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Measurement Error and the Hot Hand

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  • Daniel F. Stone

Abstract

This article shows that the first autocorrelation of basketball shot results is a highly biased and inconsistent estimator of the first autocorrelation of the ex ante probabilities with which the shots are made. Shot result autocorrelation is close to zero even when shot probability autocorrelation is close to one. The bias is caused by what is equivalent to a severe measurement error problem. The results imply that the widespread belief among players and fans in the hot hand is not necessarily a cognitive fallacy.

Suggested Citation

  • Daniel F. Stone, 2012. "Measurement Error and the Hot Hand," The American Statistician, Taylor & Francis Journals, vol. 66(1), pages 61-66, February.
  • Handle: RePEc:taf:amstat:v:66:y:2012:i:1:p:61-66
    DOI: 10.1080/00031305.2012.676467
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    Citations

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    Cited by:

    1. Jeremy Arkes, 2013. "Misses in “Hot Hand†Research," Journal of Sports Economics, , vol. 14(4), pages 401-410, August.
    2. Jeremy M. Losak & Andrew P. Weinbach & Rodney J. Paul, 2023. "Behavioral Biases in Daily Fantasy Baseball: The Case of the Hot Hand," Journal of Sports Economics, , vol. 24(3), pages 374-401, April.
    3. 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.
    4. Evans, Andrew E. & Crosby, Paul & Shin, Sunny Y., 2023. "Psychological momentum among non-experts: Evidence from club golfers," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 104(C).
    5. Robert M. Lantis & Erik T. Nesson, 2019. "Hot Shots: An Analysis of the ‘Hot Hand’ in NBA Field Goal and Free Throw Shooting," NBER Working Papers 26510, National Bureau of Economic Research, Inc.
    6. 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.
    7. Wen‐Jhan Jane, 2023. "Hot hand or choking under pressure – Evidence from professional basketball," Kyklos, Wiley Blackwell, vol. 76(2), pages 223-254, May.
    8. Daniel J. Benjamin, 2018. "Errors in Probabilistic Reasoning and Judgment Biases," NBER Working Papers 25200, National Bureau of Economic Research, Inc.
    9. 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.
    10. Robert Lantis & Erik Nesson, 2021. "Hot Shots: An Analysis of the “Hot Hand†in NBA Field Goal and Free Throw Shooting," Journal of Sports Economics, , vol. 22(6), pages 639-677, August.
    11. Daniel F. Stone & Jeremy Arkes, 2016. "Reference Points, Prospect Theory, and Momentum on the PGA Tour," Journal of Sports Economics, , vol. 17(5), pages 453-482, June.
    12. Joshua B. Miller & Adam Sanjurjo, 2015. "Is it a Fallacy to Believe in the Hot Hand in the NBA Three-Point Contest?," Working Papers 548, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. Miller, Joshua Benjamin & Sanjurjo, Adam, 2018. "A Visible (Hot) Hand? Expert Players Bet on the Hot Hand and Win," OSF Preprints sd32u, Center for Open Science.
    14. Miller, Joshua Benjamin & Sanjurjo, Adam, 2018. "Is it a Fallacy to Believe in the Hot Hand in the NBA Three-Point Contest?," OSF Preprints dmksp, Center for Open Science.
    15. 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.
    16. Brett Green & Jeffrey Zwiebel, 2018. "The Hot-Hand Fallacy: Cognitive Mistakes or Equilibrium Adjustments? Evidence from Major League Baseball," Management Science, INFORMS, vol. 64(11), pages 5315-5348, November.
    17. Robert Wrathall & Rod Falvey & Gulasekaran Rajaguru, 2020. "Do (Australian) jockeys have hot hands?," Australian Journal of Management, Australian School of Business, vol. 45(2), pages 223-239, May.
    18. Marius Ötting & Roland Langrock & Christian Deutscher & Vianey Leos‐Barajas, 2020. "The hot hand in professional darts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(2), pages 565-580, February.
    19. Miller, Joshua Benjamin & Sanjurjo, Adam, 2018. "A Cold Shower for the Hot Hand Fallacy: Robust Evidence that Belief in the Hot Hand is Justified," OSF Preprints pj79r, Center for Open Science.
    20. 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.
    21. Morgulev, Elia, 2023. "Streakiness is not a theory: On “momentums” (hot hands) and their underlying mechanisms," Journal of Economic Psychology, Elsevier, vol. 96(C).
    22. 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.
    23. 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).
    24. Ala Avoyan & Robizon Khubulashvili & Giorgi Mekerishvili, 2020. "Call It a Day: History Dependent Stopping Behavior," CESifo Working Paper Series 8603, CESifo.

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