Constructing Schedules for Sports Leagues with Divisional and Round-robin Tournaments

We analyze a sports league that wishes to augment its traditional double round-robin tournament into a longer season. The method for doing so, chosen by the top Swedish handball league Elitserien, is to form two divisions that hold an additional single round-robin tournament to start the season. This format introduces new constraints since pairs of teams in the same division meet three times during the season, while others only meet twice. Though motivated by the concerns of a specific league, the requirements addressed are general enough to be useful for other leagues. We enumerate the number of minimum break home-away pattern sets that satisfy the league’s requirements, not all of which are schedulable. We propose a sequence of increasingly restrictive necessary conditions that remove most of the unschedulable home-away pattern sets from consideration. We lastly discuss the final steps of assigning teams to a schedulable home-away pattern set; such an approach was used to construct the 2013-14 Elitserien schedule.