Bayesian hierarchical modelling of basketball team performance : an NBA regular season case study

Abstract

The main goal of this study is to propose two Bayesian hierarchical modelling approaches using basketball game data from the 2008/2009 NBA regular season. The aim of the first approach is to estimate the results of each match during the season. This is done by considering each scoring method in basketball separately, that is, free throws, 2-point shots and 3-point shots, and estimating the offensive and defensive ability with respect to each scoring method for each team. These attributes are then used to produce a final score for each match. We attempt both the Poisson and the negative binomial distribution to model the scoring propensities. Both models are used to predict game outcomes and final standings, and since we find the negative binomial approach to be considerably superior, we use it to determine overall attack and defense abilities of each time for each scoring method. The second modelling approach, on the other hand, focuses on finding the probability of the home team winning a particular match in the season. Due to MCMC convergence issues, this model is represented by just one parameter representing overall strength for each team rather than two. When comparing the winning probability approach with the scoring propensity approach, we find that the latter is superior at predicting game outcomes, the former is superior at predicting final standings, while both are comparable in predicting which teams will qualify to playoffs.