Solo/Duo Queue Idea
The league system is currently very frustrating for unlucky players. Whether or not you think elo hell exists, it's obvious that some players are put at very wrong spots. Otherwise, you wouldn't have players at Bronze 5 MMR who consistently have very strong KDA's. They may not be good enough to carry themselves out of B5 MMR alone, but they would clearly hold their own in higher leagues. (Imagine a Silver-quality player who, because of bad luck, ends up with a very bad MMR.)
There is an easy way to fix this without drastically changing the league system. In sports analytics, there is a stat called "Win Percentage Added". It's very easy to calculate. You just take a team's current game state, and see how many past teams have gone on to win from that game state. Every time a player changes the game state, you get a new chance to win. The difference between the new percentage and the old is the WPA for that play.
For example, say a team has zero turrets down, the score is 2 kills to 10, and the game time is 10:00. It might be the case that past teams in this situation went on to win 5% of the time. A player on this team downs a turret at 10:01. Teams with that score, with one turret down, went on to win, say, 7% of the time. The player who downed the turret would be credited 0.02 WPA.
Each game, you would simply apply each player's WPA to their League Point change. In a win, you would use WPA x LP. The more you do to help your team win, the more points you should gain. In a loss, you would use (1-WPA) x LP. You'll still lose points, but the more you help your team the fewer you lose.
Why would this be an easy fix? Because WPA is a stat that is impossible to abuse. There is no way to earn it except by helping your team win. How would this help unlucky players? It adds a strong link between player performance and LP change. And the best part of WPA is that it's extremely easy to calculate. It is a memory-intensive stat, because there are billions of game states to remember. But actually performing a WPA calculation can be done in constant time. It is the sort of stat an MMO could handle very easily.