8 Ball League Scheduling

[rcoups]

I need your help again Ian.  You helped me via email in 2012 with a modification of your BalancedRoundRobin v4.3 Excel file.  Everything has gone well with our 24 team League.  It looks like the League will expand to 26 teams in February.  I have used your file to generate a 26 team schedule that will work, but the League manager wants to split the League into 2 divisions of 12 and 14 teams.  Since we play 16 week sessions, each team would have to play a few teams twice during the session.  Your file that I use does not permit scheduling for a number of weeks that exceeds the number of teams.  I'm sure you can provide files for 12 and 14 team schedules that extend to 16 weeks, but there are problems.   When a team plays another team for the 2nd time, if they were the visitors the first time, they must host the 2nd time and still give all teams 8 Home matches and 8 Away matches.  Can you come to my rescue again ?

Bob Coups

[wbport]

One idea is to split into a pair of 13 team leagues and the teams with the bye that week play each other.

[rcoups]

Thanks for the response. I'll look into that idea.

It may be possible, but there are other problem areas with scheduling our League that Ian is aware of,  that I didn't detail in my post.

[Ian Wakeling]

Bob,

Unfortunately I no longer have a record of our discussions from 2012, so I am not sure of the specifics of those problem areas.   But this may not matter, as I think that what I am about to describe should work well for doubling up any of these home/away schedules.  Specifically you need to take copies of the 12 and 14 team schedules and expand them in the same way as I show for the 6 team schedule.  Note that when you cut the resulting schedules off at 16 weeks, then you will find that not all teams have exactly 8 home and 8 away matches, but I believe what you will get will be as close as possible.

The simplest way to schedule a double round-robin is to start with the a single round-robin, and then repeat the same match-ups in the same order, but reverse the pattern of home and away venues.  There is a useful side effect as all re-matches are well spaced (and equally spaced) in time.  The attached diagram, in 4 parts, illustrates how to make a double schedule for an even number of players, by editing the output from the Excel generator.  Here the output has been made using the 'do not randomize' option.  Each row of the schedule corresponds to one team, and reading from left to right, lists their opponents through the course of the tournament.  A green cell in the table is used to indicate that the match-up with an opponent is to be played at home, a yellow cell indicates an away match-up.  In particular, note that each game occupies two cells in the table.

Part 1: Here rounds 6 to 10 have been copied from rounds 1 to 5, but the pattern of green and yellow background colours, respectively the home and away assignments, have been reversed.  Note that this will create a problem for the last team; so here team F is scheduled to play 3 away games in a row in rounds 4 to 6.  If possible we would like to avoid the run of away games.

Part 2: Identify both entries in the schedule corresponding to the game in the middle of the run of 3 games (see the two highlighted entries in round 5).  We would like to change the home/away assignments of these two cells in the schedule, but note that while this will break the run of 3 for team F, it will introduce a new run of 3 for team A.  So in addition, the match-up from the previous round involving team A is also identified for change (see the two highlighted cells in round 4).  Finally, since rounds 6 to 10 are the mirror of the first 5 rounds, we identify the same games in rounds 9 and 10.

Part 3: The background colours in the highlighted cells are swapped.

Part 4: The highlighting is removed to make it easier to see that there are no longer any runs of 3 home or away games.  A quick check also confirms that all teams have exactly 5 home games and 5 away games.  It can be shown that no other schedule is possible with fewer runs of two home or two away games.

Hope that helps,

Ian.

[rcoups]

     Thanks for the quick reply Ian.  Sometime today, after my Grandkids go home, I'll work with your solution to see if I can get it to work for our League.  

      It sounds like the same thing I tried to do manually after generating the 12 and 14 team schedules with your Excel file.  It became apparent very quickly that there was going to be trouble maintaining the balanced 8 home and 8 away format among other things.  That format is important to our League because the sponsoring establishments like to have a match in their place of business every other week for the income it generates.

      As you know, once you start trying to manually tweek a schedule, it can go badly in a hurry.  I'm leaning toward using the 26 team schedule that your file generated.   A big problem for me is that our current session ends this coming Wednesday.  The following Wednesday is our Captains Meeting and the new session starts the following week.   We don't actually know how many teams we will have and where they will be based  until the end of the meeting, so I have less than a week to create a schedule, team schedules, and update all files on our website.  Finding this forum and your Excel file has saved me many a sleepless night from the days of manual scheduling.

      I will still try to make your solution work because dividing the League into two divisions seems like a good idea if it can be made to work.

      Thanks again. It's good to know there is a place where one can get help with scheduling problems.  Keep up the good work !  

[Ian Wakeling]

Warren's idea of 2 groups of 13 has both pros and cons. If you experiment with 13 rounds (use the do not randomize setting on the Excel generator), then you will see this is the closest you can come to an alternating home/away pattern that will satisfy the sponsors; the pattern does alternate, apart from the break in the schedule where there is a bye.  The problem comes if you try to play 16 rounds, then 3 of the teams will have two byes, while the remaining 10 teams only have 1 bye, so the number of within league games is not balanced.  I don't know how important this would be for your league.  For an even number of teams balancing the number of within league games is easy, but getting an alternating pattern of byes, for more than two teams is impossible, see B and F in my example above who do alternate and so would be the best to use if two teams share a venue.  If the modified schedule looks bad, it is necessarily bad, as it is known that the home/away pattern in this double round-robin is optimal, it has exactly 12 places where a team plays in the same condition (home or away) as they did in the previous round, there is a mathematical proof that there can not be fewer than 12 such places in the 6 team schedule (the formula is 3n - 6 places if there are n teams).

[dave]

POOL 1 (12 Teams)

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

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

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

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

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

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

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

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

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

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

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

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

Week 13
11       v      1
10       v      12
2       v      9
8       v      3
4       v      7
6       v      5

Week 14
1       v      10
9       v      11
12       v      8
7       v      2
3       v      6
5       v      4

Week 15
9       v      1
8       v      10
11       v      7
6       v      12
2       v      5
4       v      3

Week 16
1       v      8
7       v      9
10       v      6
5       v      11
12       v      4
3       v      2



P O O L  2 (14 Teams)
Week 1
26       v      13
14       v      25
24       v      15
16       v      23
22       v      17
18       v      21
20       v      19

Week 2
13       v      25
26       v      24
23       v      14
15       v      22
21       v      16
17       v      20
19       v      18

Week 3
24       v      13
25       v      23
22       v      26
14       v      21
20       v      15
16       v      19
18       v      17

Week 4
13       v      23
24       v      22
21       v      25
26       v      20
19       v      14
15       v      18
17       v      16

Week 5
22       v      13
23       v      21
20       v      24
25       v      19
18       v      26
14       v      17
16       v      15

Week 6
13       v      21
22       v      20
19       v      23
24       v      18
17       v      25
26       v      16
15       v      14

Week 7
20       v      13
21       v      19
18       v      22
23       v      17
16       v      24
25       v      15
14       v      26

Week 8
13       v      19
20       v      18
17       v      21
22       v      16
15       v      23
24       v      14
26       v      25

Week 9
18       v      13
19       v      17
16       v      20
21       v      15
14       v      22
23       v      26
25       v      24

Week 10
13       v      17
18       v      16
15       v      19
20       v      14
26       v      21
22       v      25
24       v      23

Week 11
16       v      13
17       v      15
14       v      18
19       v      26
25       v      20
21       v      24
23       v      22

Week 12
13       v      15
16       v      14
26       v      17
18       v      25
24       v      19
20       v      23
22       v      21

Week 13
14       v      13
15       v      26
25       v      16
17       v      24
23       v      18
19       v      22
21       v      20

Week 14
13       v      26
25       v      14
15       v      24
23       v      16
17       v      22
21       v      18
19       v      20

Week 15
25       v      13
24       v      26
14       v      23
22       v      15
16       v      21
20       v      17
18       v      19

Week 16
13       v      24
23       v      25
26       v      22
21       v      14
15       v      20
19       v      16
17       v      18

[rcoups]

Thanks for the schedules Dave.  Turns out we only have 24 teams for the spring session, but when we hit 26, we intend to try to split the league like this.    A big problem we have, however, that I didn't mention here( because Ian already knew about it), is that we have some venues that have more teams than pool tables, so we have to make sure any schedule takes that into account.

[Ian Wakeling]

Bob,

Are you looking for one 24 team schedule or two divisions of 12, this is not clear?

Teams 1 and 2 in Dave's 12 team schedule could share a venue, assuming left and right correspond to home and away.  I did not check the others, but may be there are more that you could pair up - actually I don't recall how many of your teams need to share a venue.  

Ian.

[rcoups]

Ian,

I am using a 24 team schedule for the session beginning Feb. 12.  I used your generator in "do not randomize" mode as it provides  a number of compatible lines to accommodate the team/table situation.   When I first asked you for help in 2012, we had a venue with 5 teams / 3 tables, another with 4teams / 2 tables, 1 with 3 teams/2 tables and several with 2 teams and 1 table.  With your modified file, there were ample spots on the schedule to place teams that would avoid conflict.  The team/table situation can change from session to session.

I am now looking at the 2 division (12 and 14 teams) for next session (Fall 2014) when we anticipate adding 2 more teams.   I have copied the schedules provided by Dave above and converted them into a usable grid, but checking it for the team/table conundrum manually will definitely take some time.   Thanks again for your generous help.