Fairness & Equity Dilemma

[SimSanity]

Hi, need some help.

The problem/ scenario goes like this:

I have been given the task to create a fair and reasonable roster for a tennis team.
This tennis competition is a doubles-only competition. that is, no singles matches played .

Typically teams are compromised of 4 or more players. In this scenario, there are 6 players on "my" team, who would like to play equal number of sets and play with as many different teammates as possible/equitable.

This is how it works, Its simple for a 4-player team system:

Each match has 3-rounds of sets (using a 4 player system only here (1-4)):


Rd1: Our 1 & 2 v Their 1 & 2
Our 3 & 4 v Their 3 & 4

Rd2: Our 1 & 3 v Their 1 & 3
Our 2 & 4 v Their 2 & 4

Rd3: Our 1 & 4 v Their 1 & 4
Our 2 & 3 v Their 2 & 3

So 6 sets are played and a team winner determined.

Here is the difficulty (for me)
Rd1 games are played to first to 9 games (e.g. Team A beats Team B 9-6 (in games). Rd2 & Rd3 are played to 6 (radiational ending). So there is greater importance on the Rd 1 matches

As stated previously, you can have more than 4 players in your team, obviously they all can't play at the same time as only 4 players can play at any one time. But it is possible to sub player(s) in (and out) before any rotation of games. E.g., Player 5 could come in for player 4 in rotation Rd2 so it would be Our 2 & 5 v Their 1 & 4. So with 6 players the same substitution apply.

However, players have to be ranked or have a pre-designation from 1-6 before the start of the season. If player 2 is subbed out, 3 moves into the '2 spot', 4 to the 3 etc. Furthermore, if Players 1 and 3 sit out the first round, when they substitute in for the second round for 2 other players. Player 1 must play in the "1" spot and player "3" must fill the 2 or 3 spot only (if number 2 is subbed out). In other words, a player cannot play higher than their designation.


I need help developing a team roster which would allow this occur. Its a 12 round competition and 6 players are assumed to be available.

Need help, don't know where to start. Happy to provide any clarity

Sim

 

[Cubist]

...Need help, don't know where to start.

It "serves" you right for agreeing to manage the team! ?

There are 15 ways to select 2 players from 6. Is there a way to use ALL of these during one competition? I guess that's what you're asking. You'd need to use 5 combinations in each round. To balance in a ratio closer to the 9:6:6 sets that you mention, you could use 7,4,4 combinations (they sum to 15) or perhaps 6,5,4.

I'm not sure how many courts are in use at one time (is the example of 4 that you gave played on two courts, or are all of the combinations played after each other on one court?). I don't understand the substitution restrictions either.

A simple way would be to make it fair across more than one competition. Do this by keeping a record, writing down the following numbers, and cross off combinations as they are used...

12     23     35
13     24     36
14     25     45
15     26     46
16     34     56

...or would this upset people because they want it to be even within the one competition? (I'll bet this is the case, life can be complicated!)

 

[SimSanity]

Cheers.
Reckon I'm okay with this
Legend