League Competition Fixture Patterns
Question. How are round by round fixtures for an all-play-all
league competition generated?
Answer. Using a 10 player or 10 team league as an example:-
The Basics
The numbers 1 to 10 are written in two columns beginning in the top left corner and moving in an anti-clockwise direction, so that 1 to 5 are paired opposite 10 to 6.
| 1 | 10 |
| 2 | 9 |
| 3 | 8 |
| 4 | 7 |
| 5 | 6 |
Pairings for subsequent rounds are formed by leaving 10 fixed and moving all the other numbers one step in a clockwise direction.
Interleaving
The initial order has 10 opposite 1,2,3,4,5,6,7,8 and 9 in that order. A good alternation between home and away fixtures (or black and white colour allocations) needs to be introduced. Rounds 6 to 9 are therefore interleaved with rounds 1 to 5 so that the order is now 10 opposite 1,6,2,7,3,8,4,9,then 5.
The left hand column of the interleaved rounds is designated as the home team (or perhaps the player with white pieces where a all-play-all chess tournament is concerned), except for slot 10 where the home team alternates between the left and right columns. Thus:-
| 1 | 10 | 6 | 10 | 2 | 10 | 7 | 10 | 3 | 10 | 8 | 10 | 4 | 10 | 9 | 10 | 5 | 10 |
| 2 | 9 | 7 | 5 | 3 | 1 | 8 | 6 | 4 | 2 | 9 | 7 | 5 | 3 | 1 | 8 | 6 | 4 |
| 3 | 8 | 8 | 4 | 4 | 9 | 9 | 5 | 5 | 1 | 1 | 6 | 6 | 2 | 2 | 7 | 7 | 3 |
| 4 | 7 | 9 | 3 | 5 | 8 | 1 | 4 | 6 | 9 | 2 | 5 | 7 | 1 | 3 | 6 | 8 | 2 |
| 5 | 6 | 1 | 2 | 6 | 7 | 2 | 3 | 7 | 8 | 3 | 4 | 8 | 9 | 4 | 5 | 9 | 1 |
Complementary Teams
This interleaving together with the home and away allocation has the side characteristic that teams (or players) 1 & 6, 2 & 7, 3 & 8, 4 & 9, and 5 & 10 are never both at home (or both on the same colour) in the same round: an attribute which can be made good use of in the case of teams that have to share the same venue.
Standard Berger Pattern
This standard fixture pattern is called a berger table (for reasons not
known). As a template for generating a double round all-play-all, it presents a minor
problem. Unaltered it would give three consecutive home fixtures for one team and 3
consecutive away fixtures for another between to two halves of the season. This is easily
overcome however by simply reversing rounds 8 and 9. 
Improved Patterns
By starting the cycle of rounds at the round where team 10 plays either 6
, 7
, 8
, or
9
, or
by using a mirror image of the round order and starting the cycle where team 10 plays
either team 1
, 2
, 3
, or
4
, an
improved variation on the standard fixture pattern can be generated. Some of these
variations have the additional benefit that each team has an home and away fixture in the
first two rounds.
Teams from same Club
Where a club has 4 teams in a league, and it is required that they play each other in early rounds, it is best that the variant mirror 1 modified (see below) be used and the 4 teams be allotted slots 2,7,3 and 8.
The two modified patterns below have had the round order changed so that the all the fixtures betweens 2,3,7, and 8 teams are optimally placed towards the start of the season.
Where there are two clubs with 3 teams it is advisable to use slots 3,8 and 6 for one club (all met by 5th round) and slots 5,10 and 1 (all met by 4th round) for the other, again with variant mirror 1 modified. This will then leave slots 2 and 7 available if there is a 3rd club with 2 teams.
All the following variations on the berger pattern have the fixtures between the complementary teams highlighted with a yellow background. Other fixtures between teams 2,3,7, and 8 have a tan background.
The Variations
| Pattern | Mirror | ||
| 1
|
5 |
||
| 6
|
1
|
Modified
|
|
| 7
|
2
|
||
| 8
|
3
|
||
| Modified
|
9
|
4
|
Fixture Patterns for 12 Team Leagues