Article by How-Hie Ling (h.ling@qut.edu.au)

I came up with the following scheme in 1982 for generating pairings for for N players in a round robin competition. It has been used in some regional football competitions.

The scheme works as follows:

- In the the first row, list out the player (or team) numbers in sequential order.
- If the largest number is odd, add the next number (the ghost player) to make even.
- Keep the the last number fixed at the last column.
- For subsequent rows, rotate the numbers to the right (except the last number) until the rotation is complete.
- Apply the pairing rainbows which arch from the first to the last, the second to the second last, and so on.
- Write out the pairs.
- The player who matches up with the ghost player has a bye.

Here is a simple example for 4 players. The rows of numbers are the result of applying steps 1 to 4. The rainbows at the top are the pairing operators (step 5).

1 | 2 | 3 | 4 |

3 | 1 | 2 | 4 |

2 | 3 | 1 | 4 |

Reading out the pairing gives:

round 1 | 1-4 | 2-3 |
---|---|---|

round 2 | 3-4 | 1-2 |

round 3 | 2-4 | 3-1 |