A round-robin schedule is not invented, it is constructed by a method more than a century old. Below are grids you can paste straight into the tournament chat, and an explanation of how they are produced so you can build one for any number of teams.
How the circle method works
Line the teams up in two rows facing each other. The opponents are the teams standing opposite. That is round one. Now keep the first team where it is and rotate everyone else by one position. That is round two. And so on.
After N−1 rotations the circle closes and every team has played everyone. That is why an eight-team tournament has exactly seven rounds and not eight: each team plays once per round and has seven opponents.
| Teams | Rounds | Matches per round | Total matches |
|---|---|---|---|
| 4 | 3 | 2 | 6 |
| 5 | 5 | 2 | 10 |
| 6 | 5 | 3 | 15 |
| 7 | 7 | 3 | 21 |
| 8 | 7 | 4 | 28 |
| 10 | 9 | 5 | 45 |
| 12 | 11 | 6 | 66 |
The match count grows faster than it looks. Going from eight teams to twelve is half as many entrants again, but 2.4 times as many matches. A twelve-team round robin does not fit into one playing day.
Grid for 8 teams
Seven rounds, 28 matches. Replace the numbers with team names, by draw or any other principle. The structure does not change.
| Round | Match 1 | Match 2 | Match 3 | Match 4 |
|---|---|---|---|---|
| 1 | 1 – 8 | 2 – 7 | 3 – 6 | 4 – 5 |
| 2 | 1 – 7 | 8 – 6 | 2 – 5 | 3 – 4 |
| 3 | 1 – 6 | 7 – 5 | 8 – 4 | 2 – 3 |
| 4 | 1 – 5 | 6 – 4 | 7 – 3 | 8 – 2 |
| 5 | 1 – 4 | 5 – 3 | 6 – 2 | 7 – 8 |
| 6 | 1 – 3 | 4 – 2 | 5 – 8 | 6 – 7 |
| 7 | 1 – 2 | 3 – 8 | 4 – 7 | 5 – 6 |
Grids for 4 and 6 teams
| Round | Match 1 | Match 2 |
|---|---|---|
| 1 | 1 – 4 | 2 – 3 |
| 2 | 1 – 3 | 4 – 2 |
| 3 | 1 – 2 | 3 – 4 |
| Round | Match 1 | Match 2 | Match 3 |
|---|---|---|---|
| 1 | 1 – 6 | 2 – 5 | 3 – 4 |
| 2 | 1 – 5 | 6 – 4 | 2 – 3 |
| 3 | 1 – 4 | 5 – 3 | 6 – 2 |
| 4 | 1 – 3 | 4 – 2 | 5 – 6 |
| 5 | 1 – 2 | 3 – 6 | 4 – 5 |
Grids for 10 and 12 teams
These are no longer one-day events: 45 and 66 matches is a league running over several weeks. The method is the same, the rows are just longer.
| Round | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 |
|---|---|---|---|---|---|
| 1 | 1 – 10 | 2 – 9 | 3 – 8 | 4 – 7 | 5 – 6 |
| 2 | 1 – 9 | 10 – 8 | 2 – 7 | 3 – 6 | 4 – 5 |
| 3 | 1 – 8 | 9 – 7 | 10 – 6 | 2 – 5 | 3 – 4 |
| 4 | 1 – 7 | 8 – 6 | 9 – 5 | 10 – 4 | 2 – 3 |
| 5 | 1 – 6 | 7 – 5 | 8 – 4 | 9 – 3 | 10 – 2 |
| 6 | 1 – 5 | 6 – 4 | 7 – 3 | 8 – 2 | 9 – 10 |
| 7 | 1 – 4 | 5 – 3 | 6 – 2 | 7 – 10 | 8 – 9 |
| 8 | 1 – 3 | 4 – 2 | 5 – 10 | 6 – 9 | 7 – 8 |
| 9 | 1 – 2 | 3 – 10 | 4 – 9 | 5 – 8 | 6 – 7 |
| Round | Match 1 | Match 2 | Match 3 | Match 4 | Match 5 | Match 6 |
|---|---|---|---|---|---|---|
| 1 | 1 – 12 | 2 – 11 | 3 – 10 | 4 – 9 | 5 – 8 | 6 – 7 |
| 2 | 1 – 11 | 12 – 10 | 2 – 9 | 3 – 8 | 4 – 7 | 5 – 6 |
| 3 | 1 – 10 | 11 – 9 | 12 – 8 | 2 – 7 | 3 – 6 | 4 – 5 |
| 4 | 1 – 9 | 10 – 8 | 11 – 7 | 12 – 6 | 2 – 5 | 3 – 4 |
| 5 | 1 – 8 | 9 – 7 | 10 – 6 | 11 – 5 | 12 – 4 | 2 – 3 |
| 6 | 1 – 7 | 8 – 6 | 9 – 5 | 10 – 4 | 11 – 3 | 12 – 2 |
| 7 | 1 – 6 | 7 – 5 | 8 – 4 | 9 – 3 | 10 – 2 | 11 – 12 |
| 8 | 1 – 5 | 6 – 4 | 7 – 3 | 8 – 2 | 9 – 12 | 10 – 11 |
| 9 | 1 – 4 | 5 – 3 | 6 – 2 | 7 – 12 | 8 – 11 | 9 – 10 |
| 10 | 1 – 3 | 4 – 2 | 5 – 12 | 6 – 11 | 7 – 10 | 8 – 9 |
| 11 | 1 – 2 | 3 – 12 | 4 – 11 | 5 – 10 | 6 – 9 | 7 – 8 |
What to do with an odd number of teams
Add a phantom team. With five entrants you take the six-team grid and declare the sixth slot empty: whoever draws it that round sits out. You keep the same number of rounds as a six-team grid, but each round has two matches instead of three.
The side effect: a five-team tournament lasts as long as a six-team one and somebody is always waiting. If you can find a sixth team, find one. It is cheaper than explaining to people why they are standing around for half an hour.
Ordering matches when you only have one pitch
The grid says who plays whom, not in what order. On a single pitch the matches of a round run back to back, and the order within the round decides whether the day feels comfortable.
- Nobody plays two matches in a row. Put at least one other match between a team's games.
- Nobody waits through three matches. People cool down and then go home.
- Matches that decide qualification are played simultaneously on separate pitches. With one pitch, at least play them last.
- The first match of the day should not be a grudge match: nobody is warmed up and the referee has not settled in.
With two pitches the rounds run twice as fast, but read the grid first: in some rounds both matches assigned to one pitch involve the same team.
One round robin or two
A second round robin doubles the matches and removes the main complaint about the format, that a single circuit leaves a lot to the draw and to luck. But eight teams twice over is 56 matches, which is a full season rather than a tournament.
A working rule: one circuit for a weekend event, two for a league that plays every week. The middle option is one circuit plus a knockout between the top four.
On fellasport the schedule is generated by exactly this method: enter the teams, get the rounds, and every result moves the table by itself.
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