Sports scheduling affects incentives: The case of the UEFA Champions League

A team might lose a powerful incentive to win in a round-robin contest if its final rank does not depend on the outcome of the matches still to be played. The current paper introduces a classification scheme to identify these weakly (where one team is indifferent) or strongly (where both teams are indifferent) stakeless games. The probability of such matches can serve as a novel fairness criterion to compare and evaluate timetabling alternatives. An optimal sequence of games with respect to the proposed metric increases the utility of all stakeholders at almost no price if the scheduling constraints are appropriately defined. Its application is illustrated through the 2021/22 season of the UEFA Champions League. According to our simulation model, the same schedule is optimal across all groups and the option followed in four of the eight groups is the best under a wide set of parameters. Avoiding strongly stakeless matches is verified to be a likely goal in the computer draw of the fixture that remains hidden from the public.