Classroom Investigations of Recent Research Concerning the Hot Hand Phenomenon

ABSTRACT

Many players and fans of basketball believe in the “hot hand” phenomenon, yet for years there has been little statistical evidence that such a phenomenon exists (hence the “hot hand fallacy”). However, recent research of Miller and Sanjurjo suggests that previous analyses of the hot hand have been subject to a bias, and after correcting for this bias, there is in fact evidence that the hot hand is real. Miller and Sanjurjo's analyses are based on permutation tests. In this work, we discuss the ideas behind the permutation test procedure, illustrate an online Shiny app we developed for conducting the test, and present related simulation-based inference activities for introductory statistics courses. Our examples are based on data from the NBA Three Point Contest, in which we do find evidence of an average hot hand effect. Furthermore, we discuss additional topics concerning the bias in previous hot hand studies which can be introduced in courses with a stronger emphasis on probability or mathematical statistics. In particular, we discuss a simple coin flipping problem with a surprising solution which has been the subject of much recent media coverage and debate.

KEYWORDS:

• Bias
• Conditional probability
• Expectation
• Hot hand in basketball
• Hot hand fallacy
• Permutation test
• Probability puzzles
• Shiny app
• Simulation-based inference

Acknowledgments

The author thanks the two anonymous reviewers and the editor of the Datasets and Stories section for many insightful comments that improved the article in general and Section 4 in particular. The author thanks Bradley Lubich for many helpful discussions which motivated the work in this article. Bradley also wrote the core of the streak_stats.r function used in the Shiny app, and he provided valuable feedback on previous versions of the app. The author also thanks participants at the 2016 Joint Statistical Meetings for feedback on a presentation of parts of this work.

Supplemental Material

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