## Ghostcrawler on the mechanics behind Armor Penetration

There is a great thread over on the Damage Dealing Forums started by a Rogue about the mechanics of the Armor Penetration cap/observed effectiveness. Armor Pen is a statistic that will allow an attack to ignore a given amount of armor.

The thread and the contents inside it are notable in that it is, by my recollection, the first time a Blizzard employee has given out the complete rundown of an in-game formula. While there have been hints and comments about how certain statistics impact the game from patch notes and game designer posts in the past, there has never been a "step a, step b, step c" like algorithmic definition to all those stats contained within the black box of theorycrafting.

In giving out the computations behind Armor Penetration, Ghostcrawler makes note to point out that Blizzard is not, and will not, get in a habit of delivering theorycrafting to players. They like the idea that players have to test out game mechanics, and that while the starting and end results are known, what happens in the middle of combat isn't written in stone. In the case of the Armor Penetration rating, they released it due to quite a bit of (somewhat) inaccurate information out there.

The armor penetration formula, and an example, after the break.

Ghostcrawler delivers the formula for the Armor Pen cap in the following bit of pseudo code (I've cleaned it a bit for readability sake):

Let C be the Armor Penetration constant.

if ( level < 60 )

Thus where a level 80 mob is being attacked, C = 15232.5. For a level 83 mob C = 16635.

The cap for Armor Penetration is then: (Armor + C) / 3

A quick example, used originally by Ghostcrawler but extrapolated upon here:

Assume a level 80 death knight NPC (note: non player character) has 9729 armor. C for level 80 mobs is 15232.5. The Armor Penetration cap is (9729 + 15232.5) / 3 = 8320.5. At this point the game will choose the lowest of two values, either 8320.5 or 9729, to represent the most armor which can be ignored. We'll call this value X. So X = 8320.5.

A person is attacking with 30% Armor Penetration. The game will then compute the amount of armor to be ignored against the previous value X, which means the amount of armor ignored on our level 80 death knight NPC is 2496.15 (30% of 8320.5), which we'll call M. M is then subtracted from the death knight's actual armor, which means the attack goes through against 9729 – 2496.15 = 7232.85 armor present.

Now if this is all Greek for you, don't worry. I wanted to get the information out there today. Look for a detailed guide, complete with pictures and diagrams, later this week.

The thread and the contents inside it are notable in that it is, by my recollection, the first time a Blizzard employee has given out the complete rundown of an in-game formula. While there have been hints and comments about how certain statistics impact the game from patch notes and game designer posts in the past, there has never been a "step a, step b, step c" like algorithmic definition to all those stats contained within the black box of theorycrafting.

In giving out the computations behind Armor Penetration, Ghostcrawler makes note to point out that Blizzard is not, and will not, get in a habit of delivering theorycrafting to players. They like the idea that players have to test out game mechanics, and that while the starting and end results are known, what happens in the middle of combat isn't written in stone. In the case of the Armor Penetration rating, they released it due to quite a bit of (somewhat) inaccurate information out there.

The armor penetration formula, and an example, after the break.

Ghostcrawler delivers the formula for the Armor Pen cap in the following bit of pseudo code (I've cleaned it a bit for readability sake):

Let C be the Armor Penetration constant.

if ( level < 60 )

C = 400 + ( 85 * targetlevel )

else C = 400 + ( 85 * targetlevel ) + ( 4.5 * 85 * (targetlevel – 59))

Thus where a level 80 mob is being attacked, C = 15232.5. For a level 83 mob C = 16635.

The cap for Armor Penetration is then: (Armor + C) / 3

A quick example, used originally by Ghostcrawler but extrapolated upon here:

Assume a level 80 death knight NPC (note: non player character) has 9729 armor. C for level 80 mobs is 15232.5. The Armor Penetration cap is (9729 + 15232.5) / 3 = 8320.5. At this point the game will choose the lowest of two values, either 8320.5 or 9729, to represent the most armor which can be ignored. We'll call this value X. So X = 8320.5.

A person is attacking with 30% Armor Penetration. The game will then compute the amount of armor to be ignored against the previous value X, which means the amount of armor ignored on our level 80 death knight NPC is 2496.15 (30% of 8320.5), which we'll call M. M is then subtracted from the death knight's actual armor, which means the attack goes through against 9729 – 2496.15 = 7232.85 armor present.

Now if this is all Greek for you, don't worry. I wanted to get the information out there today. Look for a detailed guide, complete with pictures and diagrams, later this week.

Filed under: Odds and ends

## Reader Comments (Page 2 of 3)

## Four Apr 19th 2009 6:38PM

***head asplodes***

## Craig R Apr 19th 2009 6:41PM

yo dawg, I heard you liked functions, so we put a function in yo function so you can derive while you derive

## tonedeff Apr 19th 2009 6:46PM

Less MATHS MATHS and more PEW PEW!

## Craig R Apr 19th 2009 6:48PM

mo' like less Q - Q and more PEW + PEW

## Shinn Apr 19th 2009 6:58PM

HAH Craig, Love it.

## Nadril Apr 19th 2009 6:51PM

So how does armor pen stack? From all of my gear I have around 7.4% armor pen added up, yet blizzard's tooltip says I can ignore up to 9.99% (123 rating). The odd thing is that even the rating is wrong, added up I have around 167.

## khelavaster Apr 19th 2009 7:07PM

from most of the comments here i get the feeling that a lot of people don't understand the formula or what GC means by the numbers and constants that he put in the example. Hopefully the topic will be extrapolated upon in more detail, but the rundown is this: you ACTUALLY get LESS armor pen that the tooltip says you do, that is to say if it says you get UP TO 30% after all the math is said and done you may actually only reduce armor by 26% or something along those lines. Not all the constants GC used were for the formula, some were simply examples, so don't try to read too much into it.

## Heilig Apr 19th 2009 8:01PM

TL;DR version:

Armor Penetration doesn't actually penetrate the percentage that is shown on your character sheet. It will always be less, and the percentage goes further down the higher the mob's armor gets.

## Allenny Apr 19th 2009 7:09PM

Awsome, Great, Fantastic. Now just tell me the cap ok. It's pretty easy to assume I'm level 80 and want the cap VS a level 83 mob because, anything lower is not really a "cap" now is it?

## Vandenite Apr 19th 2009 7:37PM

the equation shows that the amount of armor avoided is based on the mob's armor and your armor pen rating, there is no cap.

## Heilig Apr 19th 2009 7:53PM

Well, that's not technically true. If you could get enough ArPen rating so your character sheet says "up to 100%" that would be a theoretical cap. of course, you'll only be doing about 200 DPS because of all the stats you gave up to get there, so it doesn't really matter.

## Allenny Apr 19th 2009 8:10PM

I copy/paste/quote...

"Ghostcrawler delivers the formula for the Armor Pen cap in the following bit of pseudo code (I've cleaned it a bit for readability sake):

Let C be the Armor Penetration constant.

if ( level < 60 )

C = 400 + ( 85 * targetlevel )

else

C = 400 + ( 85 * targetlevel ) + ( 4.5 * 85 * (targetlevel – 59))

Thus where a level 80 mob is being attacked, C = 15232.5. For a level 83 mob C = 16635.

The cap for Armor Penetration is then: (Armor + C) / 3"

I see the word cap in there a few times. If I mouse over hit rating on my rogue, I also see Armor pen rating 47 which equals -3.82% of my enemies armor. So, if I had an armor pen rating of 1230.37 my attacks would completly ingnore anyones amror?

## Dave Apr 19th 2009 8:51PM

Aside from the part where the cap is /3 which is ~30%, as is what the tooltip states your max to be... yes you have it correct. It's divided by 3 (likely 3.33 really) in order to max out your penetration at %30 of a mob's armor.

So roughly 400ish armor penetration will cap your ability to penetrate a L83 mob.

This is COMBINED with Sunder and other armor reducing things, so you're going to get more from less if someone else is debuffing the armor of your target as well as your gear doesn't appear to be able to hit the full %30.

Whether this is as useful as adding to haste or other stats... that's a different discussion. I think this does in fact prove that armor pen isn't useless on your gear, but you still aren't going to want to gem for it.

## Dch48 Apr 19th 2009 9:16PM

You can never ignore all of a target's armor. That's the reason why the calculation is done the way it is. All LK bosses have 13083 armor and the max or cap that can be ignored works out to 9906. Say you have 30% ArP rating. That would make you ignore 30% of the 9906 or 2972. Take that number from 13083 and you have 10111 for the boss's armor. A reduction of 22.7%, not the 30% given in the tooltip. 13083 armor provides 44% damage mitigation. The reduced number of 10111 works out to 37.8% mitigation. Therefore you will do 6.2% more damage with your physical attacks which is not bad.

In my case, when my Grim Toll trinket procs I have 728 ArP or 59.2%. Working out all the formulas gives me 13.8% more physical damage for the duration of the proc. That's pretty substantial.

ArP is definitely not the useless stat some people think it is.

## Heilig Apr 20th 2009 3:09AM

Unless you do some damage that isn't physical, like ret pallies and DK's. For us it still completely sucks.

## Teaspoon Apr 19th 2009 8:58PM

If their armour is less than C/2 (ie, you're attacking a level 80 target with less than 7616 armour) then 100% armour penetration will put them at zero armour.

Anyway, let's apply this to something: all Naxx bosses have 13083 armour (46.20% damage reduction), leaving the the ArmPen cap against Naxx bosses at 9906. 100% ArmPen will put a Naxx boss at an effective 3177 armour (17.26% damage reduction).

We'll flip those numbers around to learn that with no ArmPen a Naxx boss will take 53.80% of your character-sheet damage and with 100% they'll take 82.74%. That's a 53.8% increase.

## Dch48 Apr 20th 2009 1:20AM

Okay, you're right, you use the attacker's level figure. My numbers are a little off then but my point is still valid. ArP is a valid and worthwhile stat.

## Dch48 Apr 19th 2009 9:24PM

Your math is somewhat flawed. 13083 armor provides 44% mitigation ,not 46.2. Also, nobody will ever have 100% penetration since that would require a rating of 1230 or thereabouts.

## Teaspoon Apr 19th 2009 10:02PM

I was using 15223 for the magic number, which I got from http://www.wowwiki.com/Formulas:Damage_reduction - if their numbers are wrong, please update that page with the right ones. Also, remember that we're discussing boss armour against an attack from a level 80 and not the usual discussion of a player's armour against a level 83 attack - use the level 80 magic number!

100% ArmPen isn't realistic, I was just demonstrating the extreme case. We can talk about cases that'll actually come up...

The 20% ArP from a 5-sunder leaves a Naxx boss on 11101.8, which is 42.16% damage reduction = 57.84% damage taken which comes out as a 7.5% increase over zero ArP. A mace-spec arms warrior in battle stance hitting an unsundered boss has 25% ArP (assuming ArP is an addition-stacker, not a multiplication-stacker), leaving the boss at 10606.5, or 58.94% damage taken which is a 9.59% damage increase over no ArP. The 45% from a mace-arms warrior beating up a 5-sundered boss has the boss on an effective 8625.3 armour for 63.83% damage taken, which is an 18.7% increase.

## profglitch Apr 19th 2009 9:55PM

hehehehehehehe you said penetration hehehehehehe

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