Existing match classification models in the tournament design literature have two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not distinguished with respect to the incentives of the contestants. We propose a probabilistic framework to address both issues. For each match, our approach relies on simulating all other matches played simultaneously or later to compute the qualifying probabilities under the three main outcomes (win, draw, loss), which allows the classification of each match into six different categories. The suggested model is applied to the previous group stage and the new incomplete round-robin league, introduced in the 2024/25 season of UEFA club competitions. An incomplete round-robin tournament is found to contain fewer stakeless matches where both contestants are indifferent, and substantially more matches where both contestants should play offensively. However, the robustly higher proportion of potentially collusive matches can threaten with serious scandals.

翻译：现有锦标赛设计文献中的匹配分类模型存在两大局限：仅当不确定的未来结果从不影响参赛者奖金时，才认为该参赛者持中立态度；且未根据参赛者的激励差异来区分竞争性比赛。我们提出了一个概率框架以解决这两个问题。对于每场比赛，我们的方法通过模拟所有同时或稍后进行的其他比赛，计算三种主要结果（胜、平、负）下的晋级概率，从而将每场比赛划分为六个不同类别。该模型被应用于2024/25赛季欧洲足球协会联盟俱乐部赛事中采用的既有小组赛阶段及新型不完全循环赛制。研究发现，不完全循环赛制中包含双方参赛者均持中立态度的无关紧要比赛较少，而双方参赛者均应采取进攻战术的比赛显著增多。然而，潜在合谋比赛比例持续偏高的现象，可能引发严重的赛事丑闻。