Surprised by the Gambler's and Hot Hand Fallacies? A Truth in the Law of Small Numbers

IGIER Working Paper No. 552

64 Pages Posted: 7 Jul 2015 Last revised: 21 Oct 2017

See all articles by Joshua B. Miller

Joshua B. Miller

University of Alicante - Department of Economics

Adam Sanjurjo

Universidad de Alicante - Departamento de Fundamentos del Análisis Económico

Date Written: November 15, 2016

Abstract

We prove that a subtle but substantial bias exists in a standard measure of the conditional dependence of present outcomes on streaks of past outcomes in sequential data. The magnitude of this novel form of 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. The bias has important implications for the literature that investigates incorrect beliefs in sequential decision making---most notably the Hot Hand Fallacy and the Gambler's Fallacy. Upon correcting for the bias, the conclusions of prominent studies in the hot hand fallacy literature are reversed. The bias also provides a novel structural explanation for how belief in the law of small numbers can persist in the face of experience.

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

JEL Classification: C12, C14, C18,C19, C91, D03, G02

Suggested Citation

Miller, Joshua B. and Sanjurjo, Adam, Surprised by the Gambler's and Hot Hand Fallacies? A Truth in the Law of Small Numbers (November 15, 2016). IGIER Working Paper No. 552. Available at SSRN: https://ssrn.com/abstract=2627354 or http://dx.doi.org/10.2139/ssrn.2627354

Joshua B. Miller (Contact Author)

University of Alicante - Department of Economics ( email )

Apartado de Correos 99
Alicante, 03080
Spain

HOME PAGE: http://joshua-benjamin-miller.com

Adam Sanjurjo

Universidad de Alicante - Departamento de Fundamentos del Análisis Económico ( email )

Campus de San Vicente
Alicante, 03690
Spain

HOME PAGE: http://sites.google.com/site/adamangelsanjurjo/

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