Measurement Error and the Hot Hand

Abstract

This article shows that the first autocorrelation of basketball shot results is a highly biased and inconsistent estimator of the first autocorrelation of the ex ante probabilities with which the shots are made. Shot result autocorrelation is close to zero even when shot probability autocorrelation is close to one. The bias is caused by what is equivalent to a severe measurement error problem. The results imply that the widespread belief among players and fans in the hot hand is not necessarily a cognitive fallacy.