Drunkard's Walk - Leonard Mlodinow [80]
Decades later the great French mathematician Jules-Henri Poincaré employed Quételet’s method to nab a baker who was shortchanging his customers. At first, Poincaré, who made a habit of picking up a loaf of bread each day, noticed after weighing his loaves that they averaged about 950 grams instead of the 1,000 grams advertised. He complained to the authorities and afterward received bigger loaves. Still he had a hunch that something about his bread wasn’t kosher. And so with the patience only a famous—or at least tenured—scholar can afford, he carefully weighed his bread every day for the next year. Though his bread now averaged closer to 1,000 grams, if the baker had been honestly handing him random loaves, the number of loaves heavier and lighter than the mean should have—as I mentioned in chapter 7—diminished following the bell-shaped pattern of the error law. Instead, Poincaré found that there were too few light loaves and a surplus of heavy ones. He concluded that the baker had not ceased baking underweight loaves but instead was seeking to placate him by always giving him the largest loaf he had on hand. The police again visited the cheating baker, who was reportedly appropriately astonished and presumably agreed to change his ways.16
Quételet had stumbled on a useful discovery: the patterns of randomness are so reliable that in certain social data their violation can be taken as evidence of wrongdoing. Today such analyses are applied to reams of data too large to have been analyzed in Quételet’s time. In recent years, in fact, such statistical sleuthing has become popular, creating a new field, called forensic economics, perhaps the most famous example of which is the statistical study suggesting that companies were backdating their stock option grants. The idea is simple: companies grant stock options—the right to buy shares later at the price of the stock on the date of the grant—as an incentive for executives to improve their firms’ share prices. If the grants are backdated to times when the shares were especially low, the executives’ profits will be correspondingly high. A clever idea, but when done in secret it violates securities laws. It also leaves a statistical fingerprint, which has led to the investigation of such practices at about a dozen major companies.17 In a less publicized example, Justin Wolfers, an economist at the Wharton School, found evidence of fraud in the results of about 70,000 college basketball games.18
Wolfers discovered the anomaly by comparing Las Vegas bookmakers’ point spreads to the games’ actual outcomes. When one team is favored, the bookmakers offer point spreads in order to attract a roughly even number of bets on both competitors. For instance, suppose the basketball team at Caltech is considered better than the team at UCLA (for college basketball fans, yes, this was actually true in the 1950s). Rather than assigning lopsided odds, bookies could instead offer an even bet on the game but pay out on a Caltech bet only if their team beat UCLA by, say, 13 or more points.
Though such point spreads are set by the bookies, they are really fixed by the mass of bettors because the bookies adjust them to balance the demand. (Bookies make their money on fees and seek to have an equal amount of money bet on each side so that they can’t lose, whatever the outcome.) To measure how well bettors assess two teams, economists use a number called the forecast error, which is the difference between the favored team’s margin of victory and the point spread determined by the marketplace. It may come as no surprise that forecast error, being a type of error, is distributed according to the normal distribution. Wolfers found that its mean is 0, meaning that the point spreads