Classifying ball trajectories in invasion sports using dynamic time warping: A basketball case study.

Comparison and classification of ball trajectories can provide insight to support coaches and players in analysing their plays or opposition plays. This is challenging due to the innate variability and uncertainty of ball trajectories in space and time. We propose a framework based on Dynamic Time Warping (DTW) to cluster, compare and characterise trajectories in relation to play outcomes. Seventy-two international women's basketball games were analysed, where features such as ball trajectory, possession time and possession outcome were recorded. DTW was used to quantify the alignment-adjusted distance between three dimensional (two spatial, one temporal) trajectories. This distance, along with final location for the play (usually the shot), was then used to cluster trajectories. These clusters supported the conventional wisdom of higher scoring rates for fast breaks, but also identified other contextual factors affecting scoring rate, including bias towards one side of the court. In addition, some high scoring rate clusters were associated with greater mean change in the direction of ball movement, supporting the notion of entropy affecting effectiveness. Coaches and other end users could use such a framework to help make better use of their time by honing in on groups of effective or problematic plays for manual video analysis, for both their team and when scouting opponent teams and suggests new predictors for machine learning to analyse and predict trajectory-based sports.