⚽ Player Performance Analyzer — Trajectory Clustering Live

K-means is an unsupervised learning algorithm that partitions data points into k groups so that each point belongs to the cluster whose centroid (mean) it is closest to, measured by Euclidean distance. It alternates between an assignment step, where every point joins its nearest centroid, and an update step, where each centroid moves to the mean of the points assigned to it, repeating until the assignments stop changing or the centroids barely move.

Raw x,y coordinates only describe where a player is at one instant, which is dominated by whichever phase of play is happening right now. Deriving features from the trajectory history — average field position, roaming coverage area, sprint frequency and pass-network centrality — captures how a player behaves over time, which is what actually distinguishes tactical roles such as a high press forward from a deep-lying defender, even when their instantaneous positions briefly overlap.

Plain k-means picks starting centroids uniformly at random, which can produce poor clusters or slow convergence if two initial centroids land close together. K-means++ instead picks the first centroid randomly, then chooses each subsequent centroid with probability proportional to its squared distance from the nearest centroid already chosen, spreading the initial seeds out across the data. This nearly always produces faster convergence and a lower final inertia than naive random initialisation.

Inertia, or within-cluster sum of squares, is the total squared Euclidean distance between every point and its assigned cluster centroid, computed in the standardized feature space. Lower inertia means tighter, more internally consistent clusters. Watching inertia drop across the assignment/update iterations each time the match re-clusters shows the algorithm actually converging, rather than just re-colouring dots at random.

K-means itself only outputs numbered clusters — it has no idea what a "deep block" is. After each clustering pass, the simulation looks at each cluster's average raw feature values relative to the whole squad's statistics that pass, and applies simple, transparent rules to attach a human-readable tactical label, so cluster 2 today might read as "Wide Overlap" while cluster 2 tomorrow reads as "High Press" if the underlying players' behaviour has shifted.