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Ok so the idea here is to get the most damage and most practical Ryze for your dollar. Here's the legend:
D(x) - the damage of spell x
m - Ryze's maximum mana
a - Ryze's AP
u - AP Boost from Ryze's ultimate
z - Zhonya's Ring AP Boost
R - Target's Magic Resist
r - Magic Resist Factor (discussed below)
p - Ryze's Magic Penetration
b - the base damage of the skill at rank x
n - the number of times Ryze hits a single target with spell flux
l(x) - the rank of skill x
L - Ryze's level
I - Mana from Ryze's items
G - Gold Spent
Overload - 70/105/140/175/210
Spell Flux - 50/70/90/110/130
Rune Prison Duration - .8/1.2/1.6/2/2.4 @ 80 damage per second
m = 228 + 52L + I
D(Overload) = ( .1m + .45(a + u) + b) / r
D(Spell Flux) = n * ( .33(a + u) + b) / r
D(Rune Prison) = ( ( .4 + .4 l(Rune Prison) ) ( 80 + (.33(a + u) ) ) / r
For the purposes of this guide we'll be assuming that Rune Prison stays at level two for entire game. The AP ratio is also missing from the data page so I guesstimated .33, but I think its actually higher. The spell cast order will always be Ult, Rune Prison, Spell Flux, Overload.
I've been expirimenting with a main build that's Catalyst/Tear/Meja's/Zhonya's/Archangel's with swiftness booties. There are tons of available builds with Ryze; this one is just pure damage, with Catalyst for staying power and HP, ignoring magic resist.
Opening - 475 Gold. I = 200
2x Health Potion