In honor of the start of basketball season, and to commemorate the surprising victory of my Kobe-less Lakers over the Suns, I thought I’d discuss my favorite science paper on basketball. (I did a similar thing to celebrate the beginning of the football season.)
The paper is by Amos Tversky (of KahnemanandTversky fame) and Thomas Gilovich. In 1985, Tversky and Gilovich analyzed “the hot hand” among NBA players. As every basketball fan knows, players are streaky: one minute they are in the zone and can’t miss a shot, and the next minute every field goal attempt is ricocheting off the rim. But is “the hot hand” a real phenomenon, or is it just another cognitive illusion, an attempt by the brain to detect patterns inside a random process? (Kahneman and Tversky had shown a decade before that people indulge in the error of “representativeness,” which is when “people regularly exaggerate the degree to which the probability distribution in a small group will closely resemble the probability distribution in the overall population.” Think of the coin which has landed on heads a few times in a row. Most people assume that the coin is now more likely to land on tails, since “the law of averages” has to correct the imbalance. Of course, this is a false intuition. Random coin flips are statistically independent.)
After interviewing the Philadelphia 76ers, Tversky and his co-authors realized that basketball players certainly took “the hot hand” very seriously. If a teammate had made several shots in a row, they were more likely to get passed the ball. But Tversky wasn’t convinced: he thought “the hot hand” was the sporting equivalent of a coin that has landed on heads a few times in a row. In other words, it’s just random luck: players in the zone aren’t better shooters than players who aren’t in the zone. So Tversky and Gilovich began data mining, sieving through years of 76er statistics. They found absolutely no evidence of “the hot hand” phenomenon: a player’s chance of making a shot were not affected by whether or not their previous shots had gone in. Each field goal attempt was its own random event.
The 76ers were shocked by the evidence. Andrew Toney, the shooting guard, was particularly hard to convince: he was sure that he was a streaky shooter, and went through distinct “hot” and “cold” periods. But the numbers told a different story. During the regular season, Tooney made 46 percent of all of his shots. After hitting three shots in a row–a sure sign that he was now “in the zone”–Tooney’s field goal percentage dropped to 34 percent. (Ironically, when Tooney thought he was “hot” he was actually more likely to miss a shot.) The opposite phenomenon was also true: after missing three shots in a row, Tooney made 52 percent of his shots, which was significantly higher than his normal average. (Julius Erving was the only 76er player to not suffer from this inverse streakiness. When he was on a hot or cold streak, his field goal percentage remained constant.)
But maybe the 76ers were a statistical outlier. After all, 91 percent of serious NBA fans believed in “the hot hand”. Gilovich and Tversky next turned to the Boston Celtics, who had just won a world championship. But when Tversky and Gilovich analyzed the Celtics’ free throws, they found “no evidence that the outcome of free throws is affected by previous free throw attempts.” In fact, Larry Bird was like Andrew Tooney: after making several consecutive free throws, his free throw percentage actually declined.
So why do we believe in streaky shooters? According to Kahneman and Tversky, “the hot hand” is just an illusion, the standard laws of chance viewed through the prism of human cognition. That said, when Kobe is in the zone, I still want him to have the ball. Some illusions are hard to give up.