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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.

Is it possible, then, that an 8–6 wrestler might allow a 7–7 wrestler to beat him? A sumo bout is a concentrated flurry of force and speed and leverage, often lasting only a few seconds. It wouldn’t be very hard to let yourself be tossed. Let’s imagine for a moment that sumo wrestling is rigged. How might we measure the data to prove it?

The first step would be to isolate the bouts in question: those fought on a tournament’s final day between a wrestler on the bubble and a wrestler who has already secured his eighth win. (Because more than half of all wrestlers end a tournament with either seven, eight, or nine victories, hundreds of bouts fit these criteria.) A final-day match between two 7–7 wrestlers isn’t likely to be fixed, since both fighters badly need the victory. A wrestler with ten or more victories probably wouldn’t throw a match either, since he has his own strong incentive to win: the $100,000 prize for overall tournament champion and a series of $20,000 prizes for the “outstanding technique” award, “fighting spirit” award, and others.

Let’s now consider the following statistic, which represents the hundreds of matches in which a 7–7 wrestler faced an 8–6 wrestler on a tournament’s final day. The first number tells the probability, based on all past meetings between those two wrestlers fighting that day, that the 7–7 wrestler who win. The second number will show how often the 7–7 wrestler actually did win.

So the 7–7 wrestler's predicted win percentage against this 8-6 opponent is 48.7%, but the 7-7 wrestler's actual win percentage against this 8-6 opponent on this last day of a tournament is 79.6%. So the 7-7 wrestler based on past outcomes, was expected to win just less than half the time. This makes sense; their records in this tournament indicate that the 8–6 wrestler is slightly better. But in actuality, the wrestler on the bubble won almost eight out of ten matches against his 8–6 opponent. Wrestlers on the bubble also do astonishingly well against 9–5 opponents.

In a case where 7-7 wrestler's predicted win percentage against 9-5 opponent is only 47.2%, they actually win on a last day of a tournament with the eighth win at state 73.4%.

Now, as suspicious as this looks, a high winning percentage alone isn’t enough to prove that a match is rigged. Since so much depends on a wrestler’s eighth win, he should be expected to fight harder in a crucial bout. But perhaps there are further clues in the data that prove collusion.

It’s worth thinking about the incentive a wrestler might have to throw a match. Maybe he accepts a bribe (which would obviously not be recorded in the data). Or perhaps some other arrangement is made between the two wrestlers.

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.

Is it possible, then, that an 8–6 wrestler might allow a 7–7 wrestler to beat him? A sumo bout is a concentrated flurry of force and speed and leverage, often lasting only a few seconds. It wouldn’t be very hard to let yourself be tossed. Let’s imagine for a moment that sumo wrestling is rigged. How might we measure the data to prove it?

The first step would be to isolate the bouts in question: those fought on a tournament’s final day between a wrestler on the bubble and a wrestler who has already secured his eighth win. (Because more than half of all wrestlers end a tournament with either seven, eight, or nine victories, hundreds of bouts fit these criteria.) A final-day match between two 7–7 wrestlers isn’t likely to be fixed, since both fighters badly need the victory. A wrestler with ten or more victories probably wouldn’t throw a match either, since he has his own strong incentive to win: the $100,000 prize for overall tournament champion and a series of $20,000 prizes for the “outstanding technique” award, “fighting spirit” award, and others.

Let’s now consider the following statistic, which represents the hundreds of matches in which a 7–7 wrestler faced an 8–6 wrestler on a tournament’s final day. The first number tells the probability, based on all past meetings between those two wrestlers fighting that day, that the 7–7 wrestler who win. The second number will show how often the 7–7 wrestler actually did win.

So the 7–7 wrestler's predicted win percentage against this 8-6 opponent is 48.7%, but the 7-7 wrestler's actual win percentage against this 8-6 opponent on this last day of a tournament is 79.6%. So the 7-7 wrestler based on past outcomes, was expected to win just less than half the time. This makes sense; their records in this tournament indicate that the 8–6 wrestler is slightly better. But in actuality, the wrestler on the bubble won almost eight out of ten matches against his 8–6 opponent. Wrestlers on the bubble also do astonishingly well against 9–5 opponents.

In a case where 7-7 wrestler's predicted win percentage against 9-5 opponent is only 47.2%, they actually win on a last day of a tournament with the eighth win at state 73.4%.

Now, as suspicious as this looks, a high winning percentage alone isn’t enough to prove that a match is rigged. Since so much depends on a wrestler’s eighth win, he should be expected to fight harder in a crucial bout. But perhaps there are further clues in the data that prove collusion.

It’s worth thinking about the incentive a wrestler might have to throw a match. Maybe he accepts a bribe (which would obviously not be recorded in the data). Or perhaps some other arrangement is made between the two wrestlers.

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