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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 left column tallies the probability, based on all past meetings between the two wrestlers fighting that day, that the 7–7 wrestler will win. The right column shows how often the 7–7 wrestler actually did win. 7–7 WRESTLER’S PREDICTED WIN PERCENTAGE AGAINST 8–6 OPPONENT 48.7 79.6 7–7 WRESTLER’S ACTUAL WIN PERCENTAGE AGAINST 8–6 OPPONENT 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:
7–7 WRESTLER’S PREDICTED WIN PERCENTAGE AGAINST 9–5 OPPONENT 47.2 73.4 7–7 WRESTLER’S ACTUAL WIN PERCENTAGE AGAINST 9–5 OPPONENT 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. Keep in mind that the pool of elite sumo wrestlers is extraordinarily tight-knit. Each of the sixty-six elite wrestlers fights fifteen of the others in a tournament every two months. Furthermore, each wrestler belongs to a stable that is typically managed by a former sumo champion, so even the rival stables have close ties. (Wrestlers from the same stable do not wrestle one another.) Now let’s look at the win-loss percentage between the 7–7 wrestlers and the 8–6 wrestlers the next time they meet, when neither one is on the bubble. In this case, there is no great pressure on the individual match. So you might expect the wrestlers who won their 7–7 matches in the previous tournament to do about as well as they had in earlier matches against these same opponents—that is, winning roughly 50 percent of the time. You certainly wouldn’t expect them to uphold their 80 percent clip. As it turns out, the data show that the 7–7 wrestlers win only 40 percent of the rematches. Eighty percent in one match and 40 percent in the next? How do you make sense of that? The most logical explanation is that the wrestlers made a quid pro quo agreement: you let me win today, when I really need the victory, and I’ll let you win the next time. (Such an arrangement wouldn’t preclude a cash bribe.) It’s especially interesting to note that by the two wrestlers’ second subsequent meeting, the win percentages revert to the expected level of about 50 percent, suggesting that the collusion spans only two matches. And it isn’t only the individual wrestlers whose records are suspect. The collective records of the various sumo stables are similarly aberrational. When one stable’s wrestlers fare well on the bubble against wrestlers from a second stable, they tend to do especially poorly when the second stable’s wrestlers are on the bubble. This indicates that some match rigging may be choreographed at the highest level of the sport—much like the Olympic skating judges’ vote swapping. No formal disciplinary action has ever been taken against a Japanese sumo wrestler for match rigging. Officials from the Japanese Sumo Association typically dismiss any such charges as fabrications by disgruntled former wrestlers. In fact, the mere utterance of the
Page 1 and 2: FREAKONOMICS A Rogue Economist Expl
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percent. Rudolph Giuliani, however,
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The most famous gun-control law is
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other words, the net effect of crac
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earliest years of legalized abortio
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Indeed, there are plenty of people
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What the link between abortion and
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factor. Just as most people spend m
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Still, the question of how much par
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The answer will not be heartening t
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Correlation is nothing more than a
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samples of twenty children from eac
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The child’s parents speak English
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Doesn’t: The child attended Head
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To overgeneralize a bit, the first
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Amcher, had been named for the firs
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girls are given a name that is uniq
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19. Hunter 20. Colin The Twenty “
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So does a name matter? The data sho
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6. Sarah 7. Kayla 8. Amber 9. Megan
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5. William Most Common White Boy Na
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(2003); also presented in Manuel Ei
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SUPREME COURT JUSTICE LOUIS D. BRAN
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NOT AS MUCH CRIME AS THERE ACTUALLY
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papers: Cristian Pop-Eleches, “Th
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Reason, May 2003; and Richard Morin
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Thernstrom, Lisa Chase, and Colin C
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anti-communism Anti-Defamation Leag
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abandonment of adoption of conflict
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crack cocaine changes in market for
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guns: availability of buyback of de
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Wade, Henry Wade, Wyn Craig Waksal,
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HarperCollins Publishers (Australia
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