I was thinking about the tutorial and how useless it is. Well, I'm assuming it's useless because the amount of unskilled players I see is horrifying. So I came up with an idea. I don't know if I'm the first one, but here it is:
The training system. Every player has an option to select another player as a trainer. In order to become a trainer one must meet some kind of requirements like over 1000 wins or have a win % in ranked above 60. (numbers are just examples) The apprentice is bound to his trainer for X amount of days (30? 60?), his performance affecting the trainer too. There could be a new rating system, best trainers, competition etc. Every game won by the apprentice gives the trainer some rating or maybe some IP. How the trainer will train his student is up to him. (playing with the bots, 1v1 in the Proving Grounds to teach him how to play solo lane etc)
When the X amount of days has passed, the trainer can pass or fail the apprentice. This could be a visible thing when you go to someone's profile or on the forums, like the Summoner's Code agreement. If the apprentice passes the training, he receives some kind of bigger reward, like 950 RP / 6300 IP. The trainer would receive stuff that he can use, like additional rune pages, 20+ mastery pages, big RP or IP or special skins.
Let me know what do you think and if you would like something like this in the game.