Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Here is a brief overview of Ryze's abilities:
Overload (Active): Ryze unleashes a terrifying energy blast of lightning at a single enemy unit.
Arcane Mastery (Toggle): Permanently increases mana pool, and causes attacks to deal magic damage.
Rune Prison (Active): Binds the target with sealing runes, prohibiting movement and attacks, and dealing damage.
Spell Flux (Active): Releases an orb of pure energy at a target. The orb bounces from the initial target and
continues through 6 bounces. Each bounce which lands upon an enemy deals damage.
Desperate Power (Passive): While Ryze's health is below 40%, his ability power is increased.
This is a well known "cookie cutter" style build that works fantastically well on Ryze.
Offense: My top row consists of 3/3 Deadliness and 1/3 Archmage's Savvy, but you can swap out the Archmage's Savvy
for Cripple if you have chosen Exhaust as a summoner spell.
The must-have choices after this are 4/4 Sorcery and then 1/1 Archaic Knowledge.
Defense: We spend no points here as it makes it impossible to reach both the bottom of Utility and Archaic Knowledge in Offense.
Utility: In the top row I take 1/1 Spatial Accuracy to improve my teleport, 3/3 Good Hands to reduce my time spent dead and
3/3 Perseverance. In this row you'll want to take the improved Ghost if you are taking that particular skill. If you are taking
Teleport and Ghost, then take both the improves and take a point out of Perseverance. Now take 4/4 Expanded Mind in Tier 2,
3/3 Meditation in Tier 3, 3/3 Quickness in Tier 4, 3/3 Intelligence in Tier 5 and 1/1 Presence of the Master in the final tier.
The improve for flash is essentially useless compared to its surrounding skills, so I advise not to take it.