Some Leaves may Deserve At least Partial Credit (and points)
Imagine you're playing as your favorite champion and have a 6/2/10 KDA (or for you stupid good players, 30/0/15) on the winning team. You'd be feeling pretty good up until your internet goes out and the enemy team surrenders before you can reset you router or take other steps to return to the game. You get no points, no credit, no anything; you'd just wasted forty minutes of your life.
My suggestion, is a simple one which changes the way leavers are not awarded points. Using the button that would normally dispense honor, Riot could make it so that other team mates, (and maybe opponents) can vote on whether or not the leaver deserved points. For each remaining member of the team that votes "yes the leaver should get points", they get that fraction.
For example, if two people leave the game on a single team, one as a ditching troll and one as I've described above; the remaining three members vote on whether to allow either of the two leaves points. Naturally the real leaver will be awarded 0/3 of the points he would have earned. Conversely for each player that votes the other teammate should earn points that player earns 1/3 of his points all the way up to 3/3 if the vote is unanimous.
So far as described, there is one glaring issue in the system that I notice. Level farming by creating a matched game, with four alt accounts and one real, one and then intentionally leaving games and surrendering at twenty minutes. Then the real account just votes for the four alts to receive full points and everyone is happy except the real team of five that just played a shitty game. To remedy this Match-made teammates wouldn't be allowed to vote. That means that leavers on Match made team of five would be unable to get points: a minor flaw to the solution.
Let's return to the previous example, with two leavers as before. This time however, the one who played a good match was buddies with one of the summoners that stayed in. That summoner is made exempt from voting, so only two members on the team are allowed to vote. Each yes would award 1/2 of the points back to the leaver.
As additional precautions, I would recommend that voting can only take place if one; games lasting longer that twenty-five minutes, and two; the summoner being voted on must have been connected to the game for at least seventy-five percent of the time the game when on for. if it ended at the twenty-five mark, eighteen minutes and forty-five seconds connected, if the game went on for forty minutes, the champion being voted on need to be connected for thirty of those minutes.