Format guide

Round Robin Schedule Formula: Rounds, Matches, and a Worked Example

How to calculate a round robin schedule for any number of teams, plus a step-by-step circle-method example and a time estimate.

  • Formula for even and odd fields
  • 6-team worked example
  • Time estimate

The formulas

Total matches = n(n − 1) / 2 Rounds (even n) = n − 1 Rounds (odd n) = n Matches per round = floor(n / 2) Matches per team = n − 1

Each team plays every other team exactly once. The total is the number of unordered pairs, which is n choose 2. An odd field needs one extra round because one team sits out each round.

Quick reference

TeamsRoundsMatches per roundTotal matchesMatches per team
43263
552104
653155
773216
874287
994368
1095459

The circle method

The circle method builds the schedule without repeats:

  1. Fix team 1 in place.
  2. Arrange the other teams around it.
  3. Pair the top half of the list with the bottom half.
  4. Rotate the non-fixed teams one position each round.
  5. Repeat for n − 1 rounds (even field) or n rounds (odd field).

With an odd field, add a dummy “bye” entry so the list is even. Whichever team is paired with the dummy sits out that round.

Worked example: 6 teams

Using the circle method with teams 1–6:

RoundMatches
11 v 6, 2 v 5, 3 v 4
21 v 5, 6 v 4, 2 v 3
31 v 4, 5 v 3, 6 v 2
41 v 3, 4 v 2, 5 v 6
51 v 2, 3 v 6, 4 v 5

Every pair appears once. There are 5 rounds × 3 matches = 15 matches, and each team plays 5 games.

Odd field example: 5 teams

Five teams need 5 rounds. Each round has 2 matches and one bye. The total is 10 matches, and each team plays 4 games.

Time estimate

If one match takes m minutes and only one match runs at a time, the wall-clock estimate is:

Total time = total matches × m 6 teams at 30 minutes = 15 × 30 = 450 minutes = 7 h 30 min

With c courts running in parallel, divide by c (assuming matches can be distributed evenly). The TourneyDraw schedule generator uses the one-match-at-a-time estimate and lets you change the minutes per match.

Standings and tiebreaks

A basic round robin table tracks wins and losses. The TourneyDraw standings sort by wins, then fewest losses, then seed. It does not impose a points system or head-to-head rule; use your league's rules if you need those tiebreaks.

Frequently asked questions

What is the round robin formula?
Total matches = n(n − 1) / 2. Even fields need n − 1 rounds; odd fields need n rounds. Each team plays n − 1 matches.
How many matches per round?
floor(n / 2). Six teams produce 3 matches per round; five teams produce 2 matches and one bye.
Why do odd fields need an extra round?
One team sits out each round. With an odd field, n rounds are needed so every team gets n − 1 games.
What is the circle method?
A schedule construction that fixes one team, rotates the others, and pairs the top half with the bottom half. It covers every pair exactly once.
How long does a round robin take?
Total matches × minutes per match if one match runs at a time. Six teams at 30 minutes is 450 minutes, or 7 hours 30 minutes. Multiple courts reduce the wall-clock time.
Does the schedule avoid repeats?
Yes. The circle method produces every pair exactly once for a single round robin.