Round-Robin Calculator: Games, Rounds, Byes and a Full Schedule

How it works

Games (single round-robin) = n × (n − 1) ÷ 2 · Total = single × meetings · Games per team = (n − 1) × meetings · Rounds = (n − 1) × meetings for an even n, n × meetings for an odd n · Games per round = ⌊n ÷ 2⌋ · Time slots = rounds × ⌈games per round ÷ courts⌉

In a round-robin every team plays every other team, so the number of pairings is n choose 2, n(n − 1)/2. A double round-robin (home and away) doubles it, and so on. If every team plays in every round, an even field needs n − 1 rounds of n/2 games; an odd field needs n rounds, and in each round one team has a bye. The schedule uses the circle method credited to Richard Schurig and used in Berger tables: team 1 stays in place and the other teams rotate one position each round, which pairs every team with every other exactly once in n − 1 rounds. For an odd number of teams a dummy team is added and whoever meets it has the bye. In the second leg the pairings repeat with the order reversed. With fewer courts or fields than games per round, each round is split into time slots. Mixing games from different rounds can sometimes save a slot, so the calculator also shows that lower limit; it is not always reachable.

Worked example

A 10-team single round-robin has 10 × 9 ÷ 2 = 45 games, 9 per team, played over 9 rounds of 5 games. Round 1 of the circle-method schedule is 1 – 10, 2 – 9, 3 – 8, 4 – 7, 5 – 6. With 2 courts each round needs 3 time slots, so the single round-robin takes 27 slots; at 45 minutes a game that is 20.25 hours of play. Home and away doubles everything to 90 games over 18 rounds and 54 slots.

Sources: Wikipedia: Round-robin tournament (number of games and rounds, circle method, Berger tables)

Frequently asked questions