Mixed individual-pairs tournament design for 9 players

Julian D. A. Wiseman, April 2004

This 9-player individual-pairs tournament design, last updated in April 2004, is based on an original by Matt Fayers of The Department of Mathematics at Queen Mary, University of London (formerly of The Department of Pure Mathematics and Mathematical Statistics at The University of Cambridge).

Available formats:
PDF (A4) Schedule, in score-sheet, with running totals; Schedule by player; Blank score sheet, with running totals
PDF (A3) Schedule, in score-sheet, with running totals; Schedule by player; Blank score sheet, with running totals
PDF (USL) Schedule, in score-sheet, with running totals; Schedule by player; Blank score sheet, with running totals
Also see the individual-pairs explanation and the links to designs for other numbers of players.

There is also a pure 9-player design, consisting of 9 rounds, each of which has two games of two-versus-two and one player having a bye. But in this much slower mixed design, each of the 12 rounds consists of three games of two-versus-one.

Properties of this tournament design:

 ``` i ii iii 1 G+B:H A+F:D E+I:C 2 F+H:E D+I:G B+C:A 3 E+D:B G+C:F A+H:I 4 A+G:I C+H:E F+B:D 5 I+F:C E+A:B H+D:G 6 D+C:A B+I:H G+E:F 7 G+F:B H+E:A I+C:D 8 B+H:C I+A:F D+G:E 9 C+A:G F+D:H E+B:I 10 F+E:I D+B:C H+G:A 11 H+I:D C+E:G B+A:F 12 A+D:E I+G:B C+F:H ```
• This is a mixed individual pairs for 9 players.

• Each player partners each of the others exactly once, and self-partners exactly four times.

• Each player opposes each of the others exactly twice.

• Doubles play on the left, singles on the right.

• All play four times at each venue, twice in the first six rounds and twice in the last six rounds.

• No player plays singles more than twice at any venue. B does not play singles at venue iii, F not at venue i, I not at venue ii, but the other six play singles at least once at each venue. In the first six rounds, no player plays singles more than once at any venue, and likewise for the last six rounds.

• The number of times that players remain at the same venue for two consecutive rounds has been minimised (C remains at venue ii from rounds 3 to 4, and D at venue ii from rounds 9 to 10).

• If players are ranked, from A the best to I the worst, this tournament has an unfairness measure of 1431579.38867.

• This format could have been achieved using the unique Steiner triple system on the 9 players, playing every game within each threesome. But if a ‘quick’ 9-player individual pairs is wanted, the pure 9-player design would be better still. So instead this is based on a resolvable 2-(9,3,3) system, with a distinguished element in each block such that each pair of elements occurs exactly once as the pair of undistinguished elements of a block. This is easily achieved using C3×C3.

Usual disclaimer and copyright terms apply.