We present a novel representation of NBA players' shooting patterns based on Functional Data Analysis (FDA). Each player's charts of made and missed shots are treated as smooth functional data defined over a two-dimensional domain corresponding to the offensive half-court. This continuous representation enables a parsimonious multivariate functional principal components analysis (MFPCA) decomposition, producing a set of common principal component functions that capture the primary modes of variability in shooting patterns, along with player-specific scores that quantify individual deviations from the average behavior. We first interpret the principal component functions to characterize the main sources of variation in shooting tendencies. We then apply $k$-medoids clustering to the principal component scores to construct a data-driven taxonomy of players. Comparing our empirical clusters to conventional NBA position labels reveals low agreement, suggesting that our shooting-pattern representation might capture aspects of playing style not fully reflected in official designations. The proposed methodology provides a flexible, interpretable, and continuous framework for analyzing player tendencies, with potential applications in coaching, scouting, and historical player or match comparisons.

翻译：本文提出了一种基于函数型数据分析（FDA）的NBA球员投篮模式新表征方法。每位球员的投篮命中与未命中分布图被视为定义在进攻半场二维空间上的平滑函数型数据。这种连续表征使得我们能够进行简约的多变量函数型主成分分析（MFPCA）分解，得到一组捕捉投篮模式主要变异方式的公共主成分函数，以及量化个体偏离平均行为的球员特定得分。我们首先通过解释主成分函数来刻画投篮倾向变异的主要来源。随后对主成分得分应用$k$-medoids聚类算法，构建数据驱动的球员分类体系。将我们的实证聚类结果与传统NBA位置标签进行比较，发现二者一致性较低，这表明我们的投篮模式表征可能捕捉到了官方定位未能完全反映的比赛风格特征。所提出的方法为分析球员倾向提供了一个灵活、可解释且连续的框架，在教练决策、球探评估以及历史球员或比赛比较方面具有潜在应用价值。