Coordinate transformations for characterization and cluster analysis of spatial configurations in football

Current technologies allow movements of the players and the ball in football matches to be tracked and recorded with high accuracy and temporal frequency. We demonstrate an approach to analyzing football data with the aim to find typical patterns of spatial arrangement of the field players. It involves transformation of original coordinates to relative positions of the players and the ball with respect to the center and attack vector of each team. From these relative positions, we derive features for characterizing spatial configurations in different time steps during a football game. We apply clustering to these features, which groups the spatial configurations by similarity. By summarizing groups of similar configurations, we obtain representation of spatial arrangement patterns practiced by each team. The patterns are represented visually by density maps built in the teams' relative coordinate systems. Using additional displays, we can investigate under what conditions each pattern was applied.