I don't understand the gameplay mechanics of certain characters that have both AD and AP ratios on their attacks, such as Sivir's boomerang attack or Tyrnadmere's spin. Why didn't they make it flat AD? Someone help explain the game-play mechanics for giving them small scaling AP damage.
Well, we have this item called Trinity Force. 
It gives crit chance, attack speed, attack damage, and other stats including ability power. 
builds this, 
builds this, they both have ability power scaling to add to they're burst in spells; 
could probably build this too, conditionally. However, champions like 
probably wont build this, since they already have better options. That is the only realistic reason that could justify MOST ad scaling champions having ap scaling.
Most of the champions with AP and AD ratios are older ones from before there was a clear and defined meta, things like AP Ezreal and Tryndamere's AP scaling are there from before the meta was bulit and were in place to let players decide how to play the game.
Because in that one game where you just really gotta build a Zhonyas on 
, AP scaling will still make sure you have SOME damage benefit.
