Zed damage, patch 6.3, and math
OK, I've been seeing a few threads about Zed, probably cause of that new assassin item. So, for fun, I'm gonna calculate some of his damage. Not anything slippery: real, true, after taxes damage. First, I'll give the formula so if anyone's interested they can see what damage Zed can do in any given scenario, and then the Key for the formula so you can read it. Next, I'll give you a quick scenario and some numbers you can realistically expect to find. Then, I'll give you the real damage output of Zed as affected by standard stats, extra armor, and patch 6.3. Last, I'll end with a few notes.
Formula: M[(d)(Q+q+E+A)+(p)(P+T)]+M(d(R{M[...]+A+B})
M= Masteries (double edged sword + assassin) 1.05
d= ad penetration 100/(100+(armor-attack damage penetration))
Q= razor shuriken 75 / 115 / 155 / 195 / 235 + B
q= shadow razor shuriken 37.5 / 57.5 / 77.5 / 97.5 / 117.5 + .5B
E= shadow slash 60 / 90 / 120 / 150 / 180 + .8B
A= base attack damage
p= ap penetration 100/(100+(magic resist-ap penetration))
P= Passive (.06 / .08 / .10)h
T= Thunderlord's 10 / 20 /.../180 +.3B +.1ability power
R= Ulti .3 / .4 / .5 {after rework .25 / .35 / .45}
B= bonus attack damage = base bonus attack damage)(1.05 /1. 10 / 1.15 / 1.20 / 1.25)
h= target's max health
OK, so let's assume 
is lvl 6. is maxing Q and has the Rune, Mastery, and Item build from http://www.mobafire.com/league-of-legends/build/wreck-as-zed-top-and-mid-comprehensive-guide-406404
Let's also assume his inventory is 
Let's say his enemy is 
for the sake of armor, magic resist, and total health; he is also at lvl 6, has armor seals and magic resist glyphs, and has 
and an irrelevant, non-defensive item.
M=1.05 d= 100/(100+(39.9-26.32) = .880 Q= 155 + 39.95 = 194.95 q= 77.5 + 19.98 = 97.48 E= 60 + 31.96 = 91.96 A= 68 p= 100/(100+(42-4.8) = .729 P= 900 x .06 = 54 T= 60 + 11.99 + .5 = 72.49 R= .3 B= 38.05 x 1.05 = 39.95 h= 900
If Zed lands his full combo while his Ult is active 1.05[.880(194.95+97.48+91.96+68) + .729(54+72.49)] + 1.05(.880(.3{1.05[.880(194.95+97.48+91.96+68) + .729(54+72.49)] + 68 + 39.95}) = 687.45
After patch 6.3 1.05[.880(194.95+97.48+91.96+68) + .729(54+72.49)] + 1.05(.880(.25{1.05[.880(194.95+97.48+91.96+68) + .729(54+72.49)] + 68 + 39.95}) = 658.68
If Azir has 
(without stacks)
1.05[.722(194.95+97.48+91.96+68) + .729(54+72.49)] + 1.05(.772(.3{1.05[.772(194.95+97.48+91.96+68) + .729(54+72.49)] + 68 + 39.95})
= 564.35
After patch 6.3 1.05[.772(194.95+97.48+91.96+68) + .729(54+72.49)] + 1.05(.772(.25{1.05[.772(194.95+97.48+91.96+68) + .729(54+72.49)] + 68 + 39.95}) = 543.59
Notes:
Formula does not take into account the Mastery "Merciless"
Formula is calculated at Zed landing every ability and proccing his passive while Death Mark is active, but is easily adjusted.
The entirety of Zed's magic damage come from Thunderlord's and his passive. In the examples the total is 96.86.
