What if the famous study disproving the hot hand had the maths wrong?

Then the conclusion flips. Miller and Sanjurjo prove that a subtle but substantial bias exists in that common measure of how present outcomes depend on streaks of past outcomes. Correcting for it reverses the longstanding conclusions of the canonical study, and the replications are vulnerable to the same bias.

The hot hand fallacy is one of the most widely cited results in the study of human judgment. Its canonical study examined whether a basketball shot is more likely to go in after a streak of made shots, and reported that the belief in streaks was not supported.

The measure doing the work deserves scrutiny. The authors prove that a subtle but substantial bias exists in a common measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data.

This streak selection bias has a shape. Its magnitude generally decreases as the sequence gets longer but increases in streak length, and it remains substantial for a range of sequence lengths often used in empirical work. The paper’s subtitle calls it a truth in the law of small numbers.

That is enough to overturn the literature it affects. The canonical study and its replications are vulnerable to the bias, and upon correcting for it the authors find that the longstanding conclusions of that study are reversed.