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

## TL;DR

This paper identifies and corrects a bias in measuring streak dependence in sequential data, revealing that previous conclusions about the hot hand fallacy may be flawed and often reversed after bias correction.

## Contribution

It introduces a bias correction method for streak dependence measures and demonstrates its impact on established hot hand fallacy findings.

## Key findings

- Bias exists in common streak dependence measures.
- Correcting the bias reverses conclusions of key hot hand studies.
- Bias is substantial for typical empirical sequence lengths.

## 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 this streak selection bias generally 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 long-standing conclusions of the canonical study are reversed.