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Abstract:
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Using play-by-play data from all 2014-15 regular season NBA games, we build generative models for substitutions of both individual players and five-player lineups. To model substitutions more accurately, we incorporate fouls committed and received. The substitution model consists of a continuous-time semi-Markov chain, with both holding time distribution and transition rates inferred from data. Combining the substitution model with a model for how a particular group of players contributes offensively and defensively as a function of seconds played (a plus/minus rate model), we develop a Monte Carlo method to simulate plausible game trajectories and predict outcomes of games. We create and compare different linear and nonlinear regression techniques for constructing the plus/minus rate model. We quantify the predictive power of our model, comparing out-of-sample predictions with actual results for both regular season and playoff games. By running simulations with and without an injured player, we show how the substitution model helps answer "what if" questions and measure impacts of injuries on the winners of games and series.
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