# Is the hot hand fallacy really a fallacy?

Is it a fallacy that players can get on a hot streak?

Basketball players, coaches and fans have long believed that players can get a “hot hand,” when a streak of successful shots makes it more likely that the player will make the next shot. For decades, researchers have maintained that this is a cognitive illusion, because studies showed that players’ shooting percentage did not vary after a streak. Now a new analysis reveals a fundamental error in those studies, which can be illustrated by a simple coin toss. The upshot is that the hot hand may be real after all.

#### The “fallacy” explained

In 1985, Thomas Gilovich, Robert Vallone and Amos Tversky published a study of basketball streak shooting. Although most players and fans believed that a player who had made two or three shots in a row was more likely to make the next shot, the analysis in the study seemed to show that this was not the case. Field goals, free throws and controlled shooting were studied, and the authors found no evidence for the “hot hand” hypothesis. Many follow-up studies were conducted by often skeptical researchers, but no one could prove the hot hand. Nobel Prize winner Daniel Kahneman called the idea of the hot hand “a massive and widespread cognitive illusion.” Then an error was discovered.

#### The “cold hand” error

In 2015, a working paper by Joshua Miller and Adam Sanjurjo pointed out a bias that had not been taken into account by any of the previous studies. The crucial fact is that, statistically speaking, a miss is more likely than a hit after a streak of hits. This mathematical “cold hand” effect had not been accounted for in any of the studies. To illustrate the bias, Miller and Sanjurjo imagine “Jack,” who flips a coin 100 times, writing down the outcome that comes after each heads. He expects the proportion of heads written down to be one-half. “Shockingly,” they write, “Jack is wrong.” The expected proportion of heads is less than one-half, and in fact, in any sequence, the proportion of successes following a streak of successes is less than the underlying probability of success. The Coin Flip Paradox page explains this in detail. Miller and Sanjurjo state that once this bias is accounted for, the data from the original hot hand study and follow-up studies actually show that the hot hand phenomenon is real, and the fallacy is a fallacy.

#### What remains of the hot hand fallacy

The hot hand debate will continue. If Miller and Sanjurjo are correct, they confirm what fans never stopped believing: players really do shoot better when they’re on a streak. However, even if this is so, some of the insights from the hot hand investigation remain valid.

In attempting to explain why basketball fans perceived the hot hand, Gilovich et al. examined important cognitive illusions. Regardless of whether a hot hand phenomenon exists in reality, fans perceive it to exist to a greater degree than it does. This is shown by a tendency for survey participants to characterize chance sequences as streaks, known as the clustering illusion. The tendency to overstate the effects of the phenomenon may be an example of confirmation bias.