When do Risky Substitutions Improve Match Outcomes? Interpreting Causal Machine Learning Models for Insights

Abstract

We investigate the impact of risk-taking on football match outcomes within the context of substitutions. The study uses an extensive dataset of 75 thousand substitutions spanning eight seasons across six leagues, encompassing team, match and manager characteristics, and interim results. Given the intricate web of potential drivers and the absence of a well-defined theoretical framework, conventional econometric approaches fall short. Instead, Causal Forest, a black-box causal machine learning (ML) technique, was adopted to estimate the heterogeneous treatment effects, coupled with robustness checks. Its estimates are explained through Generalized Additive Models (GAM), visualizing how different factors affect the risk-taking probability and moderate the treatment effect of risk-taking on match outcomes. Fidelity of the explanation is improved by segmenting the dataset to capture strong interaction effects. The study reveals that risk-taking propensity peaks when a team trails by 2–3 goals and tapers when leading by the same margin. Considering impact of risk-taking on match outcomes, interestingly, younger managers exhibit superior performance compared to middle-aged ones, while older counterparts excel in later substitutions. The manager’s tenure with the team increases the impact, tapering in the long run. Earlier substitutions, stronger teams have greater impact when risk-taking. Teams leading by one goal stand to benefit most from risk-taking in substitutions. This research underscores the synergistic potential of black-box causal machine learning and interpretable models, given large representative datasets with all confounders. Insights into football risk-taking dynamics have implications for managerial strategies. Beyond football, it is noteworthy that manager age and tenure with the team are top first and third factors determining the effectiveness of a risky decision.

Keywords

• Football analytics
• risk-taking
• decision making
• heterogeneous treatment effect
• causal forest
• generalized additive models (GAM)