Freakonomics of Sumo

The incentive scheme that rules sumo is intricate and extraordinarily powerful. Each wrestler maintains a ranking that affects every slice of his life: how much money he makes, how large an entourage he carries, how much he gets to eat, sleep, and otherwise take advantage of his success. The sixty-six highest-ranked wrestlers in Japan, comprising the makuuchi and juryo divisions, make up the sumo elite. A wrestler near the top of this elite pyramid may earn millions and is treated like royalty. Any wrestler in the top forty earns at least $170,000 a year. The seventieth-ranked wrestler in Japan, meanwhile, earns only $15,000 a year. Life isn't very sweet outside the elite. Low-ranked wrestlers must tend to their superiors, preparing their meals and cleaning their quarters and even soaping up their hardest-to-reach body parts. So ranking is everything.

A wrestler's ranking is based on his performance in the elite tournaments that are held six times a year. Each wrestler has fifteen bouts per tournament, one per day over fifteen consecutive days. If he finishes the tournament with a winning record (eight victories or better), his ranking will rise. If he has a losing record, his ranking falls. If it falls far enough, he is booted from the elite rank entirely. The eighth victory in any tournament is therefore critical, the difference between promotion and demotion; it is roughly four times as valuable in the rankings as the typical victory.

So a wrestler entering the final day of a tournament on the bubble, with a 7-7 record, has far more to gain from a victory than an opponent with a record of 8-6 has to lose.

SOURCE: Freakonomics: A Rogue Economist Explores the Hidden Side of Everything, by Stephen D. Levitt and Stephen J. Dubner, pp. 40-44

Levitt compiles statistics that very strongly suggest that better opponents who have winning records (8-6 or 9-5) but are not in contention on the final day must have powerful (hidden) incentives to throw their bouts in order to give the 7-7 rikishi winning records of 8-7.

So, I thought I'd test that prediction against the recently completed Natsu Basho. Sure enough, on Day 14, there were 5 low-ranking (M = maegashira) rikishi with records of 7-7. And on the final day, as Freakonomics would predict, every single one of them ended up with a winning record of 8-7:

• Miyabiyama (M3) over Tamanoshima (M1, 5-10);
• Hokutoriki (M6) over Buyuzan (M12, 6-9);
• Kotonowaka (M8) over Kyokutenho (M3, 6-9);
• Aminishiki (M11) over Takekaze (M15, 9-6);
• Tokitenku (M15) over Asasekiryu (M8, 8-7).

Chances are better than even that any 7-7 rikishi will beat any rikishi with a losing record, as in the first three bouts listed. Only the last two bouts conform to the statistical pattern of Freakonomics, where 7-7 wrestlers have a record of beating 8-6 wrestlers 80% of the time on the final day, and 9-6 wrestlers almost 75% of the time on the last day, when their predicted odds would be a little under 50%.

But another factor enters into the bouts listed above. In every case except Hokutoriki (M6) over Buyuzan (M12), either a lower-ranking rikishi upset a higher-ranking one, or a rikishi with a worse record upset one with a better record. Relative rank isn't covered by Freakonomics. But the possibility of corruption is.

Several years ago, two former sumo wrestlers came forward with extensive allegations of match rigging--and more. Aside from the crooked matches, they said, sumo was rife with drug use and sexcapades, bribes and tax evasion, and close ties to the yakuza, the Japanese mafia. The two men began to receive threatening phone calls; one of them told friends he was afraid he would be killed by the yakuza. Still, they went forward with plans to hold a press conference at the Foreign Correspondents' Club in Tokyo. But shortly beforehand, the two men died--hours apart, in the same hospital, of a similar respiratory ailment. The police declared there had been no foul play but did not conduct an investigation. "It seems very strange for these two people to die on the same day at the same hospital," said Mitsuru Miyake, the editor of a sumo magazine. "But no one has seen them poisoned, so you can't prove the skepticism."

Whether or not their deaths were intentional, these two men had done what no other sumo insider had previously done: named names. Of the 281 wrestlers covered in the data cited above, they identified 29 crooked wrestlers and 11 who were said to be incorruptible.

What happens when the whistle-blowers' corroborating evidence is factored into the analysis of the match data? In matches between two supposedly corrupt wrestlers, the wrestler who was on the bubble won about 80 percent of the time. In bubble matches against a supposedly clean opponent, meanwhile, the bubble wrestler was no more likely to win than his record would predict. Furthermore, when a supposedly corrupt wrestler faced an opponent whom the whistle-blowers did not name as either corrupt or clean, the results were nearly as skewed as when two corrupt wrestlers met--suggesting that most wrestlers who weren't specifically named were also corrupt.

For more on Freakonomics, see the authors' blog, and the Stephen Levitt seminar hosted at Crooked Timber.

UPDATE: Tom of That's News to Me, who's far more conversant about sumo than I am (and who's just finishing up law school at the U. of Chicago), left an interesting comment:

I think there are a couple reasons Levitt doesn't mention that can help explain what's going on. First off, it could just be something as simple as comparative advantage; if the 7-7 rikishi has a strong tachiai, then match him up on Day 15 with someone who's not very good at tachiai defense. Second, I don't know that he gets the individual incentives quite right; the biggest marginal difference on Day 15 is a shot at the yusho or not, but that's relatively uncommon. The biggest recurring marginal difference is that between 8-7 and 7-8, so in a world strongly controlled by shared norms, we would expect to see something like this take place pretty consistently even without any other contact between the parties. Personally, I think this reason is alone in and of itself sufficient to explain everything we see that's going on, at least w/r/t 7-7's on Day 15. The sophisticated question, I think, is how much the Kyokai discounts the effects of the 8-7, W on Day 15 in doing the rankings, and, maybe more importantly, of the rikishi who took a dive to finish at 5-10 instead of maybe 6-9, and how he did relative to other 6-9's/5-10's.