Abstract: We present Possession Sketches, a new machine learning method for organizing and exploring a database of basketball player-tracks. Our method organizes basketball possessions by offensive structure. We first develop a model for populating a dictionary of short, repeated, and spatially registered ”actions”. Each action corresponds to an interpretable type of player movement. We examine statistical patterns in these actions, and show how they can be used to describe individual player behavior. Leveraging this “vocabulary” of actions, we develop a hierarchical model to characterize interactions between players. Our approach draws on the topic-modeling literature, extending Latent Dirichlet Allo- cation (LDA) through a novel representation of player movement data which uses techniques common in animation and video game design. We show that this model is able to group together possessions with similar offensive structure, allowing efficient search and exploration of the entire database of player- tracking data. We show that our model finds repeated offensive structure in teams (e.g. strategy), pro- viding a much more sophisticated, yet interpretable lens into basketball player-tracking data.