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

Joshua Benjamin Miller and Adam Sanjurjo
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Joshua Benjamin Miller: The University of Melbourne

No sv9x2, OSF Preprints from Center for Open Science

Abstract: *Econometrica Link*: https://www.econometricsociety.org/publications/econometrica/2018/11/01/surprised-hot-hand-fallacy-truth-law-small-numbers *Full Bibliographic Reference*: Miller, J. B., & Sanjurjo, A. (2018). Surprised by the hot hand fallacy? A truth in the law of small numbers. Econometrica, Vol. 86, No.6, pp. 2019–2047 ********************************************* 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.

Date: 2018-10-18
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DOI: 10.31219/osf.io/sv9x2

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