The basic Rating system logic.
In a game of skill who ever is most skilled should consistently beat lower skilled. Humans are inconsistent and skill can change over time. So, a measurement of skill needs to represent a range for human inconsistencies, as well as always react to new data and adjust for changes in skill.
The implementation.
Build an Arbitrary Skill scale where the numeric values translate into Win probability expectations. That will also convert win probability results into numeric skill values.
Common Player Confusion Issue
Gameplay is a zero factor for systems like this. A player who is all or nothing, snowballs and stomps or flops and feeds will have the same rank as you as long as your WR and Location on the scale/Curve are the same.
Subjective Vs Objective
The issue with subjective grading/judgment is that its fucking hard to automate because It requires the context of the individual games where as a "Elo" style system does not give a shit about gameplay only the results after a match.
A player can see some ones performance in game and identify, well that dude played like shit. Where as the Rating system does not care much for individual games so much as the overall trends in play. Stand out weaker players who consistently cost their team will sink. Folks who crush the competition will climb. When your representative of a majority level of skill then a lot of matches in League turn into RNG as you rely more on allies playing well or enemies failing then personally preforming above your class interval, as its something you have not consistently done.
It's very difficult to make a Training set for machine learning that will not introduce a large Bias for Skill ratings due to the nature of stat generation in Leauge/Mobas. There is a high amount of overlap between good and bad stats, and padding values is universally less work then playing for a win. Also champions have individual stat needs relateing to their kits and theres an issue for MM usage as champion and champion builds are things that happen after a lobby is made.
But MUH TEAMMATES and @ Luck
Distribution favors you If your above average for your MMR range. Always. 10 in game. 5 slots per team. Your team has you. 100% of your games. If your not the worst player in the match the distribution is 4/9 vs 5/9. A gap of 11.11% If your the best player, your team has the best player 100% and is favored to see the worst player put on the enemy team. RNG is a thing but so is LLN and the odds here are better then some Vegas games. How to filter Luck out with math is a well studied topic. So, when folks make claims about teammates, you start seeing real gaps in probability of what they say and what they claim. If you want to see the numbers on that I can give you some examples with basic Elo.
Modern Day Ratings.
Do usually take individual Stats into account as long as the stats are universally usable. Bayesian inference is commonly used to lower the calibration time for MMR. Even basic MMR is more complex then Elo due to it needing to identify skill for individuals on a team as opposed to treating the team as 1 unit, but the theory has been out and peer reviewed for quite a few years, That's why its become an Industry Standard.
Edit.
@ Riot's System.
Riot does not use a "pure" Skill system. Riot has a Progression system and Skill system that are linked together. Riot uses their Ranks and LP to cover trends from players and its made to target perceptions.
Riot does try to add features and improve MM. Role selection was pretty big deal for Mobas and a lot of Kit baised games. Positional MM is a big deal (not positional ques.)
