Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers

Econometrica · 2018 · Volume 86 · Issue 6

Abstract

We 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. The magnitude of thisstreak selection biasgenerally decreases as the sequence gets longer, but increases in streak length, and remains substantial for a range of sequence lengths often used in empirical work. We observe that the canonical study in the influential hot hand fallacy literature, along with replications, are vulnerable to the bias. Upon correcting for the bias, we find that the longstanding conclusions of the canonical study are reversed.

Keywords

Law of small numbers, alternation bias, negative recency bias, gambler's fallacy, hot hand fallacy, hot hand effect, sequential decision making, sequential data, selection bias, finite sample bias, small sample bias

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