The life and death of football team runs: survival of collective modes shapes Lévy-like transport

Abstract

Broad run-length distributions and short-lag superdiffusion have recently been reported in football players and team centroids, prompting a collective-foraging interpretation. The mechanism linking these player- and team-level signatures remains unclear. Using SoccerMon GPS data from 66 tracked team-match records across 62 fixtures in the Norwegian women's top-flight Toppserien, we asked whether player transport is inherited from a translating team mode and what controls the lifetime of that mode. We decomposed player displacement into centroid translation and motion within the formation, then modelled the switching and termination of directional centroid runs. At longer lags, centroid translation carried an increasing share of player displacement. Run lifetimes were broad but finite: termination was highest near onset, declined with age and rose modestly later. After accounting for speed and directional persistence, collective order added only limited predictive information. At the population level, an age-dependent switching-and-termination model predicted, on held-out match dates, the early enrichment and later depletion of high-order states among surviving runs. These results link player- and team-level Lévy-like movement through a finite-lived collective mode whose age and internal state shape its survival. Long displacements need not be selected in advance; they can emerge when transient collective modes persist, reorganise and selectively survive. More broadly, trajectory statistics may record which dynamical histories survive, not only the rules by which agents move.