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We develop a machine learning approach to represent and analyze theunderlying spatial structure that governs shot selection among professionalbasketball players in the NBA. Typically, NBA players are discussed andcompared in an heuristic, imprecise manner that relies on unmeasured intuitionsabout player behavior. This makes it difficult to draw comparisons betweenplayers and make accurate player specific predictions. Modeling shot attemptdata as a point process, we create a low dimensional representation ofoffensive player types in the NBA. Using non-negative matrix factorization(NMF), an unsupervised dimensionality reduction technique, we show that alow-rank spatial decomposition summarizes the shooting habits of NBA players.The spatial representations discovered by the algorithm correspond to intuitivedescriptions of NBA player types, and can be used to model other spatialeffects, such as shooting accuracy.

Factorized Point Process Intensities: A Spatial Analysis of Professional Basketball