Who is exactly the closest and farthest from average?
Top 10 and Bottom 10 by Hellinger metric
Let’s just cut to the chase (and I had some time to sit down during the holiday to just calculate the stats): Midorifuji is the farthest from the average of the Makuuchi wrestlers and Nishikifuji (for now) is the closest.
Measuring “averageness” by Hellinger
Reminder: the Hellinger metric measures a probability distribution against some standard distribution. It ranges from 0 to 1. If it’s 0, it matches exactly; if it’s 1, it’s as disparate from the “standard” distribution as much as possible.
The formula for discrete distributions is this:
I’m using as my “average” the sumo database win percentages by kimarite as of November 2023 (it doesn’t much matter what day, given how far back the database reaches).
For the Makuuchi wrestlers, I’m looking at their win percentages, as of 24 November or 25 November 2023. One day doesn’t make a big difference, especially when it’s only one among hundreds of wins for a wrestler.
Top-ranked by Hellinger metric
Not surprisingly from the earlier post, Midorifuji is the top-ranked by Hellinger metric, having a very high percentage of his wins coming from the kimarite katasukashi, which very few rikishi use.
I will note that many “Lords of Chaos” are seen in this top-ranked list — I had profiled my faves Ura and Tobizaru earlier, but Abi is also well-known for messing many wrestlers’ runs at tournament wins, for instance.
I will note there is quite a mix of both newbies and old pros in this top-ranked list. There is a question whether the newbies, who may have used their weird mix of kimarite to rise to Makuuchi, may be able to keep using those particular tricks to stay there.
Henkas may be cute in Juryo, but ….
(A discussion for later).
Bottom-ranked (i.e. most average) rikishi
Remember, this means most average in the distribution of their winning kimarite.
Now, interesting to me is that Kotonowaka wasn’t even the closest to 0 — that lowest spot (for now) goes to Nishikifuji.
The reason I say "for now” is that Nishikifuji is in danger of falling down to Juryo.
But I will note that these “typical” wrestlers do tend to be the more experienced wrestlers, and are often rank-and-filers.
I do see the supposed “Lord of Chaos” Shodai is in there, but he is designated Lord of Chaos not due to his technique, but for “showing up” and dominating… when he seems to be “on”. It’s difficult to know when he’ll be “on”, though.
I will do more with this Hellinger metric later, from other slices. I like how this might be a first slice at distinguishing wrestlers being somewhat unusual.
Spreadsheet
Note: Each wrestler has their own tab in the spreadsheet. They’re hidden (because that’s 42 tabs… it got unwieldy) - so just unhide to look at the wrestler you want to see.