Award small amounts of LP based on Grades
This idea just came to me, and I think it might solve some problems we have so here goes.
In the games I play, I tend to win/loose between 16 to 23 LP on the game depending on the enemy. That's fine, and I don't have an issue with that. But it's not lost on me that players who throw a temper-tantrum, or died 3 times in 10 minutes then AFK aren't fun for anyone. To this end, I think we can encourage people to continue to try, continue to play well, and diminish the role of these ne'er-do-well's by assigning between 1-5 LP per grade after the game.
Those numbers are subject to debate but the point I wanted to make with them is that this should be a slight dampening of the trolls effect, not a "I got an S, so I gain LP for the loss." A loss is a loss, and LoL is a team game. But unlike sports, players don't disappear midmatch so we need to find some solution here.
The benefit to this has two sides. Players who consistently play to the height of their abilities should be able to climb slightly faster than those who play champs they're unfamiliar with, or who feed. The other side is to (again) take out the pain of have 3 games in a row with an AFK.
I think it's importantly to talk about exploits to this system since should this be implemented, it will certainly be exploited. Unfortunately, because of this, you have to put some harsher-than-normal restrictions on things. For one thing, the champ you're playing has to be assigned to a role that it's listed under in the Lobby Filters. That would require some updating on Riot's part since champs like Ornn are listed as supports and not Top Laners, but that's an easily resolved situation. This option would also not be extended to duo-queues who have a higher likelyhood of queueing in Role A and playing in Role B. Duo teams also have a higher liklihood of climbing, which is benefit enough (imo).
While grades aren't meant to be LP-related, it's again a fair offering since you're being judged against other performances of the same champ, again encouraging players to use familiar champs in ranked, rather than a "I bought a new skin, I want to use it, and IDC if this is ranked" player.
tl;dr: Grades should give you an additional 1-5 LP based on certain conditions in game, to diminish AFKs and encourage people to stay in the 4v5 and try