Modeling the complexity of basketball games using marked mutually exciting point processes

Abstract

The basketball game is rarely predictable due to the complexity of its scoring process. To deal with the complexity and forecast the game results, we develop a marked mutually exciting point process model for the scoring process. In the model, the dynamic of the scoring intensity is characterized by a mutually exciting point process. A time varying background rate is used in the intensity function to account for the non-homogeneity. The dependence between scoring events is incorporated into the model with two team-specific exponential exciting kernels. The distribution of the points obtained in each scoring event is modeled as a categorical distribution with parameters from a Dirichlet prior. An empirical Bayesian method and an expectation-maximization algorithm are developed to estimate the model parameters. We design a simulation algorithm to do pre-game and in-game predictions. An empirical study is conducted with National Basketball Association games in four seasons. It is showed that the proposed model outperforms the benchmark model both in the win-loss prediction and score prediction. Moreover, our model can obtain positive returns when betting in the point spread market. Besides forecasting, an index called added winning probability is designed based on the model to evaluate the players’ performance.