Bjerring tournament templates

[cvvcdad]

Hi! The help given here is amazingly valuable! If you can help with this, it will be greatly appreciated by many, many volleyball coaches.

I often run Bjerring tournaments during practice, and also for school vb tryouts. It's not really a problem to define Bjerring tournaments for the number of players at practices. But tryouts are a completely different animal.

In general, what I need is the teams for each round of a 6v6 Bjerring tournament for n players. A Bjerring tournament is player-defined instead of team-defined, so the mixing from round to round is in terms of which players are playing together and which players are they playing against, and NOT which teams are playing each other in a particular round. There are no defined teams, just two sets of 6 players each game.

An ideal Bjerring tournament has any given player playing with every other player the same number of games and playing against every other player the same number of games. I assume that isn't possible for every value of n; if not a variance of 1 from player to player would be fine.

A quick example: the first game of a Bjerring tournament has players 1/2/3/4/5/6 vs players 7/8/9/10/11/12; the second game is players 1/3/5/7/9/11 vs players 2/4/6/8/10/12; etc. When the tournament is over, player 1 will have played x times with every other player, and z times against every other player. Again, this is the PERFECT Bjerring tournament, but a slightly-less-than-perfect format would work too.

What would be amazingly valuable is a tool that allows a coach to input the number of players, with the output being the player assignments for each game of 6v6 for the number of rounds needed. What would be even more valuable would be a tool that does this while allowing for various-sized games -- e.g., a tournament of all 6v6 games, a tournament of all 5v5 games, etc.

I know that's a LOT to ask; alternatively (and this might be a lot to ask too), tables defining 6v6 games for Bjerring tournaments for 12 players, 13 players, etc. up to 24 players would be great! I would likely never bother you again!

Thanks so much in advance for any help you can give to all of us vb coaches out here!

[Ian Wakeling]

Hi, I think if you have exactly the right number of players and number of rounds, then there may be a perfect tournament, but most of the time, with other numbers of players and rounds the only thing possible will be a long way from perfect.  How far away from perfect probably depends on the search algorithm used, and this makes it difficult to know if you you have found an optimal solution.  I don't currently have an software that might help here, but I will think about some options.

Here is one perfect solution for 12 players in 11 rounds - where each player partners with each other player 5 times and opposes each other player 6 times.

 P1 P2 P3 P4 P5 P6    P1 P2 P3 P4 P5 P6
( 3 12  9 11  5  1) v ( 4  6 10  7  8  2)
(12 10  3  9  7  4) v ( 1 11  5  8  2  6)
( 8  7 12  6  3  5) v (11  2  4  9 10  1)
( 3 11  8  2  4 12) v (10  5  1  7  6  9)
(11 10  7  5 12  2) v ( 8  1  9  6  4  3)
( 7  6  4  1 11 12) v ( 2  9  5  8  3 10)
(10  9  6 12 11  8) v ( 1  2  3  4  5  7)
( 6  1 12  3  2 10) v ( 5  4  7 11  9  8)
( 9  8  2 12  1  7) v ( 4  3 11  5 10  6)
( 5 12  1 10  8  4) v ( 2  7  6  3  9 11)
(12  5  2  4  6  9) v ( 7  3  8 10  1 11)

If P1 to P6 are 6 positions, then each player appears twice in 5 positions, and once in the other  position.

Is 11 rounds something that is practical?  I guess another perfect schedule might be possible for 13 players and 13 rounds, with each player having one bye.