Most people go AA, but with the AP ratios that ryze gets I feel that the little damage coming from that isn't worth it, but if you get the manamune it will help you to be able to actually damage towers :]
But that is going to be on my items list for other options!

For example, say ryze has 5k mana. With the AA you will get 150 AP, that will let you do 30 extra damage with overload or 90 with rune prison which honestly isn't much late game.

So instead with the manamune you'll get 100 extra ad which will let you at least put a dent in towers when you have the chance!

Its apparent this guide is still a work in progress, and i like what you have so far besides one thing.

Is pretty worthless for ryze imo. He doesnt need AD.

On the other hand, similar to that i would take instead (: