Round robin schedule generator

How to use it

1. Enter the teams or players, one per line. For numbered teams, enter just the number, such as 8.
2. Keep the format “Teams or singles”, or choose “Doubles with rotating partners” and set the number of rounds and, if you have fewer, the number of courts.
3. For teams, choose whether every pair meets once or twice. Twice means a second half with home and away swapped.
4. Tick “Draw the order at random” if the list order should not decide who plays whom in which round.
5. Select “Make schedule”. The first name of each match is the home side; for games without a home side, use it for whatever your rules give to one side, such as the first serve.
6. Use “Print schedule” for a sheet with a space for each score, or “Copy result” to paste the schedule into a message.

Worked example: 6 teams

Six teams need 5 rounds of 3 matches, 15 matches in all. Without the random order, the schedule for Team 1 to Team 6 is:

Every team meets the other five once and never plays twice in a round. Team 1 is at home in rounds 1, 3 and 5 and away in rounds 2 and 4. With 5 teams the schedule also has 5 rounds, but each round has 2 matches and one team with a bye, and every team has exactly one bye.

How many rounds and matches

With n teams there are n × (n − 1) ÷ 2 pairs, so a single round robin has that many matches. With an even n, every team plays in every round: n − 1 rounds of n ÷ 2 matches. With an odd n, one team rests in each round: n rounds of (n − 1) ÷ 2 matches. A double round robin has twice the rounds and matches.

How the schedule is made

The tool uses the circle method, the usual way to schedule a round robin. The teams are placed in two rows facing each other, and each team plays the team opposite. The first place stays where it is, and after every round all other teams move one place around the circle. After n − 1 rounds every team has faced every other team exactly once.

With an odd number of teams, an empty place called the bye is added and kept in the fixed position. Whoever is opposite the bye rests in that round. Every team is opposite the fixed place exactly once, so every team rests exactly once.

Home and away: the fixed place is at home in every other round, and in the other pairs the side at home alternates from one pair to the next. A team that moves one place therefore usually switches between home and away. With an even number of teams, every team is at home n ÷ 2 or n ÷ 2 − 1 times; with an odd number, exactly (n − 1) ÷ 2 times. In a double round robin every team is at home exactly once against each opponent.

The only random step is the optional order of the teams. It is drawn with the Fisher-Yates shuffle and the cryptographic random generator of your browser, so every order is equally likely.

Doubles with rotating partners

In social pickleball, tennis or padel, players often change partners every round. The doubles format puts four players on each court, two against two, and lets the others sit out in turn: whoever has sat out least sits out next, so nobody sits out twice before everyone has sat out once.

For the pairs, the tool tries hundreds of random line-ups per round and keeps the one that repeats the fewest partners and then the fewest opponents, and it builds the whole schedule twelve times and keeps the best. A schedule in which everybody partners everybody exactly once exists only for some numbers of players, and the search does not always find one even then. The result therefore states how it went: the most times any two players were partners, and how many pairs never played together.

Example: 8 players on 2 courts for 7 rounds. There are 28 possible pairs and 7 × 4 = 28 partnerships, so at best every pair partners exactly once; in 50 test runs the tool found such a schedule every time. With 5 players on one court, one player sits out each round, and after 5 rounds everybody has sat out once.

Common mistakes

• Adding a “Bye” team by hand. The tool adds the bye itself when the number is odd; a team named Bye would be scheduled like a real team.
• Planning one court per match. A round only needs as many courts as it has matches; with fewer courts, play the round in several waves.
• Changing the list after printing. A new team changes the whole schedule, so print again.

Sources

• Wikipedia: Round-robin tournament (circle method)