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arXiv · 2507.15320

The uncertainty of a tournament draw: Insights from the Champions League

László Csató·András Gyimesi·Dries Goossens·Karel Devriesere·Roel Lambers·Frits Spieksma
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Abstract

The group draw of major sports tournaments implies some uncertainty, with lucky teams often enjoying a substantial unfair advantage. First in the literature, we propose a technique to quantify this draw uncertainty, which, arguably, has an optimal level of zero. Our simulation-based approach requires generating a representative set 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, under both accurate and inaccurate seedings. We also break down the impact of the 2024/25 reform into various components. The new format is found to decrease draw uncertainty, but the reduction is mainly attributable to the inaccurate seeding system used by UEFA. Consequently, 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.

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László Csató, András Gyimesi, Dries Goossens, Karel Devriesere, Roel Lambers, Frits Spieksma. 2025-07-21. The uncertainty of a tournament draw: Insights from the Champions League. https://arxiv.org/abs/2507.15320

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