Is Stephen Curry really a guard? A new perspective on player typologies using functional data analysis

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 application of FDA to this area introduces a flexible, interpretable, and continuous framework for analyzing player tendencies, with potential applications in coaching, scouting, and historical player or match comparisons.