Is a Basketball Free-Throw Sequence Nonrandom? A Group Exercise for Undergraduate Statistics Students

Abstract

I describe a group exercise that I give to my undergraduate biostatistics class. The exercise involves analyzing a series of 200 consecutive basketball free-throw attempts to determine whether there is any evidence for sequential dependence in the probability of making a free-throw. The students are given the exercise before they have learned the appropriate statistical tests, so that they can come up with ideas on their own. Students spend a full class period working on the problem, with my guidance and hints. In the next class period, we discuss how each student group approached the problem. I then present several alternative ways to analyze the data, including a runs test and a contingency table analysis of transition frequencies.

• runs test
• binomial
• transition probabilities
• contingency table
• sequential independence
• randomization

Acknowledgments

I thank my students for their enthusiastic participation in this exercise. I also thank two anonymous reviewers and editors Roger Johnson and Dex Whittinghill for their many helpful suggestions.