Defensive success in football can be linked to specific spatial and numerical indicators, with model-estimated improvements in defensive-success probability ranging from 0.136 to 0.246 for passing, 0.253 to 0.387 for receiving, 0.155 to 0.279 for carrying and 0.003 to 0.019 for shooting. These findings come from an observational, scenario-specific causal machine-learning framework designed to move beyond correlation and predictive accuracy toward tactical decision support. The researchers divided passing and receiving, carrying and shooting into relatively homogeneous spatial contexts before analysing the defensive events in each.
The study, published in Complex & Intelligent Systems , combined interpretable key performance indicators with single-KPI double machine learning, joint double machine learning and a constrained genetic algorithm. The indicators described local numerical configuration, defensive distance, spatial coverage and team organisation. Single-KPI analyses estimated average marginal effects, while joint modelling examined whether selected effects persisted when multiple indicators and their interactions were considered simultaneously.
The genetic algorithm explored feasible adjustments for unsuccessful defensive events, restricting proposed changes to combinations represented in the empirical data. For the pass stage, the distance between the attacker and nearest defender showed the most stable relationship with defensive success. Its single-KPI average marginal effect ranged from −0.137 to −0.106, indicating that, across the analysed contexts, greater nearest-defender distance was associated with a lower estimated probability of successfully defending the pass.
The receiving stage produced three indicators that were jointly supported: local numerical configuration, nearby-defender positioning and defensive coverage. Their reported single-KPI average marginal effects were −0.056 to −0.026 for numerical configuration, 0.072 to 0.232 for nearby-defender positioning and 0.028 to 0.037 for defensive coverage. Carrying involved supported measures of proximal pressure, numerical configuration and team structure.
These included nearby-defender measures covering three and five defenders, numerical advantages covering five and ten players, and area and spatial defensive indicators. The corresponding single-KPI average marginal effects ranged from −0.167 to −0.038 for the nearby-defender measures, −0.134 to −0.046 for numerical-configuration measures and 0.025 to 0.119 for the area and spatial measures. In the shooting stage, the model retained one supported indicator per spatial cluster, with single-KPI effects between −0.057 and −0.032.
The representative effects passed the study’s prespecified identification diagnostics and remained broadly stable across robustness and sensitivity analyses, the research team reported. The probability gains are model estimates under the specified observational assumptions, not observed improvements from interventions performed on the pitch. Within those limits, the framework offers a context-sensitive way to examine how pressure, spacing, numerical balance and team structure relate to defensive success at different stages of a football match, rather than treating a single tactical configuration as universally optimal.
Subject of Research: Causal machine-learning analysis of context-specific defensive indicators in football
Article Title: Seeking order in football match complexity: from causal identification to strategic optimization
Article References: Liu, X., Wang, R., Huang, K., Gómez-Ruano, M.-Á., Buldú, J. M., & Zhou, C. (2026). Seeking order in football match complexity: from causal identification to strategic optimization. Complex & Intelligent Systems. https://doi.org/10.1007/s40747-026-02511-0
Image Credits: AI Generated
DOI: 10.1007/s40747-026-02511-0
Keywords: football analytics, causal inference, machine learning, defensive strategy, spatial analysis, double machine learning, genetic algorithms, tactical optimization, match performance, Seeking, order, football
News Source: Teresa Odom. (October 21, 2026). Causal machine learning identifies tactical levers in football defenses. Scienmag.
