Seeking order in football match complexity: from causal identification to strategic optimization

Abstract

Traditional football analytics centred on correlation or predictive accuracy may not fully support intervention-oriented tactical decisions. This study developed a scenario-specific causal machine-learning framework for passing and receiving, carrying, and shooting, with each scenario further divided into relatively homogeneous spatial contexts. Interpretable KPIs described local numerical configuration, defensive distance, spatial coverage, and team organisation. Under prespecified identification assumptions, single-KPI double machine learning estimated average marginal effects, joint DML examined whether the selected effects persisted when multiple indicators and their interactions were modelled simultaneously, and a constrained genetic algorithm explored feasible adjustments among unsuccessful defensive events within empirical support. The representative effects passed the prespecified identification diagnostics and remained broadly stable across robustness and sensitivity analyses. For the pass stage, nearest-defender distance showed the most stable relationship with defensive success (Avg_1_Def single-KPI AME: −0.137 to −0.106). For the receive stage, local numerical configuration, nearby-defender positioning, and defensive coverage were jointly supported (single-KPI AMEs: Adv_10, −0.056 to −0.026; Avg_5_Def, 0.072 to 0.232; Area_Def, 0.028 to 0.037). The carry stage involved proximal pressure, numerical configuration, and team structure (Avg_3/5_Def, −0.167 to −0.038; Adv_5/10, −0.134 to −0.046; Area_Def/Spr_Def, 0.025 to 0.119), whereas the shot stage retained one supported KPI per spatial cluster (single-KPI AMEs: −0.057 to −0.032). Model-estimated gains in defensive-success probability were 0.136–0.246 for the pass stage, 0.253–0.387 for the receive stage, 0.155–0.279 for the carry stage, and 0.003–0.019 for the shot stage. The framework provides interpretable, context-sensitive evidence for defensive decision support while keeping its observational assumptions and practical limits explicit.