How a round-robin fixture list is built
How many matches a league needs, how the circle method pairs teams round by round, what a bye is, and how to plan single and home-and-away leagues.
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In short
- A league in which everyone plays everyone once has n × (n − 1) ÷ 2 matches; 8 teams need 28 and 10 need 45.
- With an even number of teams there are n − 1 rounds; with an odd number there are n rounds, and each team rests once.
- The circle method fixes one team and rotates the rest one place every round, which guarantees every pair meets exactly once.
- Playing home and away doubles the matches and the rounds.
- It builds a league, not a knockout; for groups, make one list for each group.
A round-robin is the simplest fair way to run a tournament: every team plays every other team, and the table at the end settles who won. The hard part is the schedule. With six teams there are 15 matches to fit into rounds so that nobody plays twice in a round and no pair meets more than once, and doing that by hand for ten or sixteen teams is a long evening and an easy place to make a mistake. This page explains how the schedule is built and how to plan around it, and the tool above makes it for you.
How many matches?
In a league where each pair plays once, every one of n teams plays n − 1 matches, and each match involves two teams, so the total is:
matches = n × (n − 1) ÷ 2
The number grows faster than the number of teams, which is the thing organisers forget:
| Teams | Matches (once) | Rounds | Matches a round | Matches (home and away) |
|---|---|---|---|---|
| 4 | 6 | 3 | 2 | 12 |
| 5 | 10 | 5 | 2 | 20 |
| 6 | 15 | 5 | 3 | 30 |
| 8 | 28 | 7 | 4 | 56 |
| 10 | 45 | 9 | 5 | 90 |
| 12 | 66 | 11 | 6 | 132 |
| 16 | 120 | 15 | 8 | 240 |
| 20 | 190 | 19 | 10 | 380 |
Going from 8 teams to 16 doubles the teams but multiplies the matches by more than four, from 28 to 120. If you have a fixed number of days and a single ground, the number of matches decides how many teams you can afford, not the other way round. A one-day school tournament with a single pitch and matches of 40 minutes cannot fit more than about a dozen matches, so a full league suits four or five teams, and a larger entry should be split into groups.
The circle method
The standard way to build a round-robin schedule is the circle method, and it is simple enough to do on paper. Write the teams in two rows, so that the first team sits at the top left and the rest go round in a circle. In round one, pair each team with the one opposite it. For the next round, keep the first team where it is and rotate every other team one place round the circle in the same direction, then pair each team with the one opposite it again. Repeat until the pairings would return to the start.
For six teams A to F the schedule from the tool is:
| Round | Matches |
|---|---|
| 1 | A v F, E v B, C v D |
| 2 | E v A, F v D, C v B |
| 3 | A v D, C v E, F v B |
| 4 | C v A, D v B, F v E |
| 5 | A v B, F v C, D v E |
Check it for yourself: every team appears exactly once in each round, and each of the 15 pairs appears exactly once across the five rounds. That is not luck; the circle method guarantees it, which is why it has been the standard approach for league fixtures for a long time. The order in which you list the teams only decides who meets whom in which round, and every order gives a valid schedule. If you want two particular teams to meet in the first round, list them in opposite positions: first with last, second with second last, and so on.
Odd numbers of teams and the bye
With an odd number of teams someone has no opponent in each round. The standard fix is to add an imaginary team, called a "bye", to make the number even. Whoever is paired with the bye in a round rests that round. The tool does this for you and prints the resting team on its own line.
Five teams A to E, for example, give five rounds of two matches with one team resting in each:
| Round | Matches | Rests |
|---|---|---|
| 1 | E v B, C v D | A |
| 2 | E v A, C v B | D |
| 3 | A v D, C v E | B |
| 4 | C v A, D v B | E |
| 5 | A v B, D v E | C |
Each team rests exactly once, and the league takes as many rounds as there are teams: n rounds for odd n and n − 1 for even n. This matters for planning, because it costs a whole extra round to have an odd number. Seven teams need seven rounds and eight teams need only seven, so an eighth team costs nothing in time.
Home and away
Many leagues have each pair meet twice, once at each team's ground, so each team has both a home and an away fixture against every other. That doubles the number of matches and rounds. The tool builds the second half as a copy of the first with the two sides swapped, and numbers its rounds after the first half. If you play on a neutral ground, you do not need home and away at all, but a double league is still useful where one meeting would be too short a sample, such as a league of four.
The matches within each round of the tool are listed as "Team 1" and "Team 2" and the order alternates from match to match, so that no team is always listed first. If home advantage matters in your league, check that the alternation is fair to your teams, and swap any pair by hand where it is not. This is easy to do in the downloaded file.
Putting the schedule to use
- Download it. The CSV file opens in Excel or Google Sheets, with a row for each match and a row for each bye. Add a column for the date, time and ground.
- Share it with the captains. Because every team plays once in each round, you can give each round a single date, or a single day if a ground has enough pitches.
- Plan for the weather. A one-day tournament can lose a match; a weekly league can lose a whole round. Leave a spare date.
- Build the table as you go. The Cricket Points Table Maker takes the scores and works out points and net run rate for every team, and the Net Run Rate Calculator shows the arithmetic for one match.
- Make a timetable. The Timetable Maker is useful for turning rounds into a day's schedule across several grounds.
What this builds, and what it does not
A round-robin is a league: nobody is knocked out, and the winner is the team with the best record. It is the right format when the matches are few enough and every team deserves to play every other. It is not a knockout bracket, in which each loss removes a team and the number of rounds is the logarithm of the number of teams. It is also not a Swiss system, which pairs teams with similar records and is used for chess tournaments with many players.
For a big entry, the usual compromise is groups: split the teams into two or four groups, make a league fixture list for each, and send the top teams to a knockout. Make one list per group in the tool, and keep each group to six or fewer teams if time is short.
What this tool assumes
- Between 2 and 32 teams, with repeated names counted once and capitals ignored.
- Every pair plays once, or twice if you choose home and away.
- Rounds are numbered in order; the tool does not set dates, times or grounds.
- The schedule is made in your browser, and nothing is sent anywhere.