Golf League with 16 players and 4 tee times of 4 players in each tee time.

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commish

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I have golf league with 16 players and 4 tee times of 4 players in each tee time. There are 8 players in tier 1 and 8 players in tier 2. The first seven weeks of league I would like to have two different players from tier 1 play against each other and in a foursome with 2 players from tier 2. i.e 1 vs 2 with 9 vs 10 in the first group etc. Tier players are playing against each other yet as a foursome all four players are a team playing against the other foursomes. The problem I'm having is getting through the 7 weeks with as few repeats of players in the same foursome. We play one day per week. I hope this makes sense? Thank you
 
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commish said:
I have golf league with 16 players and 4 tee times of 4 players in each tee time. There are 8 players in tier 1 and 8 players in tier 2. The first seven weeks of league I would like to have two different players form tier 1 play against each other and in a foursome with 2 players from tier 2. i.e 1 vs 2 with 9 vs 10 in the first group etc. Tier players are playing against each other yet as a foursome all four players are a team playing against the other foursomes. The problem I'm having is getting through the 7 weeks with as few repeats of players in the same foursome. I hope this makes sense? Thank you
Click to expand...

How many days a week do you have game?
 
commish said:
I have golf league with 16 players and 4 tee times of 4 players in each tee time. There are 8 players in tier 1 and 8 players in tier 2. The first seven weeks of league I would like to have two different players from tier 1 play against each other and in a foursome with 2 players from tier 2. i.e 1 vs 2 with 9 vs 10 in the first group etc. Tier players are playing against each other yet as a foursome all four players are a team playing against the other foursomes. The problem I'm having is getting through the 7 weeks with as few repeats of players in the same foursome. We play one day per week. I hope this makes sense? Thank you
Click to expand...
If I am understanding you correctly, you want a pair from tier 1 and a pair from tier 2 to form a foursome. If I have not made a mistake there are 36 distinct foursomes you can form: Let tij be the jth player from tier i.
First form the six possible pairs from tier t, i.e (t11, t12), (t11, t13), (t11, t14), (t12, t13), (t12, t14), (t13, t14) where, for example, (t11, t12) indicates pair player 1 from tier one and player 2 from tier one. Now do the same with the tier two players: (t21, t22), (t21, t23), (t21, t24), (t22, t23), (t22, t14), (t23, t14).

To form a foursome choose one pair from the tier 1 set and 1 from the tier 2 . So you have 36 foursomes which you 'label on a slip of paper and put in a bowl'. Each week choose 'one slip from the bowl'.

EDIT: :oops: it was eight in each tier not 4. So, as Subhotosh Khan said, 28 pairs for each tier and 784 four-some groups.
 
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commish said:
I have golf league with 16 players and 4 tee times of 4 players in each tee time. There are 8 players in tier 1 and 8 players in tier 2. The first seven weeks of league I would like to have two different players from tier 1 play against each other and in a foursome with 2 players from tier 2. i.e 1 vs 2 with 9 vs 10 in the first group etc. Tier players are playing against each other yet as a foursome all four players are a team playing against the other foursomes. The problem I'm having is getting through the 7 weeks with as few repeats of players in the same foursome. We play one day per week. I hope this makes sense? Thank you
Click to expand...

You can make 28 distinct pairs out of 8 players.

You can pair-up each of these pairs with 28 pairs in the other group (tier).

Now we can have (28X28=) 784 four-some groups where at least one player would be different.
 
Subhotosh Khan said:
You can make 28 distinct pairs out of 8 players.

You can pair-up each of these pairs with 28 pairs in the other group (tier).

Now we can have (28X28=) 784 four-some groups where at least one player would be different.
Click to expand...


My goal is to have as few players in the same group over the 7 weeks for example, tier 1 is made up of players 1-8, tier 2 is 9-16 a sample week would be:
Week 1
1st 4some 2nd 3rd 4th
1 vs 2| 3 vs 4| 5 vs 6| 7 vs 8
9 vs 10| 11 vs 12|13 vs 14| 15 vs 16

Week 2
1 vs 3| 2 vs 4| 3 vs 5| 6 vs 8
13 vs 16| 14 vs 15| 10 vs 12| 9 vs 11

and here is where it gets tricky, when I go to put in the tier 2 players I want them playing someone different in week 2, that parts easy, but in placing them I do not want them to be
playing with anyone from the foursome from the week prior( as you can see in the list player 3 is in a foursome with player 12 2 weeks in a row)I'm aware that it's not possible to have groupings repeat in the foursome but what is a simple solution to minimize the repeats?
 
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Subhotosh Khan said:
You can make 28 distinct pairs out of 8 players.
You can pair-up each of these pairs with 28 pairs in the other group (tier).
Now we can have (28X28=) 784 four-some groups where at least one player would be different.
Click to expand...

commish said:
My goal is to have as few players in the same group over the 7 weeks for example, tier 1 is made up of players 1-8, tier 2 is 9-16 a sample week would be:
Click to expand...
I agree there are 28 distinct pairs out of 8 players. However, those are not pair-wise disjoint pairs. That means that someone could play more than once a day.

There are \(\displaystyle \dfrac{8!}{4!\cdot 2^4}=105\) ways to segregate a group of eight into four pairs. There is no overlapping of pairs in any of the groupings. We can take any pair grouping from tier I with a grouping from tier II. That way each player in both tiers play exactly once a day. Now there are \(\displaystyle 4!=24\) ways to pair the pairs from each tier. Those are huge numbers.

ALSO, that does no address any issue of individuals playing in the same grouping on a different day.
 
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