Quote:

**Drkirby**:

How my friend builds him is Tear of Goddess, Boots, Rod of Ages, Frozen Heart, Banshee's Vail, 2nd Rod of Ages, and if the game is still going, he will upgrade his Tear of Goddess to an Archangel's. The reason he has for upgrading Archangel's last is that due to how fast Ryze casts spells, the "two times every six seconds" works out to actually being faster then "Once every three seconds"

Yeah, as I said, upgrading once your tear is charged is generally best.

As to the 2nd RoA: you get more damage with a 2nd AA or a Rabadons, and probably even more from a void staff or abyssal scepter, unless no one is building MR.

RoA: adds 725 mana, and 80 + 3% of 725 in AP, for 101.25.

Q: 78.25

W: 97.0

E: 35.4375

AA adds 400 mana (you don't get an extra 1000 from a 2nd one), 45 AP, and another 3% of max mana as AP. Lets be generous and assume you had 5k mana prior to choosing between RoA, AA, and Rabadon. So 5.4k mana now, 3% of that is 162, for 207 AP and 400 mana.

Q: 73.4

W: 144.20001

E: 72.45

What about Rabadon? Well, if you had 5k mana, you have 150 AP from AA's passive, 45 AP from AA, 80 from RoA, and 10.8 from the offensive mastery tier 1 = 285.8 AP prior to rabadon. So Rabadon adds 140 base (putting you at 425.8) , and then adds 30%, or an additional 127.74. So Rabadon adds a total of 140 + 127.74 = 267.74

Q: 53.548

W: 160.644

E: 93.70899

NOTE: @Redenbacher: if you don't have a first RoA, the Rabadons adds 140 + 103.74, for

Q: 48.75

W: 146.244

E: 85.309

Abyssal & Void staff are more complicated in terms of damage added, and I won't go into much detail... they each add 70 AP, so a little over 1/4th of the damage you would get from rabadon:

Q: 14.0

W: 42.0

E: 24.5

The actual damage benefit depends on enemy MR. If you consider an enemy with 80 MR (late game squishies), you already penetrate 24 from your E, 20 from boots, 9 from runes (assuming full MPen marks), so 53 of it, leaving 27, of which you penetrate another 15%, so they have ~23 MR left, and so take 78.7% damage from you. If you got an abyssal, they would take 94.3% damage from you instead. Thats 16% more total damage you are dealing... if your Q is doing ~600, your W ~800, and your E ~250 (random figures, probably about right), then on top of the damage from AP, you are getting an additional (on top of the 14/42/24.5) 90 or so on Q, 120 or so on W, and 37 or so on E.

If an enemy has 200 MR and you get a void staff, now you penetrate 53 (boots, masteries, runes), leaving 147, and then 49% of that (see OP for explanation of why 49% and not 55%), leaving them with around 75 MR. So instead of receiving 44.5% damage from you (pre void staff you penetrate them to 147, then 15% more leaves them at 124.95, 100/(100 + 124.95) = ~44.5%), they receive 57% (penetrate to 147, then 49% more for 74.97, 100/(100+74.97) = ~57%), for a 13.5% damage increase (to your total damage).

I think its pretty much always better damage to go for an MPen or MR reduction item last if you want more damage. If you need the extra HP, the 2nd RoA does have that