If two players with similar MMR lose a game...

Because this is a team based game. This isn't a solo game where you climb just for getting kills. If you didn't contribute during teamfights ect. then it doesn't matter how many kills you got.

Because they both lost the game and it is the result that matters.

I know its not your point but LP changes are based on your hidden MMR in relation to your current rank. MMR changes can be different game to game tho based on circumstances but you can't see it.

As for why are the players the same... because I rather players on the team focus on winning rather than padding their personal score especially in a role based game.

Because it's comparing your MMR to the enemy's.

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and one player goes 20/0... and the other player goes 0/20... why do they lose the same amount of LP?

Why does a football team lose the superbowl just because one player fumbled 4 times?

It's a team game, simple as that. It's not a selfish game about padding your KDA and farm. It is a team game about killing the Nexus.

Because your score has zero effect on your MMR or LP.

Kills dont win games. In fact i see a lot of games thrown because people got too many kills and ignored objectives or defense.