NOkozuna - Exploring Near Miss Yokozuna Runs

Testing If Yusho and Jun-Yusho Are Treated Differently

We recently looked at the successful Yokozuna runs. However, to get the full story of what it takes to reach Yokozuna, you not only need to look at the men who made Yokozuna but also the men who just missed out. Today we’ll be doing just that and seeing if we can learn more about what is required to reach the zenith of the sport.

We know that you have to be at Ozeki to reach Yokozuna, and also that in modern times the lowest win total to reach Yokozuna is 23 wins over two tournaments. For this dataset, I looked at all men who reached Ozeki, and then added up their 2 tournament win totals while at the Ozeki rank. I then filtered down to all runs that include at least 23 wins to get a sample of possible Yokozuna runs.

This gave us a sample of all the runs that could be reasonably adjudicated for Yokozuna promotion or not. Today we’ll be using that to test if Yusho and Jun-Yusho are treated differently in promotions. Recall, in the Wikipedia criteria it mentions “The de facto standard is to win two consecutive championships as ōzeki or an equivalent performance”¹. It doesn’t perfectly capture the entirety of deliberations that go into the decision, but it at least gives us a hypothesis to test.

Before I get into the weeds with this post, I would like to extend a sincere thanks to Quantian (twitter link here). If you’re at all interested in finance and don’t follow him on twitter, you’re missing out. He’s a good guy in general and a saint for helping with the math and coding here.

Let’s begin.

So as said, I filtered down to any two consecutive tournaments by Ozeki with a minimum of 23 wins. Then I then coded out the Yushos, Jun-Yushos, or lack of either won for those two tournaments. So Terunofuji was promoted to Yokozuna after going 12-3 with a Yusho in May 2021 and 14-1 with a Jun-Yusho in July 2021. In my parlance, that would be expressed as a two tournament win total of 26 wins, and the coding for the tournament success would be “JY” as he got a Jun-Yusho in his final Ozeki tournament and a Yusho preceding that.

If he had instead gotten the Jun-Yusho in May 2021 and then no Yusho or Jun-Yusho in July, the coding would be “0J”. Hopefully that makes sense. With that out of the way, let’s take a quick look at the various data combinations that go into our models first

Luckily, this table looks pretty in line with what we’d expect going in. If you win two Yusho in a row, you’re gonna get promoted. If you don’t? It get’s dicier. Furthermore, if you don’t finish the second tournament of your run with a Jun-Yusho or Yusho, then you’re almost guaranteed to not be promoted. Tochinoumi is the lucky man getting promoted with a Yusho followed by no Yusho or Jun-Yusho. However, he went 14-1 then 13-2, so by no means is that a light promotion, which I have seen a lot of in the 60’s and 70’s.²

So just starting off, Quantian ran a basic logistic regression for this data. Logistic regressions are good for modelling out binary variables and percentages. For instance, “in the second tournament of a wrestlers’ potential Yokozuna run did they win the Yusho or not.” It can either be yes or no. Logistic regressions are made for cases like this. Conversely, in the future it’s possible I’ll try to chart how much weight affects a wrestler’s success. In that case, a variable like weight isn’t binary but rather linear. I could derive an equation like (career wins) = (coefficient) * (wrestler’s weight). It’s highly stylized but that weight could be 200 kg or 205 kg and so on. Not so with “did they win the Yusho or not.” Hopefully that gives a little background/justification.

With that in mind, here’s the promotion probability table from the regression.

Looking at the above I think it aligns fairly well with expectations. It also lines up quite well with the numbers above. Other than the JY, all of the numbers are decently close. I’m sure some might object that two Yushos in a row leads to only a 85% promotion probability, but rather if anything that’s impressive. No wins were included for the calculation purposes here - the code only knew the tournament results and whether the wrestler was promoted or not. With a sample size of only 12 YY tournaments the model gave overwhelmingly likely promotion odds. To put it in betting terms, a wrestler with YY would be -567 to get promoted. It’s so likely you would have to bet $567 to win $100 if they were promoted. So I think this shows the exercise was worthwhile alone for trying to apply a different approach to this question.

As a quick note, some of the eagle eyed readers might have noticed that not every single combination is listed above - the idea is that if we run a logistic regression with all distinct combos, then it will just give us the existing frequencies as the prediction. Introducing the overlap helps “smear” them together so we can get a real estimate for J independent of the others. It’s not perfect but hopefully it’s a good start, and hopefully one day someone smarter than myself is presenting on stuff like this more rigorously at Sloan.

Continuing with the numbers, we can see that there’s a large difference between the coefficients for each of the categories. This isn’t a scientific test but to paraphrase Quantian, “there’s like a six stdev difference between the coefficients so my eyeball stats package says “yes they [Yusho and Jun-Yusho] are different”.

Finally, a good question is: “does it matter which order you win the tournaments in; in other words is JY == YJ? (and so on)”. Well again, Quantian ran the numbers and in all cases p<1.96. What does that mean? Well in other words, we cannot conclude that the order the of wins matters. To put it more scientifically, which I think helps make the magnitude of the prior statement clearer if you’re at all familiar with statistics: in all cases we failed to reject the null hypothesis that there is no difference between them (the orders) at the 5% significance level.

I do think this merits follow-up. An important point here is that with these relatively low sample sizes combined with low p values, it’s hard to draw too robust conclusions from this. Failing to establish that doesn’t mean we can’t explore further. This is a pretty basic and stylized model. A good question to investigate would be if in YJ runs (so Jun-Yusho then Yusho) their number of wins are meaningfully higher than average. They have a 53% promotion rate with N=15. JY is just 30% albeit N=10. Again, with these it’s important to emphasize the small sample. I’ll probably take a look into that later.

So let’s sum up in a more plain English fashion. We had 135 tournaments featuring at least 23 wins by an Ozeki. We looked at all those based on if they won the Yusho, Jun-Yusho, or nothing. We then ran a logistic regression on that so we could try to do better than just eyeballing it. The models aligned well with our expectations going in, and it does appear that there is a big difference between getting a Yusho and Jun-Yusho. Certainly for me, I thought they could be flexible on the “Yusho-equivalent” so if anything, it’s a little stricter than I might have assumed going in. We also tried to test if the order for your tournament championships (or lack of) matter. With our numbers, we cannot conclude that. Still, it would be worthwhile to explore this further.

My takeaway is that in the future when I’m judging if an Ozeki will get promoted or not my process will be to eliminate them if they have fewer than 23 wins. I will take the Yusho equivalent more seriously. Finally, I really need to investigate those pairings and see if I can find anything, because failing to reject the null hypothesis will eat away at me.

Thank you to Quantian, again. He’s been terrific for the help here, and fortunately that’s indicative of the kind of person he is generally too.

Hopefully you enjoyed this. Feel free to reach out if you have any questions. Also, if you enjoy this/my content in general, would you mind subscribing below and/or following on twitter? Thanks!

Future Pieces

• Reader feedback suggested:

  • I was thinking about trying to further code up how many Yokozuna were present at the time of each tournament and then looking to see if more Yokozuna means less likely to be promoted when it’s “borderline” (think ~25 wins over two tournaments + Yusho and Jun-Yusho) but if this isn’t popular it’ll be on the backburner as it’s a decent amount of work so weigh in either way

  • Does beating the current Yokozuna help with promotion? Would have to look at 120 examples

• Math Deep Dive - did they get more stringent with requirements for Ozeki and Yokozuna over time?

  • Anecdotally it absolutely seems to be the case and it aligns well with when Futahaguro got drummed out in the late 80’s

    • Some of the cupcake promotions in the 60’s and 70’s - oh boy

  • I still need to think more on how to frame this to investigate/bug my more math inclined friends how I could set this up

• Sumo Development

  • How many tournaments does it take to reach Yokozuna from Ozeki?

  • How many tournaments to reach Ozeki from Makuuchi debut?

  • There’s way more to be done; however the above data I currently have reasonable access to

• A look at the most impressive tournament by Ozeki as a group ever

  • Featuring 3 future Yokozuna, the 4 of them averaged 13 wins and won the Yusho and Jun-Yusho

• Tournament winner statistics

  • How many wins is a “weak” tournament win vs a “strong” one

• A deep dive into Tochinoshin’s Ozeki run and the 3 other men who tied him with the 37 wins over 3 tournaments to reach Ozeki

• Longer term: constructing an ELO ranking of wrestlers in the Makuuchi

  • Preliminary coding work is going well - ELO system being implemented and

  • https://www.stablemasters.ca/ actually has this already and it looks great. Hopefully I can match some of the great stuff there

• Longer term: my dataset is currently just Ozeki and Yokozuna so I’m looking to further refine the existing code and pull the full Makuuchi ranks and possibly Juryo too to look at development paths for wrestlers

• Longer term: looking at volatility of win totals for wrestlers

  • Potentially related: looking into injuries

• If you have any other ideas, feel free to message me on any of my channels and I’d be happy to credit if it does become an article

1. https://en.wikipedia.org/wiki/Makuuchi#Yokozuna

2. This is a topic I want to explore and added to the future pieces section