Modelling the dynamic pattern of surface area in basketball and its effects on team performance

Due to the advent of GPS techniques, a wide range of scientific literature on Sport Science is nowadays devoted to the analysis of players movement in relation to team performance in the context of big data analytics. A specific research question regards whether certain patterns of space among players affect team performance, from both an offensive and a defensive perspective. Using a time series of basketball players coordinates, we focus on the dynamics of the surface area of the five players on the court with a twofold purpose: (i) to give tools allowing a detailed description and analysis of a game with respect to surface areas dynamics and (ii) to investigate its influence on the points made by both the team and the opponent. We propose a three-step procedure integrating different statistical modelling approaches. Specifically, we first employ a Markov Switching Model (MSM) to detect structural changes in the surface area. Then, we perform descriptive analyses in order to highlight associations between regimes and relevant game variables. Finally, we assess the relation between the regime probabilities and the scored points by means of Vector Auto Regressive (VAR)models. We carry out the proposed procedure using real data and, in the analyzed case studies, we find that structural changes are strongly associated to offensive and defensive game phases and that there is some association between the surface area dynamics and the points scored by the team and the opponent.