A Monte carlo framework for procedural fixture fairness evaluation in league competitions
开发了一个蒙特卡洛模拟框架，用于评估联赛赛程结构导致的程序性不公平，通过总公平偏差和基尼系数两个指标量化赛程扭曲，并应用于欧洲足球联赛验证其有效性。
Abstract Fairness is a critical yet underexplored dimension of tournament scheduling, where fixture asymmetries can systematically distort competition outcomes. This paper develops a Monte Carlo simulation framework as a general decision-support tool for assessing procedural fairness in league formats, isolating distortions arising from fixture structure rather than team strength or ranking rules. The approach integrates probabilistic match outcome modelling with two complementary fairness indicators: total fairness bias, capturing the magnitude of schedule-induced distortions, and the Gini index, measuring their distribution across participants. By incorporating competition-specific importance weights, the framework enables a context-aware, two-dimensional assessment applicable to any round-robin or multi-phase format, and can be embedded as a modular component into optimization, heuristics, or machine learning–based scheduling systems. To illustrate its applicability, we apply the framework to two European football leagues with structurally asymmetric designs. The results show how corrective mechanisms – such as home/away balancing phases – can significantly reduce fairness distortions compared to uncorrected triple round-robin structures. Beyond the case studies, the contribution is methodological: the framework provides a reproducible tool for fairness assessment and a foundation for fairness-aware optimization and scheduling methods applicable across sports and competition formats. Although demonstrated on football, the methodology is domain-independent and transferable to any context where fairness and equity are of relevance.