nagora

No love for Tochinoshin's psychic battle with Hoshoryu? Pity he couldn't follow through with a win at the sumo, but the face-off was excellent.

Wow. Lots to read tonight.

I've been working on a rating system for the last couple of years and I thought I'd wheel it out here. Starting from a Bayesian point of view that when we are asked to pre-judge and an event that we know nothing about, the rational prior position is to shrug and toss a coin - we say it's 50-50 who will win (or, more precisely, it's 1/n where n is the number of possible outcomes/winners). After the event is over we update our view for the contestants. If competitor A wins, we move our expectation that s/he will win to 2/3, and the loser's down to 1/3. For my purposes, I multiply these numbers by 10000 so that ratings theoretically run from 0 to 10000 but in reality 10000 is never reached and ratings are expressed as four decimal digits (sometimes three but that is very rare). If these were the only two competitors we ever saw then we would eventually get quite a good estimation about who will win each encounter. We would still have to ask ourselves some questions about how long historical information is allowed to influence our estimate, of course, but I'll come back to that. So, what happens when we add more competitors? We more or less take the same approach - new guys are given a rating of 1/2, or 5000, and then updated based on their record. If they win a match they are bumped to 2/3, then 3/4 etc (6666, 7500). Note that their opponent's rating is not involved in this updating, unlike the Elo system. To deal with the history question, I normally drop results off after six bashos have been participated in (which may be a year or more if events are skipped). An exception to this is that if basho -7 (i.e., the one about to be dropped off the end of the rating history) was a zen-sho, then it is kept for the calculation. A string of such results is treated similarly, so for example Hakuho's four 15-0 results in a row meant that at one point his calculation was based on 10 bashos. This allows ratings to continue to exceed 9891, which would be the limit for six bashos of 15-0 otherwise. However, not even Hakuho has managed to go above that score. An analogous system is used for the lower divisions where the perfect score is 7-0. Another way of looking at the rating is that a value of, say 8478, means that the rikishi has an 84.78% chance of beating the average opponent that he has been facing in the previous year. This is the truth about all rating systems for sumo, boxing, tennis, etc. where there is no objective scoring system. We can only really rate players based on how they dominate (or not) their peers. Comparing Mike Tyson to Muhammad Ali just isn't really possible based on statistics alone. Similarly Hakuho and Nishinoumi - as we will see they are far apart in rating but to what extent this is because competition in 1910 was stiffer than it was in 2010 is impossible to divine just by looking at results. You can only compete against the people in front of you. So, let's look at some numbers. Here's the standings I calculated at the start of Natsu 2022: | Rank | Rating | Rikishi | |------+--------+--------------| | 1 | 8313 | Terunofuji | | 2 | 7021 | Abi | | 3 | 6848 | Mitakeumi | | 4 | 6471 | Oho | | 5 | 6232 | Takakeisho | | 6 | 5938 | Wakamotoharu | | 7= | 5882 | Nishikigi | | 7= | 5882 | Kotoshoho | | 9 | 5862 | Kotonowaka | | 10 | 5761 | Wakatakakage | | 11 | 5747 | Takayasu | | 12 | 5732 | Endo | | 13 | 5584 | Midorifuji | | 14 | 5444 | Hoshoryu | | 15= | 5435 | Shodai | | 15= | 5435 | Ichinojo | | 17 | 5326 | Tamawashi | | 18 | 5244 | Hokutofuji | | 19 | 5211 | Ishiura | | 20 | 5195 | Ura | | 21 | 5109 | Kiribayama | | 22= | 5000 | Onosho | | 22= | 5000 | Azumaryu | | 24 | 4894 | Sadanoumi | | 25 | 4891 | Daieisho | | 26 | 4783 | Takarafuji | | 27 | 4773 | Shimanoumi | | 28 | 4719 | Tochinoshin | | 29= | 4706 | Kotokuzan | | 29= | 4706 | Kagayaki | | 31 | 4677 | Yutakayama | | 32= | 4674 | Terutsuyoshi | | 32= | 4674 | Takanosho | | 34 | 4565 | Chiyotairyu | | 35 | 4524 | Aoiyama | | 36 | 4457 | Okinoumi | | 37 | 4375 | Ichiyamamoto | | 38 | 4348 | Kotoeko | | 39= | 4239 | Tobizaru | | 39= | 4239 | Chiyoshoma | | 41 | 4130 | Meisei | | 42 | 4111 | Myogiryu | And here's the standings for the same group post-Natsu 2022 (with the pre- and post- Natsu ratings for easier comparison): | Rank | Pre | Post | Change | | Prelim | |------+------+------+--------+--------------+--------| | 1 | 8313 | 8313 | 0 | Terunofuji | | | 2 | 7021 | 6452 | -569 | Abi | * | | 3 | 6848 | 6413 | -435 | Mitakeumi | | | 4 | 5862 | 6092 | 230 | Kotonowaka | | | 5 | 5938 | 5957 | 19 | Wakamotoharu | * | | 6 | 5584 | 5882 | 298 | Midorifuji | * | | 7 | 5761 | 5761 | 0 | Wakatakakage | | | 8 | 6232 | 5652 | -580 | Takakeisho | | | 9 | 5882 | 5625 | -257 | Nishikigi | * | | 10 | 5444 | 5556 | 112 | Hoshoryu | | | 11= | 5326 | 5543 | 217 | Tamawashi | | | 11= | 5109 | 5543 | 434 | Kiribayama | | | 13 | 4894 | 5484 | 590 | Sadanoumi | * | | 14= | 5435 | 5435 | 0 | Ichinojo | | | 14= | 4891 | 5435 | 544 | Daieisho | | | 16 | 5195 | 5385 | 190 | Ura | * | | 17 | 4674 | 5326 | 652 | Takanosho | | | 18 | 5747 | 5287 | -460 | Takayasu | | | 19 | 5732 | 5244 | -488 | Endo | | | 20 | 5211 | 5211 | 0 | Ishiura | * | | 21 | 5244 | 5122 | -122 | Hokutofuji | | | 22 | 4719 | 5056 | 337 | Tochinoshin | | | 23= | 5882 | 5000 | -882 | Kotoshoho | * | | 23= | 5435 | 5000 | -435 | Shodai | | | 25 | 5000 | 4940 | -60 | Onosho | | | 26 | 4524 | 4783 | 259 | Aoiyama | | | 27 | 4773 | 4773 | 0 | Shimanoumi | | | 28 | 4375 | 4681 | 306 | Ichiyamamoto | * | | 29 | 4677 | 4545 | -132 | Yutakayama | * | | 30= | 4783 | 4457 | -326 | Takarafuji | | | 30= | 4674 | 4457 | -217 | Terutsuyoshi | | | 30= | 4457 | 4457 | 0 | Okinoumi | | | 30= | 4239 | 4457 | 218 | Tobizaru | | | 34 | 4706 | 4375 | -331 | Kagayaki | * | | 35 | 4565 | 4348 | -217 | Chiyotairyu | | | 36 | 4130 | 4130 | 0 | Meisei | | | 37 | 6471 | 4118 | -2353 | Oho | * | | 38 | 4111 | 4111 | 0 | Myogiryu | | | 39= | 4348 | 4022 | -326 | Kotoeko | | | 39= | 4239 | 4022 | -217 | Chiyoshoma | | | 41 | 5000 | 3529 | -1471 | Azumaryu | * | | 42 | 4706 | 3125 | -1581 | Kotokuzan | * | Note that Terunofuji remained at the same rating as his score of 12-3 matched the score of 12-3 from Haru 2021, which has just dropped out of the rating history for him (since it wasn't a 15-0 result). When two rikishi meet I calculate a percentage chance for East to win based on this conceptual algorithm: Each bout is the result of a sequence of attempts to end it. Each wrestler has a chance of being successful equal to their rating/10000, so Shodai has a chance of 50%; Terunofuji 83.13%. If one wrestler is successful and the other is not, then the bout is over and the successful rikishi is the winner. Otherwise (i.e., neither or both succeed), the bout continues with another pair of attempts until there is a conclusive outcome. That's the idea, but although you could Monte-Carlo it and get an estimate we can convert this algorithm into an exact formula: Ec=((Ew x Wl) ÷ (1 - ((El x Wl) + (Ew*Ww)))) Where Ew is East's rating/10000, El is 1-Ew, and similarly Ww and Wl for West. Ec is the chance that East will win as a probability; multiply by 100 to get a percentage. Yeah, in El and Wl that's an 'el' but the font isn't good at distinguishing it from a capital i. So for Terunofuji Vs Shodai we get East's chance as 83.13%. Notice that because Shodai's current rating is 5000, he neither increases nor decreases his opponent's chance to win and any rikishi's chance (according to this system) can be calulated by simply dividing his opponent's score by 100. For Terunofuji Vs Daieisho (8313 Vs 5435), Terunofuji's chance drops to 80.5%, and against Abi's 6452 it is 73%. So that's the system and now, in defiance of what I said about not being able to compare across the decades, here's the Yokozuna rated by the highest scores they reached in their careers: | Rank | Rating | | |------+--------+--------------| | 1 | 9674 | Hakuho | | 2 | 9595 | Futabayama | | 3 | 9508 | Tachiyama | | 4 | 9375 | Taiho | | 5= | 9348 | Kitanoumi | | 5= | 9348 | Chiyonofuji | | 7 | 9273 | Tanikaze | | 8= | 9239 | Tamanoumi | | 8= | 9239 | Asashoryu | | 10 | 9180 | Tochigiyama | | 11 | 9130 | Takanohana | | 12 | 9091 | Hitachiyama | | 13 | 9070 | Umegatani | | 14= | 8971 | Tsunenohana | | 14= | 8971 | Tamanishiki | | 16 | 8913 | Tochinishiki | | 17 | 8889 | Inazuma | | 18 | 8871 | Haguroyama | | 19 | 8804 | Takanosato | | 20 | 8696 | Wakanohana | | 21 | 8681 | Wajima | | 22 | 8600 | Kimenzan | | 23 | 8596 | Onogawa | | 24= | 8587 | Wakanohana | | 24= | 8587 | Kitanofuji | | 26 | 8548 | Onishiki | | 27= | 8500 | Konishiki | | 27= | 8500 | Kashiwado | | 29= | 8478 | Terunofuji | | 29= | 8478 | Sadanoyama | | 29= | 8478 | Mienoumi | | 29= | 8478 | Akebono | | 33= | 8370 | Terukuni | | 33= | 8370 | Musashimaru | | 33= | 8370 | Hokutoumi | | 36 | 8333 | Umegatani | | 37 | 8261 | Asahifuji | | 38= | 8152 | Kisenosato | | 38= | 8152 | Harumafuji | | 40 | 8143 | Yoshibayama | | 41 | 8043 | Akinoumi | | 42= | 8000 | Otori | | 42= | 8000 | Jinmaku | | 44= | 7935 | Tochinoumi | | 44= | 7935 | Kotozakura | | 46 | 7925 | Onomatsu | | 47 | 7917 | Unryu | | 48 | 7872 | Hidenoyama | | 49 | 7826 | Kakuryu | | 50 | 7813 | Musashiyama | | 51 | 7750 | Nishinoumi | | 52 | 7727 | Azumafuji | | 53 | 7722 | Futahaguro | | 54= | 7717 | Wakanohana | | 54= | 7717 | Kagamisato | | 54= | 7717 | Asashio | | 57 | 7701 | Onokuni | | 58 | 7667 | Nishinoumi | | 59 | 7609 | Chiyonoyama | | 60 | 7586 | Maedayama | | 61 | 7561 | Shiranui | | 62 | 7556 | Shiranui | | 63 | 7455 | Ozutsu | | 64 | 7358 | Sakaigawa | | 65 | 7206 | Minanogawa | | 66 | 7045 | Nishinoumi | | 67 | 6078 | Miyagiyama | | 68= | 0 | Wakashima | | 68= | 0 | Onishiki | | 68= | 0 | Okido | | 68= | 0 | Maruyama | | 68= | 0 | Ayagawa | | 68= | 0 | Akashi | It's interesting to me how little overlap there is between this list and the current ratings, Miyagiyama (intai 1931) is the only one who would not be above all the current non-Yokozuna in the top flight. Rayden's peak rating was 9444, which would slot him into 4th place on the above list. There are a few problems. Firstly, I can't easily get the results of playoffs out of the database so the ratings do not consider scores of 16-0, 15-1 etc. The second major issue is what to do when people jump from one division to the other. It's certainly possible to come out of Juryo with a high rating and immediately get slapped down a couple of thousand points and at the moment the programs I use for my own purposes mark any rikishi who has not spent an entire six-basho stint in their current division as having a "preliminary" rating. Finally, it is clear that the top division at least has a boundary between the top half and bottom half with very little mixing during a tournament. This tends to make the top wrestler's scores lower than they should be as they only face the top opponents rather than a cross-sample of the division. I've not paid enough attention to the other divisions to know if this is an issue with them too. On the plus side, it avoids the inflation problem that plagues some systems and newbies and retirees do not overly trouble it. So, there you have it. That's what I do in my spare time :)

I deliberately avoided any attempt to allow for strength of individual opposition as that way leads to circular reasoning IMO. The approach was always to assume that a rikishi can only be rated based on how they perform relative to their peer group and trust that the banzuki generates a reasonable peer group by its nature. I realised it was a confusing mistake not to mark the ratings which are preliminary because the rikishi has not been in the division long enough for their score to "settle". I've updated the second table above to show the 14 wrestlers who's current rating should be taken with a variable amount of salt; everyone else has a rating based on at least 6 basho at the current level. 5 of the marked rikishi actually outperformed their preliminary rating; make of that what you will. Here's the top division with the preliminary ratings filtered out, perhaps you'll find these more reasonable: | Rank | Rating | | | 1 | 8313 | Terunofuji | | 2 | 6413 | Mitakeumi | | 3 | 6092 | Kotonowaka | | 4 | 5761 | Wakatakakage | | 5 | 5652 | Takakeisho | | 6 | 5556 | Hoshoryu | | 7= | 5543 | Tamawashi | | 7= | 5543 | Kiribayama | | 9= | 5435 | Ichinojo | | 9= | 5435 | Daieisho | | 11 | 5326 | Takanosho | | 12 | 5287 | Takayasu | | 13 | 5244 | Endo | | 14 | 5122 | Hokutofuji | | 15 | 5056 | Tochinoshin | | 16 | 5000 | Shodai | | 17 | 4940 | Onosho | | 18 | 4783 | Aoiyama | | 19 | 4773 | Shimanoumi | | 20= | 4457 | Tobizaru | | 20= | 4457 | Terutsuyoshi | | 20= | 4457 | Takarafuji | | 20= | 4457 | Okinoumi | | 24 | 4348 | Chiyotairyu | | 25 | 4130 | Meisei | | 26 | 4111 | Myogiryu | | 27= | 4022 | Kotoeko | | 27= | 4022 | Chiyoshoma | The thing about win probability calculations is that it is the only real test of any ranking system. In overly simplistic terms, any higher ranked competitor should beat a lower one. Adding a bit more meat onto that, the ranking should give some idea as to how often that rule can be expected to be broken.

In both cases, this is at least partly the problem of carrying ranks up with a promotion from a lower division. Neither of them have had much time in the top rank (in a row, at least). Having said that, Midorifuji did slightly better than his rating predicted in this basho, and performance is all one can really go on and a rating system should recognise when someone has hit form, shouldn't it? We shall see in July. Sumo is unusual compared to most Western sports in that the matches are neither fully round-robin nor knock-out. The committee decide who will face whom - moreso as the fortnight proceeds - and that poses challenges to any system that attempts to rate contestants based on their results as the sample of opponents is not random nor "fair". I've used this as the basis of (fantasy) betting for the last year and what I've found is that it generally gives very good results against the bookies at the start of the Basho but the accuracy tails off as fatigue and injuries set in from about day-10. Dynamically updating the ratings during the basho gave much worse results, however.

It's particularly odd since the official sumo phone app is blocked in the UK. But, I'm in. Assuming it happens.

On day 12 Abi (ranked #37) hadn't fought anyone higher than #19. The next day he was facing #3. That feels a bit less than "progressively" to me. I suppose that's a bit of hindsight and I guess he did actually lose the day 7 bout. Well, tomorrow will be interesting - Sunday, probably not so much. Unless Abi wins tomorrow, that is. Then Sunday might produce some fireworks.

That's what I was getting at: they should either slide the pressure up in stages or play the ranking chips where they fell. This "oh crap, he's doing well, throw him at the top guys quickly" seems very half-arsed. I'd personally prefer them to increase the pressure more gradually than the way they've done it here. It's inelegant.

I think they should have had the courage of their convictions - if an M15 gets to day-15 with the joint top score then have a play off. Artificially jumping him from facing people around his rank straight to an Ozeki and then immediately to the Yokozuna looks something like panic. Now they effectively have the final set up for day-14.

Whoever wins will face Terunofuji on day 14, and Shodai will face him on 15 as expected. Either Abi or Takakeisho will not face Terunofuji unless the latter loses and we end up with a play-off, I think.

Simple enough question: can two wrestlers from the same heya meet on the last day or only in playoffs? Has there ever been a period with two active Yokozuna from the same heya?

I had forgotten about Chiyonofuji and Hokutoumi being from the same stable. I enjoyed watching both of them back in the day. Hokutoumi had an excellent fighting spirit as I recall.

I thought there were lots of Bob Cats in America.

If you're in the running, you shouldn't be falling for tricks like that. A guy on 6-7 isn't there to do you any favours. It's hardly Onosho's first rodeo, is it?

All the more reason to put it in the opening ceremony, which is a statement of what is special about the host country.

I guess it's just relief, then. Although I still think the interviewer might have had a few.

Had any alcohol been consumed before these interviews, perchance?

But he was somewhere, watching...

And the pendulum will swing, as it always has.

It's one of those things. I understand why women would want to do sumo or anything else they have an interest in. I don't understand why I would want to watch it. I feel the same about weight/sex-segregated sports generally. Worst of all is tennis where women are paid the same for less effort and, by and large, a lot less quality too.

Do you mean James May? From Top Gear/Grand Tour?

That'll give them something to talk about when you go into the scanner booth at security. I suppose you could slap it to show that you don't have any weapons.

Wow. That shadow-people thing is really tasteless in a Japanese setting. Although I have recently watched a documentary about Nagasaki, so maybe I'm just feeling a bit sensitive to to the imagery.

I personally felt that there was a Nuremberg feel to some of the Beijing opening which I found unpleasant. Also, of course, they faked some of it on the broadcast with CGI which is a bit crap.

Giving up fags is a no-brainer, surely? From what I've seen of ex-smokers, the improvement in lung capacity is very rapid and you need oxygen to burn fuel for energy, which you need for effective exercise and any bout longer than 30 seconds. Booze is harder to quantify, but it is a poison which your system has to neutralize or you die from quite small doses (of alcohol), so maybe that's not too surprising either. In terms of weight, it's interesting that the normal sumo build is very similar to Olympic weight-lifters, at least to my casual eye. The guys that lift the big weights don't look anything like bodybuilders or gymnasts.