I have an idea for all these hard to balance champs
Let's take Azir for example. Why doesn't Riot try buffing his BASE damage little by little, I'm talking like 5 damage per rank and see what it does? Sure it might take a while to get him into a good spot, but it will guarantee that he isn't pushed over the top from 1 patch. Don't touch his ratio's though, it's harder to balance by ratio's cause it scales far better than bases and one buff or nerf to an item can completely break him or trash him.
Just a thought IDK.