Round Robin Tournament Scheduling

20 teams, 10 dif games, 10 rounds...

sausage041 · 18 · 12367

sausage041

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on: June 14, 2011, 05:34:06 PM
20 teams, 10 dif games, 10 rounds...and each team plays a dif team each round and plays each game once. (or any variation of those numbers)  This schedule is for a lawn games tournament where we would like to have 10 games and be able to schedule any number of teams to rotate through each game once and play a new team at each game.  I know there are scenarios where playing each team once isnt possible, but for my end game I would like to have a flexible program because we are not sure that 20 teams will attend - could be 19, could be 21 teams.  I have seen alot of schedule generators out there, but they lack the ability to specify the number of rounds (obviously 19 rounds for a perfect 20team round robin - I just want 10 rounds) and distribute to the different sites (games) evenly.  I dont know if there is an algorithm that would recognize that say Team1 has played Team 2 and been to Site 5, so never again can Team 1 play Team 2 or go to Site 5 again. (unless in a complicated situation, there were 10 teams, 10 games and it was required to play each team twice but each game only once)

I have tried using the IansBalancedRoundRobin and just cutting off the last 9 rounds, but I end up with teams playing games twice and not making it to 1 game, or a team playing at 3 games twice and thus not making it to 3 games.  If push comes to shove I could go through each team's schedule individually to try to limit some of that, but hopefully someone smarter than I has a solution here!

Hope this makes sense?

THANKS so so much for any feedback


Ian Wakeling

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Reply #1 on: June 15, 2011, 06:13:17 AM
For 20 teams use the first 10 rows of the 20 team schedule that you can find here(see the 5th Reply).  It's unlikely that a general algorithm exists, but if you want to investigate mathematical constructions, then these first 10 rows would be a special case of a Howell Design (with no empty cells).   You probably want to avoid having odd numbers of teams as there is a problem, for example 21 teams, 10 games, and 10 rounds, then 10 teams will get a bye round, while 11 teams will have no bye, so it's not possible to have everyone playing the same number of times.

Hope that helps.
« Last Edit: June 15, 2011, 06:15:34 AM by Ian »


sausage041

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Reply #2 on: June 16, 2011, 01:14:25 AM
Thanks for the reply! That would certainly work for 20 teams, I am looking at 22-25 teams now.  We are tossing around the idea of creating "divisions" so we'd go back to ~12 teams per division for scheduling.  To make things harder, we won't have a definite number until starting time, so I was hoping there was a program where we could input team names and match everything up with the click of a button.


Ian Wakeling

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Reply #3 on: June 16, 2011, 03:54:35 AM
I am not aware of a suitable program, so I think I can only be of limited help.

22 teams, 11 games & 11 rounds is possible:

(0 11) (10 12) (9 13) (8 14) (7 15) (6 16) (5 17) (4 18) (3 19) (2 20) (1 21)
(2 21) (1 11) (0 12) (10 13) (9 14) (8 15) (7 16) (6 17) (5 18) (4 19) (3 20)
(4 20) (3 21) (2 11) (1 12) (0 13) (10 14) (9 15) (8 16) (7 17) (6 18) (5 19)
(6 19) (5 20) (4 21) (3 11) (2 12) (1 13) (0 14) (10 15) (9 16) (8 17) (7 18)
(8 18) (7 19) (6 20) (5 21) (4 11) (3 12) (2 13) (1 14) (0 15) (10 16) (9 17)
(10 17) (9 18) (8 19) (7 20) (6 21) (5 11) (4 12) (3 13) (2 14) (1 15) (0 16)
(1 16) (0 17) (10 18) (9 19) (8 20) (7 21) (6 11) (5 12) (4 13) (3 14) (2 15)
(3 15) (2 16) (1 17) (0 18) (10 19) (9 20) (8 21) (7 11) (6 12) (5 13) (4 14)
(5 14) (4 15) (3 16) (2 17) (1 18) (0 19) (10 20) (9 21) (8 11) (7 12) (6 13)
(7 13) (6 14) (5 15) (4 16) (3 17) (2 18) (1 19) (0 20) (10 21) (9 11) (8 12)
(9 12) (8 13) (7 14) (6 15) (5 16) (4 17) (3 18) (2 19) (1 20) (0 21) (10 11)


and I could find something similar for 24 players and 12 games/rounds.  But I guess for practical reasons there might be a  limit on the number of different games and the number of rounds you can play.


sausage041

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Reply #4 on: June 16, 2011, 12:10:30 PM
can you post the 24 team scenario? 12 games isn't out of the question, but at least I could fiddle with it.


sausage041

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Reply #5 on: June 16, 2011, 12:35:37 PM
See the attached spreadsheet.

I thought it might be easier to if we have 20 teams to create 2 divisions of 10....on sheet 1, this works out perfectly for our objective of cycling through all ten games once in 10 rounds with the added bonus of playing each team once except for the duplicate in round 10.

Now if we had 24 teams, 2 divisions of 12 as I did on sheet 2, you can see the problem areas in RED and YELLOW.  Using Team AAA as an example (you can read the note I put on the sheet), we need now 12 rounds and 12 games to complete the round robin.  If I cut the last rounds in red, AA will not play Game 7 or 8.  Is there a way if game 11 and 12 are duplicates that a schedule could be made that recognizes that fact?  If you look at AAA in the yellow portion, they play Games 11 and 12, but not Game 7 and 8 in a 10 round scenario.  If game 7 and 8 are the same as games 11 and 12 (7=11, 8=12) then this is a non issue.

I could have 12 different games, 10 rounds, and each team would just not get to play 2 of the games.  This is how I am leaning since 22 or 24 teams seems most likely...hopefully I dont get 26+

are divisions even necessary or just making things more complicated?

Thanks so much!


sausage041

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Reply #6 on: June 16, 2011, 12:36:09 PM
Can get this Zipped, so I took screen shots of both


Ian Wakeling

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Reply #7 on: June 16, 2011, 05:05:20 PM
Here is a schedule for 24 teams which has an interesting property.  Instead of playing all the games within a division, you could play all the games between divisions.

(A12 B06) (A11 B12) (A06 B10) (A05 B09) (A07 B03) (A01 B05) (A04 B07) (A02 B02) (A09 B04) (A08 B11) (A10 B01) (A03 B08)
(A05 B03) (A04 B08) (A07 B07) (A06 B04) (A11 B05) (A08 B01) (A12 B02) (A10 B06) (A01 B09) (A02 B10) (A03 B12) (A09 B11)
(A10 B12) (A09 B07) (A01 B08) (A08 B10) (A03 B09) (A06 B06) (A02 B11) (A05 B01) (A07 B05) (A12 B04) (A11 B03) (A04 B02)
(A08 B07) (A02 B06) (A10 B02) (A01 B03) (A09 B10) (A04 B12) (A03 B04) (A11 B08) (A06 B11) (A05 B05) (A12 B09) (A07 B01)
(A06 B08) (A12 B01) (A05 B11) (A07 B12) (A04 B04) (A09 B03) (A11 B10) (A03 B07) (A08 B02) (A10 B09) (A02 B05) (A01 B06)
(A07 B02) (A05 B10) (A04 B06) (A11 B11) (A12 B07) (A10 B08) (A06 B09) (A09 B05) (A02 B03) (A03 B01) (A01 B04) (A08 B12)
(A11 B04) (A06 B05) (A12 B03) (A04 B01) (A05 B02) (A03 B11) (A07 B06) (A01 B10) (A10 B07) (A09 B12) (A08 B08) (A02 B09)
(A01 B11) (A10 B04) (A09 B01) (A03 B02) (A02 B08) (A05 B07) (A08 B05) (A04 B09) (A12 B12) (A11 B06) (A07 B10) (A06 B03)
(A02 B01) (A03 B03) (A08 B04) (A10 B05) (A01 B12) (A07 B09) (A09 B08) (A12 B11) (A04 B10) (A06 B02) (A05 B06) (A11 B07)
(A03 B10) (A08 B09) (A02 B12) (A09 B06) (A10 B11) (A11 B02) (A01 B01) (A07 B04) (A05 B08) (A04 B03) (A06 B07) (A12 B05)
(A04 B05) (A07 B11) (A11 B09) (A12 B08) (A06 B01) (A02 B04) (A05 B12) (A08 B03) (A03 B06) (A01 B07) (A09 B02) (A10 B10)
(A09 B09) (A01 B02) (A03 B05) (A02 B07) (A08 B06) (A12 B10) (A10 B03) (A06 B12) (A11 B01) (A07 B08) (A04 B11) (A05 B04)

If you don't need the divisions then you could use the same schedule but simply don't tell the teams about the divisional structure - replace A1-A12, B1-B12 above with the team numbers 1-24 in a random order,  also swap around the left and right team at random.


sausage041

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Reply #8 on: June 17, 2011, 12:40:22 AM
that is an interesting property, thanks.


for what I had attached above, and from what I have gotten from you and this site...having a scenario of say 22+ teams, there is NO possible way to cycle each team through 10 games without teams sitting out or having more than 10 rounds.  It makes sense that it doesn't work out, but I've seen some crazy math here work out.

I really appreciate all your help and prompt replies!


sausage041

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Reply #9 on: May 20, 2016, 07:41:53 PM
Hello, reviving an old thread here, but have been using the schedules provided for many years now, they have been a life saver!

My event has since grown and I am wondering if a schedule with similar parameters as above can be created for 30 and 32 teams.  As a refresher, it is a round robin event.  If 30 teams, there would be 15 locations, if 32 then 16 locations.  I want each team to play each other once.  The kicker is that I also want each team to play at 1 location only once before repeating a location.  So in a 30 team schedule, Team A would play through the 15 locations before they repeat a location - a new team at each location.  I've looked at the spreadsheet in other threads, it is incredible, but I don't believe I can get it to take into consideration the 1 location requirement.  Any help would be appreciated!!!


Ian Wakeling

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Reply #10 on: May 21, 2016, 06:18:44 AM
Hello,

I am slightly confused since much of the above is about each location exactly once (no repeats) and therefore not playing a complete round robin.

You can have 32 teams scheduled in the way that you describe.  For example:

( 4 32) ( 8  2) (10 20) ( 3 29) (17 21) (19 28) (11 23) ( 9 25) (13  6) (22  1) (31  7) (16 30) (14 15) (12 18) ( 5 24) (26 27)
( 8 25) ( 6 32) ( 4  9) (12 22) ( 1  5) (20 24) (21 29) (26 14) (27 11) ( 7 16) (23  3) (31 10) (18  2) (15 17) (19 13) (28 30)
(21 16) (27  9) ( 7 32) ( 6 11) (23 13) ( 8  3) (22 25) (24  1) (15 28) (14 30) (18 10) (26  5) (31 12) (19  4) (20 17) (29  2)
(22 20) (24 18) (11 30) (10 32) (14  7) (16 26) ( 5  9) (23 27) (25  3) (17 29) ( 2 15) (12 19) (28  8) (31 13) ( 6 21) ( 1  4)
( 7 24) (22 23) (19 25) (14  2) (12 32) (15 10) (28 18) (11  8) (26 30) (27  5) (20  1) (17  4) (13 21) (29  9) (31 16) ( 3  6)
(31 18) (10 25) (26 23) (21 27) ( 4 15) (13 32) (17 12) (19 29) ( 9 14) (28  2) (30  8) ( 3 22) (20  6) (16 24) ( 1 11) ( 5  7)
( 3 14) (31 19) (27 12) (28 26) (30 24) (17  6) (16 32) (13 20) ( 1 21) (11 15) (29  4) ( 2  9) (23  5) (22  7) (25 18) ( 8 10)
(27 19) ( 5 15) (31 21) (30 13) (28 29) ( 2 25) ( 7 20) (18 32) (22 16) ( 3 24) (14 17) ( 1  6) ( 4 11) (26  8) (10 23) ( 9 12)
(12 26) (30 21) ( 8 17) (31 24) (16  2) ( 1 29) ( 4 27) (22 10) (19 32) (18 23) ( 5 25) (20 15) ( 3  7) ( 6 14) ( 9 28) (11 13)
(11 29) (13 28) (24  2) ( 9 20) (31 25) (18  4) ( 1  3) (30  6) (12 23) (21 32) (26 19) (27  8) (17 22) ( 5 10) ( 7 15) (14 16)
(10 17) ( 1 14) (29 16) (25  4) (11 22) (31 27) (19  6) ( 5  3) ( 7  2) (13 26) (24 32) (21 28) ( 9 30) (20 23) ( 8 12) (15 18)
( 9 13) (12 20) (15  3) ( 1 18) ( 6 27) (14 23) (31 30) ( 7 21) ( 5  8) ( 4 10) (16 28) (25 32) (24 29) (11  2) (26 22) (17 19)
(28 23) (11 16) (13 22) (17  5) (19  3) ( 7 30) (15 26) (31  2) (24 10) ( 8  9) (12  6) (29 18) (27 32) (25  1) ( 4 14) (20 21)
( 6 15) (26 29) (14 18) (16 23) ( 8 20) (21  5) (10  2) (17 28) (31  4) (12 25) ( 9 11) ( 7 13) (19  1) (30 32) ( 3 27) (22 24)
( 5 30) (17  7) ( 1 28) (15 19) (18 26) (22  9) (24  8) ( 4 12) (20 29) (31  6) (27 13) (14 11) (10 16) (21  3) ( 2 32) (23 25)
( 1  2) ( 3  4) ( 5  6) ( 7  8) ( 9 10) (11 12) (13 14) (15 16) (17 18) (19 20) (21 22) (23 24) (25 26) (27 28) (29 30) (31 32)
(29  6) (18  8) ( 2 27) (20 16) (25 17) (10 21) (23  7) ( 3 11) (30 19) ( 5 31) (28 14) (13 12) (15  9) ( 4 22) (32  1) (24 26)
(16  5) (25 30) (17 13) (24 15) ( 7 19) ( 6 22) ( 9  1) (27 18) ( 3 31) (26 11) (10 12) ( 8 14) ( 2 20) (32 29) (28  4) (21 23)
(24 27) (15 12) (21 14) (18  6) (20  4) (29  8) (25 16) ( 1 31) (23  9) (10  7) (11  5) (30 17) (32 28) ( 2 26) (13  3) (19 22)
(14 10) (19 11) (16  4) ( 2 17) ( 5 28) (24 13) (29 31) ( 8 22) ( 6  7) ( 9  3) (15 27) (32 26) (30 23) ( 1 12) (21 25) (18 20)
(18  9) ( 2 13) (30 15) (26  3) (21 12) (28 31) (20  5) ( 6  4) ( 8  1) (25 14) (32 23) (22 27) (29 10) (24 19) (11  7) (16 17)
(30 12) (14 27) (23  1) (19 10) (26 31) ( 3 17) ( 2  4) (29  5) (11 24) (32 22) (25 20) (28  7) (21 18) ( 9  6) (16  8) (13 15)
(25 11) (29 22) (18  7) (23 31) (15  1) (30  2) ( 3 28) (21  9) (32 20) (24 17) ( 6 26) (19 16) ( 8  4) (13  5) (27 10) (12 14)
(20 28) (16  6) (22 31) (29 14) (27 30) (26  1) ( 8 19) (32 17) (21 15) (23  4) (13 18) ( 5  2) (12  3) ( 7 25) (24  9) (10 11)
(13  4) (20 31) (28 11) (27 25) (29 23) ( 5 18) (32 15) (14 19) ( 2 22) (16 12) ( 3 30) (10  1) ( 6 24) ( 8 21) (17 26) ( 7  9)
(17 31) ( 9 26) (25 24) (22 28) ( 3 16) (32 14) (18 11) (20 30) (10 13) ( 1 27) ( 7 29) ( 4 21) ( 5 19) (23 15) (12  2) ( 6  8)
(23  8) (21 24) (20 26) (13  1) (32 11) ( 9 16) (27 17) (12  7) (29 25) ( 6 28) (19  2) (18  3) (22 14) (10 30) (15 31) ( 4  5)
(19 21) (23 17) (12 29) (32  9) (13  8) (25 15) ( 6 10) (28 24) ( 4 26) (30 18) ( 1 16) (11 20) ( 7 27) (14 31) (22  5) ( 2  3)
(15 22) (28 10) (32  8) ( 5 12) (24 14) ( 4  7) (26 21) ( 2 23) (16 27) (29 13) (17  9) ( 6 25) (11 31) ( 3 20) (18 19) (30  1)
(26  7) (32  5) ( 3 10) (11 21) ( 2  6) (23 19) (30 22) (25 13) (28 12) (15  8) ( 4 24) ( 9 31) ( 1 17) (18 16) (14 20) (27 29)
(32  3) ( 7  1) ( 9 19) ( 4 30) (22 18) (27 20) (12 24) (10 26) (14  5) ( 2 21) ( 8 31) (15 29) (16 13) (17 11) (23  6) (25 28)


and by the time you have played the round (row) where the team numbers are in natural order, then each team will have occurred exactly once in each of the locations (the 16 columns).

30 teams is much more problematic.  There is no problem making the first 15 rounds:


(30  1) (19 14) (25  4) (27 10) (20  6) (17 13) (28 15) (26  5) (22  3) (29  9) (23  2) (21  8) (18  7) (24 11) (16 12)
(19  9) (30  2) (22  1) (16 15) (29  7) (26 14) (17  8) (24  4) (23 11) (27  6) (18  3) (20  5) (28 12) (25 10) (21 13)
(29  4) (21  5) (30  3) (28 11) (25  8) (16  1) (23  6) (22  9) (26  7) (17 12) (19 13) (27 14) (24 15) (20  2) (18 10)
(23  7) (25  3) (18 11) (30  4) (26 12) (24  2) (20 14) (27 15) (21  6) (19  5) (16  9) (22 10) (29  8) (28 13) (17  1)
(20 13) (29 12) (27  9) (24  1) (30  5) (22  7) (21 10) (25 11) (16 14) (18  2) (26  8) (23  3) (19  4) (17 15) (28  6)
(22  5) (20 11) (16 13) (23  8) (17 10) (30  6) (27 12) (18 14) (25  2) (24  7) (28  4) (19 15) (21  1) (29  3) (26  9)
(21  2) (27  4) (19 10) (18 12) (22 15) (28  5) (30  7) (23 13) (20  8) (16 11) (29 14) (25  9) (17  6) (26  1) (24  3)
(28 14) (26 10) (23  5) (29 13) (21 11) (20 15) (24  9) (30  8) (17  4) (25  1) (22 12) (18  6) (16  3) (27  7) (19  2)
(26  6) (18 15) (17 14) (21  3) (27 13) (29 11) (22  2) (19  1) (30  9) (28  8) (24 10) (16  7) (25  5) (23 12) (20  4)
(24 12) (17  9) (29  6) (25 14) (23  4) (19  8) (26  3) (20  7) (18 13) (30 10) (21 15) (28  1) (27  2) (16  5) (22 11)
(17  3) (16  8) (20 12) (26  2) (28  9) (21  4) (18  5) (29 10) (27  1) (23 15) (30 11) (24 13) (22 14) (19  6) (25  7)
(25 15) (22 13) (28  2) (20  9) (19  3) (23 10) (29  1) (16  6) (24  5) (21 14) (17  7) (30 12) (26 11) (18  4) (27  8)
(16 10) (28  7) (24  8) (22  6) (18  1) (25 12) (19 11) (17  2) (29 15) (20  3) (27  5) (26  4) (30 13) (21  9) (23 14)
(18  8) (24  6) (26 15) (19  7) (16  2) (27  3) (25 13) (21 12) (28 10) (22  4) (20  1) (17 11) (23  9) (30 14) (29  5)
(27 11) (23  1) (21  7) (17  5) (24 14) (18  9) (16  4) (28  3) (19 12) (26 13) (25  6) (29  2) (20 10) (22  8) (30 15)


But it is not known how to complete the round robin giving something similar to the 32 team schedule.   As with some of the schedules above, each game in the 30 player schedule has one team from 1-15, and one team from 16-30.

Hope that helps.


sausage041

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Reply #11 on: May 21, 2016, 08:32:52 AM
Thanks for the reply.  You are correct, we only play the first 10-12 rounds.  I guess I assumed it was probably easier to come up with the full schedule and I would just use the first 10/12 rounds.  If that changes things let me know.

Appreciate the response!


sausage041

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Reply #12 on: May 25, 2017, 11:09:21 AM
Hi Ian, wondering if you can assist me again on this scheduling.  My event has grown over the years and am now in need of a 34, 36, and 38 team schedule.  As a reminder, we only play 10 rounds (we don't play through the entire round robin), each team will only play once at a location, each team will only play another team once.  Like I have done with the 32 team schedule above, I cut the match-ups after round 10 and only use the scheduling for rounds 1-10.  In the 32 team schedule above, teams do not repeat at a location until round 17 I believe, so that is no problem.  With only 10 rounds, teams will not play at all the locations, which is fine, as long as they do not repeat at a location or against a team in the first 10 (maybe 12) rounds.

Also, as a side, is there a schedule with the above requirements for 18 teams? In my book of schedules, I have a gap between 16 and 20 teams.  With an 18 team schedule, I could make 2 divisions of 18 teams to complete the 36 team schedule that way if there is not a cleaner way.

Hopefully you'll see this today or tomorrow.  Event is Saturday morning, the late registration numbers have me nervous!

Thanks so much!


Ian Wakeling

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Reply #13 on: May 25, 2017, 12:19:29 PM
Here are some more schedules as requested.


34 teams
(3 34) (33 2) (31 14) (19 13) (6 28) (24 29) (18 7) (32 23) (5 9) (22 26) (20 11) (27 8) (16 21) (30 17) (10 15) (12 25) (1 4)
(33 4) (1 34) (16 17) (15 29) (22 31) (7 26) (21 30) (20 6) (28 24) (8 12) (5 25) (18 10) (19 32) (13 23) (9 27) (11 14) (2 3)
(30 16) (14 20) (8 34) (33 5) (1 18) (17 23) (10 31) (28 4) (11 22) (27 2) (13 9) (29 26) (15 24) (32 12) (25 19) (3 21) (7 6)
(18 15) (13 32) (33 7) (6 34) (21 19) (4 20) (1 26) (11 29) (25 3) (24 10) (28 31) (12 16) (30 9) (22 14) (2 23) (17 27) (8 5)
(8 25) (23 30) (3 19) (18 24) (12 34) (9 33) (6 22) (27 21) (14 1) (31 7) (15 26) (32 5) (17 13) (29 4) (20 28) (16 2) (10 11)
(32 21) (27 5) (20 22) (17 2) (11 33) (10 34) (25 23) (24 7) (29 6) (4 15) (30 8) (14 28) (31 1) (19 16) (3 13) (26 18) (9 12)
(5 19) (31 24) (30 12) (27 3) (8 23) (28 22) (16 34) (13 33) (10 26) (32 25) (18 6) (11 1) (29 20) (2 9) (17 21) (7 4) (15 14)
(29 22) (17 8) (2 25) (9 32) (26 24) (21 5) (15 33) (14 34) (27 30) (28 11) (4 10) (20 7) (3 12) (31 18) (6 1) (23 19) (16 13)
(7 11) (25 21) (23 9) (1 28) (3 16) (8 32) (12 27) (31 26) (19 34) (33 17) (14 29) (30 2) (22 10) (6 15) (24 4) (13 5) (18 20)
(27 23) (6 10) (26 4) (21 12) (30 5) (13 2) (29 28) (25 9) (33 20) (18 34) (3 32) (31 15) (7 14) (24 11) (16 8) (22 1) (17 19)
(9 17) (7 28) (11 15) (30 25) (13 27) (31 6) (8 19) (12 2) (16 32) (1 29) (23 34) (21 33) (18 4) (5 3) (14 26) (20 10) (24 22)
(26 6) (19 12) (27 32) (10 14) (29 7) (16 25) (9 3) (17 5) (4 31) (30 13) (24 33) (22 34) (2 8) (1 20) (18 11) (28 15) (23 21)
(14 24) (29 18) (21 13) (31 11) (20 15) (3 30) (17 32) (1 10) (12 23) (16 5) (19 2) (6 4) (27 34) (25 33) (7 22) (8 9) (26 28)
(20 31) (22 15) (29 10) (23 16) (2 32) (18 14) (11 4) (30 19) (13 8) (21 9) (1 7) (17 3) (28 33) (26 34) (5 12) (24 6) (25 27)
(12 13) (26 11) (28 18) (4 22) (17 25) (15 1) (24 20) (8 3) (21 2) (6 14) (16 27) (19 9) (23 5) (7 10) (32 34) (33 30) (31 29)
(28 10) (9 16) (24 1) (26 20) (14 4) (27 19) (5 2) (18 22) (15 7) (3 23) (17 12) (13 25) (6 11) (8 21) (33 31) (29 34) (32 30)
(1 2) (3 4) (5 6) (7 8) (9 10) (11 12) (13 14) (15 16) (17 18) (19 20) (21 22) (23 24) (25 26) (27 28) (29 30) (31 32) (33 34)

36 teams
(17 36) (13 34) (15 35) (19 33) (16 25) (18 31) (10 27) (11 30) (12 26) (2 29) (8 32) (9 28) (24 5) (1 22) (23 3) (21 7) (4 14) (6 20)
(13 35) (15 36) (17 34) (16 31) (18 33) (19 25) (11 26) (12 27) (10 30) (8 28) (9 29) (2 32) (23 1) (3 24) (22 5) (20 4) (6 21) (7 14)
(15 34) (17 35) (13 36) (18 25) (19 31) (16 33) (12 30) (10 26) (11 27) (9 32) (2 28) (8 29) (22 3) (5 23) (24 1) (14 6) (7 20) (4 21)
(14 33) (20 25) (21 31) (22 36) (23 34) (24 35) (7 29) (4 32) (6 28) (5 27) (1 30) (3 26) (15 10) (11 17) (13 12) (18 2) (8 19) (9 16)
(20 31) (21 33) (14 25) (23 35) (24 36) (22 34) (4 28) (6 29) (7 32) (1 26) (3 27) (5 30) (13 11) (12 15) (17 10) (16 8) (9 18) (2 19)
(21 25) (14 31) (20 33) (24 34) (22 35) (23 36) (6 32) (7 28) (4 29) (3 30) (5 26) (1 27) (17 12) (10 13) (15 11) (19 9) (2 16) (8 18)
(19 29) (16 32) (18 28) (17 27) (13 30) (15 26) (5 36) (1 34) (3 35) (7 33) (4 25) (6 31) (21 2) (8 14) (20 9) (24 10) (11 22) (12 23)
(16 28) (18 29) (19 32) (13 26) (15 27) (17 30) (1 35) (3 36) (5 34) (4 31) (6 33) (7 25) (20 8) (9 21) (14 2) (23 11) (12 24) (10 22)
(18 32) (19 28) (16 29) (15 30) (17 26) (13 27) (3 34) (5 35) (1 36) (6 25) (7 31) (4 33) (14 9) (2 20) (21 8) (22 12) (10 23) (11 24)
(22 27) (23 30) (24 26) (14 29) (20 32) (21 28) (2 33) (8 25) (9 31) (10 36) (11 34) (12 35) (18 7) (4 19) (16 6) (15 5) (1 17) (3 13)
(23 26) (24 27) (22 30) (20 28) (21 29) (14 32) (8 31) (9 33) (2 25) (11 35) (12 36) (10 34) (16 4) (6 18) (19 7) (13 1) (3 15) (5 17)
(24 30) (22 26) (23 27) (21 32) (14 28) (20 29) (9 25) (2 31) (8 33) (12 34) (10 35) (11 36) (19 6) (7 16) (18 4) (17 3) (5 13) (1 15)
(12 4) (2 9) (10 8) (1 5) (11 6) (7 3) (24 16) (14 21) (22 20) (13 17) (23 18) (19 15) (28 36) (25 33) (31 34) (30 26) (35 29) (32 27)
(8 11) (5 12) (1 3) (2 10) (7 4) (9 6) (20 23) (17 24) (13 15) (14 22) (19 16) (21 18) (35 31) (30 36) (27 26) (34 25) (32 28) (33 29)
(5 9) (11 10) (12 7) (4 6) (2 3) (1 8) (17 21) (23 22) (24 19) (16 18) (14 15) (13 20) (33 30) (35 34) (32 36) (29 28) (25 27) (26 31)
(6 3) (1 7) (2 11) (12 9) (8 5) (4 10) (18 15) (13 19) (14 23) (24 21) (20 17) (16 22) (27 29) (26 32) (35 25) (33 36) (31 30) (28 34)
(7 10) (6 8) (9 4) (3 11) (1 12) (5 2) (19 22) (18 20) (21 16) (15 23) (13 24) (17 14) (34 32) (29 31) (28 33) (35 27) (26 36) (30 25)
(1 2) (3 4) (5 6) (7 8) (9 10) (11 12) (13 14) (15 16) (17 18) (19 20) (21 22) (23 24) (25 26) (27 28) (29 30) (31 32) (33 34) (35 36)


38 teams
(19 38) (7 33) (9 31) (29 5) (3 35) (13 23) (27 17) (11 25) (21 15) (37 1) (8 16) (10 14) (12 6) (18 4) (32 24) (28 36) (30 26) (22 34) (20 2)
(26 16) (38 21) (35 29) (27 33) (17 23) (31 19) (1 25) (9 5) (11 13) (7 15) (37 3) (18 30) (10 34) (36 24) (20 14) (2 8) (28 6) (32 12) (22 4)
(28 14) (12 18) (38 23) (11 21) (31 25) (35 15) (7 3) (1 27) (33 19) (13 9) (29 17) (37 5) (22 30) (32 8) (34 36) (26 4) (2 10) (16 20) (24 6)
(24 12) (10 16) (30 4) (38 25) (15 13) (3 27) (35 19) (17 31) (1 23) (5 11) (33 9) (21 29) (7 37) (34 14) (22 28) (18 20) (36 32) (2 6) (26 8)
(18 22) (6 36) (14 8) (32 34) (27 38) (1 21) (11 15) (19 29) (25 5) (3 17) (35 23) (31 7) (13 33) (37 9) (2 4) (16 30) (20 12) (26 24) (28 10)
(6 32) (2 14) (18 34) (22 10) (20 4) (38 29) (16 24) (26 36) (7 9) (31 23) (13 19) (33 35) (27 21) (1 3) (37 11) (5 15) (17 25) (8 28) (30 12)
(10 36) (8 20) (22 26) (2 18) (34 30) (5 33) (38 31) (23 21) (28 12) (27 35) (1 7) (25 3) (19 17) (15 29) (16 6) (13 37) (24 4) (9 11) (32 14)
(8 30) (28 24) (10 20) (14 36) (2 12) (17 7) (6 4) (33 38) (22 32) (29 25) (5 27) (1 9) (35 31) (11 19) (18 26) (3 23) (37 15) (21 13) (34 16)
(34 4) (32 30) (2 16) (6 20) (8 24) (28 26) (29 9) (13 3) (38 35) (33 21) (11 31) (15 19) (1 5) (25 23) (27 7) (10 12) (22 14) (37 17) (36 18)
(20 37) (26 34) (28 32) (30 24) (36 22) (6 14) (10 18) (12 8) (4 16) (38 2) (15 25) (13 27) (23 11) (17 21) (31 5) (9 35) (7 29) (3 33) (1 19)
(25 33) (22 37) (36 12) (16 28) (18 6) (2 32) (26 20) (10 24) (14 30) (34 8) (4 38) (11 17) (15 9) (5 35) (13 1) (19 7) (23 27) (29 31) (3 21)
(31 27) (11 35) (37 24) (4 12) (26 14) (18 16) (8 22) (28 20) (2 34) (10 32) (36 30) (38 6) (29 3) (13 7) (17 33) (21 25) (19 9) (15 1) (5 23)
(29 23) (27 15) (11 3) (37 26) (16 32) (4 10) (36 2) (14 18) (20 24) (30 6) (34 28) (12 22) (38 8) (31 33) (21 9) (17 1) (13 35) (5 19) (7 25)
(21 35) (17 5) (25 13) (31 15) (28 37) (22 20) (12 34) (2 30) (8 6) (36 4) (24 18) (32 26) (14 16) (38 10) (19 3) (33 29) (11 1) (23 7) (9 27)
(5 13) (31 1) (15 17) (3 9) (21 19) (37 30) (33 23) (7 35) (26 10) (14 24) (20 32) (16 36) (4 28) (2 22) (38 12) (34 6) (8 18) (27 25) (11 29)
(9 17) (19 25) (21 7) (35 1) (11 33) (34 24) (37 32) (6 22) (27 29) (28 18) (26 2) (8 4) (36 20) (16 12) (15 23) (38 14) (5 3) (10 30) (13 31)
(7 11) (9 23) (27 19) (13 17) (29 1) (8 36) (5 21) (34 37) (31 3) (12 26) (6 10) (28 2) (18 32) (20 30) (35 25) (22 24) (38 16) (4 14) (15 33)
(3 15) (13 29) (33 1) (23 19) (7 5) (25 9) (28 30) (4 32) (37 36) (22 16) (14 12) (34 20) (2 24) (6 26) (10 8) (27 11) (21 31) (38 18) (17 35)
(1 2) (3 4) (5 6) (7 8) (9 10) (11 12) (13 14) (15 16) (17 18) (19 20) (21 22) (23 24) (25 26) (27 28) (29 30) (31 32) (33 34) (35 36) (37 38)

18 teams (note all games are of the form 1-9 vs 10-18
( 1 10) ( 9 11) ( 8 12) ( 7 13) ( 6 14) ( 5 15) ( 4 16) ( 3 17) ( 2 18)
( 3 18) ( 2 10) ( 1 11) ( 9 12) ( 8 13) ( 7 14) ( 6 15) ( 5 16) ( 4 17)
( 5 17) ( 4 18) ( 3 10) ( 2 11) ( 1 12) ( 9 13) ( 8 14) ( 7 15) ( 6 16)
( 7 16) ( 6 17) ( 5 18) ( 4 10) ( 3 11) ( 2 12) ( 1 13) ( 9 14) ( 8 15)
( 9 15) ( 8 16) ( 7 17) ( 6 18) ( 5 10) ( 4 11) ( 3 12) ( 2 13) ( 1 14)
( 2 14) ( 1 15) ( 9 16) ( 8 17) ( 7 18) ( 6 10) ( 5 11) ( 4 12) ( 3 13)
( 4 13) ( 3 14) ( 2 15) ( 1 16) ( 9 17) ( 8 18) ( 7 10) ( 6 11) ( 5 12)
( 6 12) ( 5 13) ( 4 14) ( 3 15) ( 2 16) ( 1 17) ( 9 18) ( 8 10) ( 7 11)
( 8 11) ( 7 12) ( 6 13) ( 5 14) ( 4 15) ( 3 16) ( 2 17) ( 1 18) ( 9 10)


I am thinking that as the number of teams rise, the proportion of the locations visited by each team is getting less since you are restricted to 10 rounds.  So with 38 teams, each team visit only 10 of the 19 locations.


sausage041

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    • Posts: 10
Reply #14 on: May 25, 2017, 12:26:07 PM
You're a lifesaver! Yes, teams will only ever visit 10 of the XX locations. It is a downside to only playing 10 rounds, but we only have 1 afternoon to get everything in (the 10 rounds are used to seed a 16 team bracket).  Thanks agan!