You keep saying this, but now I’m not sure what you mean. You seem to be ascribing multiple functions to MMR.
MMR is a number from -3 to +3. It roughly approximates your skill in terms of standard deviations from 0, where 0 is average.
Jeff Kaplan reveals what MMR boundaries are in this interview:
So, there are two other things that also deal with MMR. The MMR gain or loss after a match, which Jeff has said is sometimes a gain / loss of 0. There’s THAT formula that might be made public, but I don’t think that would do anything but let people game the system to make their numbers go up.
Then, there’s another part of the system, which is the Matchmaker itself, and that is basically asking the question “who will play in a match?”.
This article talks quite a bit about the matchmaker, mostly in terms of how groups get involved, but I think there are some key phrases of value:
The following quote and others in the article lead me to conclude that the matchmaker is just trying to find a 50% win rate match for people as often as is possible while minimizing wait time.
The matchmaker was designed to try and create games with equivalent-sized groups,
Overall, though, the matchmaker tries to give you a game with a 50% win rate, but it has to compromise, and it won’t compromise past a 40% win rate.
There are limits to how much we compromise, however.
… If one of the teams doesn’t have at least a predicted 40% win rate, then we simply don’t create the game.
The problem with having the math available for SR gains (once again, not the same as MMR) is that people would game the system. There’s good honest reasons to keep this information vague and hand wavy.
And a reminder here: SR is not used by the matchmaker in any way.