16 Player - 4 Players per Court Round Robin

[roller55]

Looking to schedule a 16 player pickleball doubles league where each week players are assigned to one of 4 courts so that each player partners with all 15 other players only once during each 5 week scheduling cycle.  (Each player will partner for one game with the other 3 players assigned to their court each week.)  Sort of a round robin within a round robin.  I'm figuring a 5 week scheduling cycle, since each player has 15 players to partner with and should partner with 3 different partners each week. (15 players / 3 partners per week = 5 weeks).  I get through 3 weeks pretty easily, but then the schedule starts to fall apart with some partners repeating.  Any suggestions, please?    

[Ian Wakeling]

See this thread.  There is a second link there for the schedule itself.   You can assign each groups of 4 to be partners and opponents in any way you like, no matter how you do it, a player will always have exactly 5 different partners and 10 different opponents.

[roller55]

Thanks for helping and I've got the 4x4 concept down.  How can additional players be added, thereby creating a player or players with byes each week.  Right now 17 players, so 1 bye each week.

[Ian Wakeling]

Not having a multiple of four adds complexity to the problem and in many cases there will be no fair schedule.  For example you would need to have 17 rounds with 17 players before you could have a schedule where everyone played the same number of times (16 times each).  I can make a schedule with fewer rounds, but I would need to know the number of rounds first.

[roller55]

I believe that your answer confirms my conclusion in attempting to create this schedule .  Attempting to set up a "balanced" schedule becomes impossible unless the league runs 17 weeks, since it would take 17 weeks for each player to have their bye.  The league is supposed to play once a week for 8 weeks.  Any suggestions on making it as fair as possible?  Additionally, what would the new scheduling sequence look like with the 17th player added?  

[Ian Wakeling]

Here is something for 17 players and 8 rounds.  With non-balanced scenarios like this, it is difficult to know if it is possible to do better or not.

  ( 9 16 v  3  4) ( 1 12 v  6 14) (11  7 v 15  2) (17  5 v 13 10)    8
  ( 5  7 v 17 12) (15 14 v 16  8) ( 6 11 v  4  9) ( 3 10 v  2  1)   13
  ( 7 16 v  5  1) (13 14 v 11  3) ( 8 10 v  6  9) (17  2 v 12  4)   15
  ( 4 17 v  8  1) (12 13 v 10 15) ( 5 11 v  3  6) ( 2  7 v 14 16)    9
  (11 14 v 17 10) (12  9 v 16 13) ( 6  8 v  7  3) ( 4  1 v 15  5)    2
  (11  1 v 12  8) ( 2 14 v  9  5) ( 3 13 v  4  7) (15 16 v 10  6)   17
  (10 12 v  3  8) ( 9 11 v  7  1) (16  2 v 17 13) ( 5 14 v  6 15)    4
  (15 17 v  3  9) (14  7 v 10  4) ( 5 16 v  8 11) ( 6  1 v  2 13)   12

There are problems, for example pairs (2 8), (6 17) & (8 13) do not occur together either as partners or opponents.

[tjb3]

I have run similiar leagues.  There are two factors that you need to address before beginning the League.  Every Team must have the same number of byes over the entire League schedule or otherwise you can get into unfair situations.  Second, if you are running a truncated League schedule (not a complete round robin) then you must have some provision in place to handle ties between Teams that do not compete against each other.

[Ian Wakeling]

I certainly agree about the byes, it can't be fair when, as in the schedule above, players do not have the same number of games.  Can you give an example regarding your second point, are you thinking about adjustments to the scoring?