Past Event: Oden Institute Seminar

Is Basketball Scoring Just a Random Walk?

Sid Redner, Professor, Physics, Santa Fe Institute

Abstract

Believe it or not, watching basketball is nearly the same as watching repeating coin tossings!  By analyzing available data from recent NBA basketball seasons, basketball scoring during a game is well described by a continuous-time anti-persistent random walk, with essentially no temporal correlations between successive scoring events.  We show how to calibrate this model to account for many statistical season-long metrics of NBA basketball.  As further illustrations of this random-walk picture, we show that the distribution of times when the last lead change occurs and the distribution of times when the score difference is maximal are both given by the celebrated arcsine law---a beautiful and surprising property of random walks.  We also use the random-walk picture to construct the criterion for when a lead of a specified size is "safe" as a function of the time remaining in the game.  The obvious application to game-time betting is left as an exercise for the interested.

Biography

Sid Redner is a faculty member at the Santa Fe Institute.  From 1978-2014, he was on the physics faculty at Boston University, where he served as acting chair (twice), and also department chair.  His research interests are in non-equilibrium statistical physics, and on these topics he as published more than 300 articles and two books—“A Guide to First-Passage Processes" (Cambridge, 2001) and “A Kinetic View of Statistical Physics" with Eli Ben-Naim and Paul Krapivsky (Cambridge, 2010).  He is a Fellow of the APS and the 2021 recipient of Leo P. Kadanoff Prize from the American Physical Society.