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

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  • Joshua B. Miller
  • Adam Sanjurjo

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.

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  • Joshua B. Miller & Adam Sanjurjo, 2019. "Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers," Papers 1902.01265, arXiv.org.
    • Handle: RePEc:arx:papers:1902.01265
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    References listed on IDEAS

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    Cited by:

    1. David M. Ritzwoller & Joseph P. Romano, 2019. "Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives to Random Bernoulli Sequences," Papers 1908.01406, arXiv.org, revised Apr 2021.
    2. Evans, Andrew E. & Crosby, Paul, 2021. "Does a cool head beat a hot hand? Evidence from professional golf," Economic Modelling, Elsevier, vol. 97(C), pages 272-284.
    3. Brañas-Garza, Pablo & Estepa-Mohedano, Lorenzo & Jorrat, Diego & Orozco, Victor & Rascón-Ramírez, Ericka, 2021. "To pay or not to pay: Measuring risk preferences in lab and field," Judgment and Decision Making, Cambridge University Press, vol. 16(5), pages 1290-1313, September.
    4. Miller, Joshua B. & Sanjurjo, Adam, 2021. "Is it a fallacy to believe in the hot hand in the NBA three-point contest?," European Economic Review, Elsevier, vol. 138(C).
    5. Hajikhameneh, Aidin & Iannaccone, Laurence R., 2023. "God games: An experimental study of uncertainty, superstition, and cooperation," Games and Economic Behavior, Elsevier, vol. 139(C), pages 88-116.
    6. Bar-Eli, Michael & Krumer, Alex & Morgulev, Elia, 2020. "Ask not what economics can do for sports - Ask what sports can do for economics," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 89(C).
    7. Meier, Philippe & Flepp, Raphael & Ruedisser, Maximilian & Franck, Egon, 2020. "Separating psychological momentum from strategic momentum: Evidence from men’s professional tennis," Journal of Economic Psychology, Elsevier, vol. 78(C).
    8. Chen, Wanyi, 2021. "Dynamic survival bias in optimal stopping problems," Journal of Economic Theory, Elsevier, vol. 196(C).
    9. Salaghe, Florina & Sundali, James & Nichols, Mark W. & Guerrero, Federico, 2020. "An empirical investigation of wagering behavior in a large sample of slot machine gamblers," Journal of Economic Behavior & Organization, Elsevier, vol. 169(C), pages 369-388.
    10. Jeremy Arkes, 2020. "Teaching Graduate (and Undergraduate) Econometrics: Some Sensible Shifts to Improve Efficiency, Effectiveness, and Usefulness," Econometrics, MDPI, vol. 8(3), pages 1-23, September.
    11. Robert J. Batt & Jordan D. Tong, 2020. "Mean Service Metrics: Biased Quality Judgment and the Customer–Server Quality Gap," Manufacturing & Service Operations Management, INFORMS, vol. 22(5), pages 975-995, September.

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