually be quite difficult to obtain, but also incredibly useful.

The problem here is quantifying when wrestlers actually “go.” I have two potential ideas neither of which is easy.

First and more possible: having high FPS (frames per second) footage from the same vantage point for every match. It’s still likely imperfect but with an algorithm you could potentially identify the frames on which wrestler begins moving. It is important to have the same vantage point for all of these as otherwise it could interfere with the measurement and make times non-standard.

Second: sensors in the Mawashi. With technological advancements, I think this is likely feasible but also a bit of a pipe dream at the same time. As we know when the wrestlers make a big movement at the tachiai to start the match, they’re generating a ton of force and quite quickly. I think you could configure a wearable motion tracker to detect that and accurately, but I very much doubt that the Sumo Association will be implementing something like this any time soon.

Assuming we did obtain this data and it was reliable it’d be useful. I often compare sumo to other sports and the tachiai is probably the one instance that these large violent men are most comparable to the lithe drivers of Formula 1. In both cases it’s all about reaction.

Also like F1, smarter wrestlers would likely be able to take advantage of knowing opponent’s tendencies - not unlike in a restart at F1 (the race is slowed down due to debris on the track) there is an advantage to be gained for the leader by tactically taking off and resuming the race when least expected.

Furthermore, beyond knowing if reaction times are quick or slow in general it would also be useful to know if they’re consistent. Some wrestlers likely have a quick tachiai, but only occasionally. Coaching up that consistency would be valuable.

New Sumo Stat 4 - First Step: Stride Length, Time

This is in certain ways a continuation of the stat above. But knowing how far the initial stride of the wrestler is along with how long it took them to get the foot down from the first step would be useful and usable information.

I’ll be honest: here’s where I think it could be tougher to implement in a reliable way. For this one you might need a Hawk-eye multi camera high FPS (frames per second) system like in tennis.

The rewards would be worth it for wrestlers and coaches with access to this data however. They would get more value out of it than the audience at home because unlike us they would know each wrestler’s game plan. Depending on strategy in match, your steps could vary greatly. In a henka for instance, the wrestler is jumping to the side and hoping the other wrestler over committed to going straight. That might be obvious but if the wrestler is going for a belt grip vs a push then the footwork and how long (or short) of a step they aim for could be quite different in this case.

Even still, knowing that time to first step would be useful for us viewers too. In running they say that you can change stride length and you can change stride frequency but that’s what you’re working with. In a sport where one wrong step can mean a loss, more info about the first step could only enrich our understanding.

Conclusion

I joked about consulting for a sumo stable up top, but in writing this piece I tried to think like a data scientist, or a statistician, or a member of the analytics department for a professional sports team. I tried to keep the discussion relatively grounded, but I think there are some valuable lessons in there that are widely applicable.

Knowing how the data is obtained is incredibly important. In fact, sometimes data will have been poorly collected. At PFF they’ll often have employees watch the same plays and chart it with whatever stats they try to get from it to ensure that folks are grading them the same. Election pollsters are always assessing if the people they ask questions are representative - thinking more about where data comes from and how reliable it is has only becomes more and more important.

There will likely be a part two of this sooner or later, but if you want to try and get a little smarter and think more like a data scientist or hedge fund manager then I’d encourage you to think about what other stats might help. To help, think of the Target as being predicting who will win a sumo match. The data you would get will be a feature. Let’s assume there’s a working Elo (the chess ranking system) so your goal is to come up with a feature that will improve your algorithm that predicts a Target. Or in plain English: what’s a stat that doesn’t exist that you think would allow you to better predict who wins? I think that adding wingspan of a feature to my model would allow me to more accurately predict the target being who will win a given match.

Extra Credit: sumo match outcomes are best modeled as a binary. In other words, the wrestler either wins or loses; two choices - binary. In computer science and stats this will often be portrayed as a 0 or a 1 (with 0 representing a loss and 1 a win or vice versa). This is actually a bit problematic because a common method - linear regression - is unavailable because it assumes that numbers can go continuously beyond 0 and 1. In this case when you’re modeling a binary outcome you’ll typically use a Logistic Regression. Much of the same terminology and even lots of the math is similar (but not the same) except the result you’re returned will be somewhere starting from 0 up to 1. So key takeaway: linear regressions are used for predicting quantities like how much money a company will earn whereas logistic regressions are used for calculating odds like what percent chance will the company make the predicted earnings for instance. Going forwards I think I’ll put more math/in-depth stats stuff at the end under this Extra Credit section so it can hopefully be educational but also not overwhelming and more optional.

Glad to be back, and hopefully more frequently.

I’ve watched probably 5+ years of sumo every tournament and a year and a half doing data analysis on sumo. I also keep up with many other sports and the more analytic aspects of them. If it’s baseball then it’s WAR, OPS+, pitch mixes; if it’s a sport I follow, odds are I’m looking at the advanced stats. As a result, I think I have some accumulated lessons and wisdom that help me think about sumo more intelligently, and to hopefully have a deeper and more accurate idea of what is going on. So I decided to start with this as the first in a series on lessons I’ve learned that I think can help readers think more deeply about sumo too. They often have direct analogues in other sports, so I’ll connect the ideas to show their validity and also teach you a bit about sports beyond sumo. Finally, I’ll also try to bring in the statistical reasoning behind these lessons but in an approachable way.

As a quick sidenote: I’m trying to integrate more videos into my writing going forwards. So if I mention a guy I’ll try to include highlights - the analysis is fun for me but at the end of the day it’s the guys wrestling we care about. I’m also trying to explain more sumo concepts when I mention them. The latter was due to reader feedback so please feel free to drop advice for improvements. Let’s begin.

Lesson 1: Development is Not Linear

Development is not linear. It sounds simple, but it’s become an important phrase across many sports. In American sports with drafts, a very important advance in statistical analysis was the realization that the younger a player is at the time of the sports draft - NBA, NFL, MLB, all the same - the higher their overall potential. It makes obvious intuitive sense: across all sports, including sumo as we’ve discussed here before where we found they peak at age 27, athletes tend to peak in their mid to late 20’s. You’re likely at your best physical performance but experienced enough in the sport to make better use of your physical attributes than in your early 20’s. If a college wide receiver has a 1,000 yard season as a 19 year old that’s obviously more impressive than doing it at 23. The former is a kid and has presumably more room for development vs the latter a man among boys with more experience in college football.

Similarly, if a sumo prospect reaches the top division Makuuchi at age 21 then that’s more impressive than doing it at age 25. In fact, we did some analysis and found that future Yokozuna debut in the top division a year younger on average than wrestlers whose highest rank is Ozeki (the rank below Yokozuna). Again, this makes intuitive sense so it’s great that the numbers backed us up there.

However, it’s very easy to fall into recency bias. We see a young wrestler rocketing up the lower divisions and even into the Joi (the top part of the top division) and assume it’s a matter of time till they’re an Ozeki or even a Yokozuna only for them to struggle towards the top. Suddenly the prospect shine comes off them and it seems they’ll only ever be a mid Maegashira wrestler. Atamifuji more or less fits this mold to a tee and I have seen people souring on his potential. However, Tochinoshin - the Georgian wonder wrestler of such great strength - fit a similar mold. He made the top division by 21 and stuck in Maegashira for years even winning a runner up and going 12-3 multiple times but never stuck in the Joi. With injuries dropping him down to Makushita (third division), he could have easily been written off. In fact even after he dominated on the way back to the top division, he didn’t seem destined for Ozeki until at age 30, nearly a decade after debuting in Makuuchi he put everything together, and won a tournament en route to making Ozeki finally fulfilling that potential.

The flip side is that we see guys that never did anything special and assume that’s all they’ll ever be. If you watched sumo in the 80’s and saw a 25 year old making his debut in the Makuuchi, you likely assumed he would peak as a mid Maegashira guy, maybe make Komosubi once or twice and that would be the best case scenario. If you watch enough sumo you’ll start to recognize wrestlers having career archetypes like that. Except in this case that wrestler was Kirishima the elder who slowly grinded his way to the top making Ozeki at over 30. He would go on to win his first top division tournament and get several more Jun-Yushos (runner up) along the way in his 30’s before gracefully descending down the Banzuke similarly slow to his methodical advance to the top.

Finally, a more depressing scenario in which it’s important to keep in mind that development is not linear is the case of Takakeisho. As an Ozeki at 23 having already won a tournament from the Joi at 13-2 he looked like a surefire Yokozuna. Unfortunately injuries and an inability to string together two Yokozuna quality tournaments in a row ultimately doomed that dream. He arguably peaked much younger than 27 and at 28 is retired from wrestling himself.

We’ve done the research and found that wrestlers peak at 27, but that’s ultimately just the average of all wrestlers. Each of them has their own unique path and some will be early bloomers while others will hit a wall maybe even for years only to finally unlock a new level of skill. If you’re an NFL fan the latter example is akin to Zack Baun who broke out at 28 years old making First Team All Pro and being a key cog on a Super Bowl winning team1.

In all these cases it’s easy to overindex on the most recent results. In other words, we see someone stalling and we assume that’s all they’ll ever do. Or we see a high flying prospect and assume they’re destined to be a Yokozuna. This is what we call recency bias.

But the truth is, every wrestler is unique as is their developmental path. I imagine if you reflect on your life or career, it hasn’t been a continuous journey but rather ebbs and flows; successes and failures but not in a predictable way. We often think of development and skills as monotonic. That is a fancy word for something that is always going up (or down) and here’s a helpful graph that illustrates it2.

Ultimately, I think this concept of development not being linear or monotonic makes sense when you think about it and relate it to your life and even sports careers you’re likely familiar with. We all have our ups and downs. Nevertheless, it is worth constantly keeping this as a refrain in the back of your mind. I find it helpful for when a guy I expected more of hits a wall in the Makuuchi (I still believe in Atamifuji for instance) - a young and injury-free wrestler always has more time to put things together. Similarly, it gives me hope that some non-prospect wrestler with a fan friendly style might actually have more skill than his record suggests. Tobizaru debuted in the top division at an age that suggested he didn’t have much more to unlock, but luckily for fans of high octane wrestling he has showed he can keep up with the best while providing endless entertainment.

Sumo is hard to predict and we’re better off for it. I like learning about it with my spreadsheets and math and data, but at the end of the day wrestlers are humans like us and just as unpredictable. That’s what makes it worth watching.

Hopefully you enjoyed this because Part 2 is coming soon and will give us a related lesson.

But first I want to say another thank you! The reception I’ve received has been almost universally positive, and I think that even some of the detractors might be coming from a place of frustration that what we’re presenting here isn’t in its final form yet. Worry not, we aim to continue to advance the frontier of analytics and data on sumo wrestling.

Ozeki Analytics’ Long Term Goal

I can distill this project to a single goal, and that would be: “to be able to indefinitely simulate sumo tournaments into the future with a relatively high degree of plausibility for all the underlying assumptions required for that.”

That might be a bit technical sounding so I’ll phrase it a bit less concisely while also highlighting some important considerations I keep in mind. This blog has a statistics focus. By looking at past results and data related to sumo, we can begin to understand the general rules, exceptions, and unknowns in our sport.

Sometimes we have fairly explicit rules - promotion to Yokozuna, the apex of the sport, requires two Yusho equivalents. However, those rules aren’t also as ironclad as they seem or can be massaged if you prefer it that way. If there aren’t many Yokozuna, and a wrestler has hit 26 wins over 2 tournaments (hard win requirement - so a rule) then that Yusho (tournament win) equivalent can be a bit squishier. That might be a good example of an exception or perhaps even an unknown. quick note: don’t get too hung up on exceptions/unknowns - it’s just a way to express the inherent uncertainty we’ll have.

In fact, a better example of exceptions and unknowns would be the Banzuke (the ranking of every wrestler) making process. If you have spent any amount of time working on Banzuke - Guess the Banzuke for instance - you’ll know that while they follow general rules and guidelines in putting the Banzuke together, what will determine who guessed the Banzuke best each time involves some luck. They also have been known to make a couple quirky decisions each tournament. In other words, there are exceptions and unknowns.

It’s similar to trying to figure out who will win each match. Using Elo (a chess system) can provide a good start. Furthermore, our intuition is often good; Hakuho is gonna win more matches than he loses. But we also can’t know every match; Hakuho did in fact lose matches. By the way, better prediction matches is actually a major goal for 2025.

So we look to be able to have a framework in place to predict everything related to sumo from who will win matches, to what the matches will actually be, to how that will affect the following tournament.

Furthermore, this framework should be based on the existing data we have about sumo and we should be able to test how well our predictions compare to the reality. This will allow us to find areas for improvement and further research.

I thought putting it this way might help. A testable framework is preferable to non-structured guesses. Frameworks can be improved upon and weaknesses identified. Semi-structured (at best) guesswork cannot (so easily).

The above is for me. It’s not a hard and fast rule. But also, when you’re talking about repeatable processes - which is required for indefinite simulation - then you do need this kind of process. There was a minor controversy over some Banzuke predictions I posted last year. I know the algorithm requires further refinement, but its very existence is a goal in and of itself. Without the algorithm, the kind of improvement we’re looking for isn’t possible!

So if 2025 is a success, by the end of year, we’ll be able to simulate till Atamifuji (or whomever is the last current wrestler) retires in the 2030’s and ideally the results will look realistic from the matchups, to the number of new rikishi, to who is winning matches and so on.

It’s ambitious I know, but that’s what we aim for!

2024 Achievements - Where We Got to in 2024

Looking at the above, honestly we could probably pull that off.

If you want the minutiae of everything covered, the Sumo Knowledge Encyclopedia has been updated to have everything from 2024 in it. Even better, it’s organized by topic too!

But to go a bit in, we began by looking at what determines what is required to be a top dog - Yokozuna or Ozeki - promotion-wise. We also looked at how many Sekiwake and Komosubi there should be each tournament because that’s also not pre-determined/allotted. In fact, we did a decent amount looking at what determines the Banzuke.

We also took a look at how wrestlers careers begin and end. We have an algorithm with some decent results that can predict retirements, albeit after each tournament is done. We even looked at when wrestlers peak - about age 27, similar to other sports, but mathematically confirmed now.

Now to begin the transition: we also looked at determining matchups, which will require further work. It actually only covers the top division and I need to do further testing and verification. In fact, I also have a few improvements for the Banzuke prediction algorithm in mind too. Finally, determining who will win matches also requires further work.

2025 Roadmap - Where We Hope to Reach in 2025

As I said above, “Frameworks can be improved upon and weaknesses identified.” We have frameworks for almost everything that we want to learn in place. But those improvements and weaknesses need to be identified and implemented.

This is less sexy, but I do need to work this year on improving my data and code pipeline. I have all the programs and data, but it’s much less smooth to run in practice. Fixing this shouldn’t lead to a large improvement in terms of how accurate estimates are (although it might by preventing manual errors caused by the messy process), at least in the short term. However, getting my environments more “productional” and “professional” for lack of better terms will lead to improved results because testing different hypotheses, models, factors and so on will be smoother and quicker. This one is more for me than the readers.

As mentioned above, there are some identified Banzuke prediction algorithm improvements. Additionally, the above mentioned data pipeline improvements will make further refinement quicker and easier.

Torikumi or the art of matchmaking requires further refinement on my part. This will also benefit greatly from the data pipeline 2.0.

Last year I began a framework to determine things like “what is mid-Maegashira” and so on. A piece you can expect to see in the near future will finish that for the lower divisions as it previously left off at the bottom of Makushita (3rd highest division).

This leads into the final major topic for 2025: determining who will win matches. I have done some work with Elo (originally a chess ranking system, but it’s widely applied across sports) but I seek to combine that with the above framework and perhaps other features (or independent variables, or if you prefer predictors (I probably won’t use it, but you could imagine using height as a predictor - i.e. the taller wrestler is likelier to win))

We also have some fun pieces planned too. I mentioned a potential “Dynasty Score” or a way to weigh who has had the best sumo run of all time (well, I mean besides Hakuho, and how those runs measured up). I also might look to do what a “Typical Banzuke” might look like by taking the guys who occupied each position on the Banzuke since 1989 the most. Presumably Hakuho will be no 1, but who was most commonly second in the Banzuke? I genuinely don’t know but it interests me, so I’m hoping that’s reflective of others too.

Finally, I do speak some Japanese and read it much better. I might eventually look to translate some important passages from books on sumo or important newspaper articles and such.

Personal Bits (Skippable)

I’m incredibly grateful how well this first year went. I actually set a goal to write an article a week for the year. If you check the archives I was actually just about doing that through July or August. Unfortunately, I do tend to trail off from a productive standpoint after summer. If I wanted to cut myself some slack I have a decent excuse that a lot of the work I do tends to be more deeply researched pieces. Those often require tons of prep work just to get the data ready much less running the models, interpreting the results, and writing them up. In fact, I have probably 3-5 articles in my drafts in varying states of readiness. Some require more research, others rewriting and others I just haven’t had the time to finish.1

It’s kind of hard to believe but we hit 100 subscribers last year starting from a total of 0. Who knew 100 people wanted to read in depth pieces on the numbers behind sumo wrestling? Well I certainly didn’t, but I have had a great time getting to know some of my readers better, and also just good interactions with fans. Related to that I will try to hopefully be more active on socials this year.

I’ll also say that I’m an ideas guy. Believe me, I have tons of balls in the air of which this is just one. That said, this is one that I have relatively large amounts of follow-through on. As I review what I still think needs to be refined and further researched, I’m actually incredibly heartened by the progress we made through 2024. While the remaining urgent areas are some of the toughest and most important, if I wanted to, I could work with the existing programs and data and simulate indefinitely albeit with no new wrestlers to replace the current ones. I actually don’t know how I’ll tackle that yet, but that’s a problem for future me and one I’d be happy to have as my most pressing.

Hopefully my other projects go well enough that I have time to cross promote them here where relevant.

Other than that, just wanted to thank everyone for reading this far. I had a few folks that took some of my work in what I see as an uncharitable light and denigrated it as such. They even had some good points on improvements to be made that I agreed on although the dismissiveness I found less agreeable. That is not at all the spirit which the majority of folks I’ve interacted with had. Almost everyone I’ve had the pleasure of meeting (online) throughout this project has been incredible. We’ve exchanged ideas and improved each other. Beyond that, we’ve had a good time. I said it before, but I’m thankful for that and thankful for the readers. I hope we can all have a great 2025 and even further! Thank you so much again.

Prospect Review - Ozeki Analytics September Basho Guys to Watch

If you want to look at the old piece it’s here, but I actually summarized their records in the September Basho to see how they did:

I chose a really good time to start keeping track given that all 7 of the selected wrestlers went Kachikoshi and Shimizuumi won a Yusho too. Furthermore, 5 of the 7 were promoted divisions. I honestly don’t know if I’ll top this for a while.

Prospects for Kyushuu and This Feature’s Future

As I reviewed the prospects I got thinking about what I’m actually trying to do here by listing out prospects. While it was nice that I got a bunch of guys that did well last tournament, I think that’s actually not what I’m shooting for primarily. Furthermore, as I looked at guys I thought might do well I noticed we have more and more ex-college wrestlers in line with our research findings previously. A lot of those guys will tear it up in Jonokuchi or Jonidan and even Sandanme but start to top out around mid-high Makushita. So I think I have a goal with my prospect rankings going forwards.

This feature is meant to highlight wrestlers that through a combination of youth and overperformance look like they could become future Makuuchi wrestlers, particularly successful ones. It’ll definitely be a balancing act between the youth and overperformance because there are top tier college wrestler prospects under this category - you may even have heard of one, newest Ozeki, Onosato - but also, I don’t want this to just be a list of 23 year olds going 6-1 against fresh entrants to the Jonokuchi.

Furthermore, since people featured on this are usually at or around their career high ranks, Kachikoshi and greater validate selection and push expectations higher. I won’t get into Bayesian statistics, but the basic idea here is that I’m selecting these men on the idea that they’ve already performed well, and if they continue to perform well at higher and higher ranks then we should revise our expectations upwards for their potential. To analogize, if your basketball team signed a player and you expected him to shoot 40% on the season, but they shot 45% instead, you should likely expect more of that player going forwards. That’s all I’m saying here. If this is confusing let me know and maybe we’ll have a post on that topic.

I’ll also try to put a (Top Division ETA) next to each guy. I’m not super confident in this but I also figured it’d be fun to provide, it reminds me of baseball prospect watching, and hopefully writing it down will force me to work harder to actually project it in the future better.

So without further ado here are some additional guys I’m high on for Kyushuu 2024 Basho.

Kotoeiho J13W - (Late 2025 Makuuchi Debut)

Making your Juryo debut at just 21 years old is going to get you on this list. He’s been in the upper Makushita for a hot minute, so I would not be surprised if he’s able to hang in the lower Juryo. In terms of opponents, he’s already fought some of the lower Juryo itself. He has solid size and favors a Yorikiri to get guys out of the ring. If he is able to stick in the Juryo like I anticipate, I’m guessing he still might have a little more seasoning needed to make it past the upper Juryo into the Makuuchi hence the ETA.

Seihakuho Ms47E - (Late 2025-Early 2026 Makuuchi Debut)

I don’t have as many prospects I’m singling out this time around, but I’m calling my shot here.

Seihakuho not only shares the name connection with sumo GOAT (greatest of all time) Hakuho, but he’s also a Mongolian countryman with a folk wrestling pedigree from there. As the first foreigner in Hakuho’s stable, a collegiate champion, and a well sized man, I’m betting on all of this. If anything, I’m going a bit conservative - if he is good and goes ~5-2 or better in lower Makushita, he might be able to make it up to Makuuchi by mid 2025. That said, not everyone can replicate the instant success of Onosato or Takerufuji. Even so, if I have to place my chips on one of the new crop of top collegiate wrestlers to do it, it would be Seihakuho.

Ieshima Ms54E (ETA Late 2026-2027)

This one is also a bit of a shot call albeit in a different way. I don’t want to inundate you with college wrestlers tearing it up in the lower divisions and so above I pushed all-in (for this Basho at least) on Seihakuho. Here I’m plucking a lower Makushita debutant wrestler. Still just 19 years old and of slighter stature, he might still be considered what we call “a big boy.” I think the big reason I gravitated towards him is that he reminds me a bit of a discount Takakeisho. He’s also a smaller Oshidashi (pushing) specialist. I really hope he does reward my faith in him and can at least Kachikoshi, because if he does I think we could have a fun wrestler on our hands.

New Debutants

We have two new men to Makuuchi this time around, and we’ve already brought up one of them! Shishi is one of 2 Ukrainian wrestlers in sumo right now and the other is Asakoryu.

Shishi M16E

Shishi has good size and definitely has the better pedigree of the two debutants in my opinion. He hit a bit of a wall in Makushita, and took a little time to get through Juryo, but he looks like a well deserved top division wrestler. I would not be surprised to see him stick around, and even if he doesn’t, he seems like the kind of guy that could easily make it back up to the top division. Given his size, he is a fairly straightforward style where he’s looking primarily for Yorikiri and then Oshidashi as his winning methods. Hopefully he’s around for a while because I love seeing non Japanese non Mongolian wrestlers. It makes the sumo world more interesting in my opinion.

Asakoryu M17E

I’m not trying to be mean but I do think Asakoryu likely finds himself overmatched here and won’t be a stalwart at least this time in the top division. Unlike Shishi he does not have tremendous size. Additionally, he honestly got a bit lucky with his promotion; he went 11-4 from Juryo 8 and still got into the top division. He had previously gone 6-9 and 7-8 from Juryo 4, so even upper Juryo looks a bit too advanced for him. That said, the 26 year old is still just entering his prime and only has ~3-4 years of pro sumo experience. Hopefully it’s a learning experience and he can grow from it. Despite his size, Oshidashi is his go to Kimarite (winning technique)

Retirement Odds

So the full explanation can be found here but generally what I’m doing is looking at the prior tournament and using some key criteria to figure out who is most likely to retire going forwards. Age is one, if you were demoted is another, and most importantly is how many injury losses you had in the prior tournament. In other words, if you miss a bunch of matches and lose them because you were injured, that more than anything else will make you more likely to retire based on my research.

As a reminder, this is backwards looking - i.e. the odds they would have retired after the Basho. Still, if your odds are high right now, and you do poorly in Kyushuu, then that’s probably not making it less likely to retire. The other key criteria is that this is Sekitori - aka the top two divisions of Makuuchi and Juryo. Also, the Cumulative Loss Percentage is out of total matches - so 100% means all 15 were lost via injury loss.

The algorithm is humming. It honestly probably wasn’t too hard a call for a 38 year old coming off a full tournament of injury losses, but with Myogiryu, accurate is accurate. Aoiyama is probably a little more marginal but at least it had him in the top 10 of most likely to retire Sekitori.

As always I’d keep in mind for Terunofuji that he’s less likely to retire given his Yokozuna status so that’s probably pushing his odds higher than they would be otherwise. But by the same dint he is less likely to participate in a match he can because his Yokozuna status is not loseable, which also artificially pushes high odds lower. I guess what I’m saying is Yokozuna are special cases.

Thanks for reading!

Seriously though, I think we’re in a more stable era for our Ozeki going forwards. I might have said and though that earlier this year, but all 3 men have clean slates for now (Onosato is a fresh promotee, and Kotozakura and Hoshoryu both had 8 wins last time around) so we should have the same set January and likely February too.

As for Yokozuna, this tournament would be the first in any rope run for any of the current Ozeki. Still, I think they’re interesting to talk about and to see if my piece linked here on who I think will be next Yokozuna ends up being right.

Potential Yokozuna Preview

The big question is if Onosato can continue his record breaking ways and make it to Yokozuna in only 2 tournaments at Ozeki - which would be the minimum tournaments required and the record for quickest ascension to Yokozuna (both tournament wise, and from Ozeki, I believe).

If he does want to make Yokozuna, he needs to keep the magic 26 wins in two tournaments in mind. That said, winning the Yusho on the first tournament of a Yokozuna run is less important than the second tournament.

26 wins + Yusho on second tournament is the quick and dirty version, but we have some more analysis under the Yokozuna section on the Sumo Knowledge Primer here too. Let’s look at the men now.

Kotozakura - O1E

Sometimes when you’re doing sports analysis you can uncover some statistic or tendency and you feel really smart and can cheer for your guys to press the ball better, or run this play or defend that player tighter or whatever. Other times you’re doing sports analysis and the results seem comically simple: you just need to play better.

Unfortunately, the advice for Kotozakura is of the latter type. He has every skill and physical asset you could want, but he just needs to be more consistent. Easier said than done and “win more” sounds almost patronizing as advice, but that’s what he has to do. If he puts it together for 2 consecutive tournaments - something he did going 13-2 January ‘24 - then he’s a Yokozuna. Sounds simple, and he has shown he can do it. But will he? That’s why we watch.

Hoshoryu - O1W

On the other hand with Hoshoryu I think I have more concrete advice. His problem - to my amateur eyes of course - is that he just doesn’t dominate enough. Put another way: he lets far too many guys into matches that he shouldn’t.

Watching a dominant wrestler at the peak of his powers, you start to think he’ll win every match before it’s started. A lot of the times they’ll just blast guys out of the ring. When they’re taken to the brink - few times it may be - they can recover and turn that into a win, or at last avoid an embarrassingly quick and basic loss.

When I watch Hoshoryu I don’t get that feeling of dominance. I think he can beat anyone on any given day, however the opposite feels true to me too. He seems like he can throw away a match against a worse wrestler on any given day also. With the margin for error on a Yokozuna run I just don’t see his current level being enough. When there are guys at the top like Onosato, Kotozakura, and when healthy, Terunofuji, you cannot afford to throw away losses in week 1 cheaply.

If the above strikes you as overly pessimistic, I promise I still like his long term prospects. He’s generally healthy and still relatively young. Time is on his side, so hopefully this tournament he proves me wrong and starts dominating lower ranked wrestlers. But the good news is even if it’s not this tournament, he has plenty more to do that in too.

Onosato - O2E

Last but certainly not least. In fact, “last but most importantly” is a phrase I’ve never heard but would apply to Onosato here.

Onosato has put together a truly unbelievable resume in just a couple years of professional Sumo. I honestly don’t have too much to add here other than it will be interesting to see how he does after his Ozeki promotion. Anecdotally there seems to be a bit of a hangover effect from newly promoted Ozeki which makes sense as there is ceremony on top of the usual Sumo for those promotees. This is empirically born out as we discovered in my first piece on Ozeki Analytics in the graphic below:

If he can avoid the Ozeki hangover, then he should be in a great place. My one lingering doubt with Onosato was him reaching 13 wins in a tournament. After all, you need 13 wins twice in a row to hit the magic 26. Well last time around he showed he can easily reach 13 wins en route to Ozeki. As long as the health is there, it’s a matter of when, not if.

Potential Ozeki Preview

The main attraction here is Kirishima. He might even be on the third of three tournaments in an Ozeki run stealthily already. I’ll explain that below. But with that in mind we actually have more contenders than I thought.

Before I get ahead of myself, the Ozeki requirements can be a little less rigid than Yokozuna especially depending on the Ozeki roster. Right now we have 3 solid Ozeki so I expect when evaluating candidates they’ll stick to the general rule we’ve found which is 33 wins over 3 tournaments (Ozeki section here has more).

Kirishima S1E - 12-3 (September), 8-7 (July)

Technically speaking if Kirishima gets 13 wins this next tournament (a total he reached in the Kyushu Basho last year) then he would be on 33 wins over 3 tournaments below Ozeki.

One: I don’t think that’s likely, although it certainly looks more so after his terrific outing in September

Two: I don’t think they would count that first tournament (8-7) in July as being part of an Ozeki run. After all, had he won 10 then, he wouldn’t have to be fighting to regain his rank the hard way.

I really am rooting for him because if last tournament wasn’t a mirage then it really looks like he lost his spot due to some bad injury luck. I’ll put the number he should be shooting for as 10.5 wins. If he does that November and January it puts him at 33 wins for 3 tournaments. You might be saying, “how could he get a half a win?,” and I hear you and I think that means he should ambitiously shoot for 11 wins to make it even easier next time around only needing 10 wins in January. Best of luck to the once (and hopefully future) Ozeki.

Daieisho S1W - 8-7 (September)

Maybe one day I’ll figure out how to calculate the most underrated wrestlers. If I do come up with a decent way to rank based on that, I imagine Daieisho will be near the top of that list. He’s been steadily getting Kachikoshis and better from the Joi, and in particular the Sekiwake and Komosubi spots the past several years. Maybe this tournament he could go on the start of a run that’ll ensure he’s no longer so underestimated.

Wakamotoharu K1E - 11-4 (September) from M3

A late bloomer in sumo, Wakamotoharu arrived in the top division in his late 20’s, but has looked comfortable up here ever since. He went 11-4 last tournament which from the Maegashira 3 spot should be high enough to be included on an Ozeki run if he gets 22 wins over the next two tournaments.

It would be a really fun story if he did, because I believe based on my research he would be the oldest Makuuchi debutant to make Ozeki in the modern era. And by a couple years too!

Shodai K1W - 10-5 (September) from M4

The enigmatic Shodai is having himself a bit of a run right now. He actually has 20 wins over the past two tournaments. I only included the September record, as his July 10-5 came from Maegashira 10 and would be too low to be included in an Ozeki run. Still, the former Ozeki has demonstrated he still has some fights left to give. We’ll see how he does this time around being firmly in the Joi facing top wrestlers daily.

Oho M1E - 9-6 (September) from M2

I’m including him as I have a bit of a soft spot for him and he seems to finally be fulfilling some of his potential. Yokozuna Taiho’s grandson made his Makuuchi debut quite young in his early 20’s and seems to finally be putting it together. For reference, him and Hoshoryu came up around the same time, so who knows? Maybe these rivals can finally meet as peers at Ozeki sooner or later?

Wakatakakage M2E

If not for an injury last Spring, he might already be an Ozeki. Wakatakakage had looked that good with solid records to back it up. He’s finally back in the Joi and has looked good since his return. Can he complete his comeback story?

Last time around we had the gift wrapped narrative of whether Onosato would make Ozeki or not. We don’t have anyone on the final tournament of a Yokozuna or Ozeki run around this time, and yet the cast of characters might be more compelling. I’m excited to see how everyone does. Hopefully you enjoy this tournament and all the rikishi can stay safe and unharmed while continuing the excellent year of Sumo.

Today we’re going to be talking about why prediction markets aren’t necessarily the solution to a lot of the problems we encountered last week in trying to figure out the issues with election polling and polling aggregation. The same as last week, this is meant to be a plain English, non-partisan explainer that goes over some of the issues with predictions markets. I think that this is a lot closer to the problems with markets (like the stock market) in general. Certainly some statistical lessons can be gleaned, but today I’ll flex some knowledge accumulated more from the finance parts of my day job.

The Basics of Prediction Markets

In many ways, finance is the art of transformation. When a company sells its stock in the private markets (typically Venture Capital or Private Equity) they are transforming a share in all future profits of the business into cash today. Similarly if I am a farmer and want to ensure that I have enough money to make it through to the next year, I might transform the future crops I will be harvesting from an uncertain future sum of cash (selling at whatever the price in the market will be) into a guaranteed price for a guaranteed amount of crops (depending on structure this is either a future or forward contract). In the latter case this also might be called a hedge - as in I am hedging against the risk that I receive a price lower than I expect and hope for.

In fact, markets and trading allow us to transform quite a few different things into dollar values. For instance, continuing on the crops example from above, let’s just assume that I’m locking in selling crops at the current market price today - call it $100 a bushel. So if the contract is to sell you my crops tomorrow at $100 (the current market price) then my hedge likely isn’t that valuable - how much could the crops change in price in the next 24 hours? But if the contract is to sell you my crops 1 year from today at $100 that could be very valuable indeed. After all, who knows what price the crops will be at next year? There could be a crop shortage due to poor weather. Maybe there will be an abundance next year on the other hand. Depending on a whole variety of factors, that uncertainty that time breeds will increase the value of locking in that price for someone, and decrease it for someone else. But the bottom line is that we’re transforming time into a dollar amount to be haggled over.

Continuing beyond time, we can also transform the credit worthiness of a counter party (the person you are doing business with) into a dollar value. If Microsoft decided to raise money to build out data centers, you would likely lend to them rather cheaply. This will be reflected in the interest rate that is paid. Now if your multiple-times-bankrupt buddy from college approached you to raise money to build out data centers, I am guessing you would charge him a higher interest rate than Microsoft.

These are basic and stylized examples, but the bottom line is that by using the same medium to express different more abstract concepts - creditworthiness, time, risk - we can turn them into concrete dollar values. That is the medium we are using to express our various opinions - and the value you place on time is an opinion in its own way - in dollars.

So markets and transformation to dollars give us a way to have a shared language for expressing and predicting things that otherwise might be impossible to clearly communicate to each other. We might have a completely different model for voter turnout, who women-under-35 will vote for, how to weigh the Quinnipiac Polls, and so on, but when I tell you that I am 40% sure that Jim Exampleson will win the election, suddenly you can either agree or disagree.

Efficient Market Hypothesis

With our shared language - percentages or dollars for now - we’re now in a much better place as we are no longer talking past each other. I might have a different model and a different prediction than yours, but so long as we’re using that same language - dollars or percentage - then we are in a coherent conversation with each other. I agree with your price or odds or I disagree and then try to profit off of that.

That’s something, but betting markets promise us more. In fact, this screenshot I took as I’m writing this from Polymarket - one of the larger prediction markets - promises “Live and accurate forecasts”

Let’s make a bold assumption for a second that this company actually does care about more than profits (bold indeed) and aspires to provide more accurate predictions. Why should prediction markets provide more accurate forecasts?

Well there are actually quite a few theoretical justifications for markets providing more accurate predictions. In fact, you’ll find some economists who defend price gouging during natural disasters because they see it as a price signal. Flights are more expensive out of an area because a hurricane is coming should signal to the market to provide more flights out of that pending disaster area1.

But let’s skip over justifications besides the profit motive and instead go to the end result of all of those incentives that markets provide (according to some): Efficient Market Hypothesis.

Efficient Market Hypothesis essentially states that asset prices reflect all available information. At a basic level the thinking isn’t too far from the joke I opened this piece with: if you’re buying a stock today, you (per this theory, if it holds true) should not be able to make any money through the efforts of your research into it. All of that information has already been incorporated into the stock price. What that does not mean is that you are guaranteed to lose money; there are bound to be random gyrations of the stock throughout trading periods. Furthermore, it is possible that the stock you bought has an unexpectedly strong quarter, and goes up as a result. Note, I said unexpectedly, because again in stronger forms of Efficient Market Hypothesis (EMH henceforth) all available information should be incorporated into the stock price.

Now from an outsider’s perspective if you haven’t heard this theory before, it can sound rather silly, hence the joke. But I would advise against dismissing it out of hand. Through a combination of legal constraint and other constraints, there are certain kinds of trades that you can reasonably expect to be positive that the market has not competed away. However, for the rest of the market when we discuss highly liquid (meaning trading frequently) stocks in major public markets, some version of EMH has solid explanatory power. After all, some of the smartest people in the world try to beat the market and often fail. Furthermore, when greater understanding of what drives prices are discovered - often described as and called factors such as bigger companies being more valuable, or companies that are focused on growth instead of maximizing value at current size, etc. - those factors tend to quickly lose their (superior) value.

Above I alluded to there being multiple forms of EMH. These forms will be based on how much information is hypothesized to be “baked in” to the price. A weak form EMH will posit only historic stock prices are incorporated whereas a strong form will speculate that even private information is included in the price information. Who knows, perhaps in the future insider trading laws are relaxed so much that becomes a reality!

How Does That Work Though?

So markets will lead to predictions that are in line with public data, and possibly even private data too. But how?

Continuing with EMH, we have a stock Example Industries LLC that is priced at $100. Everyone that owns it agrees that it is worth about $100 and as such it trades at $100 moving up or down a random bit each day but always closing around that $100.

Now Scrooge McDuck realizes that he’s missing out on profit by keeping his money in gold coins in a vault in his house and decides he’ll reinvest it. He goes to the stock market and decides he needs to get market exposure ASAP, prices be darned. So he begins by saying he’ll buy Example Industries LLC for $105. He’ll tell his stock broker to go to the market and convey that information; incidentally this would be called being bid $105. As an owner of Example Industries LLC I know that there’s a potential $5 worth of profit there (105-100=5) so I agree to sell at $105; this would be called being offer $105.

Great, right? However, we’re in EMH world, and everyone else in the market (somehow) knows that we should be selling this stock for anything above $100 as that would be a premium to it’s true value (if the assumptions hold). So the next guy says, “well anything above $100 is a premium, I’d feel good selling to Scrooge at $104.” Then the next guy says “well $103 is still profitable” and so on until Scrooge is buying for more or less about $100. Again, if EMH holds then we’ll all sell as that’s a premium.

In fact, this is a bit how markets work generally. There are High Frequency Traders looking to see if a stock selling at $101 on Exchange A can be bought for $100 at Exchange B. When that happens I will buy from B, and sell to A and lock in $1 profit. Everyone will do this until that price difference is eliminated. That guaranteed profit is called an arbitrage and is what will keep prices relatively the same across and between exchanges.

Using this language, we can think of EMH as a theory that all information in the markets will be arbitraged away. In the Scrooge McDuck example we all would have competed to sell him the stock at a premium until that competition ultimately drove the price down to ~$100.

Please note again that this is a highly stylized version of EMH and markets as a whole. Furthermore like I said there are $20 bills laying on the ground so to speak because of various restrictions that limit arbitrage. In fact, as a trader those are the opportunities you should be looking for. But also by that same logic, you should make sure you can understand why that arbitrage or opportunity exists, because chances are if you don’t understand it then you might be the Scrooge McDuck squandering money.

Back to Political Betting Markets - Less Liquidity, More Problems

So we now know that transforming to dollars will give us a shared language. Furthermore, we have a hypothesis that posits that in markets, new information will be arbitraged away. Sounds like prediction markets, and markets in general are the way forwards then?

Unfortunately there are limits.

Earlier I brought up, “when we discuss highly liquid (meaning trading frequently) stocks in major public markets, some version of EMH has solid explanatory power.”

Regarding the high liquidity, one way to characterize liquidity would be how much an individual trade or trader can impact the market. If we’re trading a penny stock (a cheap, generally lightly traded, and small company) and I buy $1mm (million, more finance speak) of it, that’ll likely push the price meaningfully upwards. If I do the same $1mm buy of Apple stock then there will be minimal if any price impact to that purchase. Hence we could refer to liquidity as a spectrum with some stocks being more liquid than others. As it is a spectrum it is a bit difficult to define how liquid the various prediction markets are, but I can tell you for a fact there are whales in those betting markets.

When I refer to a “whale” that essentially means somebody that is throwing around a lot of money. In the case of these prediction markets the whale represents about $30mm (million) worth of bets on Trump. Again as someone who works in public markets, $30mm is generally a pretty small amount if you’re talking an institutional or larger fund in the stock market, but these prediction markets are less liquid, and hence are impacting the prediction odds. I’ve seen reported that the impact of those purchases in particular have moved the odds ~5-8% more than they otherwise would have.

Again, when defining liquidity there’s no strict cutoff for how much any purchase should move the market, but I would say that if indeed $30mm worth of bets moves odds 5-8% ceteris paribus (meaning: assuming no other changes) then that hardly qualifies as “highly liquid”. So there we have our first issue with prediction markets; insufficient liquidity means that they can end up less reflections of all information and more reflections of large traders’ opinions.

Does EMH Hold for Prediction Markets? Experiment in 2024?

I think this is a much more academic and difficult question than people would want to accept. There’s a sort of critique of EMH that goes “well there was a big price move and thus EMH is wrong.” I think given that there tend to be few glaring opportunities for profit in the market and that many of those opportunities for profit can be explained by legal and size constraints for investment means we should treat EMH with more respect than simply dismissing it out of hand because it fails to explain every market move.

That said, to go with the more snarky dismissal we do have this:

To give a better justification than showing a time that prediction markets were big time wrong, let’s think about an investing philosophy that’s in contrast to EMH, generally.

Value investors tend to be folks that subscribe to an investment philosophy akin to what Warren Buffett preaches: by doing research into companies and figuring out which ones are good, you can be rewarded for holding those high quality companies over a long period of time. Sometimes those companies might suffer in the markets, but over time you’ll be rewarded for holding high quality companies.

If we extrapolate this to prediction markets and you can apply a value investing philosophy and be rewarded for it, then it would act as a repudiation to the idea that EMH holds in prediction markets and that prediction markets ought to provide a more accurate vision of events.

The thing is, this election looks to be a genuine 50/50 or so. Maybe it’s 55/45, maybe it’s even 60/40, but at least from my perspective, it looks like Kamala is favored in the popular vote, and Trump is doing alright in the swing states he would need. If we apply the logic from last week’s piece on polling, I’d put it more like: “based on some polling where they seek to correct for misses from the prior election and seek to cover ~95% of scenarios, then when we include the margin of error in polling at the current stage, this election looks like it should be somewhere between 40-60 favoring either candidate to win.”

Unfortunately, that doesn’t provide a neat falsifiable counter scenario for us. For instance, if the election polls had it Kamala 70/30, and Polymarket still had it 60/40 towards Trump, that would be perfect for us. In this case you could “value invest” based on the underlying polls, hold until the election when Kamala would be much more likely to win, and then cash out. Were that the case, it would be a potentially decisive blow that these markets aren’t efficient and more accurate.

Another Problem: Infrequent Marks to Market; Also, Prediction Markets’ Value?

A publicly traded company does just that: it publicly trades everyday that the markets are open. If I own a share of Apple stock, 5 days a week I will know exactly what that stock (and the larger company) is valued at.

Private Equity (PE) and Venture Capital (VC) are investment classes that focus on private companies. They will invest money in a company, and periodically if there is a large piece of news, or a material change in the value of the company they will update the value. For instance, we’ve heard frequently about how much in value Twitter has deteriorated since Elon Musk bought it and took it private.

Something interesting that has emerged in financial literature is that pensions, endowments, and various other long last institutional investors invest in and like PE and VC because they so infrequently update the value of the investments. We don’t need to get into the nitty gritty of it beyond the fact that it’s very convenient to not worry about updating values (for better or for worse) more or less daily.

Rather, I bring PE and VC up because these betting markets are more or less the same. There will only be one mark to market for these bets/predictions, and that’s when the bet settles and you either won or lost. Just as we can only know how good our election polling was after the fact, we’re in the same situation for our prediction markets.

Now that doesn’t mean they are worthless. In fact, they do have some value which is quite different than what the owners and boosters claim: these markets are liquid enough that they serve as useful barometers of the change in election odds based on recent events in real time.

To give a good example: after the debate between Trump and Biden (2024), Biden’s odds went down precipitously. That was a real time vindication of what we were seeing in terms of what looked like a poor performance. Before anyone answered a polling question about it, we could go to these various sites in real time and see that it augured poorly for Biden. That was borne out by history too (him dropping out).

But note that what I’m claiming here is starkly different from what these sites advertise. Real time prediction markets can be useful for gauging how the larger populace might be reacting to the latest news. That is a far cry from those markets being the most accurate, or whatever is being claimed.

EMH Failed to Account For:

People being stupid.

I’m being a bit reductive here for a punchline above, but the general thrust of this piece is related to prediction markets on politics in particular. We have quite a few different phrases to convey “someone is letting their emotions dictate their gambling” such as being on tilt, throwing bad money after good, etc.

Letting your emotions dictate how you allocate capital as opposed to a sound and repeatable process is - and this is my opinion here - stupid. And I promise as someone who has followed these kinds of markets (and other irrational markets) for a while that you could classify many of these traders as dictated by emotion rather than rational analysis. Politics does that to us!

At the end of the day we have countless examples beyond prediction markets of folks letting tribalism, memes, or excessive opportunism separate themselves from their money. Bed Bath and Beyond was raising capital from retail investors more or less till the day they went bankrupt. A few years ago Hertz announced it was essentially bankrupt but was still going to sell shares in the company despite that. People were lining up to buy stock in a self-admitted essentially worthless company until a court order halted that.

I said earlier that EMH actually does have decent explanatory power. You probably aren’t going to discover something looking through Apple’s various financial statements that will allow you to make superior returns on investing in it. But when we get to penny stocks or prediction markets? Suddenly markets aren’t so efficient, and the Hypothesis part of Efficient Markets Hypothesis starts to become the key word. We as a people let that stupidity and emotion affect our decisions, and few places will you see that more than in these political prediction markets.

Conclusion

We set out to look at prediction markets and examine a few questions. What is the theory behind why prediction markets should give us more accuracy? I used mostly EMH to explain it, but the profit motive (i.e. there’s a price dislocation and you look to make money off of it) is of a similar type of thinking and provides a similar justification.

We discussed how there are whales in these markets, and the larges moves they’ve made show that the markets aren’t highly liquid because those moves impact price/odds so much. Furthermore, we talked about how with political prediction markets in particular when folks are investing based on emotions that makes it more likely that the odds we’re seeing reflect sober analysis.

But not everything is bad here; the challenges above might affect the predictions as a whole, but there is still some utility in seeing the change in those flawed odds to get a sentiment check on how news affects candidates odds.

At the end of the day, we might not get a clean example to show why prediction markets aren’t necessarily more accurate, but I do think we saw why as they are currently there are structural problems that mean they aren’t as accurate as the websites portray them as.

In my mind, one of the defining features of the modern age is data. Nowadays we are more than awash in it. We collect it anywhere and everywhere we can. We’re constantly generating new data and trying to tease out insights from it. This blog/project is absolutely a part of that. In the past 100 years or so, with the aid of computers we’re now able to apply statistical techniques cheaply and easily in a way that would have been inconceivable before the mid 1900’s. Alongside this increase in data and the ability to process and analyze it, we also have invented many different techniques to actually do the analysis with. I’m frequently surprised reading up on statistical analysis and finding out that some technique that seems omnipresent nowadays was invented in the 1980’s, if not later.

However, with the proliferation of all this data and analysis and new techniques, comes the simultaneous increase of the odds of us tricking ourselves. As Twain said, there are lies, damned lies, and statistics. Today I’m going to be looking at polling at large and why I think we pay too much attention to minor differences between polling aggregators. While this post will talk about some more advanced statistical concepts, the underlying motivation is to explain in relatively simple language some of the issues with polls and polling aggregation. Ideally by the end of the piece you’ll be able to understand the polling landscape and how to think about it a little better.

Furthermore, it’ll be about statistical thinking in general, and how that relates to predicting elections.

Step One: Defining the Goal

First off, we want to define our goal. It sounds relatively simple, but it’s always important to have a concrete goal in mind. Maybe you’re trying to test a hypothesis, maybe you’re trying to learn something about data you have; it could be essentially almost anything but the important thing is to have that goal in mind and ensure that you’re always working towards that goal. If you don’t, then it’s easier than you think to lose track of it and you end up answering a slightly (if not majorly) different question.

Today, our goal is to be able to accurately predict elections.

How Can We Predict Elections - Just Polls?

So now that we defined our goal let’s think about how we can get closer to it. What we want is a data series that correlates highly (be that positive or negative) to the election. The last sentence is worth expanding on. Again, our goal remains to accurately predict the election. While asking potential voters who they intend to vote for is (likely) correlated to the election outcome, they are not the only data series correlated to it. Additionally, there are reasons that polling data might not be as strongly correlated to election results as we would like.

I also included the bit about correlation being highly positive or negative because either correlation could serve our purposes. Positive Correlation is when A happens, B is more likely to happen and when A doesn’t happen, B is more likely to not happen. Negative Correlation is when A happens then B is less likely to happen, and the opposite. The common format to express correlation is a single number between -1 and 1. If correlation is 1, then A and B are perfectly correlated and A happening guarantees B happening. -1 is perfectly inversely correlated and means A happening guarantees B does NOT. 0 means that there is no relation between A and B.

So with the correlation explanation aside, our goal is the most highly correlated data series to election results1. I wanted to cover this, in addition to stressing the importance of keeping our goal in mind to make a point: if there is data that is more correlated to election results than polling, then we should be using that instead of polling data.

To give an example, economic indicators will be correlated to election results. If lots of people are unemployed, incumbents will likely do worse. If wages are up and filling up at the gas tank is cheap, incumbents will likely do better. So do keep in mind that polls aren’t the only way to predict an election, or necessarily the best.

Why Not Use Polling Data

We just covered that there might be data that’s better for our purposes than polling data. For the rest of the piece, we’ll treat that as if it is not the case, and that we should be using polling data if we want to best predict election results. Still, keep that in mind and ask yourself if the person you’re reading is trying to predict the election or if they’re trying to generate ad revenue on their website by getting people to click on it, for instance. In fact, just as there might be people writing about the election trying to generate clicks instead of accurate predictions, we can imagine a pollster doing the same.

It’s hopefully not controversial to say that polling data influences political reality. I cannot say how much it does, but bad polls ended the candidacy of Joe Biden (or had a very strong influence). Not all polls will be that significant, but there are partisan pollsters who seek to influence political outcomes by publishing biased poll results.

However, we’re still statisticians and we can say that a biased poll can be useful if certain conditions hold. Imagine that there is a pro Trump polling company, and they consistently are 6 points more biased to Trump than actual results. So if they showed Trump +8 then you would expect the actual results to be Trump +2. If that held consistently over time, that would be very useful indeed!

So now we’re getting to the idea of polling aggregation. We won’t have a perfect idea of how biased every poll is, but if we do a good job of adjusting a bunch of polls and averaging them out, then in theory we should have a good idea of how the election will play out.

I’m speaking in highly general terms here, but that is basically what Nate Silver, New York Times, or any polling aggregator is doing. They are taking a bunch of polls, adjusting if there is a bias, and then doing some kind of weighing mechanism to arrive at a final prediction.

I think as a whole, the approach is sound and makes sense. However, I believe that for several reasons, there will always be a minimum amount of uncertainty or guesswork involved. In other words, certain polls or even aggregators can be correct in any given election, but a certain amount of that accuracy is due to luck. If that does not make sense, hopefully the next few sections will make my point clearer. Additionally, it’ll explain what it means for data to be non-stationary and why you would use an Autoregressive Model.

Defining Our Goal: Addendum on Modeling

Above I said that our goal is to be able to accurately predict elections. That is still the case but I thought it would help to go a little more into how we will do that. In statistical literature, we would define our goal as the dependent variable or y (footnote2).

Our goal is to find the independent variables or x’s that would lead us to an accurate y. At the end of the day our equation will look something like this:

Predicted Election Results = Our Input Polling Data * Beta Coefficient That Maximizes Odds of Prediction Election Result Correctly

That’s a mouthful and a half, but that’s what we’re trying to do. This is a fancy version of what you’ll see as a basic linear regression which is something like:

y = x * Beta

Y is the election prediction. x will be the polls that we’re weighing. Beta is just the coefficient that will give us the most accurate results of y. So to make this “real world” we would have:

Predicted Election Result = New York Times Poll * Beta

I don’t want to use tons of mathematical notation, but you can imagine that the real version of this equation we’d have many many more polls all with their own Betas - after all, we’ll weight the NYT differently from the Washington Post to get the most accurate results. This is where you would be using a Sigma symbol (that E looking symbol below) to indicate that you’re iterating over a bunch of different polls.

y = Σ x * β

In fact, we could get even more specific. In this case we’re trying to get a y or dependent variable that is most accurate for 2024 (or whichever election we’re trying to predict).

Again, it sounds like a minor distinction, but it’ll be important to keep in mind for our first major problem with the election prediction.

Problem 1 - Non-Stationarity

Imagine we lived in a world where we didn’t know that you have a 50% chance of getting Heads when you flip a coin. I set out to determine the odds of landing Heads on any given coin flip. So I pull some datasets of how many times a coin was flipped, and how many times it turned up Heads. Generally speaking, if there’s a solid sized sample set - it shouldn’t matter if I’m pulling data from yesterday, 10 years ago, or 100 years ago. I will likely come to a model that puts the odds of Heads at around 50% because coins intrinsically will have a 50% odds of landing on either side.

Now we’re in a slightly parallel world. We still don’t know about the odds of getting Heads on a coin flip, but there’s one key difference: in our world 100 years ago the weighting on the coins were different. For whatever reason, the metals they used and the way the coin was designed, there was actually a 55% chance of getting heads on any given coin flip. Again, that was 100 years ago but our current coins are a true 50/50.

Now, instead of being able to use any data to predict a coin flip, we would have to be sure what kind of coin we’re trying to predict. Is it the century old coin biased towards heads? Or is it the modern coin that’s a true 50/50.

It sounds like a silly example, but it explains an important concept: stationarity in our predictors

Errors are stationary if they are generally the same over time. They’re non-stationary if they change over time. In our example, the weighting of the coin changed over time, so if we didn’t have something in our model to account for that, then we would have a model that performed poorly as a result. To make it clear, this is assuming we’re using one model that covers that coin from 100+ years ago when you were 55% likely to get heads but then the coin changed and now it’s a true 50/50.

Why Is US Election Prediction Non-Stationary?

Just like the coin example, when you’re thinking of non-stationarity you want to be asking: would using the same independent variables, or predictors, work equally well over time?

We assumed that polling data works for our purposes here. Part of polling is looking at various breakdowns of the polls themselves. Can we draw conclusions about who someone is likely to vote for based on their gender? Their race? Things of that nature.

In fact, this is a lot of what polling is. You’re looking at historical correlations between various demographic markers, and then applying those to the people who you ask who they’re going to vote for. If you call only women, or only elderly people, then you’ll be adjusting based on that. Finding representative samples of the electorate is a problem that continues to bedevil pollsters. Books can be (and are) written over how to optimize polling processes.

However, you might have realized what I’m leading to already: different demographic groups’ preferences change over time. It’s an extreme example, but if you were modelling US elections over time, and you had African American voters, it would be very important to account for the fact they were a reliable Republican voting bloc until they weren’t (say pre 1960’s if not earlier) and became a reliable Democratic voting bloc. But even further, the slim margins here matter quite a deal given how close presidential elections can be. That’s without even getting into the fact that all of these polls have margins of error or confidence bands built in.

The main point here is that various demographic voter preferences change over time, and that makes polling accurately (and thus prediction) difficult.

So how do we deal with non-stationarity?

Well keeping up with the coin example, what we’ll likely do is insert an additional variable. So what we’ll use is called a Dummy Variable. It’s just a basic binary variable that is often either 0 or 1. In this case, we would look to see if our coin is from the 55% era, or the 50% era, and use that dummy variable to express that. You could imagine it being 1 for the 55% coins and 0 for 50% coins, which would inform our model which probability distribution to use.

Using dummy variables or some other way to allow the model to account for the fact that preferences change over time is one way to deal with stationarity in models, if it breaks down cleanly like above.

Unfortunately, I don’t think it would be so clean using US elections. So we are forced to move to a different method to account for the non-stationarity of demographics’ polling preferences.

Another way to deal with non-stationarity is to simply zoom in to the data so you are covering a time period where the underlying data is stationary. Using the coin example, we would simply just model the likelihood the coin lands on heads since they moved to the 50% coin design.

Perfect, we’re going to zoom into more recent data. It’s a pretty difficult problem if we should be doing say, 1960-present, 2016-present, or whatever period. In fact, part of that problem with figuring out where our data cut-off should be is related to our next problem.

Problem 2 - Low Sample Size with Low Frequency

I began this piece talking about how one of the defining features of modern society is how much data we collect. Generally speaking if you ask a statistician or data scientist they’ll tell you: more data is better. Even if data seems “useless” right now, it’s possible that it could be useful in the future so collect it anyways. There are actually quite a few techniques in statistics and modelling related to removing data that is useless, or even worse, damaging to predictions. In fact, in our AI age, the selling point of many models is how many parameters they use and how large their datasets are.

When it comes to presidential elections, we have had 59 since our countries founding. But saying our sample size (henceforth referred to as N) is 59 oversells the data quantity. I imagine that the insights we could mine from the 2020 election are likely much more valuable than the 1796 election where women, non-white men, and even non-propertied men (often) could not vote.

The problem with small sample sizes is simple: it makes it much harder to deduce general characteristics of the electorate. Here’s a good example: George W Bush (43) actually did well with Muslims in 2000 (there’s conflicting data, but some estimates have him with 40%+ of the Muslim vote). He also did quite well with Hispanics. Donald Trump in comparison did rather less well with both of those groups.

We only have a presidential election every 4 years, and are forced to draw sweeping conclusions from those results. One way to get more data to predict presidential elections is to use results from other elections, and trying to establish the correlation between that election and the presidential one. For instance, pollsters are generally going to recalibrate their models based off of how midterm elections go. This serves to give us more data, but simultaneously this data can be misleading as it will not correlate perfectly to the presidential election. You can imagine that a particularly popular governor wins an election against a particularly bad opponent with a larger than expected margin. How do you account for that governor’s popularity and their opponent’s unpopularity? So this data is not useless, but also must be treated skeptically in the sense of wanting to not assume it will directly translate3.

Ideally, from a pollster’s perspective, if we had presidential elections once a week or so, we could likely predict elections with a high degree of confidence. We would be able to zoom in so that our data is stationary, and we would have enough instances to be able to sus out any changes in a demographics’ voting preference and how that translates between polls and actual ballot boxes in real time.

Unfortunately, again from the pollster’s perspective, we only have elections once every 4 years. So we get new election data and we update our models for the various race, age, gender, etc. splits. In particular, we will look at where our previous predictions failed and we’ll look to correct them. Alas, that leads us to the final error we’re covering today.

Problem 3 - Autocorrelated Errors

We’re almost at the end, and luckily I think this one might be the easiest to explain now that we’ve gotten into the nitty gritty above.

As I said before, we’ll look at what our models predicted, and then compare to what the actual election results were. If we missed by underestimating Republican strength, then we’ll likely be adjusting our polls to so that future iterations will capture the Republican part of the electorate better. It’s the exact same with Democrats; if we overestimated their voter share with the elderly, then in subsequent polls, we’ll assume the elderly are less likely to vote Democratic (than we previously assumed).

This means that our errors for our current prediction are likely to be the opposite of our errors the previous time due to over-correction. We saw this in 2016 when the polls underestimated Trump, and then 2017-2020 the polls (generally) overestimated Republican strength. It makes sense as pollsters were trying to correct their previous error, but ended up overdoing it.

How do we deal with this?

We use an Autoregressive model. If you’re not familiar with this, no worries and in fact the name is fairly self explanatory. Auto in this case means self, and regressive just means you’re looking at the past results. So basically what we’re doing is looking at where we had errors last time, and then assuming there will be a correction based on that in the current period. Over time we’ll ideally have enough data (including errors) that our model can minimize how those errors affect our predictions.

However, we run into a similar problem as to our demographic non-stationarity: we simply don’t have enough elections to have confidence that we’re properly correcting for the errors, even as we use our autoregressive model. As a result, it will be more difficult to accurately anticipate how large the errors will be, and how to correct for them.

This post in many ways could have been: we don’t have enough elections to reduce the margin of error in election polls as much as we would like to

A Few More Problems to Think Of

We covered a lot here, but this is a topic that could be written about endlessly. Here are a few other things I didn’t cover here in depth that are also going to be potential issues with polling.

• Turnout. Even if we modeled perfectly how each demographic will vote, if we don’t do a good job predicting who will actually go to the polls and vote, then we’ll be liable to have errors

• October Surprises. Does something happen right before the election that has the potential to shift voter preferences or turnout that wasn’t previously expected? A good example would be the James Comey letter on Hillary Clinton’s emails coming out right before the election in 2016. In fact, there were arguably two October Surprises in 2016 given the Access Hollywood tape that came out on Trump. What a crazy election!

• Third Parties. For good reason they tend to receive less attention when calibrating models, but the breakdown in who votes Third Party and who ends up “returning home” to a major party, so to speak, can prove decisive in states won on a small margin

Conclusions

What should we make of all this?

I recognize that a lot of what I said above makes it seem like predicting elections is a fool’s errand. This may come as a surprise then but I think that by combining a bunch of polls together that we actually can end up with a decent snapshot of how the election might play out. In fact, despite all the issues, even in elections like 2016 which greatly “defied the conventional wisdom”, polling reflected that it was expected to be a tight election. In fact, I recall seeing the Wisconsin polls narrowing consistently in the leadup to November. If you add in the fact that all of these polls have a built in margin of error or confidence interval they start to look less bad. We are accustomed to seeing that Trump is 3 points up, but to be more accurate, it ought to be expressed as “in the latest poll Trump is 3 points up with us being confident that if you add or subtract 5% to that +3 it would cover almost every conceivable scenario with some basic but justified (by data) assumptions.”

That’s a mouthful, but all these polls have what we call confidence intervals or margin of error. Those convey that with it’s actually a range of outcomes they predict. Furthermore, that range of outcomes won’t cover literally every scenario but rather will cover say 95% of scenarios. Those “scenarios” furthermore are based on built in assumptions. Those assumptions are trying to apply all of the above lessons we have covered such as adjusting for the latest elections, trying to correct for prior errors, etc.

Suddenly when we see that these predictions are actually based on lots of assumptions and made with models we know have built in shortcomings, we start to see that it actually is kind of impressive that we’re able to predict elections this well.

That leads me to my position: there is going to be a degree of uncertainty inherent to election forecasting. Someone “getting it right” might be a credit to their rigorous modeling and great assumptions. Maybe they correctly had the right set of data where voter preferences were relatively stable, and the pollster’s correction was handled correctly. It also might be based on luck. In either of those scenarios, getting it right once is hardly a guarantee of getting it right in the future. In this sense, paying attention to whether a modeler is open about their shortcomings and assumptions becomes a credit to them, in my mind.

In fact, I’ll lay my cards out on the table here: this genesis of this post was in decent part due to the proliferation of people doing poll aggregation models as amateurs. I have no problem with folks doing open-source work with data and this blog is based on that. However, I have seen far too many folks have one decent model or result and suddenly thinking it means they know how to win elections. To be very clear, modeling how the electorate will vote and what could change those voting patterns are completely different questions and success in one by no means guarantees success in the other. That goes back to one of our first rules: know what question you are trying to answer.

So that’s it: making an accurate model of who will win the presidency, and the breakdown of votes that leads to that is extremely hard. There are lots of inherent difficulties to this modelling, and at the end of the day the best we can do is acknowledge these are models that are inherently providing a range of outcomes based on assumptions. However, if we stay honest and humble, we also have the opportunity to provide a generally correct view of the election.

One way to make sense of this number is to look at the number of debutants by each year. Unlike “how many men wrestled in Makuuchi since 1988”, I do have heuristics and a sense on the question “how many people debut in Makuuchi each year.” It feels like generally each tournament there are 1-3 debutants, so 2 on average times 6 tournaments a year to give 12 Makuuchi debutants a year on average. Luckily I ran the numbers and can offer something better than my heuristic. Here’s the graph of debuts by year

To give explain this data, I have the full Banzukes all the way back to the 50’s. I simply took the names of every wrestler who had wrestled in the Makuuchi at least once since 1988 - so that’s the ~320 men from above. Then I looked for the Makuuchi debut of each of those wrestlers and charted it above. As a note, I actually cut it off at 1988. There were some wrestlers in the dataset who debuted before 1988 but to keep this an apples-to-apples comparison, I did not include them in this data. That gives us 275 wrestlers.

Here are some additional stats on the sumo debuts by year:

Minimum: 2 (2021)
Maximum: 14 (2011)
Average: 7.64
Median: 7.00
Standard Deviation: 2.62

The minimum debutants in a year being 2021 the year after Covid makes a decent amount of sense. On the maximum being in 2011 I don’t have such an easy story. As it turns out, my earlier heuristic about there being 2 debuts per tournament on average seems to be twice as optimistic as it should be and in fact there’s a little over 1 debutant on average per Basho.

Looking at the data I can’t really sense or see any trends.

I am writing this as of October ‘24 and by my count I believe there are 7 men who made their Makuuchi debut this year (Onosato, Shimazuumi, Takerufuji, Oshoma, Tokihayate, Onokatsu and Shirokuma). Furthermore I believe Shishi will be the only debutant in the final Basho of the year in November so if I am correct on those, then very neat that we basically ended up right on average and almost on the median perfectly too.

This is a bit of a shorter piece, but I do expect to have some further analysis related to Makuuchi debuts in the near future. Thanks for reading!