In a sumo tournament, all wrestlers in the top division compete in 15 matches and face demotion if they do not win at least eight of them. The sumo community is very close-knit, and the wrestlers at the top levels tend to know each other well. The authors looked at the final match, and considered the case of a wrestler with seven wins, seven losses, and one fight to go, fighting against an 8–6 wrestler. Statistically, the 7–7 wrestler should have a slightly below even chance, since the 8–6 wrestler is slightly better. However, the 7–7 wrestler actually wins around 80% of the time. Levitt uses this statistic and other data gleaned from sumo wrestling matches, along with the effect that allegations of corruption have on match results, to conclude that those who already have eight wins collude with those who are 7–7 and let them win, since they have already secured their position for the following tournament. Following condemnation of the claims by the Japan Sumo Association, the 2011 Grand Tournament in Tokyo was canceled- the first time since 1946 -due to allegations of match-fixing.
Great point; there's more to sumo matches than just numbers. For example, a wrestler has to decide whether they're going to "go all out" for a match or not. If they do, they'll perform better but there's a higher chance of injury.
You can see Takayasu make this calculation when he gets up against the rope, a lot of time he'll just nope out of it. I imagine a lot of things go into this kind of decision: their age, the state of their injuries, the quality of their opponent, and how much they actually need this victory. Obviously if they've already got their winning ratio then they don't need it as much.
Unfortunately that wikipedia article makes it sound like the book caused the 2011 cancelation and match-fixing scandal. On the contrary it was caused by a police investigation into baseball gambling which uncovered incriminating text messages with sumo wrestlers. cite: https://www.bbc.co.uk/news/world-asia-pacific-12375649