A doubly self-exciting Poisson model for describing scoring levels in NBA basketball.

This article focuses on developing and applying a doubly self-exciting Poisson time series model, based on the INGARCH(1,1) specification, to analyze the number of field goals made by National Basketball Association (NBA) teams and players during the 2018–2019 season at both the game (within-season) and minute (within-game) levels. The model captures temporal dependence by incorporating self-exciting effects and includes covariates such as playing at home and within-game temporal segments. Estimation is performed within a Bayesian framework using a divide-and-conquer strategy and Wasserstein barycenters to combine posterior distributions. Results indicate that while self-exciting dynamics are generally weak at the team level, certain high-scoring players exhibit notable excitation patterns, reflecting variability in scoring streaks. Additionally, the model facilitates clustering of players based on their scoring dynamics, offering insights into individual scoring behaviors, and suggests potential applications to other sports and performance-related variables.