Context-aware event clustering with consensus model selection: A large-scale study of EuroLeague timeouts

This study addresses the problem of segmenting decision-intervention events in sequential, high-frequency processes using unsupervised learning applied to play-by-play-derived game-state representations. Using play-by-play–derived key performance indicators (KPIs) from 3,743 EuroLeague games (2008–2023), we represent 25,032 timeout events as feature vectors capturing efficiency, score state, possession control, and playmaking/discipline. We benchmark partitional clustering methods (k-means, k-medoids / Partitioning Around Medoids (PAM), MiniBatch k-means, Clustering Large Applications (CLARA), and Fuzzy c-means (FCM)) under Euclidean, Manhattan, and Minkowski (r = 3) distances. Candidate solutions are evaluated with Silhouette, Calinski–Harabasz, Davies–Bouldin, Dunn, Gap, and an elbow heuristic, and selected via a prespecified consensus rule prioritizing parsimony and stability across k. The primary taxonomy selects k-means (Euclidean) with k = 3, with k = 2 and k = 4 providing coherent robustness views. To interpret clusters, we combine inferential contrasts via analysis of variance (ANOVA), supervised importance screening using Random Forest mean decrease in accuracy and mean decrease in Gini (MDA/MDG), and low-dimensional structure via principal component analysis (PCA). Across methods, a compact discriminative core emerges: performance-index differentials, score differential, free-throw volume/accuracy, and assists; offensive rebounding (and secondarily defensive rebounding and turnovers) captures possession-control stress co-occurring with score/efficiency pressure. We translate these patterns into an operational heuristic: monitor a composite pressure signature and consider intervention when it deteriorates, particularly in late-phase profiles consistent with momentum disruption and half-court re-organization.