Possible scenarios for season registration

When team registrations for the next season finish the scheduling has to take place.

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.

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.

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