# Carry-Over tournament design for 8+8=16 players

Julian D. A. Wiseman, March 2002

This is a carry-over tournament design for 8+8=16 players. It therefore assumes that two qualifying leagues (called ‘Roman’ and ‘Italic’) have played an all-play-all, and that the top 8 players from each are through to the final. In the final these 16 players are then to play each other, except that games already played between them are ‘carried over’. The players in the Roman league are called A, B, C, etc, and those in the Italic league a, b, c, etc.

It was last updated in March 2002, and is based on an original by Dr Nicholas F. J. Inglis 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; Blank score sheet, with running totals
PDF (A3) Schedule, in score-sheet, with running totals; Blank score sheet, with running totals
PDF (USL) Schedule, in score-sheet, with running totals; Blank score sheet, with running totals
Also see the carry-over explanation and the links to similar designs for other numbers of players.

Properties of this tournament design:

i ii iii iv v vi vii viii f:C e:D A:h B:g G:b H:a d:E c:F F:d E:c b:H a:G h:B g:A D:f C:e E:b F:a G:d H:c A:f B:e C:h D:g D:h C:g B:f A:e H:d G:c F:b E:a c:B d:A a:D b:C g:F h:E e:H f:G e:G f:H g:E h:F a:C b:D c:A d:B g:H h:G e:F f:E c:D d:C a:B b:A A:a B:b C:c D:d E:e F:f G:g H:h
• Each player plays exactly once each of the players in the other league.

• Each player plays exactly once at each venue.

• Each player plays four times on each side (left and right).

• It is seeded, so that important games come late in the tournament. It is assumed that player A is better than B, etc, and that a is better than b, etc. (Usually rankings are determined by the players’ scores in the qualifying rounds.)

• It has a permutation score of 2595.631802528725, which is maximal.

• It has a left-right asymmetry measure of 101481/78400 = 1.29440051, which is minimal.

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