In this weekend, I've got asked about sumo match-fix scandal and realized that the news spreads the world over and people outside Japan are also interested in. I said to my friend "they have been doing that and media keep on hiding the fact. So, it's no surprise to me". After checking some blogs, I found out that a controversial book, Freakonomics by Levitt, mentioned sumo wrestlers are match rigging. I haven't read the book yet but there's a pdf file of his paper about corruption in sumo wrestling. Some quotes here:
The key institutional feature of sumo wrestling that makes it ripe for corruption is the existence of a sharp nonlinearity in the payoff function for competitors. A sumo tournament (basho) involves 66 wrestlers (rikishi) participating in 15 bouts each. A wrestler who achieves a winning record (eight wins or more, known as kachi-koshi) is guaranteed to rise up the of cial ranking (banzuke); a wrestler with a losing record (make-koshi) falls in the rankings. A wrestler’s rank is a source of prestige, the basis for salary determination, and also influences the perks that he enjoys
"Figure 1" on the paper demonstrates the importance of an eighth win to a wrestler.
The critical eighth win—which results in a substantial promotion in rank rather than a demotion garners a wrestler approximately 11 spots in the ranking, or roughly four times the value of the typical victory. Consequently, a wrestler entering the final match of a tournament with a 7-7 record has far more to gain from a victory than an opponent with a record of, say, 8-6 has to lose.
He found out the peak on 8-7 records. See below.
Figure 2 provides clear visual evidence in support of the model’s prediction. Approximately 26.0 percent of all wrestlers finish with exactly eight wins, compared to only 12.2 percent with seven wins.
There're some more interesting analysis such as a give-and-take case "What Happens When Wrestlers Meet Again in the Future" so download the pdf file to read a whole paper.
You might be disappointed with the fact but don't get wrong. Sumo is "professional" wrestling and you won't be noticed how they cheat. Just enjoy watching two naked fat guys hugging each other. ;p