What the numbers can reveal

OVER a quarter-century of serious cycling, I’ve heard the rumors about performance-enhancing drugs -- stimulants in the 1970s, steroids in the 1980s and blood boosters such as erythropoietin (EPO) in the 1990s. A friend who knows my penchant for exposing fraud suggested I track Tour de France winners’ speeds and note the increase after 1991, the year he says EPO was introduced. Because my friend won the Tour three times, I figured it was worth checking.

From 1949 to 1962, the Tour winners averaged 34.7 kilometers per hour (about 21.5 mph). From 1963 to 1976, the average increased to 35.4 kph, a 2% difference. From 1977 to 1990, the average increased another 2% to 36.2 kph. From 1991 to 2004, the average speed jumped to 39.5 kph, a 9% increase. Something must have happened in the 1990s to trigger such a leap in speed.

EPO? Maybe. But composite materials led to lighter, stronger bikes. Clothing became more aerodynamic. Nutrition and training became more scientific. The number of racers grew from an average of about 120 in the ‘50s to about 190 in the ‘90s. (More riders accentuates drafting and increases speeds on the flat stages.) Also, the race has been shortened about 620 miles over the last 50 years. Can these factors account for the spike in the ‘90s? We could compare the split times on crucial mountain stages between top riders and average riders, pre- and post-1991, with the presumption that elite riders would be using the best performance-enhancing drugs under the direction of the most knowledgeable sports physicians. A significant difference between top riders, but not among average riders, pre- and post-1991, would be compelling evidence of artificial performance enhancement.

My model for this exercise in data comparison came from Steven D. Levitt, an economist at the University of Chicago who is shaking up his profession by applying standard methods from the social sciences to very nonstandard questions from the real world.

A 2003 New York Times Magazine article about Levitt by journalist Stephen J. Dubner led to their collaboration on the new book “Freakonomics,” which was primarily written by Dubner and is a hodgepodge of Levitt’s polymathic interests. Although the authors eschew any central theme, I took from it two messages: Science can answer the broadest range of questions (even freakish ones) about human behavior, and incentives and motivations are intimately linked in driving human behavior.

For example, Levitt devised an algorithm to analyze Chicago public school data, revealing that some teachers inflated student scores on state exams by filling in answers to harder questions (always the same block of correct answers). There also was a spike in the scores one year, followed by a drop to earlier levels. Retests on these same students proved that they did not know the answers to those harder questions. The teachers were fired.

Levitt also discovered that sumo wrestlers were fixing some of their matches. To rise in rank and earn more money, a wrestler must finish a tournament of 15 matches with a winning record. Levitt found a pattern of cheating whenever a wrestler with a 7-7 record (and a lot to gain by winning one more) was pitted against an 8-6 wrestler (with little to lose) in the final bout of a tournament. A 7-7 wrestler’s predicted win percentage against an 8-6 opponent was 48.7%, whereas the actual win percentage was 79.6%. The next time these wrestlers competed and there was nothing at stake, the 7-7 wrestlers won only 40% of the rematches. “The most logical explanation,” Levitt concludes, “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.”

Levitt’s most controversial computation involves the dramatic 1990s drop in crime rates. The reason, he says, is not tougher gun control laws, capital punishment, decreasing unemployment or a stronger economy. It is Roe vs. Wade. Research shows that children from impoverished and adverse environments are more likely to become criminals. After the 1973 court decision made legal abortions possible, millions of poor, single women aborted unwanted fetuses; 20 years later, the pool of potential criminals had shrunk, as did the crime rate. (The solution isn’t more abortions, he says, but “better environments for those children at greatest risk for future crime.”)

Of course, correlation does not always mean causation, and explaining the causes of crime is a complex, multivariate problem. But Levitt also shows that the five states that legalized abortion two years before Roe vs. Wade saw a drop in crime earlier than the other states. Further, those states with the highest abortion rates in the 1970s experienced the greatest drop in crime in the 1990s, and the entire decline in crime was among the age group born after 1973, not among older groups.

More generally, Levitt demonstrates that the crime rate also dropped when three additional factors shrank the pool of criminals: Increased rates of imprisonment accounted for a third of the drop (compared with capital punishment, which led to 4% of the decrease); increased numbers of police officers accounted for 10% of the crime drop; and the collapse of the crack cocaine market caused profits to drop along with the incentive to sell it (and thus the accompanying violence declined), accounting for an additional 15% of the crime plunge.

Levitt employs statistical tools that are simple yet elegant. He cuts to the heart of a question and picks topics that are fascinating. All social scientists should ask themselves if the problems they are working on are as interesting or important as those in this superb work. *