How to make win chances equal and account for draws in any team FFA

We have a team FFA with N teams. We can describe it with 3 N-dimensional vectors:
- a vector p of the teams' win probabilities calculated by my generalization of the elo system for team FFA (or even more general systems); The sum of its components must be 1.
- a vector res of the teams' ressource factors (has been 100% for any team in earlier systems, but can now be changed arbitrarily as a handycap)
- a vector R of result ratings that describes the game outcome, usually 1 for the winner team, 0 for all other teams; The sum of its components must be 1. For exampe if there is a draw between two teams, their ratings are 1/2. If 3 teams die in a FFA and there is a draw between the remaining teams, their ratings are 1/(N-3) and so on.

Then the probability vector has to be changed to account for different res:

 p'_k = res_k * p_k / (scalar product of res and p). 

The elo change of team number k must then be c(R_k - p'_k), where c is the elo change constant (usually around 30; becomes higher if players have low weightings, but is the same for all teams). I have proved that this solution makes the sum of win probabilities=1, the sum of elo changes=0 and the expectation value of elo change for any team=0.

Any res would be possible, but in order to give every team a win chance of p'_k=1/N, we have to use

 res_k = 1/((N-1)p_k) * sum from j=1 to N with j not= k (res_j p_j). 

It can still be freely chosen if the better team should get less ressources, the worse more or a bit of both, which is the same as multiplying the vector res with a factor.

This "res" is only a mathematical value. It is not defined how it is realized ingame. There are many possibilities. The best approach is probably as a ressource income factor, maybe with ressource income factor of team k = sqrt(res_k) because win probability might be proportional to the square of resource income factor because of Lanchester's square law.

This kind of ressource handycap is not meant to be the normal way to play, but maybe a good alternative for a 1v1 with high skill difference. The worse player wouldn't have to fear higher loss probability and the better player wouldn't have to fear unjustified elo loss when playing with handycap. Maybe make handycap an option in lobby and a room "1v1 skill dependent ressources -> equal win chances"?

quote: unjustified elo loss

If i derp away 50 elo by starting amphs in water where commander is defenseless, or by blocking my factory with a mex, then i fully deserve to lose 50 elo. There is no undeserved Elo loss.

quote: So if I 1v1 Anarchid I'd get 16x his res/4x his metalmult? I could live with that! Go go implement it

If your 1v1 elo is 1541±6, that's correct.

Rewarding bad play with more ressources is somewhat the same as rewarding it with better team members. But ressource handycap would only have a noticable effect in 1v1 and non-team FFA (and unbalanced small teams), because balancing by player constellation comes first and only if this is still unbalanced, the rest is compensated by ressources. Thus someone who throws team games, will get better team members rather than ressources.

Rewarding better players with worse allies is precisely the opposite of how elo works in every other game (ones with proper playerbases) and is precisely the problem with our team games, and the source of much agony and trolling.

It's the last thing we want.

You should win FFA because you are good. Hell you should win team games because you are good, and get better allies as you get good.

Isn't that part of the point of matchmaking, to ensure that larger playebase would actually play more (and higher quality) games?

The fact you have to do the legwork of convincing them and seeding a new room is the problem with the system.

We used to play 4v4 as 'large teams' and considered anything larger to be 'ridiculous' and 6v6 to be 'unplayable'. Trust me. People would play 30v30. Probably on Icy Run.

Teams room is currently limited to 32 players. Let's start a petition to get Licho to raise this number :P