8 team league in a double-dual format

[lifesagas]

You may laugh at this one, but I need help :-)

We have 8 wrestling teams in our district.  My goal is to get a schedule where each team wrestles three "double-duals" and a dual.

A double-dual is where you have four teams and each team competes against two of the teams - and not the third team.   Like this:

Round 1:
Team 1 vs. Team 2
Team 3 vs. Team 4

Round 2:
Team 1 vs. Team 3
Team 2 vs. Team 4

This is better than a "tri" format where you wrestle two teams, but have to sit out a round.

Can you work out a formula where each team will wrestle a "double-dual" against all the other teams without repeating any teams.  I believe that this will leave each team with someone they haven't faced yet.  For those teams I'd like to schedule a dual against the remaining team.

Parents, coaches and kids are staying up way to late to get this all in now, so your help is greatly appreciated.

[Ian Wakeling]

If I understand correctly, then you have 2 venues and for each of 3 sessions of wrestling you send 4 teams to each venue where they play 2 rounds.  It is possible to arrange the round robin like this, for example:

    Venue 1   Venue 2

  (CH) (EG) | (DF) (AB)
  (CE) (GH) | (AF) (BD)
  ---------------------
  (BC) (FG) | (DH) (AE)
  (BG) (CF) | (AH) (DE)
  ---------------------
  (EF) (BH) | (AG) (CD)
  (BF) (EH) | (CG) (AD)
  ---------------------
  (DG) (FH) | (BE) (AC)

Team A always plays at  Venue 2, so you might like to swap the venues around for one of the three sessions to get a better balance.

Will that work for you?

[lifesagas]

You are the best!  Many, many thanks!
 

[lifesagas]

Could you help me with this configuration??  

The above setup is perfect! but is it possible to have 2 duals instead of just 1?

The purpose still is for each team in this division to only meet once, so we could substitute a team from another division if needed.

It's not critical that absolutely every team has 2 duals, but if we could 2 or 3 teams with them that would be great.

[Ian Wakeling]

I don't think I fully understand your request, so it would help if you could give a few more details.  Are you combining two divisions of 8 somehow?  It would help if you showed the basic parameters of the problem, number of divisions, players per division, number of venues, number of rounds and an example of a typical round.

Thanks,  Ian.

[lifesagas]

Hi Ian,  

I can't thank you enough for helping me!!  You are a gem!!

Here's the scenario:

We have a district with 8 teams in it.  We all need to go against each other exactly once.  We like the 3 double-dual format and 1 dual schedule you gave us previously, but we have a team (at least 1) that wants to have 2 duals (to better highlight that match-up).  
We have no limit on # of locations.  We have other teams from nearby that we can use to substitute in a double-dual, but the dual events should always be between teams in the same district.  Not every team needs to have 2 duals, but if we could get 1 or 2 or whatever number of teams necessary to have 2 duals, that would make this perfect!!

Week 1:
Location: 1  l  Location 2
 
  (CH) (EG) | (DF) (AB)
  (CE) (GH) | (AF) (BD)
  ---------------------
Week 2:
Location: 1 l  Location 2

  (BC) (FG) | (DH) (AE)
  (BG) (CF) | (AH) (DE)
  ---------------------
Week 3:
Location: 1 l  Location 2

  (EF) (BH) | (AG) (CD)
  (BF) (EH) | (CG) (AD)
  ---------------------
Week 4:
Location 1
(DG)
Location 2
(FH)
Location 3
(BE)
Location 4
(AC)

Week 5:
Location 1
(??)
Location 2
(??)

etc. as necessary

Does that help?  You must have an amazing brain to be so good at this!!!

[Ian Wakeling]

lifesagas,

I am Still not sure exactly what you are looking for. I think we need to have the list of team match-ups which you would like to play twice before we can construct a schedule.  

But there is an interesting modification that can be made to the original schedule above.  Consider adding the last row below to convert week 4 into the double-dual format as follows:

   Venue 1   Venue 2 
 
  (CH) (EG) | (DF) (AB) 
  (CE) (GH) | (AF) (BD) 
  --------------------- 
  (BC) (FG) | (DH) (AE) 
  (BG) (CF) | (AH) (DE) 
  --------------------- 
  (EF) (BH) | (AG) (CD) 
  (BF) (EH) | (CG) (AD) 
  --------------------- 
  (DG) (FH) | (BE) (AC) 
  (DF) (GH) | (AB) (CE)

So the four match-ups in the last row (AB), (CE), (DF), & (GH) are the ones that occur twice in the schedule, and conveniently the first time all four of those same match-ups occured was week 1, so these re-matches are as far apart as possible.  Now if we have last season's ranking of the 8 teams, then it would make most sense to assign the teams as follows:

old     new
rank team letter
  1   A
  2   B
  3   C
  4   E
  5   D
  6   F
  7   G
  8   H

Doing this means that all four of the repeated match-ups are between teams who are very close in ability.

Does that help?

Ian.

[lifesagas]

Ian, you're a good man to help me.

Here's the list of teams in our district...

Aubrey
Lakeside
Lexington
Southville
Trent County
West Port
West Schofield
Woodford

We can only wrestle each team once.

The  teams that want to meet in single duals (head-to-head) are:

Aubrey vs. Lakeside
Aubrey vs. South County

Lakeside vs. ?

We can add teams from outside the district into the double duals or we can have more duals if needed to make the system work, but single duals should always be against teams from the same district.

THANKS AGAIN!

[Ian Wakeling]

I think this breaks the symmetry of the whole schedule and there will be no good solutions.

We could assign the teams as follows:

Aubrey (A)
Lakeside (B)
South County (C)
? (E)

(BE) & (AC) are singles anyway, so no problem yet.  But in week 1 you can not allow the match-up (AB), however A & B will still have to turn up in order to play F & D respectively, so this leaves a situation where 2 teams compete twice, and the other two teams just once.