Bayesian hierarchical modelling of basketball tracking data - a case study of spatial entropy and spatial effectiveness.

Spatio-temporal data in sport is increasing rapidly, however suitable statistical methods for analysing this data are underdeveloped. The current study establishes the need for spatial statistical methods, propose a Bayesian hierarchical model as an appropriate method for comparing spatial variables, and test this model across three spatial scales. The need for spatial statistical methods was established through the identification of spatial autocorrelation. This necessitated the use of a Bayesian hierarchical model to test for an association between spatial ball movement entropy and spatial effectiveness. Posterior distribution results showed a generally positive association such that increases in entropy were associated with increases in effectiveness. The strength and confidence of the associations were impacted by the spatial scale, with the 6 × 6 grid showing the most conclusive evidence of a positive relationship; the 4 × 4 grid was mostly positive, however with a large variation; and finally, the basket-centric scale results were less conclusive. The results of the current study demonstrate the suitability of a Bayesian hierarchical model for testing for associations or differences between spatial variables. With the increase in spatial analyses in sport, this study presents an appropriate statistical method for dealing with complex problems associated with spatial analyses.