| Abstract: |
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. |