Statistically speaking, Your impact in a game with 9 other people is just 10%
So yes, the quality of matchmaking matters a lot more than your individual performance.
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That's not how statistics work. That's like saying LeBron only has a 7% impact on the games he plays. People who do well in a match have more impact. You only would flatline at 10% if everyone in your matches are equally skilled. AKA your true ELO
Do you actually believe that everyone in every game performs and contributes the exact same amount of value as every other player in every single game?
statistically speaking? maybe. In reality? that is not how the game works in the slightest. You can have a huge impact on the game or an insignificant one depending on how good you are at the game
How do you suppose anyone ever climbs if only everyone's impact is only 10%? How do elo boosters climb with 70%+ winrates?
But every game feels like its 100% your responsibility.
What you say applies to the people who are able to climb.
Not really. Higher performance results in you having more gold than others. Whether that gold came from successful roams, solokills, or just proper CSing, solid performance came to fruition. If gold determines whether you can 1v1, 1v2, or 1v3, that means higher performance can give you the strength of multiple players.
This fact then leads into why players wouldn't have a 10% influence on the game's outcome even in the most balanced scenarios. You probably think perfect matchmaking means every player has the same performance and thus contribution, but that's an impossibility. Even in the most even of fights, a 50%-50%, one player will lose and the other will get a gold lead. That gold lead then shoots one player's contribution and lowers their enemy's.
Sure if you want to take a raw 10 players = 10% each approach.
Unfortunately not all 10 players or their champions are of equal value. Some champions perform better against certain champions (hence counter pricks like 
vs 
) Even then it is based on the overall skill and experience each player has with the respective champion. Sure Sivir counters Blitzcrank in many ways, but if the player behind the blitzcrank has a great deal of experience in dealing with Sivir while the Sivir player is relatively unskilled with Sivir or in Bottom Lane in general, then the Blitzcrank will perform better.
So it is inevitable that some players will be more than 10% and others less than 10% even by the most modest calculation of contribution.