Possible scenarios for season registration

Unfortunately, there are 5 possible scenarios that can arise that are not ideal but which must be addressed. Here are the range of possible scenarios:

42 teams registered: 7 divisions of 6 teams Best case 43 teams registered: 7 divisions of 6 teams + 1 extra Last divisions has 7 teams. 44 teams registered: 7 divisions of 6 teams + 2 extra Last divisions has 8 teams. or 2 last divisions of 4 teams. 45 teams registered: 7 divisions of 6 teams + 3 extra Last divisions has 9 teams. or 2 last divisions of 4 teams and 5 teams. 46 teams registered: 7 divisions of 6 teams + 4 extra Last divisions has 10 teams. or 2 last divisions of 5 teams and 5 teams. or 2 last divisions of 6 teams and 4 teams. 47 teams registered: 7 divisions of 6 teams + 5 extra 2 last divisions of 6 teams and 5 teams. 48 teams registered: 8 divisions of 6 teams Best case

Scheduling Unbalanced Divisons in CSVA

While the normal CSVA division has 6 teams. This means that over a 10 week season, each team plays each other twice; once at home and once away. Hopefully, each session will have N divisions of 6 teams, i.e. Nx6 teams.

With a normal 6 team division, here is a typically 'ideal' schedule.

A 6 Team Division

[Week01]<=>[1-3 6-4 2-5] [Week02]<=>[4-1 6-5 3-2] [Week03]<=>[5-1 2-6 4-3] [Week04]<=>[6-1 2-4 3-5] [Week05]<=>[1-2 6-3 5-4] [Week06]<=>[3-1 4-6 5-2] [Week07]<=>[1-4 5-6 2-3] [Week08]<=>[1-5 6-2 3-4] [Week09]<=>[1-6 4-2 5-3] [Week10]<=>[2-1 3-6 4-5] All teams play each other twice, once at home and once away.

Please note that any week theoretically can be switched with any other week on the schedule and not impact the schedule. The starting ideal schedule has the property that two teams play each other 5 weeks apart. When weeks are switched, it is best to switch those 5 apart, e.g. Week02 and Week07. Switching other weeks will loose the symmetry of team play.

Unfortunately, the registrations may require that CSVA have less or more than 6 teams. In these cases, the choices for setting the number of teams in a division is not always pleasant. Here are the possible basic (ideal) schedules for the non-six team divisions:

A 4 Team Division	A 5 Team Division
[Week01]<=>[1-3 2-4] [Week02]<=>[4-1 3-2] [Week03]<=>[2-1 4-3] [Week04]<=>[3-1 4-2] [Week05]<=>[1-2 3-4] [Week06]<=>[3-1 4-2] [Week07]<=>[1-4 2-3] [Week08]<=>[1-2 3-4] [Week09]<=>[1-4 2-3] [Week10]<=>[2-1 3-4] teams 1 & 2 play 4 times teams 1 & 3 play 3 times teams 1 & 4 play 3 times teams 2 & 3 play 3 times teams 2 & 4 play 3 times teams 3 & 4 play 4 times	[Week01]<=>[1-3 4-BYE 2-5] [Week02]<=>[4-1 5-BYE 3-2] [Week03]<=>[5-1 2-BYE 4-3] [Week04]<=>[1-BYE 2-4 3-5] [Week05]<=>[1-2 3-BYE 5-4] [Week06]<=>[3-1 4-BYE 5-2] [Week07]<=>[1-4 5-BYE 2-3] [Week08]<=>[1-5 2-BYE 3-4] [Week09]<=>[1-BYE 4-2 5-3] [Week10]<=>[2-1 3-BYE 4-5] Each team plays every other team twice once at home and once away. Each team also has 2 BYEs
A 7 Team Division	A 8 Team Division
[Week01]<=>[3-4 2-1 7-5 BYE-6] [Week02]<=>[1-3 6-2 4-BYE 5-7] [Week03]<=>[3-1 2-4 7-BYE 5-6] [Week04]<=>[6-3 5-1 BYE-2 4-7] [Week05]<=>[7-3 2-6 1-4 BYE-5] [Week06]<=>[5-3 7-2 6-4 1-BYE] [Week07]<=>[3-5 2-BYE 4-1 6-7] [Week08]<=>[BYE-3 4-2 5-6 1-7] [Week09]<=>[3-BYE 2-5 1-6 7-4] [Week10]<=>[3-2 4-5 6-1 BYE-7] Each team plays each other once and has a BYE Five teams play three teams twice. Three teams have 2 BYEs and 2 teams twice. Team 1 plays team 3 twice, team 4 twice, team 6 twice Team 2 plays team 4 twice, team 6 twice, 2 BYEs Team 3 plays team 1 twice, team 5 twice, 2 BYEs Team 4 plays team 1 twice, team 2 twice, team 7 twice Team 5 plays team 3 twice, team 6 twice, team 7 twice Team 6 plays team 1 twice, team 2 twice, team 5 twice Team 7 plays team 4 twice, team 5 twice, 2 BYEs Team 8 plays team 2 twice, team 4 twice, team 7 twice	[Week01]<=>[3-4 2-1 7-5 8-6] [Week02]<=>[1-3 6-2 4-8 5-7] [Week03]<=>[3-1 2-4 7-8 5-6] [Week04]<=>[6-3 5-1 8-2 4-7] [Week05]<=>[7-3 2-6 1-4 8-5] [Week06]<=>[5-3 7-2 6-4 1-8] [Week07]<=>[3-5 2-8 4-1 6-7] [Week08]<=>[8-3 4-2 5-6 1-7] [Week09]<=>[3-8 2-5 1-6 7-4] [Week10]<=>[3-2 4-5 6-1 8-7] Each Team plays each other 1 and 3 other teams twice: Team 1 plays team 3 twice, team 4 twice, team 6 twice Team 2 plays team 4 twice, team 6 twice, team 8 twice Team 3 plays team 1 twice, team 5 twice, team 8 twice Team 4 plays team 1 twice, team 2 twice, team 7 twice Team 5 plays team 3 twice, team 6 twice, team 7 twice Team 6 plays team 1 twice, team 2 twice, team 5 twice Team 7 plays team 2 twice, team 5 twice, team 8 twice Team 8 plays team 2 twice, team 4 twice, team 7 twice
A 9 Team Division	A 10 Team Division
[Week01]<=>[1-2 3-BYE 7-4 5-9 6-8] [Week02]<=>[4-3 9-BYE 6-1 5-7 2-8] [Week03]<=>[9-3 7-8 1-BYE 6-4 2-5] [Week04]<=>[6-5 7-BYE 1-3 2-4 8-9] [Week05]<=>[4-1 9-BYE 7-2 3-6 8-5] [Week06]<=>[4-5 9-6 2-1 8-BYE 7-3] [Week07]<=>[5-BYE 3-4 8-7 2-6 1-9] [Week08]<=>[5-1 3-8 4-9 2-BYE 6-7] [Week09]<=>[4-BYE 9-7 5-6 3-2 1-8] [Week10]<=>[9-2 6-BYE 7-1 3-5 8-4] Each team has 1 BYE and plays each other team once. Team 1 plays team 2 twice Team 2 plays team 1 twice Team 3 plays team 4 twice Team 4 plays team 3 twice Team 5 plays team 6 twice Team 6 plays team 5 twice Team 7 plays team 8 twice Team 8 plays team 7 twice Team 9 has 2 BYEs	[Week01]<=>[1-2 10-3 7-4 5-9 6-8] [Week02]<=>[4-3 9-10 6-1 5-7 2-8] [Week03]<=>[9-3 7-8 1-10 6-4 2-5] [Week04]<=>[6-5 10-7 1-3 2-4 8-9] [Week05]<=>[4-1 10-9 7-2 3-6 8-5] [Week06]<=>[4-5 9-6 2-1 8-10 7-3] [Week07]<=>[5-10 3-4 8-7 2-6 1-9] [Week08]<=>[5-1 3-8 4-9 10-2 6-7] [Week09]<=>[4-10 9-7 5-6 3-2 1-8] [Week10]<=>[9-2 10-6 7-1 3-5 8-4] All teams play each other team once. Teams 1-5 play one team twice from team 1-5. Teams 6-10 play one team twice from teams 6-10.

Here is an Alternate Perfect Schedule for 5 team division

In this variation, the 5 BYEs are all placed in the first half of the season.

[Week01]<=>[1-3 4-BYE 2-5] [Week02]<=>[4-1 5-BYE 3-2] [Week03]<=>[5-1 2-BYE 4-3] [Week04]<=>[2-4 1-BYE 3-5] [Week05]<=>[1-2 3-BYE 5-4] [Week06]<=>[3-1 3-4 5-2] 3 dbl [Week07]<=>[1-4 2-5 2-3] 2 dbl [Week08]<=>[1-5 1-2 3-4] 1 dbl [Week09]<=>[5-1 4-2 5-3] 5 dbl [Week10]<=>[2-1 4-3 4-5] 4 dbl

Looking at it another way:

AWAY TEAM 1 2 3 4 5 ------- ------- ------- ------- ------- H 1 5_ 8* 1_ 6_ 8* O M 2 0_ 7* 4_ 1_ 7* E 3 6* 2_ 6* 8_ 4_ T E 4 2_ 9_ 3_ 0* 0* A M 5 3_ 9* 6_ 9* 5_

where:
  N is week number (0 is week 10)
  N_ is single match for week N
  N* is double match for week N

Each team play each team twice and
  1 plays 2 three times
  2 plays 5 three times
  3 plays 4 three times
  4 plays 3 three times
  5 plays 1 three times

Note: In the scheduling process, in order to meet the limitations of gym availability and other dependencies, any week theoretically can be switched with any other week in the above sets without affecting the overall schedule.