Random Walk Picture of Basketball Scoring

TL;DR

This paper models basketball scoring as a weakly-biased continuous-time random walk, accurately capturing various statistical properties of NBA game scoring and team performance using play-by-play data.

Contribution

It introduces a novel random walk framework for basketball scoring, incorporating game-specific features and team heterogeneity, to explain scoring dynamics and team success.

Findings

Scoring intervals follow an exponential distribution.

The model accurately predicts score differences and lead durations.

Inclusion of team heterogeneity explains win/loss records.

Abstract

We present evidence, based on play-by-play data from all 6087 games from the 2006/07--2009/10 seasons of the National Basketball Association (NBA), that basketball scoring is well described by a weakly-biased continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between different scoring intervals. Using this random-walk picture that is augmented by features idiosyncratic to basketball, we account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead. By further including the heterogeneity of team strengths, we build a computational model that accounts for essentially all statistical features of game scoring data and season win/loss records of each team.