Tournament schedules and incentives in a double round-robin tournament with four teams

TL;DR

This paper develops a classification scheme for weakly and strongly stakeless matches in double round-robin tournaments with four teams, using a fairness criterion based on match probabilities, and applies it to UEFA Champions League data.

Contribution

It introduces a novel classification and fairness metric for match schedules in four-team double round-robin tournaments, aiding in designing more engaging schedules.

Findings

Some schedules are dominated by others in fairness.

Optimal match sequence depends on team strength and organizer preferences.

Choosing the right schedule can reduce uninteresting matches.

Abstract

In a round-robin tournament, a team may lack the incentive to win if its final rank does not depend on the outcome of the matches still to be played. This paper introduces a classification scheme to determine these weakly (where one team is indifferent) or strongly (where both teams are indifferent) stakeless matches in a double round-robin contest with four teams. The probability that such matches arise can serve as a novel fairness criterion to compare and evaluate match schedules. Our approach is illustrated by the UEFA Champions League group stage. A simulation model is built to compare the 12 valid schedules for the group matches. Some schedules are shown to be dominated by other schedules. It is found that the strongest team should play at home in the last round against one of the middle teams, depending on the preferences of the tournament organiser. Choosing an optimal sequence of matches with respect to the proposed metric can help to avoid uninteresting matches.