According to recent empirical studies, the group draw of major sports tournaments can imply a high level of uncertainty, and some lucky teams enjoy an unfair advantage over the other teams. We propose a novel technique to quantify this draw uncertainty, which, arguably, has an optimal level of zero. Our simulation-based approach requires generating a high number of random draws to compute the variance of qualifying probabilities for each team. The method is applied to compare draw uncertainty in the former group stage and the current incomplete round-robin league phase of the UEFA Champions League. We also break down the impact of the 2024/25 reform into various components. The new format is found to decrease draw uncertainty; the reduction can mainly be attributed to the inaccurate seeding system used by UEFA. Our results reveal that the primary benefit of an incomplete round-robin tournament compared to the standard group stage lies in the robustness of its draw uncertainty to the seeding of the teams, which is a crucial aspect of fairness.

翻译：根据近期的实证研究，大型体育赛事的抽签分组可能蕴含高度的不确定性，部分幸运球队因此享有相对于其他球队的不公平优势。我们提出一种新颖的技术来量化这种抽签不确定性，其理想水平应为零。我们的模拟方法通过生成大量随机抽签结果，计算每支球队晋级概率的方差。该方法被用于比较欧洲冠军联赛旧有小组赛阶段与当前不完整循环联赛阶段的抽签不确定性。我们还将2024/25赛季赛制改革的影响分解为多个组成部分。研究发现新赛制降低了抽签不确定性，这种减少主要可归因于欧足联采用的种子队分级系统不够精确。结果表明，相较于标准小组赛阶段，不完整循环赛制的主要优势在于其抽签不确定性对球队种子排位的稳健性，这是公平性的关键维度。