Pros: +Very strong mid-late game +Tanky +Spamable spells +High DPS +High sustain late game +AoE ultimate

Cons: -Weak early game -Blue dependent early -Doesn't farm well -Needs farm

Ryze is a tanky, DPS caster and his runes should reflect that. The Magic Pen marks, as well as the Magic Resist glyphs, are very standard rune choices for AP mids. These runes give you the best possible advantage during the laning phase, allowing you to win trades and harass your opponent.

Health per level seals allow Ryze to scale well into mid to late game, helping him become even tankier.

The movement speed quints give Ryze a lot of utility. With extra movement speed, Ryze and dodge skill shots, avoid ganks, catch running enemies, kite enemies, and even perform ganks of his own.

When I first started playing Ryze I read a few guides that suggested mana runes... so I bit and wasted my IP. The only thing the mana runes really help with is a early game mana pool, but you should be getting blue the second time around so mana shouldn't be a problem after that. Having tankier runes and MP runes allow you be more of a brute force in the game.

Lets say you pick up scaling mana seals and flat mana glyphs (like I so dumbly did). At level 18 you'll have 291 mana.
Overload 291*.065=18.915
Rune Prison 291*.045=13.095
WOOT!! An extra 32 damage compared to 175 health and 12 magic resist. Even though 12 magic resist doesn't sound like a lot, it helps a ton when trading early game.

I go with a 9/0/21 masteries page for Ryze, focusing on CDR and getting to late game. I pick Intelligence over Strength of Spirit becasue the health regen Strength of Spirit gives early to mid game isnt very strong, and late game you should have enough spell vamp to sustain yourself very easily. Focusing on the CDR masteries allows you to get 40% CDR (the cap) without blue buff.

The 3 points in Brute Force is to help you farm creeps easier since Ryze is poor at auto attack farming and needs to be farmed to be effective. The 4 ability power you would gain from Mental Force will not make any difference in your damage so its better to just focus on getting that cs up.

Explanation: Very standard AP mid summoner spells. Flash is very versitle. It can be used to secure kills or escape ganks. Ignite helps allow you to burst your opponant down very rapidly and secure kills.

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Other Options

Ghost goes well with Desperate Power, allowing you to chase down low health targets or run away from enemies.

Teleport will allow you to buy and get back to lane more quickly, in particular when you get your Tear of the Goddess. It could also allow you to help your team mates out if they fall into trouble.

Heal could allow you to live a little longer in fights, but with the spell vamp Desperate Power gives you should be able to heal yourself fairly nicely. I would not suggest getting this.

Yes, your spells cost a high amout of mana. Yes, you do spam your spells. And yes, you can run into some mana problems very early on if not careful. But no, Clarity is not a great idea. Ryze's power comes from a huge mana pool, not a lot of mana regen. Plus, at around 7 or 8 minutes you should have blue buff so mana wont be a problem.

Passive: Arcane Mastery

When Ryze casts a spell, all other spells have their cooldown reduced by 1 second.

Explanation:

This is what makes Ryze's damage output so high. Basically you can just spam your abilities, Overload in particular, and keep refreshing your cool downs to keep your damage rolling.

Q: Overload

Passive: Ryze gains 2 / 4 / 6 / 8 / 10% cooldown reduction.
Active: Ryze blasts enemy unit for 60/85/110/135/160 (+40% of ability power) plus 6.5% of his max mana in magic damage.
Cooldown 3.5 seconds
Cost 70 mana
Range 650

Explanation:

This is your main source of damage. This becomes a very very very spamable spell when you are comboing because of Arcane Mastery and your capped CDR. Oh, and you get 10% CDR, what more can you ask for?

W: Rune Prison

Ryze traps an enemy unit, preventing them from moving for .75 / 1 / 1.25 / 1.5 / 1.75 / and dealing 60 / 95 / 120 / 165 / 200 (+60% of ability power) plus 4.5% of his max mana in magic damage.
Cooldown 14seconds
Cost 80/90/100/110/120 mana
Range 625

Explanation:

This spell deals a good amount of damage and provides a snare. It is absolutely great for setting up ganks or escaping ganks. In team fights you can keep the AD bruiser away from you while you burst them down. When chasing you can pick someone off, allowing your team to catch up and blow them up. The only problem with this is it costs a lot of mana early game. Try not to use it very often early usless you need it for ganks (both setting one up or escaping one) or you have blue.

E: Spell Flux

Ryze unleashes a bouncing orb of magical power which bounces to enemy units or himself, up to 5 times. Each bounce deals 80/90/100/110/120 (+35% of ability power) (+1% of max mana) magic damage and reduces the target's Magic Resistance by 15.
Cooldown 14seconds
Cost 60 / 75 / 90 / 105 / 120mana
Range 675

Explanation:

This spell can deal a very good amount if damage late game if you get good bounces. When combo'ed with Desperate Power this spell can be used to deal a large amount of AoE damage which can be very useful in team fights or simply just farming.

R: Desperate Power

Ryze becomes supercharged, passivly grants 75 / 150 / 225 mana, also gaining 15/20/25% spell vamp and causing his spells to deal 50% AoE damage for 5 / 6 / 7 seconds.
Cooldown 70 / 60 / 50 seconds
Range 200

Explanation:

This ult is amazing. The AoE effect of this ultimate makes you a team fight force, dealing amazing amounts of damage. The spell vamp allows you to tank a ton of damage, which is why Ryze is so strong late game. If you are being focused by the enemy team, simply pop your ult and watch your life magically come back (but try not to get focused as you will die eventually). On top of that it passively grants mana which means more damage!

Use it. Period.
Desperate has an extremely short cool down, 50 seconds at lvl 3. With your 40% CDR that makes the cool down 30 seconds. Do a quick combo right after popping your ult, your down to roughly 25 seconds. See what I'm getting at? Even at earlier levels, the cool down is very short, and if you really want to get it back fast you can spam your abilities (I would highly suggest having blue if you plan on doing this early to mid game). Use Desperate Power to farm, use it to get blue on your own, use it to sustain your self in lane if your getting fairly low.

Basically what I'm trying to say is, unless you are 5 seconds away from fighting (1v1 or teamfight) feel free to use your ult. With how short the cool down is you will have it back by the next team fight.

So basically: Desperate Power > Overload > Rune Prison > Spell Flux

This skill order helps you maxamize your damage output and set yourself up for the best success in fighting both 1v1 and team fights.
Desperate Power goes first because... well come on, it's your ult.
Overload goes second because of the passive CDR you gain from it as well as its extremely short cool down, making it a spamable spell
Rune Prison is third because with each point the damage increases greatly as well as the snare time.
Spell Flux is last because, sadly, its cool down doesn't shorten with levels so it is just better to level it last

The reason I do not get 2 early points in Overload by level 3 is because in a lvl 3 fight, you will have a much higher damage output with you 3 spells than with your lvl 2 Overload.

Start: Boots + Health Potionx3
If you think you are going to have an easy lane you can consider going Sapphire Crystal + Health Potionx2