Spell Vamp Ryze

Ryze is a high burst damage character with a large mana pool. I play Ryze as my main and this is the build I use. What makes this build unique is that I include the Hextech Revolver as one of the core items giving Ryze a passive Spell Vamp, which when combined with his Ultimate, Desperate Power, makes him nearly invincible.

Pros
Burst Damage
Mana Pool
Spell Vamp
Stun

Cons
Weak Tower Damage

CDR

Cooldown Reduction is capped at 40% and should be Ryze’s #1 priority. By increasing CDR you increase the frequency of your burst damage. Also once CDR and Desperate Power are capped, Desperate Power will have a 30 second cooldown.

I obtain 40% CDR as follows:
9% from Masteries, 1% from runes, 10% from Overload passive, 20% from Frozen Heart.

Mana

Priority #2 is mana. Because the damage from Overload and Rune Prison scales with mana, more mana = more damage. I use Runes, Masteries, and Items to effectively increase Ryze's mana pool.

Spell Vamp

Ryze deals massive amounts of magic damage. Desperate Power provides temporary Spell Vamp but adding Hextech Revolver and later upgrading it to either Hextech Gunblade or Will of the Ancients improves Ryze's survivability tremendously.

Magic Penetration

Magic Penetration is crucial against opponents with Magic Resistance. After Archaic Knowledge (Mastery) penetrates 15% of opponents magic resistance, Spell Flux, Sorcerer's Shoes, 3x Greater Quintessence of Magic Penetration and 9x Greater Mark of Magic Penetration's provide between 34.22-58.22 magic penetration, depending on the level of, and whether or not you cast Spell Flux on the target. This should provide enough Magic Penetration to counter champions with some Magic Resistance, however sometimes a Abyssal Mask or Haunting Guise may be necessary.

Core Items

The core items for this build are:
Tear of the Goddess
Boots
Catalyst the Protector
Glacial Shroud
Hextech Revolver

These items are cheap, easily obtainable, and are essential to this build. They combine for the following stats:

290 Health, 2100 Mana, 15% CDR, 15% Spell Vamp, 7 Mana Regen, 40 Ability Power, 45 Armor, Movement 1, on leveling up restores 250 Health and 200 Mana over 8 seconds.

Upgrade

All of the Core Items are upgradeable. After getting the 5 core items, and sometimes sooner, I upgrade the boots. If you have 10% CDR from Runes and Masteries I recommend Sorcerer's Shoes. If you don't have the CDR Ionian Boots of Lucidity are a great option because they provide 15% CDR and upon purchasing them you would have CDR capped which as I stated before is Priority #1. In some matches the magic penetration from Sorcerer’s Shoes could be sacrificed for Boots of Swiftness. I usually do this if playing against faster characters like Teemo and Warrick.

To take advantage of the per minute stacking I upgrade the Catalyst the Protector to the Rod of Ages next.

If you have 10% CDR from runes and masteries and went with Sorcerer’s Shoes next you should upgrade the Glacial Shroud into the Frozen Heart so that you reach 40% CDR. If you have the Ionian Boots of Lucidity you can wait to upgrade the Frozen Heart until later.

From this point on all upgrading and building is done on an as needed basis.

Hextech Revolver upgrades to either Hextech Gunblade or Will of the Ancients. If your team will benefit from WoTA I recommend it, however if your group wouldn't benefit from the aura then I recommend the Gunblade because the added attack damage will help you destroy towers, which is Ryze's biggest weakness, and the active ability is also great, provided you remember to use it once every 60 seconds.

Optional 6th Items

The 6th item is situational and should be built to counter your opponents.

Abyssal Mask provides magic resistance and lowers nearby enemies magic resistance.
Haunting Guise inexpensive way to add 20 magic penetration.
Thornmail is great against high physical damage characters especially ones with fast attack speed.
Banshee's Veil is great against casters and adds more mana.
Rylai's Crystal Scepter adds a slow to your spell damage.
Warmog's Armor adds a ridiculous amount of health.
Hextech Gunblade or Will of the Ancients whichever you didn't already get. Combined with Desperate Power would yield 75% spell vamp which is probably unnecessary.

At this point everything except for the Tear of the Goddess should be upgraded. Since Archangel's Staff's unique passive builds mana slower than the Tear of the Goddess and converts 3% of maximum mana to AP I save this for last.

I always get Clarity to restore mana and keep me in the fight. I use clarity as soon as my mana is half empty so that its cooldown will begin to cycle.

On the 5v5 map I get Exhaust to help kill champions. On the 3v3 map I instead get Fortify because keeping the towers up on the smaller map is of the utmost importance.

Blue Glyphs have the highest CDR stats of all the runes and the highest mana/level. To reach the CDR cap I recommend getting 1% CDR from runes. All of the other runes are mana/level except for the Red Marks and the Quintessences where I get Magic Penetration. I do this to maintain enough magic penetration without the Abyssal Mask to keep it optional.

You could sacrifice the 14.22 magic penetration from the 9x Greater Mark of Magic Penetration and 3x Greater Quintessence of Magic Penetration for 414.72 mana at level 18 from 9x Greater Mark of Knowledge and 3x Greater Quintessence of Knowledge.

The masteries are focused on CDR, mana, and mana regeneration.

Ryze is at his best when soloing a lane because he can out level and out farm the competition. However, getting Insight (Mastery) and Will of the Ancients makes Ryze the ideal companion for any caster.

Use Spell Flux to try and get multiple last hits.

The splash damage from Desperate Power makes it very effective for clearing groups of minions.

Jam whatever button is not on cooldown.