Understanding why shooters shoot -- An AI-powered engine for basketball performance profiling

Understanding player shooting profiles is an essential part of basketball analysis: knowing where certain opposing players like to shoot from can help coaches neutralize offensive gameplans from their opponents; understanding where their players are most comfortable can lead them to developing more effective offensive strategies. An automatic tool that can provide these performance profiles in a timely manner can become invaluable for coaches to maximize both the effectiveness of their game plan as well as the time dedicated to practice and other related activities. Additionally, basketball is dictated by many variables, such as playstyle and game dynamics, that can change the flow of the game and, by extension, player performance profiles. It is crucial that the performance profiles can reflect the diverse playstyles, as well as the fast-changing dynamics of the game. We present a tool that can visualize player performance profiles in a timely manner while taking into account factors such as play-style and game dynamics. Our approach generates interpretable heatmaps that allow us to identify and analyze how non-spatial factors, such as game dynamics or playstyle, affect player performance profiles.

Testing Unsatisfiability of Constraint Satisfaction Problems via Tensor Products

We study the design of stochastic local search methods to prove unsatisfiability of a constraint satisfaction problem (CSP). For a binary CSP, such methods have been designed using the microstructure of the CSP. Here, we develop a method to decompose the microstructure into graph tensors. We show how to use the tensor decomposition to compute a proof of unsatisfiability efficiently and in parallel. We also offer substantial empirical evidence that our approach improves the praxis. For instance, one decomposition yields proofs of unsatisfiability in half the time without sacrificing the quality. Another decomposition is twenty times faster and effective three-tenths of the times compared to the prior method. Our method is applicable to arbitrary CSPs using the well known dual and hidden variable transformations from an arbitrary CSP to a binary CSP.