Duncan was an unlikely candidate to hold such a powerful job. He was only thirty-six when appointed, a onetime academic all-American at Harvard who later played pro basketball in Australia. He had spent just three years with the CPS—and never in a job important enough to have his own secretary—before becoming its CEO. It didn’t hurt that Duncan had grown up in Chicago. His father taught psychology at the University of Chicago; his mother ran an after-school program for forty years, without pay, in a poor neighborhood. When Duncan was a boy, his afterschool playmates were the under-privileged kids his mother cared for. So when he took over the public schools, his allegiance lay more with schoolchildren and their families than with teachers and their union.

The best way to get rid of cheating teachers, Duncan had decided, was to readminister the standardized exam. He only had the resources to retest 120 classrooms, however, so he asked the creators of the cheating algorithm to help choose which classrooms to test.

How could those 120 retests be used most effectively? It might have seemed sensible to retest only the classrooms that likely had a cheating teacher. But even if their retest scores were lower, the teachers could argue that the students did worse merely because they were told that the scores wouldn’t count in their 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 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? 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.

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.