Yokozuna Strength, Opponent Strength, and Yokozuna Dominance

[Randomitsuki 2,843]

Hiya.

There have frequently been discussions (here and elsewhere) about the strength and/or dominance of Yokozuna. Is Hakuho just the best ever, or is he just lucky to have a bunch of mediocre rikishi around him?

A couple of days ago I realized that I have the data to address some of these questions. It was quite an epic undertaking, with 20+ hours of work going into it. I had all the data available, but they were distributed over hundreds of files, and took a while to extract. Anyway, here is what I did.

A couple of years ago, I began collecting Elo ratings for all SumoDB bouts since 1934. Elo ratings can be quite fickle: it is harder, though not impossible, to achieve high ratings with less bouts in a basho, less basho in a year, and less rikishi on the banzuke. Therefore my analyses began with all Yokozuna since the advent of the 6-basho era. I took the Elo ratings of all their bouts during their respective Yokozuna tenures. Moreover, in order to address the issue of dominance, I also recorded the Elo ratings of all their opponents. This allowed me to compute average Elo ratings for each basho of a Yokozuna, and, if the Yokozuna weren't kyujo, the average Elo ratings of their opponents for each basho.

I will present the data in four charts.

YOKOZUNA STRENGTH

The first chart shows the Elo ratings of Yokozuna during their Yokozuna careers (click to enlarge).

Some observations:

There are rikishi who made Yokozuna while still improving, thus giving us something like a bell curve for their careers (Taiho and Kitanoumi are good examples). Other Yokozuna probably "fluked" into their promotion as a career highlight, and went downward from there on (Asashio, Tochinoumi, Kotozakura, Mienoumi, Takanosato, Asahifuji, Wakanohana; potentially also Harumafuji and Kakuryu).

As can be seen from the overall gestalt of the graph, Yokozuna from the 1960s onward were much stronger than the first two on the list (for instance, at the end of his career Asashio had an Elo rating of about 2080. To put this into perspective, that is the current level of a guy like Sadanoumi on the current banzuke).

Starting with Asashoryu, ratings went through the roof, a potential effect of the internationalization of sumo. Asashoryu bested age-old Elo ratings of Taiho, and Hakuho simply annihilated Asashoryu's records. The highest moment-to-moment rating of Hakuho was incredible 2690 points during Natsu 2011. Even Harumafuji and Kakuryu are not much weaker than Chiyonofuji, according to these data! Consequently, one could say that the most unfortunate Yokozuna of all time is Harumafuji - better than most on the list, but still a perennial also-ran

There has also been talk about great rivalries recently. And the classic candidates show nicely on this graph: Kashiwado was second fiddle to Taiho for about five years, but then his rivalry (but not his career) ended. Wajima/Kitanoumi were also a nice couple, spiced up later by guys like Wakanohana and Mienoumi. Akebono/Takanohana was also a great matchup, specifically as the Japanese had the upper hand from 1994 to 1997, but Akebono was slightly better after that.

It would be interesting to see what would have happened if Tamanoumi didn't die aged 27. He was about to potentially become a rikishi with incredible dominance.

Wajima and Takanohana have very interesting curves with a very notable dip, followed by a comeback to former glory.

Nice to see how Chiyonofuji became better and better during his tenure. I also had not known that Akebono had to finish his career while being on his highest rating ever!

OPPONENT STRENGTH

Now onto the second graph, charting the average Elo ratings of the Yokozuna's opponents.

Some notes:

There are some zigzag patterns with a particularly low opponent rating. This typically happens when a Yokozuna went kyujo after few days, having faced only low-rankers thus far.

Once again, we can see two boosts in average opponent strength. One steady improvement from 1958 to 1965. And the internationalization effect kicking in since the Akebono tenure.

On average, Yokozuna opponents have never been as strong as in the last few years! This puts the talk about mediocrity among current rikishi into some perspective, hopefully.

On a final note, one can nicely see the Futagoyama effect in the mid-1990s. Akebono had a much, much tougher schedule than Takanohana.

YOKOZUNA DOMINANCE

Now onto the dominance patterns. I computed this graph by looking at the average difference between a Yokozuna during a basho and his opponents during the same basho. Here are the data:

First, we can see that there is no general trend. Throughout modern history, the average difference between a Yokozuna and his opponents was between 150 and 300 rating points. Of course, there are some phases of incredible Yokozuna dominance. The first mention goes to Taiho who had very weak opposition during the second half of the 1960s. At the end of the 1970s, Kitanoumi was without serious opposition for some years. The late 1980s saw incredible dominance by Chiyonofuji, though not quite on Taiho levels. It appears that Takanohana was very dominant in the late 1990s, but keep in his mind that his opponents were in fact much weaker than Akebono's due to Futagoyama-beya's overall dominance. Asashoryu was without serious rival until Hakuho began an era of unprecedented dominance, even surpassing Taiho levels.

What does that mean with regard to Hakuho? On the one hand, he is the best ever by pure Elo rating levels. On the other hand, his opponents are no muppets, and many of them have the strength of former Yokozuna (Kisenosato and Terunofuji come to mind with Elo ratings of more than 2300 points). On the third hand, however :-), Hakuho has no trouble coping with the better opponent levels, easily playing in a league of his own, dominance-wise.

THE BOTTOM LINE

On a final note: here is a graph for those people who find the upper graphs to wiggly. It shows the average career Elo rating of each modern Yokozuna during their tenure, and the average Elo rating of all their respective opponents. This graph is somewhat difficult to interpret, as some Yokozuna prolonged their careers to their bitter ends, while others miss the downward spiral due to injuries, death, or the benefit of still being active.

In terms of average Elo ratings, Hakuho is numero uno, with Asashoryu a very distant second. Harumafuji and Kakuryu are currently in third and fourth place, but this might change (probably not upwards...). Among retired rikishi, Taiho, Tamanoumi, and Chiyonofuji also stick out.

Kakuryu, Harumafuji, and Hakuho are the top three when it comes to opponent strength, another indicator that sumo might be much more high-profile right now than in ages past.

As for the biggest difference between Yokozuna and their opponents, Hakuho easily leads, with Taiho and Chiyonofuji being far behind in second and third, respectively.

Any comments on that?

Edited August 16, 2015 by Randomitsuki

[ScottyJoyJrBebe 97]

May I just give my thanks and admiration for such a well-presented, well-explained and well-researched topic. If your ever in Hawaii, let me know, you have earned dinner on me!!!

(One day, a game manufacture will take a chance, and create a sumo game with all the greats in it, able to challenge one another in fantasy bouts we can only dream of. One day)

[Asashosakari 19,614]

Many thanks! (I am not worthy...)

OPPONENT STRENGTH

Once again, we can see two boosts in average opponent strength. One steady improvement from 1958 to 1965. And the internationalization effect kicking in since the Akebono tenure.

I suspect the first part of that late 1990s/2000s increase is due to the extremely strong recruiting numbers in the first half of the 1990s. Similarly, I wouldn't be surprised if the dip around the late 1970s/early 1980s is based mostly on the ailing nature of Ozumo's recruiting about 10 years earlier.

Still though, neither deviation seems all that large, perhaps lending support to my contention from a few months ago that getting 200 shindeshi a year isn't necessarily that much of a competitive boost for (upper) makuuchi compared to getting just 80-ish.

That further increase over the last 10 or so years, though...wow.

[torquato 1,075]

Wow. Very Impressive!

However, one question. Did you take possible inflation into consideration? https://en.wikipedia.org/wiki/Elo_rating_system#Ratings_inflation_and_deflation

[Gurowake 4,099]

Impressive work.

What I really want to know is how many Yokozuna were better than Kisenosato. He's not that much worse than the two lowly Yokozuna we have now, and you're saying that those two Yokozuna rank only behind Asashoryu and Hakuho.

[sesom 55]

Very impressive! Thank you for providing this data!

[Randomitsuki 2,843]

Wow. Very Impressive!

However, one question. Did you take possible inflation into consideration? https://en.wikipedia.org/wiki/Elo_rating_system#Ratings_inflation_and_deflation

I am aware of ratings inflation. My method to counteract for it involves adjusting the ratings after every basho so that the average ratings on the banzuke (set at 1500 points) remains the same.

[Randomitsuki 2,843]

What I really want to know is how many Yokozuna were better than Kisenosato. He's not that much worse than the two lowly Yokozuna we have now, and you're saying that those two Yokozuna rank only behind Asashoryu and Hakuho.

Harumafuji and Kakuryu rank only behind Hakuho and Asashoryu when you look at the Elo totals. However, it is highly probable that their average will drop down as they wander along the downward path of the bell curve.

Maybe a better (and new) statistic is the highest Elo rating ever achieved (assuming that Harumafuji and Kakuryu have already peaked). Here are the 27 modern Yokozuna, sorted by peak rating.

 1 Hakuho         2690    Natsu 2011 after day 12
 2 Asashoryu      2558    Hatsu 2007 after day 15
 3 Taiho          2524    Kyushu 1967 after day 10
 4 Kitanoumi      2517    Aki 1978 after day 8
 5 Chiyonofuji    2502    Kyushu 1988 after day 14
 6 Harumafuji     2488    Haru 2013 after day 2
 7 Tamanoumi      2483    Aki 1971 after day 4
 8 Takanohana     2467    Hatsu 1997 after day 3
 9 Akebono        2448    Kyushu 2000 after day 15
10 Kakuryu        2442    Natsu 2014 after day 3
11 Mienoumi       2412    Haru 1980 after day 1
12 Musashimaru    2409    Nagoya 2001 after day 10
13 Kitanofuji     2404    Aki 1970 after day 2
14 Wakanohana II  2403    Nagoya 1979 after day 9
15 Takanosato     2398    Haru 1984 after day 4
16 Wajima         2395    Aki 1977 after day 5
17 Hokutoumi      2381    Haru 1989 after day 11
18 Kashiwado      2371    Aki 1967 after day 1
19 Asahifuji      2355    Aki 1990 after day 12
20 Sadanoyama     2351    Nagoya 1965 after day 11
21 Onokuni        2330    Kyushu 1987 after day 1
22 Futahaguro     2325    Aki 1986 after day 2
23 Kotozakura     2322    Nagoya 1973 after day 15
24 Wakanohana III 2312    Nagoya 1998 after day 5
25 Wakanohana I   2308    Aki 1960 after day 14
26 Tochinoumi     2265    Natsu 1964 after day 15
27 Asashio        2215    Natsu 1959 after day 2

For convenience, I did not look at the current Ozeki on a day-by-day basis, but only at their ratings at the end of each basho. That being said, Kisenosato's peak rating was at least 2434 points, so he would feature in 11th place out of 28 Yokozuna, directly behind Kakuryu. Or, if you only look at the relatively recent ones, Kisenosato in his prime was better than Musashimaru at the top of his game.

BTW, the peak ratings of Kotoshogiku and Goeido are 2361 and 2347, respectively.

Edited August 17, 2015 by Randomitsuki

[Chiyozakura 148]

I really like these kind of ratings and yours is well structured so good job! What surprises me is the high rankings of Kakuryu and Harumafuji. Kakuryu had just two outstanding basho in his whole career and as a Yokozuna has ranged between 9-6 and 12-3. How come that he is equal to Chiyonofuji and Taiho? Kotoshogiku's ranking also appears too high. Why does he surpass Asahifuji, who averaged 12 wins for quite some time? At the same time Wakanohana I's ranking appears very low which makes me believe that there indeed is an "inflation".

[Gurowake 4,099]

I think it's partly a numbers thing, just taking the results of crunching the numbers. If you want a more theoretical explanation, I would suggest that it's those at the top are more reliably beating those that are not at the top, and those just below the top are more reliably beating those that are a little further below the top, etc. Is that really true? Well, it's certainly true for Hakuho, and for everyone else, well, we have the results of running the numbers to suggest that it's true. It's hard to point to exactly what the deal is that's causing the ratings to come out higher, but if as he suggests the average rikishi on the banzuke maintains a steady rating while those on top end up with higher ratings, the cause of the inflation at the top must be due to them actually being relatively better compared to average than those in the past. It's hard to say whether they are absolutely better since they'll never face each other at their respectively peaks, but given the results we've seen, they're relatively better than their competition.

[Randomitsuki 2,843]

I really like these kind of ratings and yours is well structured so good job! What surprises me is the high rankings of Kakuryu and Harumafuji. Kakuryu had just two outstanding basho in his whole career and as a Yokozuna has ranged between 9-6 and 12-3. How come that he is equal to Chiyonofuji and Taiho? Kotoshogiku's ranking also appears too high. Why does he surpass Asahifuji, who averaged 12 wins for quite some time? At the same time Wakanohana I's ranking appears very low which makes me believe that there indeed is an "inflation".

Fair enough.

There is the classical problem of inflation/deflation which is caused by the overall average ratings going up or down, and all I can assure that this problem has been taken care of. The average rating stays at 1500. What indeed happened is that the difference between the best and the worst rikishi on the banzuke has widened over the last decades: Makuuchi, Juryo, Makushita, and Sandanme ratings have slightly gone up, and this is balanced by Jonidan and Jonokuchi ratings going down. I think there is good reason to believe that this widening of the gap is a "truth", and not some statistical artifact. Isn't it to be expected that the difference between good and bad rikishi increases when more people are recruited (including more international recruitments)?

Edit: Or, as Gurowake says (who beat me to it).

Edited August 17, 2015 by Randomitsuki

[Kasutera 258]

This is a fantastic compilation of data. Thanks for putting the effort into the gathering and analysis.

[Gurowake 4,099]

Also, I have my own independently conceived rating system, although based on an Elo form, and I concur about the times of peak ratings of Hakuho and Harumafuji, although I have them closer by 12 points. For Kakuryu, for the peak indicated, I have him almost exactly the same number of points below Hakuho's peak (I have 249, Rando says 248). However, I also have Kakuryu currently higher rated than he was then, although only by 2 (and peaked 5 higher before his Day 15 loss to Hakuho last basho). I also have Kisenosato peaking 7 points higher (Day 15 Kyushu 2013) than Kakuryu's Natsu 2014 peak, so for those we're in disagreement around 15 points.

I'm using only relative values as we definitely have a different base value we're starting with, while I assume we're using the same Elo-based curve for win probabilities (1/(1+10^(dR/400)). We're almost certainly using different K-values and handling new rikishi differently, and I'm not doing any normalization (and my data is only back to Hatsu 2007, and I can't suggest that it's even close to accurate for 3 years after that, so I can't say anything about when Asashoryu peaked).

Edited August 17, 2015 by Gurowake

[Asashosakari 19,614]

What indeed happened is that the difference between the best and the worst rikishi on the banzuke has widened over the last decades: Makuuchi, Juryo, Makushita, and Sandanme ratings have slightly gone up, and this is balanced by Jonidan and Jonokuchi ratings going down. I think there is good reason to believe that this widening of the gap is a "truth", and not some statistical artifact. Isn't it to be expected that the difference between good and bad rikishi increases when more people are recruited (including more international recruitments)?

I think it's more because "bad" rikishi stay around much longer these days, so they get beaten by a greater number of better rikishi along the way. The sandanme and jonidan divisions were much younger and more of a mixed bag in the past, nowadays they're full of rikishi who will definitely not get much better anymore, but still stay in sumo for a long time.

By the same token, the average quality in the higher divisions has likely gone up. There used to be loads of makushita-quality rikishi who would quit around or before age 25 (sometimes even after proving their talent with a handful of juryo appearances) - these rikishi are much more career-oriented now and will stick around with the hope of moving up further, even after temporary setbacks. Considering most rikishi with talent don't peak until around age 27-29, there's almost certainly more depth now because of that.

At the same time Wakanohana I's ranking appears very low which makes me believe that there indeed is an "inflation".

There might be an effect of the smaller number of tournaments pre-1958 (fewer opportunities for top-quality rikishi to demonstrate their skills and improve their rating), though perhaps there's a correction factor for that in the system - Randomitsuki?

In addition, the scheduling exemptions were more complex - various rikishi who would face off under current rules didn't at the time (Wakanohana and Taiho, Chiyonoyama and Tochinishiki, and so on), which likely depressed everyone's ratings: considering those softer schedules, many high-rankers in the 1950s really should have won more bouts than they did. Not so coincidentally the whole decade was known to have fairly unimpressive and often injured high-rankers (the latter leading to yet even softer schedules). It's conceivable that Tochinishiki [not covered here, as pre-1958] and Wakanohana with their 10 yusho apiece weren't nearly as impressive in quality terms as those yusho totals imply, much like Musashimaru was the beneficiary of some good timing late in his career (though for a shorter amount of time, and he took greater advantage of it due to his consistency).

Edited August 17, 2015 by Asashosakari

[Suwihuto 133]

With the availability of data for Sumo, I was thinking of doing something similar until I saw this thread! I already am working on similar data for rugby league.

[Randomitsuki 2,843]

At the same time Wakanohana I's ranking appears very low which makes me believe that there indeed is an "inflation".

There might be an effect of the smaller number of tournaments pre-1958 (fewer opportunities for top-quality rikishi to demonstrate their skills and improve their rating), though perhaps there's a correction factor for that in the system - Randomitsuki?

Very early ratings are probably shaky, so I did not go back to Yokozuna until 1934.

I am not using any correction formula to account for fewer basho a year or fewer rikishi on the banzuke. This, of course, creates some "problems" (or maybe "truths"?).

For instance, in Hatsu 1953, 13% of all rikishi on the banzuke were in Makuuchi! If we look at the numbers today, the top 13% cover the range not only of Makuuchi, but also Juryo and Makushita-joi. This in itself might explain why ratings were much lower back then. If a Yokozuna fought guys who were M6 back then, this would be tantamount to a Yokozuna of today meeting M16 rikishi on a regular basis. Yokozuna of 1953 simply could not gain that many Elo points. Add to that the fact that few Yokozuna of the 1950s had zensho yusho (in spite of weak opposition), and their low ratings might be explained.

In 1959, only six years later, the number of total rikishi doubled, and only 6.5% of all rikishi were in Makuuchi. That number is much more in line with current standards. As these effects have a non-immediate impact, it might have taken a while until the ratings accommodated to this "modern" standards.

[Doitsuyama 1,192]

I did a quite similar undertaking some years ago (2004, 2005, 2006, 2010) without these nice graphs but with some numbers and not restricted to Yokozunae. Many results are of course similar, with the biggest deviation being that I took only results from juryo and makuuchi as the lower divisions varied so much during the decades that I feel the assumption of a constant average of 1500 is a fallacy possibly leading to bad results. Anyway, I do have Asashoryu behind Taiho, Kitanoumi, Tamanoumi and Chiyonofuji which seems like a good debate coming up. [;)]

Hakuho of course is the best yokozuna ever and any argument to put him behind somebody else has to resort to "feeling" or other non-logic, well demonstrated in the other thread.

[Randomitsuki 2,843]

I did a quite similar undertaking some years ago (2004, 2005, 2006, 2010) without these nice graphs but with some numbers and not restricted to Yokozunae. Many results are of course similar, with the biggest deviation being that I took only results from juryo and makuuchi as the lower divisions varied so much during the decades that I feel the assumption of a constant average of 1500 is a fallacy possibly leading to bad results. Anyway, I do have Asashoryu behind Taiho, Kitanoumi, Tamanoumi and Chiyonofuji which seems like a good debate coming up. [;)]

Wow, there are really some striking differences between your ratings and mine (e.g. Chiyonofuji's peak is 88 points behind Taiho's according to your scheme, while I have the difference at only 22 points). And here I thought that every Elo ratings system using the same weighting factors (I think we both use K = 20), would eventually settle on identical or at least highly similar differences among rikishi!

I guess the only way to determine which system works better would be to "predict" historical sumo results based on Elo ratings alone. If you are interested in setting up such a comparison, please let me know!

Edited August 17, 2015 by Randomitsuki

[Asashosakari 19,614]

For instance, in Hatsu 1953, 13% of all rikishi on the banzuke were in Makuuchi! If we look at the numbers today, the top 13% cover the range not only of Makuuchi, but also Juryo and Makushita-joi. This in itself might explain why ratings were much lower back then. If a Yokozuna fought guys who were M6 back then, this would be tantamount to a Yokozuna of today meeting M16 rikishi on a regular basis. Yokozuna of 1953 simply could not gain that many Elo points. Add to that the fact that few Yokozuna of the 1950s had zensho yusho (in spite of weak opposition), and their low ratings might be explained.

That's a good point about the early post-WWII period. My gut feeling is that talent levels don't quite scale linearly across the whole spectrum - if there are 400 rikishi in total and 20 of them are above a given talent level, I suspect there will be somewhat fewer than 40 with 800 total. But certainly more than 20, so it's bound to have at least some effect on the overall competition. (The greatest relative increase in the number of rikishi should be somewhere around the middle of the talent distribution.)

And a related factor is the eternal debate about the effect of the increasing number of rikishi joining out of high school and university. (The older foreign recruits belong in here, too, of course.) The filtering process between age 15 and 23 still takes place, it's just that it takes place outside of the Ozumo framework - where it might have taken 20 middle school recruits to "produce" one makuuchi-caliber rikishi in the past, perhaps it now takes only 10 recruits out of high school or 5 out of university. The other 10/15 kids still exist, they just never show up on a banzuke, so it should take fewer official recruits to get to the same competitive landscape as before. (Of course, it's possible that today's shindeshi numbers are still relatively low even in age-adjusted terms.)

Anyway, this might explain why things already started to accelerate in the late 1990s - very high overall recruiting plus an improvement in the age structure of those recruits, for a massive influx of talent (centered around the famed 1976 generation with its 16 makuuchi rikishi). And then from about 2000 onward the massive wave of foreign recruiting added to it and kept it going, even while the overall shindeshi numbers declined again.

[Asashosakari 19,614]

Wow, there are really some striking differences between your ratings and mine (e.g. Chiyonofuji's peak is 88 points behind Taiho's according to your scheme, while I have the difference at only 22 points).

Perhaps your re-averaging is the cause of that? Taiho's peak came right in the middle of a massive retirement wave. I can't even guess if that resulted in upward or downward adjustments though.

[Randomitsuki 2,843]

Wow, there are really some striking differences between your ratings and mine (e.g. Chiyonofuji's peak is 88 points behind Taiho's according to your scheme, while I have the difference at only 22 points).

Perhaps your re-averaging is the cause of that? Taiho's peak came right in the middle of a massive retirement wave. I can't even guess if that resulted in upward or downward adjustments though.

That couldn't explain it. First of all, a retirement wave would increase rather than decrease ratings, making the difference between Taiho and Kitanoumi even more difficult to explain. Moreover, the adjustments are relatively small, sometimes zero points, sometimes 1 or 2 between bashos. Even the mother of all retirement waves (yaocho scandal of 2011) led to an increase of only 6 points per rikishi.

[Gurowake 4,099]

Many results are of course similar, with the biggest deviation being that I took only results from juryo and makuuchi as the lower divisions varied so much during the decades that I feel the assumption of a constant average of 1500 is a fallacy possibly leading to bad results.

This almost certainly will lead to different results, and it has nothing to do with differences between the decades: not everyone enters Juryo at the same skill level relative to others there. If you assign Ichinojo and Mitakeumi the same initial rating upon entering Juryo as Kotoeko and Wakanoshima, you're throwing away a lot of information. While any deviations from their true relative rating will be corrected over time, the cumulative effect is to not be injecting enough points into those rikishi who are far more likely to make it through Juryo and the bottom of Makuuchi and thus depressing ratings in the top of the division.

Edited August 17, 2015 by Gurowake

[Asashosakari 19,614]

That couldn't explain it. First of all, a retirement wave would increase rather than decrease ratings, making the difference between Taiho and Kitanoumi even more difficult to explain. Moreover, the adjustments are relatively small, sometimes zero points, sometimes 1 or 2 between bashos. Even the mother of all retirement waves (yaocho scandal of 2011) led to an increase of only 6 points per rikishi.

I should have clarified that it was a wave of retirements all over the banzuke, not just sekitori, hence my notion that it might have driven ratings up because it also involved a boatload of unremarkable rikishi probably rated below 1500 points (just possibly not enough of them). But if the magnitude of the adjustments isn't nearly large enough anyway then that idea goes out the window. Never mind. :-) Edited August 17, 2015 by Asashosakari

[Asashosakari 19,614]

This almost certainly will lead to different results, and it has nothing to do with differences between the decades: not everyone enters Juryo at the same skill level relative to others there. If you assign Ichinojo and Mitakeumi the same initial rating upon entering Juryo as Kotoeko and Wakanoshima, you're throwing away a lot of information. While any deviations from their true relative rating will be corrected over time, the cumulative effect is to not be injecting enough points into those rikishi who are far more likely to make it through Juryo and the bottom of Makuuchi and thus depressing ratings in the top of the division.

I may have an error in my thinking here, but doesn't that also depend on the observed average entry level in the more finely-detailed approach? If Ichinojo ends up reaching juryo with 1900 points in your system and Kotoeko does with 1700, would that make a significant difference to the overall (longer-term) results compared to both coming in with 1800 each? And beyond that: If Kotoeko is coming in with an artificially high rating and then goes 4-11, he's going to transfer a lot more points to the sekitori regulars before he drops out of sight again, so I'm not sure the "not enough points being injected" notion fully holds.

[Gurowake 4,099]

This almost certainly will lead to different results, and it has nothing to do with differences between the decades: not everyone enters Juryo at the same skill level relative to others there. If you assign Ichinojo and Mitakeumi the same initial rating upon entering Juryo as Kotoeko and Wakanoshima, you're throwing away a lot of information. While any deviations from their true relative rating will be corrected over time, the cumulative effect is to not be injecting enough points into those rikishi who are far more likely to make it through Juryo and the bottom of Makuuchi and thus depressing ratings in the top of the division.

I may have an error in my thinking here, but doesn't that also depend on the observed average entry level in the more finely-detailed approach? If Ichinojo ends up reaching juryo with 1900 points in your system and Kotoeko does with 1700, would that make a significant difference to the overall (longer-term) results compared to both coming in with 1800 each? And beyond that: If Kotoeko is coming in with an artificially high rating and then goes 4-11, he's going to transfer a lot more points to the sekitori regulars before he drops out of sight again, so I'm not sure the "not enough points being injected" notion fully holds.

It may well be the case that due to enough mixing between the divisions that any lack of points weak rikishi bring in tend to pull down the average in the top of the banzuke in the same way that those with more points are bringing them up comparatively. I don't have any sort of proof or anything to demonstrate why I think the injection of more points among those that head to the top of the banzuke will do more than the overall effect of injecting fewer with those that hang around Makushita more. I have a general feeling that those that are just barely good enough to be sekitori a few times will be in general much closer in a system that ignores deshi tournaments to where they would be in a system that considers them compared to the difference that would manifest between those of Ichinojo's caliber. Now, there are a lot more of the former, so maybe the effects actually tend to be a wash. I don't have any idea really. But I do know that you're going to be systematically underrating those that come hot into Juryo and speed their way up, and those are the folks who will tend to make up the top ranks, and those that make it there the slow way will be overrated. While these effects will eventually wash out through the magic of Elo, with new rikishi always making their way up the effect is continually being renewed. So basically you're causing a bias in your system towards rikishi who weren't that good when they hit Juryo comparatively, and I think in general that those people make up fewer of the top ranks.