A probabilistic match classification model for low-scoring sports

All existing match classification models in the tournament design literature suffer from 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 for the three main outcomes (win, draw, loss), thereby classifying each match into six categories. The suggested model is applied to the last round of the previous group stage and the new incomplete round-robin league, introduced in the 2024/25 season of UEFA club competitions. The incomplete round-robin tournament is found to contain fewer unimportant matches with two indifferent teams, and substantially more matches where both teams should play offensively. However, the robustly higher proportion of potentially collusive matches can threaten with serious scandals.