tHoops: A Multi-Aspect Analytical Framework Spatio-Temporal Basketball Data Using Tensor Decomposition

The shot selection process in basketball can be thought of as an indicator of the identity of a player/team. Characterization of these processes is important for player and team comparisons, pre-game scouting etc. Typically, shot charts are compared in a heuristic manner. Recently though automated ways have appeared in the sports analytics literature that aim into identifying a set of prototype shooting patterns that can be used as a basis for describing the tendencies of a player/team. However, these approaches are almost exclusively focused on the spatial distribution of the shots. However, there is a multitude of other parameters that can affect the shot selection by a player. For example, the time remaining on the clock, the score differential, etc. are some contextual factors that can impact the shot selection of a player. In this work, we propose a framework based on tensor decomposition for obtaining a set of prototype shooting patterns based on spatiotemporal information and contextual meta-data, that can be used to describe the overall shot selection process for a player or a team. The core of our framework is a 3D tensor X, whose element X(i,j,k) is equal to the number of shots entity i took from location j during time k. The granularity of time and location can be defined depending on the application. Using the PARAFAC decomposition we decompose the tensor into several interpretable patterns, that capture a group of entities, that take shots from similar locations during similar times in the game. Using the tensor components, we express every entity as a combination of these components with the weights being the corresponding elements in the entity factor of the decomposition. The framework introduced in this paper can have further applications in the analysis of the spatiotemporal data available from optical player tracking as we showcase by analyzing a small dataset.