How Freakonomics explains Hakuho’s non-promotion

A brief pause from the serious events of the world to ask a key question:

Dude, how did Hakuho not get promoted to yokozuna?

After a slow start to his basho – two losses by day 9, Hakuho won the remainer of his bouts to finish 13-2. That last, thirteenth win wasn’t exactly a minor achievement – it was the defeat of Asashoryu in what sounds like an excellent, tense bout. And the powers that be had indicated that Hakuho would likely be promoted if he won 13 of 15 and either won the tournament or was runner-up. 13, check. Runner-up, check. Promotion, nope.

The audience thought he deserved promotion, cheering the match with great vigor. But it was not to be:

However, the Mongolian 21-year-old’s hopes of making yokozuna after only his second tournament as an ozeki were dashed by association chairman Kitanoumi, who along with other officials, confirmed that Hakuho’s promotion–and that of sekiwake Miyabiyama to ozeki–would have to wait until after September’s tournament.

“The tournament had already been decided,” Kitanoumi said in reference to Asashoryu’s triumph on Day 14. “But Hakuho did a good job chalking up 13 wins. We just want to see another tournament.”

This last comment is an interesting one – Kitanoumi is implying that Asashoryu might not have fought as hard in his final match as he would have if Hakuho had been capable of snatching the Emperor’s Cup – Asashoryu’s 17th. Given that Asa and Hakuho are countrymen – causing commentators to refer to the match as “the Battle of the Khans” – there’s additional speculation that Asa might have wanted Hakuho to have the win.

You might view this as disrespectful to Hakuho for implying that he can’t beat Asa in a fair fight – he’s 4-7, by my count, not a bad record agains the yokozuna – or to Asashoryu for suggesting that the yokozuna might throw a match. But it may just mean that Kitanoumi is a fan of Freakonomics.

One of Steven Levitt’s most discussed (though, perhaps, not one of his most read) papers is a collaboration with Mark Duggan, titled “Winning Isn’t Everything: Corruption in Sumo Wrestling”. Quoting from the abstract:

A non-linearity in the incentive structure of promotion leads to gains from trade between wrestlers on the margin for achieving a winning record and their opponents. We show that wrestlers win a disproportionate share of the matches when they are on the margin. Increased effort can not explain the findings.

To unpack a bit: Finishing a tournament 7-8 is a lot worse than finishing 8-7. The difference between 9-6 and 8-7 is pretty minor – they’re both undistinguished winning records – while the difference between the 7-8 losing record and an 8-7 winning record can mean the difference between remaining at a high rank and being demoted, with commensurate losses in sponsorship, pay and so on. So when two rikishi face off on the 15th day, with one at 7-7 and one at 8-6, the first rikishi has a lot more on the line than the second.

Using statistical techniques I don’t even pretend to understand, Levitt and Duggan demonstrate that just sheer effort can’t explain how often the 7-7 rikishi wins those matches – they speculate that rigging takes place, observing that matches with wrestlers in the same stable show strong rigging evidence, and that rigging tends to decrease in times of increased media scrutiny.

The point in this case is that there is some part of the phenomenon attributable to increased effort. Asa is going to win the Emperor’s Cup whether he finishes 14-1 or 15-0. Hakuho, however, has lots more on the line – at 13-2, he believes he’s going to get promoted, while at 12-3, the probably won’t be. Perhaps he gives just a bit more and Asa a bit less, even if the two haven’t discussed the situation, made any agreements or chosen to consciously throw the match.

One way or another, we’ve now got a rikishi who can consistently threaten the Yokozuna… unlike the other ozeki, who largely struggled to put together barely-winning records. Whether Hakuho is promoted now or after the next tournament, it’s coming soon, and it should make sumo even more exciting to watch.