The organisers of major sports competitions use different policies with respect to constraints in the group draw. Our paper aims to rationalise these choices by analysing the trade-off between attractiveness (the number of games played by teams from the same geographic zone) and fairness (the departure of the draw mechanism from a uniform distribution). A parametric optimisation model is formulated and applied to the 2018 and 2022 FIFA World Cup draws. A flaw of the draw procedure is identified: the pre-assignment of the host to a group unnecessarily increases the distortions. All Pareto efficient sets of draw constraints are determined via simulations. The proposed framework can be used to find the optimal draw rules and justify the non-uniformity of the draw procedure for the stakeholders.
翻译：大型体育赛事组织者在小组抽签约束方面采用不同的策略。本文旨在通过分析吸引力（来自同一地理区域的球队之间的比赛场次）与公平性（抽签机制偏离均匀分布的程度）之间的权衡关系，为这些选择提供理论依据。我们构建了一个参数化优化模型，并将其应用于2018年和2022年国际足联世界杯抽签。研究发现抽签程序存在一个缺陷：将东道主预先分配到特定小组会不必要地加剧抽签偏差。通过模拟计算，我们确定了所有帕累托有效的抽签约束集合。所提出的框架可用于寻找最优抽签规则，并向利益相关者论证非均匀抽签程序的合理性。
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