First guide and I decide to troll. Amazingly, however, I'm actually 19 wins to 8 losses using this build. Considering Ryze is a mana hoar now, and his ap ratio's are horrid, I decided, hey what the hell, might as well mess around. So now I have this troll build that somehow works... So ladies and gents, I give you AD Ryze.

Pro's
You push towers better, Ryze couldn't push towers due to no ap/ad but now you can.
You still have a great damage output(still have mana and you get ad with)
You have a snare AND a lot of Magic Reduction
You are not useless when your CD's are up
You are a bit tanky
You farm mana and creeps faster/better

Con's
Rage all over the place
You don't do major magic damage/phys damage. You do a decent amount of both.
Spell Flux loses all usefulness except MR reduction and Passive reduction
Magic Damage is reduced do to no AP (why does that matter, Your a mana hoar)

I am cheap. Yes I am. I use these runes for all characters (with a change with armor pene instead of ap pene on AD champs). You save IP from the runes saved, and you get a bit tanky and a bit of damage early game. So yeah, Armor, Magic Resist, Pene, and Hp. What more can you ask for?

Getting 26 in offense because I lied. This isn't a full AD Ryze. It's a hybrid... Both pene's, crit because everyone loves crits. Extra Armor pen. And more damage. Easy and done.

Start off with a Saphire crystal + hp pot+ mana pot. Like any other Ryze build. It gives damage and spamability(did i spell that right?). Prioritize your tear. Like always. After tear you get lvl 1 boots and finish off the Manamune. So, why Manamune? It gives the 50 mana less than a archangels BUT you build mana faster. Lots and lots faster. 3 mana per spell every second + 1 mana for every basic attack = More mana faster. After which get a malady for attack speed and MR reduction. This MR reduction + spell flux = a lot of MR reduction, possibly negative MR for your target. So what does this mean? In that awkward second or so when your all on cd, or you just wanna toss some dmg, or you want to make your spells hurt MORE.
So what kinda boots should you get? Well what does your team need exactly? The extra speed from the boots help malady debuff and increases your AD damage. Or you can get Sorcerer Boots for EVEN MORE magic damage. After boots you can build tanky while building up more mana or get a phantom dancer to build your AD damage with your speed, as well as build Mana for magic damage from your Overload and Rune Prison. Either way you still dish out a load of Magic and Physical damage. :D

Overload and Rune Prison will be your main spells to focus on. Overload is 8% mana and Rune Prison is 5%. I get one of everything as soon as possible to make use of my passive. Overload gives a tone of magic damage and is spammable due to its 4 second cooldown + Ryze's passive. Rune prison gets maxed out next because it allows for catching and escaping. The instant damage from this thing and the snare KILLS (also if u feel like being a d*ck, this is the best ksing spell you could ever wish for(not that I do it, hehe)). Now I may get some rage for not bumping his ult at lvl 11 but hey, I think this build is already encouraging rage. But after playing Ryze after his remake, I find his ult is only useful for mobbing creepkills and healing. Even in team fights, its only useful when the team is all huddled up in in a small circle which is practically never. (Using the old ryze this wasn't much of a problem since his old main spell was spell flux which bounces away with insane damage but this isnt the old ryze anymore... T.T) So his ult gives him a bit more sustain and possibly that kill when a enemy runs close enough to a fleeing "IM GONNA DIE!" squishy. So yeah, Rune Prison > Ult. After that it's just finishing everything off.

Tele and flash. OK flash got super nerf but hey, It's the best juking(jooking(Once again, no idea how to spell)) tool you can use. Teleport is just for getting back faster in lane/ganks. You can replace teleport if your teammates have it covered and replace with surge, exhaust, ghost, or anything you feel would be helpful. Like smite. Or rally. Or tele. Or not.

In conclusion pie is not better than cake because cake is a fake and pie is a lie. Oh wait what? I mean don't judge this guide to seriously, like I said, its my first as well as its a semi-troll. It works, but the goal here is to have fun. LIKE ALL GAMES ARE SUPPOSED TO DO. Have fun with it. Now about the guide: I'm sorry for the grammatical/spelling errors I have done. I'm sorry for encouraging an ELO hell. I'm sorry for typing so much. And I'm sorry for all the serious players who eventually get teamed up with me(or with my build). It actually works though, give it a try before you rate. Comments are appreciated (be nice kind peoples T.T). And remember, have fun and good luck.

p.s. Play smart aggressive. You have a great harass. Use it. I hate seeing passive players playing aggressive champs. I.E. a passive Irelia.