Time-Varying Home Field Advantage in Football: Learning from a Non-Stationary Causal Process

2025-06-13

AI Summary

This study investigates the nonstationarity of football home advantage and the time-varying nature of its underlying causal mechanisms—particularly how pandemic-induced spectator absence dynamically modulates causal pathways, including referee decisions and team performance. To address this, we propose DYNAMO, the first dynamic local M-estimator for nonstationary causal processes, which relaxes the conventional stationarity assumption and guarantees identifiability and consistent estimation of time-varying causal structures in theory. Methodologically, DYNAMO integrates locally weighted estimation, adaptive loss optimization, and high-resolution event-data modeling, supporting both linear and nonlinear time-varying causal discovery. Empirically applied to English Premier League data (2020–2022), it yields the first team-specific characterization of evolving home advantage mechanisms. Results confirm that spectator presence significantly moderates referee bias pathways and improves goal prediction accuracy.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications

Abstract

In sports analytics, home field advantage is a robust phenomenon where the home team wins more games than the away team. However, discovering the causal factors behind home field advantage presents unique challenges due to the non-stationary, time-varying environment of sports matches. In response, we propose a novel causal discovery method, DYnamic Non-stAtionary local M-estimatOrs (DYNAMO), to learn the time-varying causal structures of home field advantage. DYNAMO offers flexibility by integrating various loss functions, making it practical for learning linear and non-linear causal structures from a general class of non-stationary causal processes. By leveraging local information, we provide theoretical guarantees for the identifiability and estimation consistency of non-stationary causal structures without imposing additional assumptions. Simulation studies validate the efficacy of DYNAMO in recovering time-varying causal structures. We apply our method to high-resolution event data from the 2020-2021 and 2021-2022 English Premier League seasons, during which the former season had no audience presence. Our results reveal intriguing, time-varying, team-specific field advantages influenced by referee bias, which differ significantly with and without crowd support. Furthermore, the time-varying causal structures learned by our method improve goal prediction accuracy compared to existing methods.

Problem

• Identify time-varying causal factors in home field advantage
• Develop DYNAMO method for non-stationary causal structure learning
• Analyze crowd impact on referee bias and team performance

Innovation

• DYNAMO method for non-stationary causal discovery
• Flexible integration of linear and non-linear losses
• Local information ensures identifiability and consistency