12 player pickleball round robin on 3 courts with 2 options

[Cindi]

Hi Ian,

I have more pickleball schedule questions for you:

Option 1: For this schedule I have 3 courts and 12 players and have enough time for 8 rounds. I'd like a schedule where in each round you partner with a different player and play against different opponents so that at the end each person has played with 8 unique partners and against each opponent once and sometimes twice, but not opposing the same team twice. The preference would be to have new players on each court from one round to the next -- for example, if in round 1 players A and B play against C and D, then in round 2 player A is not on the same court as B, C or D. It doesn't have to be perfect for everyone, but just a preference for variety. If possible  could you finish this schedule for the full 11 rounds for when time permits?

Option 2: Sometimes I have a wider range of skills among players and in this case I'd like an option to rank them from 1-12 with 1 being the strongest and 12 the weakest player. Is it possible to create 8 games where you can have somewhat equal teams playing against each other? If done randomly sometimes the 2 strongest players play the 2 weakest and that isn't much fun for anyone. Again I'd prefer for each player to have 8 unique partners and to favor variety from round to round instead of having 2 of the same players on the same court in consecutive rounds.

Thanks again for all your help. I organize a lot of pickleball games and you are helping me to keep my games organized and fun! :-)

Cindi

[Ian Wakeling]

Hi Cindi,

Regarding Option 1 - I am not sure if this can be solved or not.  I have tried a few things and I can find 9 rounds with the basic properties that you ask for; that is to say different partners, and once or twice for opponents.  I can't find anything similar for 8 rounds.  The 2nd part to your question about variety is hard, certainly what you want is impossible unless there are 4 or more courts, and 16 or more players.  However, I can see that it may be possible to have a schedule for 12 players where no more than 3 pairs of players who have played together on a court in one round, play together in the next round. The completion to 11 rounds is a harder problem still, and I can't really offer an useful suggestions.

For Option 2 all I can suggest is that you try mixed doubles schedules. Split the players into two ability groups based on ranks, then consider one group to be men and the other women and play a mixed doubles schedule, this will make sure that every partnership consists of one player from each ability group. You will be limited to fewer than 8 rounds, but that is a natural consequence of saying that you don't want certain pairs of players to partner, as they would either be too weak or too strong.  Turning this around, you could approach the problem by first deciding which parnterships were allowed, and then try to construct a schedule from them.

Here is the 9 round schedule that I mentioned for option 1.  It is interesting to note that it cannot be completed into an 11 round schedule since the partnerships (1 2) (1 3) and (2 3) are yet to be played, and no two of them can occur together in a valid round of play.

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

Ian

[Cindi]

Thanks, Ian! That looks a lot better than what I've been using for Option 1!😁
For Option 2 I will try what you recommend with splitting my women into M and F groups and using a mixed doubles schedule. The only problem will be when we go beyond the 6th round as you will then repeat partners instead of playing with someone new. Any thoughts on constructing maybe an additional 2-3 rounds so that the weaker and stronger players aren't paired together? 

[Ian Wakeling]

Hi Cindi,

Short of writing software specifically to try to optimize this problem, I don't really have any further ideas.  The schedule here at the Wiseman web site might be worth considering. The schedule is optimized for an unfairness criterion, but as it assumes that the whole Whist schedule is to be played, it may not be what you want - nevertheless it may be worth throwing away 2 or 3 of the rounds you least like the look of (rounds 2 and 8 for example).

I looked again at Option 1 above, and it surprised me that it is possible to have six rounds where all partners are different and all opponents are once or twice.  Here is an example:

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

there is a catch, three pairs of players are on court together three times, these are (4 11), (5 12) & (6 10), while there are plenty of other pairs who only meet once, for example (7 8), and many who meet twice.  My take from this is that schedules for 7 and 8 rounds are possible.

[Ian Wakeling]

Here is an 8 round schedule.

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

My impression from a quick glance at all the schedules above is that they may be optimal for the variety between successive rounds.