Need help putting together 7 league schedule

[jorgie97]

I am going crazying trying to put together a seven team league baseball schedule. Essentially, we have two fields with two games being able to played on each field. We have 7 teams and do not want any byes. We want each team to have an equal number of double headers and play each other as close to as the same times as possible as we are looking to play for 20 weeks. Would any of you guys be able to help put together. Thanks!

[Ian Wakeling]

It is best to start by looking for a 21 week schedule, as this can be fully balanced, and then throw away the last week.  With 21 weeks there are 84 games in total which can be arranged so that all teams:

• play each other exactly 4 times
• play on each field exactly 12 times
• play 12 games at the earlier start time
• play 12 times at the later start time
• play exactly 3 double headers

For example the following schedule has all these properties - the dashed line separate the 21 weeks.

 F1    F2
(1 7) (4 6)
(1 2) (3 5)
------------
(1 4) (5 7)
(3 6) (2 4)
------------
(3 7) (2 6)
(4 7) (1 5)
------------
(2 5) (3 4)
(1 6) (2 7)
------------
(2 3) (4 5)
(1 3) (6 7)
------------
(3 7) (5 6)
(2 4) (1 5)
------------
(1 6) (3 4)
(5 7) (2 6)
------------
(5 6) (1 3)
(4 7) (1 2)
------------
(2 5) (1 7)
(3 6) (4 5)
------------
(1 4) (6 7)
(3 5) (2 7)
------------
(4 6) (2 3)
(1 4) (5 7)
------------
(2 7) (1 3)
(2 4) (5 6)
------------
(2 5) (1 6)
(3 6) (4 7)
------------
(3 6) (4 5)
(1 7) (2 3)
------------
(1 5) (2 6)
(4 6) (3 7)
------------
(3 5) (1 2)
(6 7) (3 4)
------------
(4 7) (2 5)
(3 5) (1 6)
------------
(1 2) (3 7)
(5 6) (2 4)
------------
(1 4) (6 7)
(2 3) (1 5)
------------
(5 7) (3 4)
(2 6) (1 7)
------------
(2 7) (4 6)
(4 5) (1 3)

Note that the team with the double header in the week that you throw away will end up with one less game than the other 6 teams, so removing the last week above will mean that team 4 has 22 games, while the others all have 23 games.