Round Robin Calculator

A round robin is one of the fairest ways to run a competition: every team or player meets every other one. It's used for everything from five-a-side leagues and table tennis clubs to esports groups and pub quiz leagues. The challenge is working out how many matches you'll need and scheduling them so nobody plays twice at once.

This guide explains the maths and the scheduling. To generate a full fixture list, use the round robin calculator.

What is a round robin?

In a round robin, each participant plays every other participant once. In a double round robin, they play each other twice, often home and away, as in most football leagues.

Because everyone faces everyone, the final table reflects overall performance rather than the luck of the draw, unlike a knockout where one bad game ends your tournament.

How many matches are there?

The number of matches in a single round robin is:

matches = n × (n − 1) ÷ 2

where n is the number of teams. Each team plays n − 1 matches. For a double round robin, multiply by two.

The number of matches grows quickly. Twenty teams playing home and away, like many football leagues, need 380 matches.

How many rounds?

A round is a set of matches in which each team plays at most once. With an even number of teams, you need n − 1 rounds, with n ÷ 2 matches in each. With an odd number of teams, one team has to sit out each round, called a bye, so you need n rounds.

So 8 teams need 7 rounds of 4 matches, while 7 teams also need 7 rounds, of 3 matches each with one team resting.

Scheduling fixtures: the circle method

The standard way to schedule a round robin is the circle method:

1. Number the teams and arrange them in two rows facing each other.
2. Each pair facing each other plays in the first round.
3. Keep team 1 fixed, and rotate all the other teams one position around the circle.
4. Repeat until every team has played every other.

With an odd number of teams, add a dummy "bye" team. Whoever is paired with the bye rests that round.

The round robin calculator uses the circle method to build a complete fixture list for up to 20 teams, and alternates which team is listed first so home and away matches are spread fairly.

Planning time and venues

If you know how long a match lasts and how many courts or pitches you have, you can estimate the total time needed. Matches in the same round can be played at the same time if you have enough venues.

For example, 8 teams with 4 matches per round on 2 courts need 2 time slots per round. With 7 rounds of 20-minute matches, that's 14 slots, or about 4 hours 40 minutes of playing time, before breaks. The calculator works this out when you enter match length and courts.

Points and tiebreakers

Agree a points system before you start. Common systems include:

• Football-style: 3 points for a win, 1 for a draw, 0 for a loss
• Win-loss: 1 point for a win, 0 for a loss, for sports without draws

When teams finish level on points, typical tiebreakers are:

1. Head-to-head result between the tied teams
2. Goal, point or game difference
3. Goals or points scored
4. A play-off match, if time allows

Writing these down in advance avoids disputes later.

Round robin vs knockout

Making a round robin feel fair

A few small decisions can make a big difference to how fair a round robin feels to the people taking part. Spread byes evenly so no team rests twice in a row, and try to avoid any team playing several matches back to back without a break. If some courts or pitches are better than others, rotate teams between them. In a double round robin, make sure each pair of teams plays once at each venue or side.

Publishing the full fixture list in advance helps players plan and reduces disputes. It also lets you spot problems early, such as two teams that share players being scheduled at the same time.