How to work out fixtures

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Rough and Ready or Scientific?

Working out fixtures is a science and it is not easy to ensure that every club has a game in every round and that no clubs more than, say, two consecutive home or away games. Add to that the desire to keep certain teams from playing at home at the same time, e.g. Liverpool/Everton, Man Utd/Man City, and it is a very complex science. The rough and ready approach, of course, can be perfectly adequate for our fantasy leagues, but if you want a bit of realism, then the scientific approach is what you need. So, I will go into the science of calculating fixtures but first I will illustrate the basic system for 16 teams, whcih does not fully achieve the aims but works outreasonably well. The reason it works is because 16 is a power of two and divides evenly down to one.

Basic 16-team method

With 16 teams, you can divide the division down into groups of two teams, which aids the calculation of a proper fixture list. This system can be analysed by looking at the LOGacta fixtures and results chart. For the first set of fixtures, the division is divided into two halves of eight teams each. The fixtures are then created by matching the two halves against each other and then varying the opponents by one in the list each time (for the ease of reference we will call these Stage A fixtures - all remaining fixtures are Stage B) :

Round 1
Team 1 v. Team 9
Team 2 v. Team 10
Team 3 v. Team 11
Team 4 v. Team 12
Team 5 v. Team 13
Team 6 v. Team 14
Team 7 v. Team 15
Team 8 v. Team 16

Round 2
Team 9 v. Team 8
Team 10 v. Team 1
Team 11 v. Team 2
Team 12 v. Team 3
Team 13 v. Team 4
Team 14 v. Team 5
Team 15 v. Team 6
Team 16 v. Team 7

 Round 3
Team 1 v. Team 11
Team 2 v. Team 12
Team 3 v. Team 13
Team 4 v. Team 14
Team 5 v. Team 15
Team 6 v. Team 16
Team 7 v. Team 9
Team 8 v. Team 10		 Round 4
Team 9 v. Team 6
Team 10 v. Team 7
Team 11 v. Team 8
Team 12 v. Team 1
Team 13 v. Team 2
Team 14 v. Team 3
Team 15 v. Team 4
Team 16 v. Team 5

This will produce 16 out of the 30 fixtures for each club. At the next stage the division is divided into four groups of four, with the first group playing the seconf group and the third group playing the fourth. Using the same method as above, this produces the next 8 fixtures.

Round 17
Team 1 v. Team 5
Team 2 v. Team 6
Team 3 v. Team 7
Team 4 v. Team 8
Team 9 v. Team 13
Team 10 v. Team 14
Team 11 v. Team 15
Team 12 v. Team 16

Round 18
Team 5 v. Team 4
Team 6 v. Team 1
Team 7 v. Team 2
Team 8 v. Team 3
Team 13 v. Team 12
Team 14 v. Team 9
Team 15 v. Team 10
Team 16 v. Team 11

 Round 19
Team 1 v. Team 7
Team 2 v. Team 8
Team 3 v. Team 5
Team 4 v. Team 6
Team 9 v. Team 15
Team 10 v. Team 16
Team 11 v. Team 13
Team 12 v. Team 14		 Round 20
Team 5 v. Team 2
Team 6 v. Team 3
Team 7 v. Team 4
Team 8 v. Team 1
Team 13 v. Team 10
Team 14 v. Team 11
Team 15 v. Team 12
Team 16 v. Team 9

The league is then broken down into 8 groups of 2 and, with each group of two playing the next group of two, another four fixtures are created, a total of 28 out of 30. The final two fixtures are created by the playing the teams within the groups of two against each other home and away, thus completing a standard 16-team fixture list.

The Scientific Method

The method described above is workable because 16 breaks down to 2 or 1 without any remainder, but what if it was a league of 18 teams, or 20, or 22? The method would not work because you would end up with an odd number of clubs in the groups for the later stages. So, for this method we will look at a half-season's fixtures (the second half of the season is just the same fixtures but reversed).

If we take an 18-team division as an example, the first 9 fixtures would be easy enough, as each half of the league would play the other half, the Stage A fixtures . The problem arises at the next stage, Stage B, where the teams within each group of nine play amongst each other - there would always be an odd team out. The solution, however, is easy: there will be an odd team out in both groups, thus they play each other in that round. This will, of course, duplicate fixtures from Stage A, but if it is done so that all the duplicated fixtures take place in just one Stage A round, then that round can be exlcuded from Stage A. This then produces 8 Stage A fixtures and 9 Stage B fixtures (i.e. each club in each section of nine plays the other eight clubs from their own section, plus one club from the other half of the division).

The next problem is to ensure that no club is given more than two consecutive away or home fixtures. There is a way of doing this but it is quite difficult to explain, so the following list will hopefully illustrate this as well as showing how the Stage B fixtures are worked out. This example shows how the Stage B fixtures are worked out for one half of the division, with the clubs from the other half shown in italics:

Round 9
1 v 10
2 v 9
3 v 8
4 v 7
5 v 6 		Round 10
6 v 15
7 v 5
8 v 4
9 v 3
1 v 2 		Round 11
2 v 11
3 v 1
4 v 9
5 v 8
6 v 7 		Round 12
7 v 16
8 v 6
9 v 5
1 v 4
2 v 3 		Round 13
3 v 12
4 v 2
5 v 1
6 v 9
7 v 8 		Round 14
8 v 17
9 v 7
1 v 6
2 v 5
3 v 4 		Round 15
4 v 13
5 v 3
6 v 2
7 v 1
8 v 9 		Round 16
9 v 18
1 v 8
2 v 7
3 v 6
4 v 5 		Round 17
5 v 14
6 v 4
7 v 3
8 v 2
9 v 1

The full fixture list

Based on the above, the entire fixture list for an 18-team league is as follows (half-season). Note that I ususally place the Stage B fixtures in the middle of the Stage A fixtures rather than do all of the Stage A fixtures first. Thus, the round numbers are slightly different from those in the examples above. The final list in italics is the Stage A round that is excluded due to the fixtures being included in Stage B (also shown in italics).

Round 1
1 v 11
2 v 12
3 v 13
4 v 14
5 v 15
6 v 16
7 v 17
8 v 18
9 v 10 		Round 2
10 v 8
11 v 9
12 v 1
13 v 2
14 v 3
15 v 4
16 v 5
17 v 6
18 v 7 		Round 3
1 v 13
2 v 14
3 v 15
4 v 16
5 v 17
6 v 18
7 v 10
8 v 11
9 v 12 		Round 4
10 v 6
11 v 7
12 v 8
13 v 9
14 v 1
15 v 2
16 v 3
17 v 4
18 v 5 		Round 5
15 v14
16 v 13
17 v 12
18 v 11
1 v 10
2 v 9
3 v 8
4 v 7
5 v 6 		Round 6
11 v 10
12 v 18
13 v 17
14 v 16
6 v 15
7 v 5
8 v 4
9 v 3
1 v 2 		Round 7
16 v 15
17 v 14
18 v 13
10 v 12
2 v 11
3 v 1
4 v 9
5 v 8
6 v 7 		Round 8
12 v 11
13 v 10
14 v 18
15 v 17
7 v 16
8 v 6
9 v 5
1 v 4
2 v 3 		Round 9
17 v 16
18 v 15
10 v 14
11 v 13
3 v 12
4 v 2
5 v 1
6 v 9
7 v 8
Round 10
13 v 12
14 v 11
15 v 10
16 v 18
8 v 17
9 v 7
1 v 6
2 v 5
3 v 4 		Round 11
18 v 17
10 v 16
11 v 15
12 v 14
4 v 13
5 v 3
6 v 2
7 v 1
8 v 9 		Round 12
14 v 13
15 v 12
16 v 11
17 v 10
9 v 18
1 v 8
2 v 7
3 v 6
4 v 5 		Round 13
10 v 18
11 v 17
12 v 16
13 v 15
5 v 14
6 v 4
7 v 3
8 v 2
9 v 1 		Round 14
10 v 5
11 v 6
12 v 7
13 v 8
14 v 9
15 v 1
16 v 2
17 v 3
18 v 4 		Round 15
1 v 16
2 v 17
3 v 18
4 v 10
5 v 11
6 v 12
7 v 13
8 v 14
9 v 15		 Round 16
10 v 3
11 v 4
12 v 5
13 v 6
14 v 7
15 v 8
16 v 9
17 v 1
18 v 2 		Round 17
1 v 18
2 v 10
3 v 11
4 v 12
5 v 13
6 v 14
7 v 15
8 v 16
9 v 17
(1 v 10)
(2 v 11)
(3 v 12)
(4 v 13)
(5 v 14)
(6 v 15)
(7 v 16)
(8 v 17)
(9 v 18)

This system also works for 22 teams. The system for 20 teams is slightly different and rather than going onto the details of it here is an example of the system that I use for the Premier League. (Requires Adobe PDF Reader).

Fixtures 20

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