Fair Schedules for Single Round Robin Tournaments with Ranked Participants

• A new measure capturing fairness of a schedule in a tournament: ranking fairness • We provide real-life examples illustrating the relevance of ranking fairness • An intricate construction providing ranking-fair single-break schedules • Integer programming-based solutions for computing ranking-fair single-break schedules • The Canonical Pattern Set does not admit ranking-fair schedules 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 if the number of participants is a multiple of 4. Further, we give a formulation that outputs ranking-fair schedules if 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 if the number of teams exceeds 8. These findings impact the type of schedules to be used for SRR tournaments.