Approaching the limit: Modeling the physiological bounds of playable space in football

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Abstract
A bstract: Pitch control models quantify spatial dominance in football by estimating which player can arrive first at each pitch location, but they treat all players as equivalently capable regardless of preceding effort. We introduce physiology-aware pitch control (Phys-PC), a model-agnostic time-to-arrive correction that imposes two physiological capacity channels calibrated from tracking data: a transient recoverable burden capturing incomplete recovery from recent high-intensity efforts, and a cumulative non-recoverable drain accumulating across match play. Both channels reduce a bounded access scale that modulates kinematic TTA before any downstream pitch-control computation. All parameters are anchored to exercise-physiology benchmarks; no laboratory measurements are assumed. Applied to a 64-match international tournament, Phys-PC reveals structure that kinematic models cannot detect. In head-to-head races, the dominant burden channel shifts from transient to cumulative over the course of a match, with a transient resurgence in the final 15 minutes. These physiological asymmetries predict match outcomes: relative reserve advantage is associated with higher odds of winning ground challenges (OR = 1.20, p = 0.006; +4.2 pp), completing over-the-top passes past recovering defenders (OR = 1.45, p = 0.034; +8.3 pp), and progressing possession sequences into the final third (OR = 1.31, p = 0.013; +5.1 pp). At the player-profile level, an acute-cumulative decomposition of contested space access separates roles and individuals whose territorial reach is maintained through sustained positioning from those whose access is rebuilt through repeated high-intensity actions, providing a physiological lens on team tactical structure.

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