This means that no pairing will be repeated in a future round. Restricting ourselves to horizontal stripes ensures that no segment is a rotation or reflection of another segment. The restriction that no vertex has more than one segment drawn to/from it ensures that no team is scheduled for more than one game in each round. Therefore, the schedule could look like this: Round One more rotation will bring the polygon back to its original position. one vertex point.) The new segments represent the pairings for round two. Rotate the polygon 1/Nth of a circle (i.e. Each segment represents teams playing each other in the first round. The vertex that has been left out gives the idle team. Each vertex represents one team.ĭraw horizontal stripes as shown below. Draw a regular N-gon (heptagon for 7 teams). Let us work out the schedule for 7 teams, numbering the teams from 1 to 7. There will be N rounds (since each team will play every other team once, and will be idle for exactly one round ). Let N = number of teams in the tournament. Round Robin scheduling: Odd number of teams. We can also rotate the teams around so that each team plays in every field / pitch / court at least once (at present team 8 always plays in D). If A, B, C and D are the fields / pitches / courts, the schedule could look like this: Round So (6, 5), (7, 4), (1, 3) and (2, 8) play the second round.Ĭontinue rotating the polygon until it returns to its original position. The new segments represent the pairings for round two. Rotate the polygon 1/(N-1)th of a circle (i.e. Then, join the vertex that has been left out to the centre. Each vertex and the centre point represents one team.ĭraw horizontal stripes as shown below. Let us schedule a round-robin tournament for 8 teams numbered from 1 to 8.ĭraw a regular (N -1) sided polygon (i.e., a heptagon for 8 teams). Since each team will play every other team once, no team will be idle during any of the rounds. There will be N -1 rounds (each team will play N-1 games). Round Robin scheduling: Even number of teams. The technique is called the polygon method. This method assumes that there are enough fields / pitches / courts so that all the games in a round can be played simultaneously. There is a systematic approach to scheduling a Round Robin tournament. In a Round Robin tournament every team plays every other team. Then, 4 of those teams (randomly selected) could get a bye and the other 8 teams would play to find the other 4 contestants for the next round. If you have 24 teams, you could have everyone compete in a preliminary round this would leave 12 teams. The four winners would then join the other twelve to fill out the sixteen-team field. With 20 teams, you might select eight of those teams to have a preliminary round. The first step is to get the number of teams to a power of two: 2, 4, 8, 16, 32. Scheduling a single elimination tournament is relatively easy. In this format, one defeat is enough to eliminate a team from the tournament. There are 2 well-known types of tournament formats that sport schedulers use. Scheduling games is a little more challenging than one might desire.
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