12 Player Golf League - 9 week schedule

[HGGolf]

Looking to fit a balanced 12-player schedule into a 9 week season. My idea is to have 3x 4-Player Divisions. Play the 8 players outside your division 1x each (8 matches); play the other 3 players in your division 3x each (9 matches). Total of 17 matches.

For weeks 1-8, everyone plays 2 opponents (in the other cart, in the foursome) for a total of 16 matches. Week 9, simply play your final opponent.

Is this possible and will everyone end up in a foursome with everyone else? What does the schedule look like?
Is there a better way to structure the league?

Thank you in advance for the help!

[Ian Wakeling]

I don't think I have understood the problem correctly.  It sounds like each foursome is 2 vs 2, but then you would have to consider balancing both partners and opponents.  Can you give an example of what the first couple of weeks might look like?

Thanks.

[HGGolf]

Division X: Player A, Player B, Player C, Player D
Division Y: E, F, G, H
Division Z: I, J, K, L

Week 1:
Foursome I: A/E/B/F
Carts: A&E / B&F
A vs. B
A vs. F
B vs. E
E vs. F

[HGGolf]

So, the schedule would end up something like this:

Week 1:
A,E / B,F ; C,I / D,J ; G,K / H,L [ AvsE, AvsB, BvsE, EvsF...]
Week 2:
A,F / C,G ; B,J / D,K ; H,I / E,L

...

After 8 weeks, A will have played: E/F/G/H/I/J/K/L and B/B/B/C/C/C/D/D, leaving one game vs. D in week 9.

[HGGolf]

I think I have a passable schedule. It could probably be optimized a little better to reduce the duplication of players in a cart together and more evenly distribute the number of times non-divisional players are in the same foursome. I will switch up the weeks to distribute match-ups more intuitively, but that doesn't change the format.

Any help on optimizing this basic structure would be much appreciated.

[Ian Wakeling]

I think you may already have a good solution, so I would be interested to know what you have done to get to the schedule in the Excel file.   My insitinct is to try to make 8 weeks where all the foursomes are of the 'Mixed Type' where there are two players from each of two groups, and then have a final round (or two rounds) where the foursomes are of the 'Group Type', with foursomes corresponding to group membership.  I can then think of two strategies for searching for a solution:

(1) There are exactly 48 possible pairs of two players where the two players come from different groups.  You could try rearranging these pairs to form an 8 week schedule.  Of course this automatically gives balance for players in a cart together.  I have not tried this option.

(2) I noted that there are exactly 1728 possible ways to assign play for a week, where all 3 foursomes are of the Mixed Type.  So I looked for ways of selecting 8 weeks from 1728 to give a schedule.  This was not totally successful, and the method is only finding schedules like the one below, where you would need to add two Group Type rounds, both with 2 matches per player.  This gives 4x replication of the within division matches.

The schedule below uses numbers rather than letters, so A=1, B=2, C=3, etc., and it is presented with the same layout as your Excel file, where weeks are rows, and pairs of adjacent columns are carts.

1  8  3  5  2 12  4 10  6 11  7  9
1  7  2  8  3  9  4 11  5 12  6 10
1  5  3  6  2 11  4  9  7 10  8 12
1  6  4  7  2 10  3 11  5  9  8 12
2  7  4  5  1  9  3 10  6 12  8 11
2  7  3  6  1 10  4 12  5 11  8  9
3  8  4  6  1 12  2  9  5 10  7 11
2  5  4  8  1 12  3 11  6  9  7 10

1  3  2  4  5  8  6  7  9 11 10 12
1  3  2  4  5  8  6  7  9 11 10 12

[HGGolf]

Thanks for the input. I am restricted to fitting my schedule into 9 weeks, though.

I approached the problem by working out Division X (teams A,B,C,D) vs. division Y (E,F,G,H), but keeping the division matchups balanced, sticking with one of each divisional combination.
Over 6 weeks, I used the combinations of AB, AC, AD, BC, BD, and CD vs. EF, EG, EH, FG, FH, GH. This can be set up leaving exactly one unplayed opponent for everyone. (side note: Interestingly, I wasn't able to figure out a combination that allowed for everyone to ride in the cart once with the other division opponent they don't play. At best, I always ended up with one combination that was never in the same foursome).

Anyway, after figuring out the Division X vs. Division Y teams for 6 weeks, I figured out X vs. Z and Y vs. Z.

So, through 6 weeks, everyone needed to play just one team from each of the other two divisions and their 3 divisional opponents one more time. If I worked it out properly in the first part, fit nicely into the final 3 weeks.

[HGGolf]

^wrong attachment.

[Ian Wakeling]

In the last attachment above you are giving priority to the pairs in a cart, as these are all unique, so I am now confused as to what you want to give priority to.   If you want to have something like your original schedule, then I think the following is better:

1  7  2  5  3 11  4 12  6 10  8  9
3  5  4  6  1  9  2 12  7 11  8 10
1  5  2  8  3  9  4 10  6 11  7 12
3  8  4  7  1 12  2 10  5 11  6  9
2  5  3  6  1 10  4 11  7  9  8 12
1  8  3  6  2 12  4 11  5  9  7 10
2  7  4  8  1 11  3  9  5 10  6 12
1  6  4  7  2  9  3 10  5 12  8 11
1  2  3  4  5  6  7  8  9 10 11 12

In the last round both opponents should be played.  However since the pairs (1 2),  (5 6) & ( 9 10) oppose 4 times, you would have to reduce these by one somewhere in the first 8 weeks.