Round Robin Tournament Scheduling

Basketball 3 v 3 Tournament - 15 players

SCNickerson · 9 · 323

SCNickerson

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on: August 16, 2020, 09:33:04 AM
Seen lots of threads for 7-13 players and one for 15, but what im hoping to find is a tournament schedule for 3 on 3 with 15 players.

We have 2 nets available to play on, so 12 players can be playing at any one time and 3 of them sitting.

It doesn't have to be perfectly balanced in the sense that everyone plays with each other X number of times. Also the number of games doesn't matter either, just enough to fill a 2 hour slot with games being 5 minutes each.

Any help would be appreciated. Thanks


Ian Wakeling

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Reply #1 on: August 16, 2020, 11:38:00 AM
I can make a reasonably balanced schedule with 20 rounds.  For example in the following :

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

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

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

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

each person has exactly 4 byes, plays on the same teams as the other 14 players either 2 or 3 times, and plays against each of the other 14 either 3 or 4 times.

It would be a good idea to change the order in which rounds 11 to 20 are played, as this would break up the pattern of back-to-back byes.  A similar schedule with 15 rounds would be possible if the above is too much to achieve in 2 hours.


SCNickerson

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Reply #2 on: August 21, 2020, 07:31:20 AM
I can make a reasonably balanced schedule with 20 rounds.  For example in the following :

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

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

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

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

each person has exactly 4 byes, plays on the same teams as the other 14 players either 2 or 3 times, and plays against each of the other 14 either 3 or 4 times.

It would be a good idea to change the order in which rounds 11 to 20 are played, as this would break up the pattern of back-to-back byes.  A similar schedule with 15 rounds would be possible if the above is too much to achieve in 2 hours.


Thanks so much! This will make tonight easy :) If I want to do the 15 rounds how do I do that? 20 rounds is too much for 2 hours, worst case scenario is I will just chop the last 5 off. These are 9-12 year olds they wont know the difference / care, they just want to play!
« Last Edit: August 21, 2020, 10:19:29 AM by Ian Wakeling »


Ian Wakeling

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Reply #3 on: August 21, 2020, 10:27:42 AM
Here is a new 15 round schedule, it should work a lot better than simply chopping off the last 5 rounds above, and I think I have the  byes well distributed too, so most players have at least two games between byes (player 11 is the one exception).

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

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

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


SCNickerson

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Reply #4 on: August 22, 2020, 03:30:16 PM
I put the schedule for 15 to use last night and the boys enjoyed it!

I was a tad bit nervous as I only counted 14 at one point and that is one number I don't have a 3v3 schedule for. Is it easy to create one?


Ian Wakeling

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Reply #5 on: August 23, 2020, 03:20:22 AM
It's good to know that it worked!  14 players and 14 rounds is actually easy to create a schedule for, then each team can have exactly 2 byes and 12 games.  In the schedule below each player is on the same team as all other players either once or twice, and against all other players two or three times.

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



SCNickerson

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Reply #6 on: September 04, 2020, 08:55:53 AM
I guess I may as well see if I can fill in the holes.

I believe I now have 6-16 players, and saw posts for 20/21.

Is it possible to get something for 17-19? I will browse through some posts here in a bit to see if I can find a schedule.


Ian Wakeling

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Reply #7 on: September 05, 2020, 10:24:11 AM
The only way I have of making a schedule for 17 is to have 17 rounds (because 17 is a prime number).  So I offer the following with 5 byes per round:

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

If you have 18+ do you want to play with three nets?  Of course 19 is also prime, but is 19 rounds too many?
« Last Edit: September 05, 2020, 10:26:01 AM by Ian Wakeling »


SCNickerson

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Reply #8 on: September 16, 2020, 06:30:59 PM
The only way I have of making a schedule for 17 is to have 17 rounds (because 17 is a prime number).  So I offer the following with 5 byes per round:

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

If you have 18+ do you want to play with three nets?  Of course 19 is also prime, but is 19 rounds too many?

I'd have to stay with 2 nets as that's all we have with our current venue. I had to put the 17 schedule to use last week, popularity is picking up. Might need an 18-20 soon.