Round Robin Tournament Scheduling

Volleyball Doubles and Triples

ndodge · 23 · 19386

ndodge

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on: January 27, 2010, 07:28:54 PM
Looking to organize volleyball tournaments, either doubles or triples.

I've seen the whist schedules, which are perfect for doubles, but in my situation I have to account for having people not show up, so even if I planned a 12 person tournament, I'd like to have backup plans for 11, 10, 9 players, etc.  If there were a balanced or near-balanced whist schedule for player counts from 8 to 12 that would be ideal.  Is there such a thing for the numbers not 4n ?  

Is there software available for the general public for whists other than the ones that show schedules for 4n player counts ?  Are there topics for posts I should look at that might be similar to what I'm trying to do ?

Also, I'd like to do some schedules for volleyball triples, where there is some pattern for at least minimizing the playing with/against other players.  I realize this is a more open-ended and vague question, and was mostly wondering if there was existing material I could be pointed to.  


ndodge

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Reply #1 on: January 28, 2010, 12:54:06 AM
I think I can use and adjust the schedules found here:  http://www.jdawiseman.com/papers/tournaments/individual-pairs/individual-pairs-links.html

for the doubles tournaments, at least.  I have to do some more thinking about the practicality of the triples idea.  I might not have enough time for it to really be anything other than essentially a random selection of a few out of many possible combinations.


Ian Wakeling

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Reply #2 on: January 30, 2010, 07:29:34 AM
As you have found,  the Wiseman website has the double schedules for 4n+1 players.  These are well known, but unfortunately are not implemented in the schedules area here.  This still leaves a gap for 10 or 11 players - it's possible to come up with nearly balanced solutions, I think, I will have a look later.

You may like to look at this old thread, it has a triples schedule for 7 players that may be of use.


Ian Wakeling

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Reply #3 on: January 30, 2010, 11:56:53 AM
When generalizing the Whist problem to schedules with byes, then I think the one thing that it is important to plan for, is that all players should play the same number of games, otherwise the schedule will be perceived as unfair by the players who have fewest games.

Definition:

A whist schedule with byes WSB(4t+b) is a schedule for 4t+b players and 4t+b rounds of play. Each round consists of t tables of whist play, and b players (1<=b<=3) who receive a bye. The schedule should have the following properties:

- Each player plays in exactly 4t rounds and has exactly b bye rounds.
- A player's 4t partners are all different.
- Each player opposes every other player at least once and at most twice.
- Pairs of players who never partner should play in opposition twice.

If all of these conditions are met then the schedule will be have optimal social balance, in the sense that the number of times players sit together at a table, either as partners or opponents, is at least twice and at most three times.  Other properties that may be desirable are:

- Players should never have byes in consecutive rounds.
- Pairs of players who both have a bye in the same round, should never have byes together again.

When b=1 then the situation reduces to the classic whist schedule for 4t+1 players that you have already seen.  If b=2 or 3, then things are more interesting, for example here are some cyclic solutions for 10 and 11 players:

   Table 1          Table 2        Byes
( 1  5 v  7 10)  ( 6  4 v  9 3)  ( 2  8)
( 2  1 v  8  6)  ( 7  5 v 10 4)  ( 3  9)
( 3  2 v  9  7)  ( 8  1 v  6 5)  ( 4 10)
( 4  3 v 10  8)  ( 9  2 v  7 1)  ( 5  6)
( 5  4 v  6  9)  (10  3 v  8 2)  ( 1  7)
( 7  6 v  4  8)  ( 1  9 v  5 3)  (10  2)
( 8  7 v  5  9)  ( 2 10 v  1 4)  ( 6  3)
( 9  8 v  1 10)  ( 3  6 v  2 5)  ( 7  4)
(10  9 v  2  6)  ( 4  7 v  3 1)  ( 8  5)
( 6 10 v  3  7)  ( 5  8 v  4 2)  ( 9  1)

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


I think many such schedules for b=2 and b=3 exist, although I have no general proof of this.


ndodge

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Reply #4 on: February 23, 2010, 07:25:17 PM
I also do events where volleyball players play 4 on 4.  These schedules that you posed for 10 and 11 players work perfectly for foursomes, if I just treat what had been a game in doubles as a team, with the opponent being the other set of 4 players in what had been the other doubles game in that round (with the players who had byes before still having byes).  I did a little number crunching in a VBA macro just to ensure that things are still balanced, and they appear to be.

However, if I look at a 12 player whist schedule and try to do the same approach to convert that schedule to 4's, then that schedule does not come out balanced.  I believe I used the 12 player whist schedule from Wiseman and tried to treat one of the courts as the group of players having a bye.  

What I am looking for is a 12 player, 1 court, 4v4 schedule (with 4 players having a bye in each round), with about 12 rounds, with balancing of with/against for each player.  


ndodge

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Reply #5 on: February 24, 2010, 01:59:12 PM
For the 12 player scenario, a solution for playing 3 on 3 with 2 courts would be desirable also (perhaps in place of the 4v4 with 4byes scenario, but I'd take either or both!

I came up with good, balanced formats for doubles for 4 to 12 players, and came up with some other good options for using 3 or 4 players on a side for player counts of 5, 6, 7, 9, 10, and 11 (still have to check doing 4's with 8 players), and this 12 player scenario hasn't been solved yet.  But I'm close.


Ian Wakeling

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Reply #6 on: February 26, 2010, 04:15:13 AM
I am a little surprised that the schedules above worked out well when you collapsed the doubles matches into teams of 4 - I will have to think some more why that works.  Below is some output from my program for the 4 against 4 option with 4 byes.  I can get a reasonable solution in terms of the number of times pairs are on court together, and the number of time pairs are on the same team, however the opponent balance could be a little better.  I have included some concurrence matrices that count pairs, this must be the something similar to your VBA code.


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

Byes :
 7  1  3  5
 8  2  1  6
 9  3  2  4
10 11  3  6
11 12  1  4
12 10  2  5
 7  2  8 11
 8  3  9 12
 9  1  7 10
 5 11  6  9
 6 12  4  7
 4 10  5  8

Overall Concurrence:
  0 . . . . . . . . . . .
  5 0 . . . . . . . . . .
  5 5 0 . . . . . . . . .
  5 5 5 0 . . . . . . . .
  5 5 5 5 0 . . . . . . .
  5 5 5 5 5 0 . . . . . .
  6 5 5 5 5 5 0 . . . . .
  5 6 5 5 5 5 5 0 . . . .
  5 5 6 5 5 5 5 5 0 . . .
  5 5 5 5 6 5 5 5 5 0 . .
  5 5 5 5 5 6 5 5 5 5 0 .
  5 5 5 6 5 5 5 5 5 5 5 0

Within Team Concurrence :
  0 . . . . . . . . . . .
  2 0 . . . . . . . . . .
  2 2 0 . . . . . . . . .
  2 3 2 0 . . . . . . . .
  2 2 3 2 0 . . . . . . .
  3 2 2 2 2 0 . . . . . .
  2 2 2 2 3 2 0 . . . . .
  2 2 2 2 2 3 2 0 . . . .
  2 2 2 3 2 2 2 2 0 . . .
  2 2 3 2 2 2 2 3 2 0 . .
  3 2 2 2 2 2 2 2 3 2 0 .
  2 3 2 2 2 2 3 2 2 2 2 0

Opponent Concurrence :
  0 . . . . . . . . . . .
  3 0 . . . . . . . . . .
  3 3 0 . . . . . . . . .
  3 2 3 0 . . . . . . . .
  3 3 2 3 0 . . . . . . .
  2 3 3 3 3 0 . . . . . .
  4 3 3 3 2 3 0 . . . . .
  3 4 3 3 3 2 3 0 . . . .
  3 3 4 2 3 3 3 3 0 . . .
  3 3 2 3 4 3 3 2 3 0 . .
  2 3 3 3 3 4 3 3 2 3 0 .
  3 2 3 4 3 3 2 3 3 3 3 0


Ian Wakeling

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Reply #7 on: February 26, 2010, 05:41:22 AM
It looks like the 3 against 3 on two courts may be a better option - there is a perfect solution in 11 rounds where all possible pairings within teams occur twice and all possible opponents occur three times.

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


For round 12 you could play anything, but of course the nice balance would be lost.


ndodge

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Reply #8 on: March 28, 2010, 03:27:47 AM
Wondering if there are formats that are balanced for doing 3v3 for player counts of 8 or 9, preferably in 6 to 8 rounds.  Doesn't need to be perfectly balanced, e.g., would be fine, for example, if each player played with 4 players 2 times and with 3 players 3 times (or something to that effect, and something similar for the against part).  Also, what I tried doing manually, was to have it so that pairs of players didn't play each other (e.g. A doesn't play B, C doesn't play D, etc. (for the 8 player scenario anyway).  Doing it manually didn't work so well, of course.


Ian Wakeling

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Reply #9 on: March 30, 2010, 02:11:05 AM
The following two schedules may help you, they both have the property you asked for, where the number of times players meet on the same team or play against each other is as balanced as it can be.  The 9 player schedule has one more round than you were looking for - the alternative was 6 rounds but I could not find any good solution for that.

Hope that helps.

   7  4  1  v  8  3  6    2  5
   8  1  2  v  5  4  7    3  6
   5  2  3  v  6  1  8    4  7
   6  3  4  v  7  2  5    1  8
   4  8  5  v  1  7  3    2  6
   1  5  6  v  2  8  4    3  7
   2  6  7  v  3  5  1    4  8
   3  7  8  v  4  6  2    1  5


   3  5  6  v  9  1  8    2  7  4
   1  6  4  v  7  2  9    3  8  5
   2  4  5  v  8  3  7    1  9  6
   9  3  4  v  1  8  7    6  2  5
   7  1  5  v  2  9  8    4  3  6
   8  2  6  v  3  7  9    5  1  4
   4  6  7  v  3  1  5    2  9  8
   5  4  8  v  1  2  6    3  7  9
   6  5  9  v  2  3  4    1  8  7


ndodge

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Reply #10 on: May 29, 2010, 07:45:03 PM
Triples formats have worked very well for volleyball tournaments this year (as have the doubles formats).  I have formats for 6 to 9 players for triples, and I double that if I have 2 courts, so I can handle players counts from 6 to 9 or from 12 to 18.  I don't have a balanced format for triples for player counts of 11 or 12 though.  Any ideas ?


ndodge

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Reply #11 on: May 29, 2010, 07:56:29 PM
Sorry, I meant I don't have triples formats for 10 or 11.


Ian Wakeling

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Reply #12 on: June 03, 2010, 03:50:35 AM
Here are some similar schedules to the ones above, but for 10 and 11 players.   Hope that helps.


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

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


ndodge

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Reply #13 on: June 03, 2010, 10:00:36 AM
Thank you very much.  One last request (hopefully), for triples:  I was able to find a solution for 6 people sort of by hand, but by having 2 people not play together (it cut down the combinations enough to make finding a solution doable by hand).  Is it easy to find a better solution for 6 players, 3v3 ?  

What this is being used for is a volleyball club, about 400 members strong, in the Twin Cities.  We have doubles, triples and sometimes 4's events.  We also do "paired 4's" where we take whist formats but apply them to pairs of people (i.e., you pair with somebody and stay as a pair the whole time).  We've had many successful events, and having solutions for every number really helps, because of course something always seems to come up regarding who actually shows up on a given day.

Thanks again,
Nathan


Ian Wakeling

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Reply #14 on: June 03, 2010, 10:38:17 AM
Nathan,

Good to know that the schedules are being put to use.   As regards the 6 people, how many rounds are you looking for?   I think I can see that you will be unable to find anything balanced for 5 rounds of triples play, however 10 rounds should work, all partners 4 times, all opponents 6 times.  But is 10 rounds too many?

Ian.