Simply change the scoring system and you change what people are trying to go after. If you want to encourage better team play you change the incentives. The score is the incentive. Make it a basic point system, you get 300 for a kill, -300 for a death, if you 2v1 a guy you get 100 and the KB gets 200, if you kill a golem you get 50 if you kill the enemy golem you get 100, kill a dragon you get 100, drop a ward 10 drop a purple ward 50... etc.
Makes incentive for actually doing stuff in the game worth while. Not trying to make this about PVE but, balance the game out and make point systems that actually contribute to doing the shit that makes a win. Sorry, you can run a 15 KDA and still lose, you see it in the pro leagues as well as lower leagues every day. Rating should be based on your average score per game. Meaning, you could still rank up if you played well but your team was garbage. Change the scoring system you make this game a insanely better.