The single consistent thing in your games is you and as being better at the game is traditionally acknowledged to consistently advantage your team
This makes it not a coin flip but rather favors you to win more then you lose.
By removing the slot you occupied (because you occupied it 100% of games) there is 11.11% value for each slot, That translates into how often The very worst player is going to be on the other team.
So 61.11% odds your team is favored not to have the LVP. Be that troll, newbie, low skill. The exception is, if your the weakest player in a match at which point your team is gonna have LVP 100%.
The coin flip side balances out because highest skilled player is also gonna land on the enemy team. For this to be true thou also means admitting hey that's not me or my team would 100% have the MVP on it.
End result of the two is average players for a MMR tend to float around their MMR with no significant gains or losses and depend on teammates or self improvement. Most players who only ever focus on teammate mistakes and plays are not doing to hot on the self improvement thing, This sentence is my opinion and inherently has some Bais.
The # of people in the systems not to big of an issue (unless it gets very low) nor Is the amount of skill on average because as a statistical system its going to adjust for this. As long as you have enough players to make statistical significance your ladder is fine.
Pretty much 50% of the ladder is always going to be under their starting MMR. For league,I doubt its exactly represented like this for the ladder. Elo was made to be Zero Sum but that does not carry over well for MMR because you need to track accounts individually and that requires independent K factors so that your Adjustment formula can be ran 10 times at a match end rather then just once. So your gonna see some variance, more so with Soft resets.
Now as far as improving MM. It will still be a coin flip for a massive # of players really fast. If your near the 50 percentile your gonna end up at the MMR your expected to be stuck in rapidly.
MMR scores are meant to represent a Mean average for an accounts performance, so its also a range. Its commonly treated like some absolute value and its not, its treated like 2 players with the same score when accurate would be identical in how they preform and they wont because the Good games and Bad games of a player can have the same range but very different impact on a match.
So, a lot of times people use the term Coin flip, then use that to explain why they have sunk down the ladder. I lost X games because RNG teammates being awfully. A high streak of losses however is increasingly unlikely in a coinflip. Put it into powers for the # of potential combinations. 2^loss/win streak.
Now im not a math guru but far as I can if see your looking for 1 specific combination that's only possible 1 time. So for a 10 game streak that's odds of 1,024 to 1. For a 15 game streak that's 32,768 to 1. For 20? 1,048,576 to 1.
This is why I harp on players treating 3-4 games as a "streak. That's 8 to 1 and 16 to 1 odds. Anyhow point being after a point its pretty clear a positive or negative streak of any significance is not likely because of luck as a factor but skill and a lot of people don't quite understand why that is.
Now, op about your comments like
We just need a better match making system.
Match people according to their skill better.
Yea I agree. First up, Reworking Duoing will go a long way. Make it off MMR not Tiers. Restrict the duoing MMR to be the same as MM considers to be Fair. Honestly completely removing it from Solo que would be better but Most the issues with Riots system are there because players like them or feel better because of them. The effort to keep players happy and content often is what makes problems.
Promo helper and demotion protector can result in an account who is sinking having a much higher Tier then MMR.
MM should spend a bit longer looking for a more fair range, MM should have a priority to put players with similar K factors into a game.
Duoings the stand out issue imo because you see it make negative impact on a lot of games.