The dual problem of space: Relative player positioning determines attacking success in elite men's football.

The concept of space has been successfully modelled in football using spatiotemporal player data and Voronoi diagrams. Current approaches, however, are narrow in scope by focusing on an inter-team allocation of space to measure space control. The present work extends this widespread perspective with an intra-team application of the Voronoi diagram and its dual Delaunay triangulation to measure space management. Both models are leveraged to derive novel performance metrics, which assess how teams use triangular positioning and how players tie up defenders during attacks. The outcome of N = 128,187 attacking sequences from 306 elite men's football matches is analysed using linear mixed-effects models to validate the proposed performance metrics. Results show that attacking success is characterized by player positioning which promotes forming of large triangles especially in ball proximity, whereas the overall number of triangles is of no relevance. Furthermore, players tie up more defenders and thus create free teammates more often during successful attacks. The results demonstrate that a new perspective on space is helpful to better quantify and understand the effect of space management and player positioning on attacking performance in football.