The thing is that we have 1000+ hours played Cuthbert and his followers, who believe the exact opposite, that after dominating for a few games, the matchmaker finds a doppelganger to put on the opposite team to balance the matches and force things back to 50%. If we all say “I played a lot and it seems to me” then we have no way distinguishing between what you say, and what Cuthbert says, and what I say.
This is why we need shared data and statistical significance analysis. That is, science, rather than just people stating their opinions.
It’s in the name → Match Making Rating. It is the rating used to make the matches.
Skill rating is a friendlier, human readable form of matchmaking rating, with the ability to implement features like decay and leaver penalties without affecting how matches are made (matchmaking rating does not change during leaving and decay). See How Competitive Skill Rating Works (Season 13) → How Competitive Skill Rating Works (Season 13) → Summary → “Summarize Matchmaking, Rating, and Progression for me” to get the key references.