Post by provomon on Jan 22, 2012 11:33:51 GMT -5
I have eight players that want to participate in a doubles pickleball tournament. Each player will compete individually but will be paired with a second player as a pair to compete against another pair.
We will use two courts and two players will compete against two other players in combinations of four on the two courts. With eight players, each player will play seven games.
For the tournament format to be fair, each player needs to play with and against each of the other players, the same number of times. With eight players selecting four at a time there are 70 combinations possible (order not being important).
As an example, in the following matrix players 1&2 play players 3&4 in the first game. However in this matrix each player plays one other player more than two times. For example, Player 1 plays against Player 4 in every game except the third game.
Game Court 1 Court 2
1 1 - 2 3 - 4 5 - 6 7 - 8
2 1 - 3 2 - 4 5 - 7 6 - 8
3 1 - 4 2 - 3 5 - 8 6 - 7
4 1 - 5 4 - 8 2 - 7 3 - 6
5 1 - 6 4 - 7 2 - 5 3 - 8
6 1 - 7 4 - 6 2 - 8 3 - 5
7 1 - 8 4 - 5 2 - 6 3 - 7
Does anyone have a way of developing the matrix or formula so that each player plays with and against each of the other players the same number of times (two I assume), or is that not possible?
We will use two courts and two players will compete against two other players in combinations of four on the two courts. With eight players, each player will play seven games.
For the tournament format to be fair, each player needs to play with and against each of the other players, the same number of times. With eight players selecting four at a time there are 70 combinations possible (order not being important).
As an example, in the following matrix players 1&2 play players 3&4 in the first game. However in this matrix each player plays one other player more than two times. For example, Player 1 plays against Player 4 in every game except the third game.
Game Court 1 Court 2
1 1 - 2 3 - 4 5 - 6 7 - 8
2 1 - 3 2 - 4 5 - 7 6 - 8
3 1 - 4 2 - 3 5 - 8 6 - 7
4 1 - 5 4 - 8 2 - 7 3 - 6
5 1 - 6 4 - 7 2 - 5 3 - 8
6 1 - 7 4 - 6 2 - 8 3 - 5
7 1 - 8 4 - 5 2 - 6 3 - 7
Does anyone have a way of developing the matrix or formula so that each player plays with and against each of the other players the same number of times (two I assume), or is that not possible?
