  Shot charts in basketball analytics provide an indispensable tool for
evaluating players' shooting performance by visually representing the
distribution of field goal attempts across different court locations. However,
conventional methods often overlook the bounded nature of the basketball court,
leading to inaccurate representations, particularly along the boundaries and
corners. In this paper, we propose a novel model-based approach to shot chart
estimation and visualization that explicitly considers the physical boundaries
of the basketball court. By employing Gaussian mixtures for bounded data, our
methodology allows to obtain more accurate estimation of shot density
distributions for both made and missed shots. Bayes' rule is then applied to
derive estimates for the probability of successful shooting from any given
locations, and to identify the regions with the highest expected scores. To
illustrate the efficacy of our proposal, we apply it to data from the 2022-23
NBA regular season, showing its usefulness through detailed analyses of shot
patterns for two prominent players.
