Is sumo rigged?

Freakonomics is a current best-seller looking at real-world applications of economics. Steven Levitt, the author, says sumo is rigged.

That’s horrible! What’s his evidence? Well, wrestlers who have a 7-7 record on senshuraku, the last day of the bimonthly fifteen-day tournaments, and therefore face demotion if they lose, win 80% of their matches against opponents who have already notched their eighth victory and are safe from demotion, even though statistically they would be expected to win only 50%.

Further, in the next match between the same two wrestlers, the win-loss percentage is precisely reversed! In other words, the wrestler in the first match who is allowed to win then “repays” his opponent in the second match by letting him win.

Statistically, I’m sure the win-loss patterns the author discovered are not attributable purely to differences in skill. But that is not enough to condemn sumo as being “fixed”.

First, by definition, a game being fixed or rigged requires some quid pro quo. The authors of Freakonomics speculate about the possibility of bribes or payoffs, but of course have no way to validate that. Personally, I doubt that money is changing hands. The entire “transaction”, or “agreement”, to lose now and get paid back later, is probably non-verbal. It’s possible that it is not even entirely conscious.

But whether non-verbal or non-conscious, such behavior still offends our Western notion of fairness. We say: the wrestlers are “cheating.”

But in a way this behavior is entirely fair: anyone who enters the last day at 7-7 can expect to be given the same favorable treatment by any opponent who is 8-6. And the effect on rankings is smaller than you might think. It certainly does not rise to the level of a structural effect, like someone throwing a World Series game. The authors make the point that big money is at stake—yokozuna can make a million dollars a year, and being demoted out of juryo cuts off your salary altogether if I recall—but in fact any biasing of the results caused by shading 7-7 matches does not cause major swings in salary-related outcome values either.

Rather, the result is simply to put a bit of a damper on the ups and downs of the game—to decrease the standard deviation, if you will. Wrestlers the fans know and love may stay around a bit longer before getting demoted or retiring to open a chanko nabe restaurant.

Instead of making the pedestrian observation that money can lead people to cheat, a phenomenon hardly worthy of their attention, it would have been great if the authors could have brought some real insight to the sumo question, namely what the value function is that is maximized by the behavior in question—in this case, the Japanese values of stability, prestige, and solidarity.

One Response to “Is sumo rigged?”

  1. steve le Says:

    Where did you get that sumo doll. Do you want to sell it.

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