  During the past few years advancements in sports information systems and
technology has allowed us to collect a number of detailed spatio-temporal data
capturing various aspects of basketball. For example, shot charts, that is,
maps capturing locations of (made or missed) shots, and spatio-temporal
trajectories for all the players on the court can capture information about the
offensive and defensive tendencies and schemes of a team. Characterization of
these processes is important for player and team comparisons, pre-game
scouting, game preparation etc. Playing tendencies among teams have
traditionally been compared in a heuristic manner. Recently automated ways for
similar 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 work, we propose a
framework based on tensor decomposition for obtaining a set of prototype
spatio-temporal patterns based on the core spatiotemporal information and
contextual meta-data. The core of our framework is a 3D tensor X, 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. The framework introduced in this paper can have further
applications in the work-flow of the basketball operations of a franchise,
which we also briefly discuss.
