Help with determining number combinations - for all you engineers and math geeks!

[Lisa99]

I have volunteered to help set up a round robin tournament for my pickleball club. Unfortunately this math challenged person has been given the task of setting up who plays against whom in each of 8 rounds.

Here's the task. There are 8 rounds and depending on the number of players there can be more than one game in each round. For each game there are 4 players (two sets of two) but they are playing as individuals rather than partners that stay together.

Once round 1 is over, rounds 2 - 8 have to be a different combination of players so that by the end of 8 rounds everyone will have played with and against all other players (this is a no elimination tournament and at the end the person with the highest total score wins)

I have to set up 8 rounds for 4 players, another for 5 players, another for 6 players, and a final one for 7 players. I believe byes will need to be involved for all but the 4 player scenario.

If you have any idea how to do this I'd love guidance! I've scoured google and have come up with nothing that I remotely understand.

 

[Midpack]

I found several helpful resources online like Tournament Scheduling : nrich.maths.org that I might be able to help with, but to clarify:

Your tournament will be all doubles matches (with individuals playing with all other players)? No singles matches correct? And number of players varies from 4 to 7?

That is a pretty complex tournament to schedule AND score!

 

[Lisa99]

I found several helpful resources online like Tournament Scheduling : nrich.maths.org that I might be able to help with, but to clarify:

Your tournament will be all doubles matches (with individuals playing with all other players)? No singles matches correct? And number of players varies from 4 to 7?

That is a pretty complex tournament to schedule AND score!

Thanks for the help! I'll take a look at the site today. You're correct, doubles tournament with individual players playing all other players.

It's a ladder league that's played to rank individual players within our club.

 

[stepford]

I'm not sure if I follow exactly what you need to do to set up the ladder. Do you just need to determine how many distinct pairings make a foursome? In the simplest case of 4 players (call them 1, 2, 3 and 4) this would make for only 3 distinct pairings: (1,2) play (3,4), (1,3) play (2,4), and (1,4) play (2,3). Would those 3 games (or just a repetition of them) constitute a complete round robin or is there something I'm missing?

If it is just a question of counting the distinct pairings in a foursome then it can be easily generalized to N players. I think it works out to be something like:
N! / (8 (N-4)! )
but maybe one of the better math folks on here should check me on that...

 

[Bestwifeever]

I would first ask the person who did it last year.

 

[Lisa99]

I would first ask the person who did it last year.

Agree completely. That's where I started but these seniors are having a senior moment and can't remember who has the files and no one will fess up to having them.

 

[Lisa99]

I'm not sure if I follow exactly what you need to do to set up the ladder. Do you just need to determine how many distinct pairings make a foursome? In the simplest case of 4 players (call them 1, 2, 3 and 4) this would make for only 3 distinct pairings: (1,2) play (3,4), (1,3) play (2,4), and (1,4) play (2,3). Would those 3 games (or just a repetition of them) constitute a complete round robin or is there something I'm missing?

If it is just a question of counting the distinct pairings in a foursome then it can be easily generalized to N players. I think it works out to be something like:
N! / (8 (N-4)! )
but maybe one of the better math folks on here should check me on that...

This is exactly what I need! But I also need the potential combinations for 5 players, 6 players and 7 players. There will be byes involved for the 5, 6, and 7 player combinations. I'll see if I can put the formula into Excel to generate the balance of what I need.

 

[stepford]

N! / (8 (N-4)! ) = 15 when N=5, 45 when N=6, and 105 when N=7. I'm not sure how you accommodate that many combinations in only 8 rounds.

For instance, for N=5 the 15 distinct pairs of pairs are:

(1,2) playing (3,4)
(1,2) playing (3,5)
(1,2) playing (4,5)
(1,3) playing (2,4)
(1,3) playing (2,5)
(1,3) playing (4,5)
(1,4) playing (2,3)
(1,4) playing (2,5)
(1,4) playing (3,5)
(1,5) playing (2,3)
(1,5) playing (2,4)
(1,5) playing (3,4)
(2,3) playing (4,5)
(2,4) playing (3,5)
(2,5) playing (3,4)

How do you get all those combinations in 8 rounds? I imagine the question now becomes more of tournament standards rather than math and Midpack's reference would probably be very helpful.

 

[Bestwifeever]

Agree completely. That's where I started but these seniors are having a senior moment and can't remember who has the files and no one will fess up to having them.

That's really funny and I can sympathize--as someone who used to handle scoring and handicapping as a volunteer for a little 9-hole golf league, I ran into this the first year I did it! She just couldn't find time to get me any information about how she had done it for maybe ten years (and she wanted to step down).

 

[HFWR]

If you have any idea how to do this I'd love guidance!

Be out of town?

 

[Lisa99]

Here's is how an 8 player series is constructed:

 

[phil70]

this sounds like a standardized test question!

 

[Live And Learn]

Combinations and permutations .... makes me want to find all those kids from algebra class who said "I'll never need this stuff !" when I was saying "this is cool" and say "told you so !!!"

 

[Lisa99]

Combinations and permutations .... makes me want to find all those kids from algebra class who said "I'll never need this stuff !" when I was saying "this is cool" and say "told you so !!!"

Agree! I loved algebra and made straight A's in it but seems to be like a foreign language... If you don't use it you lose it. I've definitely lost it!

 

[Live And Learn]

Agree! I loved algebra and made straight A's in it but seems to be like a foreign language... If you don't use it you lose it. I've definitely lost it!

Ditto --- including the "losing it" part !

 

[stepford]

I suspect the combinatorics is the easy part while the herding of cats necessary to make the tournament work takes all the true skill.

 

[Brett_Cameron]

Here's is how an 8 player series is constructed:

I don't see where 1-2 play with each other.

 

[Midpack]

I actually spent some time working on this yesterday. I did find quite a few free mixed doubles round robin schedule generators that would seemingly fit the OP's needs - but I wasn't willing to go as far as downloading them to test. Sorry...

 

[dallas27]

I'm literally studying game theory and nash equilibrium right now. However, your problem confounds me.