tHoops: A Multi-Aspect Analytical Framework for Spatio-Temporal Basketball Data

Evangelos E. Papalexakis, Konstantinos Pelechrinis

Abstract: During the past few years advancements in sports information systems and technology has allowed the collection of a number of detailed spatio-temporal data that capture various aspects of basketball. For example, shot charts, that is, maps capturing locations of (made or missed) shots, and spatio-temporal trajectories for the players on the court can capture information about the offensive and defensive tendencies, as well as, schemes used by a team. Characterization of these processes is important for player and team comparisons, scouting, game preparation etc. Team and player tendencies have traditionally been compared in a heuristic manner, which inevitably can lead to subtle but crucial information being ignored. Recently automated ways for these comparisons have appeared in the sports analytics literature. However, these approaches are almost exclusively focused on the spatial distribution of the underlying actions (usually shots taken), ignoring a multitude of other parameters that can affect the action studied. In this study, we propose a framework based on tensor decomposition for obtaining a set of prototype spatio-temporal patterns based on the core spatio-temporal information and contextual meta-data. At the epicenter of our work is a 3D tensor $\tensor$, whose dimensions represent the entity under consideration (team, player, possession etc.), the location on the court and time. We make use of the PARAFAC decomposition and we decompose the tensor into several interpretable patterns, that can be thought of as prototype patterns of the process examined (e.g., shot selection, offensive schemes etc.). We also introduce an approach for choosing the number of components to be considered. Using the tensor components, we can then express every entity as a weighted combination of these components. Finally, the framework introduced in this paper has applications that go beyond purely pattern analysis. In particular, it can facilitate a variety of tasks in the work-flow of a franchise's basketball operations as well as in the sports analytics research community.