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official record—which, in fact, all retested students would be told. To make the

retest results convincing, some non-cheaters were needed as a control group. The

best control group? The classrooms shown by the algorithm to have the best

teachers, in which big gains were thought to have been legitimately attained. If

those classrooms held their gains while the classrooms with a suspected cheater

lost ground, the cheating teachers could hardly argue that their students did

worse only because the scores wouldn’t count.

So a blend was settled upon. More than half of the 120 retested classrooms were

those suspected of having a cheating teacher. The remainder were divided

between the supposedly excellent teachers (high scores but no suspicious answer

patterns) and, as a further control, classrooms with mediocre scores and no

suspicious answers.

The retest was given a few weeks after the original exam. The children were not

told the reason for the retest. Neither were the teachers. But they may have

gotten the idea when it was announced that CPS officials, not the teachers, would

administer the test. The teachers were asked to stay in the classroom with their

students, but they would not be allowed to even touch the answer sheets.

The results were as compelling as the cheating algorithm had predicted. In the

classrooms chosen as controls, where no cheating was suspected, scores stayed

about the same or even rose. In contrast, the students with the teachers identified

as cheaters scored far worse, by an average of more than a full grade level.

As a result, the Chicago Public School system began to fire its cheating teachers.

The evidence was only strong enough to get rid of a dozen of them, but the many

other cheaters had been duly warned. The final outcome of the Chicago study is

further testament to the power of incentives: the following year, cheating by

teachers fell more than 30 percent.

You might think that the sophistication of teachers who cheat would increase

along with the level of schooling. But an exam given at the University of Georgia

in the fall of 2001 disputes that idea. The course was called Coaching Principles

and Strategies of Basketball, and the final grade was based on a single exam that

had twenty questions Among the questions:

How many halves are in a college basketball game?

1. 1

2. 2

3. 3

4. 4

How many points does a 3-pt. field goal account for in a basketball game?

1. 1

2. 2

3. 3

4. 4

What is the name of the exam which all high school seniors in the State of

Georgia must pass?

1. Eye Exam.

2. How Do the Grits Taste Exam.

3. Bug Control Exam.

4. Georgia Exit Exam

In your opinion, who is the best Division I assistant coach in the country?

1. Ron Jirsa.

2. John Pelphrey.

3. Jim Harrick Jr.

4. Steve Wojciechowski

If you are stumped by the final question, it might help to know that Coaching

Principles was taught by Jim Harrick Jr., an assistant coach with the university’s

basketball team. It might also help to know that his father, Jim Harrick Sr., was

the head basketball coach. Not surprisingly, Coaching Principles was a favorite

course among players on the Harricks’ team. Every student in the class received

an A. Not long afterward, both Harricks were relieved of their coaching duties.

If it strikes you as disgraceful that Chicago schoolteachers and University of

Georgia professors will cheat—a teacher, after all, is meant to instill values along

with the facts—then the thought of cheating among sumo wrestlers may also be

deeply disturbing. In Japan, sumo is not only the national sport but also a

repository of the country’s religious, military, and historical emotion. With its

purification rituals and its imperial roots, sumo is sacrosanct in a way that

American sports can never be. Indeed, sumo is said to be less about competition

than about honor itself.

It is true that sports and cheating go hand in hand. That’s because cheating is

more common in the face of a bright-line incentive (the line between winning

and losing, for instance) than with a murky incentive. Olympic sprinters and

weightlifters, cyclists in the Tour de France, football linemen and baseball

sluggers: they have all been shown to swallow whatever pill or powder may give

them an edge. It is not only the participants who cheat. Cagey baseball managers

try to steal an opponent’s signs. In the 2002 Winter Olympic figure-skating

competition, a French judge and a Russian judge were caught trying to swap

votes to make sure their skaters medaled. (The man accused of orchestrating the

vote swap, a reputed Russian mob boss named Alimzhan Tokhtakhounov, was

also suspected of rigging beauty pageants in Moscow.)

An athlete who gets caught cheating is generally condemned, but most fans at

least appreciate his motive: he wanted so badly to win that he bent the rules. (As

the baseball player Mark Grace once said, “If you’re not cheating, you’re not

? As Malloy saw it, all his

troubles stemmed from the one fight in which he took a dive. Otherwise, he

could have had class; he could have been a contender.

trying.”) An athlete who cheats to lose, meanwhile, is consigned to a deep circle

of sporting hell. The 1919 Chicago White Sox, who conspired with gamblers to

throw the World Series (and are therefore known forever as the Black Sox), retain

a stench of iniquity among even casual baseball fans. The City College of New

York’s championship basketball team, once beloved for its smart and scrappy

play, was instantly reviled when it was discovered in 1951 that several players

had taken mob money to shave points—intentionally missing baskets to help

gamblers beat the point spread. Remember Terry Malloy, the tormented former

boxer played by Marlon Brando in On the Waterfront

If cheating to lose is sport’s premier sin, and if sumo wrestling is the premier

sport of a great nation, cheating to lose couldn’t possibly exist in sumo. Could it?

Once again, the data can tell the story. As with the Chicago school tests, the data

set under consideration here is surpassingly large: the results from nearly every

official sumo match among the top rank of Japanese sumo wrestlers between

January 1989 and January 2000, a total of 32,000 bouts fought by 281 different

wrestlers.

The incentive scheme that rules sumo is intricate and extraordinarily powerful.

Each wrestler maintains a ranking that affects every slice of his life: how much

money he makes, how large an entourage he carries, how much he gets to eat,

sleep, and otherwise take advantage of his success. The sixty-six highest-ranked

wrestlers in Japan, comprising the makuuchi and juryo divisions, make up the

sumo elite. A wrestler near the top of this elite pyramid may earn millions and is

treated like royalty. Any wrestler in the top forty earns at least $170,000 a year.

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

PERCENTAGE AGAINST 8–6

OPPONENT

7–7 WRESTLER’S ACTUAL WIN

PERCENTAGE AGAINST 8–6

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

PERCENTAGE AGAINST 9–5

OPPONENT

7–7 WRESTLER’S ACTUAL WIN

PERCENTAGE AGAINST 9–5

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