The Famous 'Hot Hand Fallacy' Was a Math Mistake

In 1985 Thomas Gilovich, Robert Vallone, and Amos Tversky published "The Hot Hand in Basketball," a paper that became a textbook case of how intuition deceives us. They had collected shooting sequences from the Philadelphia 76ers and asked: after a player makes a shot, is the next shot more likely to go in than after a miss? The answer, they reported, was essentially no. The streaks fans saw were just the patterns the brain finds in random sequences. "Hot hand" entered the cognitive-bias canon as a textbook fallacy.

In 2015 the economists Joshua Miller and Adam Sanjurjo found a counterintuitive flaw in the original analysis. The procedure of selecting moments after a make and computing the success rate at the next attempt is biased downward in finite sequences. Conditional on a flip having come up heads, the next flip is, in a finite sample, slightly less likely to be heads — purely as an artifact of how the conditioning works. The bias is small but real, and large enough to flip the original conclusion.

When Miller and Sanjurjo reanalyzed Gilovich and colleagues' own data with the correction, the supposed evidence against the hot hand reversed. Players who had just made several shots in a row really did shoot better on the next attempt, by a few percentage points. Their 2018 paper in Econometrica called the corrected result "strong evidence of hot hand shooting."

Gilovich has not fully retracted. The dispute continues, but the cleaner finding is now that the hot hand is real and the famous fallacy was, at minimum, overstated. The cognitive bias canon picked the wrong example to make its point.