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Uncertainty in the Hot Hand Fallacy: Detecting Streaky Alternatives to Random Bernoulli Sequences

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  • David M. Ritzwoller
  • Joseph P. Romano

Abstract

We study a class of permutation tests of the randomness of a collection of Bernoulli sequences and their application to analyses of the human tendency to perceive streaks of consecutive successes as overly representative of positive dependence - the hot hand fallacy. In particular, we study permutation tests of the null hypothesis of randomness (i.e., that trials are i.i.d.) based on test statistics that compare the proportion of successes that directly follow k consecutive successes with either the overall proportion of successes or the proportion of successes that directly follow k consecutive failures. We characterize the asymptotic distributions of these test statistics and their permutation distributions under randomness, under a set of general stationary processes, and under a class of Markov chain alternatives, which allow us to derive their local asymptotic power. The results are applied to evaluate the empirical support for the hot hand fallacy provided by four controlled basketball shooting experiments. We establish that substantially larger data sets are required to derive an informative measurement of the deviation from randomness in basketball shooting. In one experiment, for which we were able to obtain data, multiple testing procedures reveal that one shooter exhibits a shooting pattern significantly inconsistent with randomness - supplying strong evidence that basketball shooting is not random for all shooters all of the time. However, we find that the evidence against randomness in this experiment is limited to this shooter. Our results provide a mathematical and statistical foundation for the design and validation of experiments that directly compare deviations from randomness with human beliefs about deviations from randomness, and thereby constitute a direct test of the hot hand fallacy.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1908.01406
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    References listed on IDEAS

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    1. Matthew Rabin & Dimitri Vayanos, 2010. "The Gambler's and Hot-Hand Fallacies: Theory and Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 730-778.
    2. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, July.
    3. Yosef Rinott & Maya Bar-Hillel, 2015. "Comments on a “Hot Hand” Paper by Miller and Sanjurjo (2015)," Discussion Paper Series dp688, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    4. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
    5. Joshua B. Miller & Adam Sanjurjo, 2015. "Surprised by the Gambler’s and Hot Hand Fallacies? A Truth in the Law of Small Numbers," Working Papers 552, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    6. Daniel J. Benjamin, 2018. "Errors in Probabilistic Reasoning and Judgment Biases," NBER Working Papers 25200, National Bureau of Economic Research, Inc.
    7. Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, May.
    8. repec:pri:cepsud:91malkiel is not listed on IDEAS
    9. Romano Joseph P. & Shaikh Azeem & Wolf Michael, 2011. "Consonance and the Closure Method in Multiple Testing," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-25, February.
    10. Robin Greenwood & Andrei Shleifer, 2014. "Expectations of Returns and Expected Returns," The Review of Financial Studies, Society for Financial Studies, vol. 27(3), pages 714-746.
    11. 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.
    12. Barberis, Nicholas & Greenwood, Robin & Jin, Lawrence & Shleifer, Andrei, 2015. "X-CAPM: An extrapolative capital asset pricing model," Journal of Financial Economics, Elsevier, vol. 115(1), pages 1-24.
    13. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, vol. 72(5), pages 1329-1376, September.
    14. Miller, Joshua Benjamin & Sanjurjo, Adam, 2018. "Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers," OSF Preprints sv9x2, Center for Open Science.
    15. Joshua B. Miller & Adam Sanjurjo, 2018. "Surprised by the Hot Hand Fallacy? A Truth in the Law of Small Numbers," Econometrica, Econometric Society, vol. 86(6), pages 2019-2047, November.
    16. Joshua B. Miller & Adam Sanjurjo, 2014. "A Cold Shower for the Hot Hand Fallacy," Working Papers 518, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    17. Carhart, Mark M, 1997. "On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
    18. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    19. Matthew Rabin, 2002. "Inference by Believers in the Law of Small Numbers," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(3), pages 775-816.
    20. Hendricks, Darryll & Patel, Jayendu & Zeckhauser, Richard, 1993. "Hot Hands in Mutual Funds: Short-Run Persistence of Relative Performance, 1974-1988," Journal of Finance, American Finance Association, vol. 48(1), pages 93-130, March.
    21. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Journal of Economic Perspectives, American Economic Association, vol. 17(1), pages 59-82, Winter.
    22. Burton G. Malkiel, 2003. "The Efficient Market Hypothesis and Its Critics," Working Papers 111, Princeton University, Department of Economics, Center for Economic Policy Studies..
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