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.
The first chart shows the Elo ratings of Yokozuna during their Yokozuna careers (click to enlarge).
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!
Now onto the second graph, charting the average Elo ratings of the Yokozuna's opponents.
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.
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?