Fair Schedules for Single Round Robin Tournaments with Ranked Participants

TL;DR

This paper introduces a fairness measure for single round robin tournaments with ranked participants, proposing explicit constructions for fair schedules when the number of teams is divisible by 4, and analyzing limitations of existing scheduling methods.

Contribution

It defines a new fairness criterion, provides explicit constructions for ranking-fair schedules when the number of teams is divisible by 4, and shows limitations of common scheduling methods.

Findings

Ranking-fair schedules exist for team counts divisible by 4.

Popular scheduling methods fail to produce ranking-fair schedules for more than 8 teams.

The proposed methods ensure fairer treatment of participants based on their rankings.

Abstract

We introduce a new measure to capture fairness of a schedule in a single round robin (SRR) tournament when participants are ranked by strength. To prevent distortion of the outcome of an SRR tournament as well as to guarantee equal treatment, we argue that each participant should face its opponents when ranked by strength in an alternating fashion with respect to the home/away advantage. Here, the home/away advantage captures a variety of situations. We provide an explicit construction proving that so-called ranking-fair schedules exist when the number of participants is a multiple of 4. Further, we give a formulation that outputs ranking-fair schedules when they exist. Finally, we show that the most popular method to come to a schedule for an SRR tournament, does not allow ranking-fair schedules when the number of teams exceeds 8. These findings impact the type of schedules to be used for SRR tournaments.