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

Joshua Miller and Adam Sanjurjo

No 552, Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University

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. JEL Classification Numbers: C12; C14; C18;C19; C91; D03; G02. 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.

Date: 2015
New Economics Papers: this item is included in nep-cbe and nep-ecm
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (17)

Downloads: (external link)
https://repec.unibocconi.it/igier/igi/wp/2015/552.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:igi:igierp:552

Ordering information: This working paper can be ordered from
https://repec.unibocconi.it/igier/igi/

Access Statistics for this paper

More papers in Working Papers from IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University via Rontgen, 1 - 20136 Milano (Italy).
Bibliographic data for series maintained by ().