Round robin schedule: how many games, rounds and byes
How a round robin schedule is made with the circle method: n × (n − 1) ÷ 2 games, n − 1 rounds for an even number of teams, a bye each round for an odd number, with worked examples.
How many games and rounds?
In a round robin everyone plays everyone else once. With n teams that is n × (n − 1) ÷ 2 games: 6 teams play 6 × 5 ÷ 2 = 15 games, 8 teams play 28 and 10 teams play 45.
An even number of teams needs n − 1 rounds, with every team playing once in each round. An odd number needs n rounds, because one team sits out each round: 6 teams take 5 rounds, 7 teams take 7.
The circle method
Bracket Maker builds the schedule with the circle method. The teams sit in a circle of slots; team 1 stays in place and every other team moves one slot along after each round. In each round the first slot plays the last, the second plays the second-to-last, and so on. After n − 1 rounds every pair has met exactly once.
With an odd number of teams an empty slot (a bye) is added to make the count even. Whoever is paired with the bye sits out that round, so each team sits out exactly once.
Worked example: 4 teams
Teams A, B, C and D. A stays in place; B, C and D rotate.
Round 1: A vs D, B vs C
Round 2: C vs A, D vs B
Round 3: A vs B, C vs D
That is 3 rounds and 4 × 3 ÷ 2 = 6 games, and each team plays the other three once.
Worked example: 5 teams
With 5 teams a bye makes 6 slots, so there are 5 rounds of 2 games and one team sits out each round:
Round 1: B vs E, C vs D (A sits out)
Round 2: E vs A, B vs C (D sits out)
Round 3: A vs D, E vs C (B sits out)
Round 4: C vs A, D vs B (E sits out)
Round 5: A vs B, D vs E (C sits out)
Total: 5 × 4 ÷ 2 = 10 games. Every team plays 4 games and sits out once.
Home and away, and playing everyone twice
With “Show home and away” on, the first-named team in each game is at home, and home games are spread evenly: no team has more than one home game more than another. A double round robin plays the whole schedule twice, the second time with home and away swapped: 4 teams then play 6 rounds and 12 games.
How the table is ranked
Teams are ranked by wins, with a draw counting as half a win. Teams level on wins are separated by head-to-head (only the games among the tied teams), then point difference, then points scored, then the order of the entry list.
Related guide
Round robin schedules, 3–12 teamsRound-by-round round robin schedules for 3 to 12 teams or players, with the team that sits out each round for odd numbers. Print a table and write your team names next to the letters.
Frequently asked questions
How many games are in a round robin?
n × (n − 1) ÷ 2 for n teams that play each other once: 4 teams play 6 games, 8 teams 28 and 12 teams 66. Playing everyone twice doubles it.
How many rounds does a round robin take?
n − 1 rounds for an even number of teams and n rounds for an odd number. 8 teams need 7 rounds of 4 games; 9 teams need 9 rounds of 4 games, with one team sitting out each round.
What happens with an odd number of teams?
One team sits out (has a bye) each round. Each team sits out exactly once, and every pair still meets once: 5 teams play 10 games over 5 rounds.
What is a double round robin?
Every pair meets twice, the second time with home and away swapped. 6 teams play 2 × 15 = 30 games over 2 × 5 = 10 rounds.
Can I split a big group into pools?
Yes. Groups + knockout plays a round robin inside each group, then the top teams of each group play a bracket. Teams are dealt into the groups in snake order (with 3 groups: seeds 1, 2, 3 to A, B, C, then 4, 5, 6 to C, B, A), so the groups are equally strong.