Steven Dubner - Freakonomics
The seventieth-ranked wrestler in Japan, meanwhile, earns only $15,000 a year.
Life isn’t very sweet outside the elite. Low-ranked wrestlers must tend to their superiors, preparing their meals and cleaning their quarters and even soaping up their hardest-to-reach body parts. So ranking is everything.
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 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 7–7 WRESTLER’S ACTUAL WIN
PERCENTAGE
AGAINST 8–6 PERCENTAGE
AGAINST 8–6
OPPONENT
OPPONENT
48.7 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: 7–7 WRESTLER’S PREDICTED WIN 7–7 WRESTLER’S ACTUAL WIN
PERCENTAGE
AGAINST 9–5 PERCENTAGE
AGAINST 9–5
OPPONENT
OPPONENT
47.2 73.4
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 words “sumo” and “rigged” in the same sentence can cause a national furor. People tend to get defensive when the integrity of their national sport is impugned.
Still, allegations of match rigging do occasionally find their way into the Japanese media. These occasional media storms offer one more chance to measure possible corruption in sumo. Media scrutiny, after all, creates a powerful incentive: if two sumo wrestlers or their stables have been rigging matches, they might be leery to continue when a swarm of journalists and TV cameras descend upon them.
So what happens in such cases? The data show that in the sumo tournaments held immediately after allegations of match rigging, 7–7 wrestlers win only 50
percent of their final-day matches against 8–6 opponents instead of the typical 80
percent. No matter how the data are sliced, they inevitably suggest one thing: it is hard to argue that sumo wrestling isn’t rigged.
Several years ago, two former sumo wrestlers came forward with extensive allegations of match rigging—and more. Aside from the crooked matches, they said, sumo was rife with drug use and sexcapades, bribes and tax evasion, and close ties to the yakuza, the Japanese mafia. The two men began to receive threatening phone calls; one of them told friends he was afraid he would be killed by the yakuza. Still, they went forward with plans to hold a press conference at the Foreign Correspondents’ Club in Tokyo. But shortly beforehand, the two men died—hours apart, in the same hospital, of a similar respiratory ailment. The police declared there had been no foul play but did not conduct an investigation. “It seems very strange for these two people to die on the same day at the same hospital,” said Mitsuru Miyake, the editor of a sumo magazine. “But no one has seen them poisoned, so you can’t prove the skepticism.”
Whether or not their deaths were intentional, these two men had done what no other sumo insider had previously done: named names. Of the 281 wrestlers covered in the data cited above, they identified 29 crooked wrestlers and 11 who were said to be incorruptible.
What happens when the whistle-blowers’ corroborating evidence is factored into the analysis of the match data? In matches between two supposedly corrupt wrestlers, the wrestler who was on the bubble won about 80 percent of the time.
In bubble matches against a supposedly clean opponent, meanwhile, the bubble wrestler was no more likely to win than his record would predict. Furthermore, when a supposedly corrupt wrestler faced an opponent whom the whistleblowers did not name as either corrupt or clean, the results were nearly as skewed as when two corrupt wrestlers met—suggesting that most wrestlers who weren’t specifically named were also corrupt.
So if sumo wrestlers, schoolteachers, and day-care parents all cheat, are we to assume that mankind is innately and universally corrupt? And if so, how corrupt?
The answer may lie in…bagels. Consider the true story of a man named Paul Feldman.
Once upon a time, Feldman dreamed big dreams. Trained as an agricultural economist, he wanted to tackle world hunger. Instead, he took a job in Washington, analyzing weapons expenditures for the U.S. Navy. This was in 1962. For the next twenty-odd years, he did more of the same. He held senior-level jobs and earned good money, but he wasn’t fully engaged in his work. At the office Christmas party, colleagues would introduce him to their wives not as
“the head of the public research group” (which he was) but as “the guy who brings in the bagels.”
The bagels had begun as a casual gesture: a boss treating his employees whenever they won a research contract. Then he made it a habit. Every Friday, he would bring in some bagels, a serrated knife, and cream cheese. When employees from neighboring floors heard about the bagels, they wanted some too. Eventually he was bringing in fifteen dozen bagels a week. In order to recoup his costs, he set out a cash basket and a sign with the suggested price. His collection rate was about 95 percent; he attributed the underpayment to oversight, not fraud.
In 1984, when his research institute fell under new management, Feldman took a look at his career and grimaced. He decided to quit his job and sell bagels. His economist friends thought he had lost his mind, but his wife supported him. The last of their three children was finishing college, and they had retired their mortgage.
Driving around the office parks that encircle Washington, he solicited customers with a simple pitch: early in the morning, he would deliver some bagels and a cash basket to a company’s snack room; he would return before lunch to pick up the money and the leftovers. It was an honor-system commerce scheme, and it worked. Within a few years, Feldman was delivering 8,400 bagels a week to 140
companies and earning as much as he had ever made as a research analyst. He had thrown off the shackles of cubicle life and made himself happy.
He had also—quite without meaning to—designed a beautiful economic experiment. From the beginning, Feldman kept rigorous data on his business. So by measuring the money collected against the bagels taken, he found it possible to tell, down to the penny, just how honest his customers were. Did they steal from him? If so, what were the characteristics of a company that stole versus a company that did not? Under what circumstances did people tend to steal more, or less?
As it happens, Feldman’s accidental study provides a window onto a form of cheating that has long stymied academics: white-collar crime. (Yes, shorting the bagel man is white-collar crime, writ however small.) It might seem ludicrous to address as large and intractable a problem as white-collar crime through the life of a bagel man. But often a small and simple question can help chisel away at the biggest problems.
Despite all the attention paid to rogue companies like Enron, academics know very little about the practicalities of white-collar crime. The reason? There are no good data. A key fact of white-collar crime is that we hear about only the very slim fraction of people who are caught cheating. Most embezzlers lead quiet and theoretically happy lives; employees who steal company property are rarely detected.
With street crime, meanwhile, that is not the case. A mugging or a burglary or a murder is usually tallied whether or not the criminal is caught. A street crime has a victim, who typically reports the crime to the police, who generate data, which in turn generate thousands of academic papers by criminologists, sociologists, and economists. But white-collar crime presents no obvious victim. From whom, exactly, did the masters of Enron steal? And how can you measure something if you don’t know to whom it happened, or with what frequency, or in what magnitude?
Paul Feldman’s bagel business was different. It did present a victim. The victim was Paul Feldman.
When he started his business, he expected a 95 percent payment rate, based on the experience at his own office. But just as crime tends to be low on a street where a police car is parked, the 95 percent rate was artificially high: Feldman’s presence had deterred theft. Not only that, but those bagel eaters knew the provider and had feelings (presumably good ones) about him. A broad swath of psychological and economic research has shown that people will pay different amounts for the same item depending on who is providing it. The economist Richard Thaler, in his 1985 “Beer on the Beach” study, showed that a thirsty sunbather would pay $2.65 for a beer delivered from a resort hotel but only $1.50
for the same beer if it came from a shabby grocery store.
In the real world, Feldman learned to settle for less than 95 percent. He came to consider a company “honest” if its payment rate was above 90 percent. He considered a rate between 80 and 90 percent “annoying but tolerable.” If a company habitually paid below 80 percent, Feldman might post a hectoring note, like this one:
The cost of bagels has gone up dramatically since the beginning of the year.
Unfortunately, the number of bagels that disappear without being paid for has also gone up. Don’t let that continue. I don’t imagine that you would teach your children to cheat, so why do it yourselves?
In the beginning, Feldman left behind an open basket for the cash, but too often the money vanished. Then he tried a coffee can with a money slot in its plastic lid, which also proved too tempting. In the end, he resorted to making small plywood boxes with a slot cut into the top. The wooden box has worked well.
Each year he drops off about seven thousand boxes and loses, on average, just one to theft. This is an intriguing statistic: the same people who routinely steal more than 10 percent of his bagels almost never stoop to stealing his money box—a tribute to the nuanced social calculus of theft. From Feldman’s perspective, an office worker who eats a bagel without paying is committing a crime; the office worker probably doesn’t think so. This distinction probably has less to do with the admittedly small amount of money involved (Feldman’s bagels cost one dollar each, cream cheese included) than with the context of the
