Volleyball Triples Schedule: 2 courts, 15 players

[VolleyFreak]

Just happened across the site.  Love the info provided.  Wish I had the time & energy to dig into the mathematics behind this.  I'd love to understand it on a deeper level.

I direct a number of different volleyball tournaments/leagues that have some unusual formats.  I was wondering if I could get some assistance on a new league format.  The playing format is triples (3v3).  I've got 2 courts and 15 total players so 3 players would have a bye each playing session.  I'm looking for each player to play with & against the other league participants and have the same amount of byes per participant.

Possible?  Any assistance would be greatly appreciated.  Thanks.

JP

[Ian Wakeling]

Can you say something about the number of rounds you would like to play?  My thinking is that the schedule must have a multiple of 5 rounds in order to meet the basic condition that everyone get the same number of games, that is to say after 5 rounds everyone will have had exactly one bye, also each player will have had 8 partners and 12 opponents.  As there are 14 possible partners and opponents, the smallest balanced schedule that can exist is when there are 7 blocks of 5 rounds, or 35 rounds in total, where all pairs play together on the same team 4 times, and oppose 6 times.  I say "can exist" as it is possible an example of this schedule is not known, but I can certainly look for one if you are interested.  However, I am guessing 35 rounds is too many, so you may need to pick a more manageable number, 5, 10 or 15 perhaps, but you will have to accept that you can not balance the number of times pairs play with and against each other.

Ian.

[VolleyFreak]

Hi Ian.  Thanks for the quick reply.

Some further details.  The league is date limited to 8 matches.  They are actually playing 2 matches per date over 4 weeks.  The preference would be that a given player's schedule would not have back-to-back BYEs where he wouldn't play at all on a given date.  I realize this will fall well short of a balanced schedule.  For those that play fewer games, we rank them based on stats like set winning %, avg. point differential, etc.  If you could assist with a 10 round schedule, I can truncate it to 8 rounds and live with the asymmetries.

Thanks again for the assist.  Love the site.

[Ian Wakeling]

Below is the best 10 round schedule I can find.  There are probably many ways of adapting to 4 groups of 2 rounds.  For example leave out rounds 1 and 2, and swap around rounds 8 and 9 to avoid the back-to-back byes for teams 8 and 10.  Hope that helps.

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

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