Friday, April 20, 2012

Building 2v2 Teams

I've been thinking a fair bit about how to properly turn internet votes for potential pairs into an actual split of 8 people into 2 teams. (Getting to sleep when I have something like this to think about is really hard...) Properly may not even be the right term because there are different ways to work it out that are different and yet still optimal depending on what your criteria are going into the decision. I thought it would be useful to look at the numbers as of early Friday morning along with different ways I could see to split the StarCraft 2 spring arena teams up.

For starters we have the restriction that there will be no same-race teams. This was handed down by MLG in the announcement post so I'm going to assume it's non-negotiable. I also happen to like the restriction if only to stop a double 6-pool from happening. At any rate, with the racial split of the players (3 terran, 3 protoss, 2 zerg) this actually significantly reduces the options. The only way to work it out with the given restriction is to have one ZT team, one ZP team, and 2 TP teams. (You can't have two ZT teams since that would leave three P for the remaining two teams. The same logic applies to two ZP teams. The only remaining option is the given one.)

After that you need to decide what the most important factor is. Each team is getting a number of YES votes and a number of NO votes. The way I see it you can use one of those as your main criteria, or the other one, or you can build a function between the two of them. The simplest would be a straight subtraction. I might go with something where the YES votes were weighted as worth twice as much as a NO vote, for example. You can also try to maximize the total sum of your main criteria across the four teams or you could try to maximize the main criteria on a team by team basis to fill in our 4 legal team options.

Answer the following questions to see where you'd fall on that spectrum:

- Should the team with the most YES votes get included no matter what?
- Should the team with the most NO votes get excluded no matter what?
- Should the team with the biggest YES-NO spread get included no matter what?
- Should you try to make the most people very happy or should you try to make everyone as happy as possible even if no one gets what they really want?

Picking the biggest number, eliminating all now illegal teams (ones containing a chosen player or ones in a race combination which is no longer legal), and iterating is pretty easy. Maximizing the total sum is less so. I feel like I should know how to do this sort of thing from my C&O days. Simplex method or something. I couldn't think of how to do it right away and let my mind wander a bit. I started thinking about how I'd write a program for it and what sort of pruning function I could use to pare down the search tree. Then I thought about how big the tree would even be... Turns out there's only 36 possible combinations. Oh. Well then, I'll just build a spreadsheet!

Before looking at how things shake out (to avoid allowing a potential MKP&Huk team cloud my judgment) I believe the way to go would be to use a straight YES-NO function to assign a value to each team and then use the spreadsheet to maximize the total sum of that value across the 4 chosen teams. I like this because if a particular team is popular relative to other options for a player it should get chosen and doesn't rest everything in the hands of the single most popular team. Theoretically just picking the biggest number and eliminating illegal options could result in the least popular team sneaking in. But would it even matter? How do things shake out?

Pick Biggest - MKP&Huk, MC&DRG, Ganzi&Parting, Heart&Violet  - 1640 votes
Maximize Sum - MKP&Huk, MC&DRG, Ganzi&Parting, Heart&Violet  - 1640 votes

CRITERIA: Fewest NO Votes
Pick Biggest - MC&DRG, Ganzi&Parting, Heart&Violet, MKP&Huk - 777 votes
Maximize Sum - MKP&Huk, MC&DRG, Ganzi&Parting, Heart&Violet - 777 votes

Pick Biggest - MKP&Huk, MC&DRG, Ganzi&Parting, Heart&Violet - 863 votes
Maximize Sum - MKP&Huk, MC&DRG, Ganzi&Parting, Heart&Violet - 863 votes

CRITERIA: Most YES-(NO/2) Votes
Pick Biggest - MKP&Huk, MC&DRG, Ganzi&Parting, Heart&Violet - 1251.5 votes
Maximize Sum - MKP&Huk, MC&DRG, Ganzi&Parting, Heart&Violet - 1251.5 votes

Ok, so it turns out as the numbers stood it doesn't actually matter what criteria you chose among any that I've considered. They all come out with precisely the same teams. On the plus side those teams all include my desired team!


Sthenno said...

Obviously all the players are very good, but for unorganized teams it seems really, really hard to beat MKP and HuK. Like I said in your other post, I think a lot of games will come down to micro with small numbers of units, and if they do then MKP + HuK should probably beat everyone else soundly.

Nick Page said...

I agree completely. They also have the match-up with the coolest trick that I remember from back in my 2v2 days. Mules+trading cash+warpgates!