AP Yi isn't completely un-viable. He's tanky as hell late game with some CDR in combo with his Meditate. 1v3+turret he can survive for a while. But Hybrid AP+AS works best. And there are some nice items that give both. Nashor's Tooth jumps straight to mind.
AP Yi sure deals tons of magic damage, but its kinda useless. U'll depend a lot on Alpha Strike and Meditate, and thats suicidal if u cant use them like normal attacks. U'd have to "Q" and run, "Q" and run, and thats not how Yi should be played.
If u want to build AP, play as a mage.
If u want to build AP, play as a mage.

AP Yi doesnt do tons of damage.
He does 1 spell with 100% AP ratio. Nothing more...
Even sion is better... 100% AP ratio x2
Srsly if you want to play AP Yi, take Sion instead, you will bring burst damage, offtakiness, and most of all CC!
He does 1 spell with 100% AP ratio. Nothing more...
Even sion is better... 100% AP ratio x2
Srsly if you want to play AP Yi, take Sion instead, you will bring burst damage, offtakiness, and most of all CC!
That's why you get a lichbane and a guinsoo's. You proc your lichbane with your spells (which gets your AS/AP up) and then DPS them down with your AS. You also need a lot of CDR and a little magic pen for the damage boost. AP Yi is more difficult, but imo it's all about play style. I suck at Master Right-click (crit/AS Yi), but I'm really good at "Alpha strike to the Face!" (AS/AP Yi).
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Yi's role has always been to take down towers and alpha to squishies taking them out quickly.
AP Yi's role is what? Harassment and running away praying they don't have CC?
Out of all those champions why play a champion wrong?
If you're looking for a secret success that will be more unique this isn't it, its been tried and denied.