Melee DPS 101: Armor Penetration
Posted by 
iTZKooPA on Tuesday, April 21, 2009 - 18 Comments Tags: algebra, armor penetration explained, dps 101, ghostcrawler, i hope my math is right!, math, math is hard, melee dps 101, my brain hurts
iTZKooPA on Tuesday, April 21, 2009 - 18 Comments Tags: algebra, armor penetration explained, dps 101, ghostcrawler, i hope my math is right!, math, math is hard, melee dps 101, my brain hurts 
Honestly, I really didn't plan on covering Armor Penetration as part of this reoccurring column. For starters, the statistic is largely a junk statistic, due to its low usage on our fancy pieces of gear. Mainly, it's because the stat has never been fully understood, until now. A Blizzard Poster by the name of Ghostcrawler - you may have heard of him - revealed the in-depth calculations behind the statistic and ultimately what has had theorycrafters confused since its inception. To my knowledge, this is the first time Blizzard has revealed a formula, and only because of all the confusion surrounding it.Thanks to Patch 3.1 and some friendly pointers from Heartbourne, I've been on a bit of a math kick, which made yesterday's post all that more interesting to me. I must warn you that this discussion is going to have Algebra, serious algebra. Before we get into the complexity of the formula, here are the three things that seem to have held the theorycrafting up for so long. If you aren't a math fan hopefully the bullet points will help you grasp the concept. Otherwise, allow your eyes to glaze until the conclusion.
Up To: This is a key phrase in the stats' tooltip that seems to be overlooked often. Simply put, the number displayed is the maximum percentage of armor that can be ignored. It isn't a guaranteed number because of the following two pieces that Ghostcrawler revealed.
Constant: Blizzard didn't want Armor Penetration to be too powerful at the high or low end (read level) of the spectrum so they came up with this little diddy. The magic Armor Constant (will be refereed to as 'K' below) is an easy to calculate number that changes significantly when a mob is over level 60.
Cap: The Cap, combined with the K, causes the "Up To" statement in the tooltip. If the Cap is lower than the target's armor, then said Cap is used in the Armor Penetration calculation rather than the actual target's armor. If this is the case, then the effective armor reduction will appear lower than the stat lists.
The numbers for the first example are being lifted directly from Ghostcrawler's post on the topic, but to try and reduce confusion, I have left some extraneous information out and added additional explanation. If you grasp the original post, then the following block will be redundant. Our formula will focus solely on endgame content, level 80 and level 83 (boss mob) NPCs.
Important numbers:
Level 80 Constant (K) = 400+85*targetlevel+4.5*85*(targetlevel-59) = 15232.5
Level 83 Constant (K) = 400+85*targetlevel+4.5*85*(targetlevel-59) = 16635
Armor Cap = (targetarmor + K)/3
Example Mob: We will stick with Mr. Street's example, a level 80 warrior creature with 9729 armor. The player attacking has 30% Armor Penetration and no other modifiers.
Calculation:
Our armor constant (K) in this case = 15232.5
Armor Cap = (targetarmor + K)/3 = (9729 + 15232.5)/3 => 8320.5
The formula choses the lower amount (Armor Cap or actual armor) to apply the penetration stat (.30) to: ArmCap * ArmPen = lost armor => 8320.5 * .30 = 2496.15
Thus 2496.15 of the target's armor is ignored, effectively leaving the creature with 7232.85 armor: armor - armor lost = effective armor => 9729 - 2496.15 = 7232.85
Comparison:
If it wasn't for the "Up To" statement then the calculation would certainly be off, since the player only sees a reduction of 25.66% of the target's armor. Due to the usage of the Armor Cap, the Armor Constant was selected, reducing the amount lost below the 30% that you may have expected.
Example Boss: For our quicker second example we have selected a boss mob with 25000 armor being attacked by a toon with 30% Armor Penetration.
Calculation:
K = 16635
Armor Cap = (25000 + 16635)/3 => 13878
lost armor = 13878 * .3 = 4163.5
effective armor = 25000 - 4163.5 = 20836.5
Percent lost = 4163.5/25000 = 16.6%
Conclusion:
Armor Penetration is certainly not a statistic that you should be gearing out for. As you can see, your penetration percentage actually goes down against a well armored opponent. The original poster of the thread claimed that the toon in question had 116% Armor Penetration, but only reduced the target's armor by 66%. Talk about a loss.
Although we may not have known the mechanics behind the calculation before, theorycrafters were correct in assuming that all our other stats are more important. Gear for Hit, Expertise, Agility, Attack Power, Strength, etc, as Armor Penetration is a third rate stat for Melee DPSers. For rogues, warriors, death knights and feral druids, the statistic should be weighed above Intellect and Spirit, but below seemingly every other modifier.
Reader Comments (18)
FIRST!
Great post btw! tho' i dont play melee.
love the image
for arms warriors in pvp armor pen+battlestance (10% armor pen buff) + Mace spec+shattering throw can definitely have some devastating effects on squishies :) Though armor pen is not really a stat you may wish to stack it certainly has it's advantages in various situations.
well glad that stat is out of the way. Thanks for crunching the numbers.
next...
ouch. My brain! :)
*eyes glaze over*
This sort of stuff takes all the fun out of WoW (for me) I perfer to keep it simple and not stress this level of detail.
Even after they explained how ArP works , it's still (if not better) equal to agility for feral druids and regemming all my gear for ArP was a boost in dps
Wow! All that just to explain how Armor Penetration can effect our DPS. I just wrote that all down (no printer) to have to read whenever I want, but I should have read it all first, lol. That took a while...
O.o!?!?!
As a rogue i am only looking at gaining Agi,AP and Hit realy. I have never looked at armor penetration and have never wanted it. Ive looked at the gear i have and jus "Hey i have armor penetration, oh joy" So as concluded i think its a waste of time. Go for the real stats!
I've always skipped gear with armor penetration (unless it had a whole bunch of other stats) because I figured it was just like what spell penetration is: Trash.
Still, the more people who learn about this, the better in my opinion. It'll save players from wasting time and gold on it, and cause them to go for better gear.
I appreciate your breakdown of the "up to" part of armor penetration rating. This indicates that even if your tool tip is indicating you are ignoring up to 100% of a mob's armor value, you still have more armor to penetrate. While your numbers and math appear accurate at showing that the display of the stat is misleading to say the least, you are overlooking how 'armor' itself works. Consider the diminishing return of stacking armor (as armor goes up in value, the % of mitigation diminishes). Judging purely by numbers, the more armor you have, the less valuable the stat becomes. Yet armor penetration works inversely of this mitigation (as the armor value goes down by a % of the total, the % of mitigation decreases increasingly). If a mob were to dis clothe by a set value... every time the mob took off 500 armor the mob would decrease his mitigation by a greater % value than before. The more armor penetration you have, the more valuable the stat becomes, simply put. If we think of armor penetration through this concept, perhaps the reason blizzard limits the % of actual penetration when calculating the application of the stat is to keep the stat from being over powered. I know no other classes that have stacked this stat other than an arms warrior, but for my feral druid, an abundance of the stat seems to scale well with my other primary stats.
http://www.warcrafthuntersunion.com/2009/01/hunter-armor-pen-rating-how-it-works-at-level-80/
This site almost explains what I am saying about understanding the concept of armor penetration but comes up short yet again in the conclusion. Pay attention to Joe's comment in the following comments. He shows that armor penetration's actual increase in dps is almost twice of that shown, based on the values in the article.
Give me some more numbers, I want to see experiments with high armor pen and low armor pen for feral druids, and compare and contrast it with Agi, and Strength. Please ^.^
[=|__|=]
[+|__|::]
Nintendo DS
I do remember ArP, it was a waste and always had been... I guess until now (or the 3.1 patch).
I think its important that we have access to this information as it makes each player (potentially) more effective. Now that could sound like boring work but when you are on a new boss and you dont have the DPS or whatever to down it and you wipe all night, its no fun.
Now one stat should not make or break a raid, but the idea of everyone being as effective as they can be is good... (or as effective as they want to be).
So the question is - how good is this stat now? depending on class, build and content (pvp, pve, etc...).
Lots of new Wrath gear has ArP on it ... even some tanking gear (which I still think is odd - even though it would help TPS, there are other stats that can also help TPS).
So, great start on the article - now more theory and stuff please! :D
I have 67% armor pen with food and flask and with sunders and ff i can estimate i have 80-85%. Just from experience every time I got new gear that had armor pen my dps went up. I would trust less random calculators that spit out numbers and take advice from someone that uses ArP as their main stat. I try and have ArP in every peice of gear I have unless its a major downgrade. I've pulled 7k on regular raid bosses with 25k ferocious bites. I've seen it on rogues, hunters and dks and as long as you have it stacked on your gear and gems (and spec maces for rogues) its a perfectly viable strategy.
Arms warrs, you still want ArP. Rogues, you still want ArP. Ferals, you still want ArP. Do a little theorycrafting before you start blathering on about agility and AP.
@Brant
"Do a little theorycrafting before you start blathering on about agility and AP."
You can't be serious. If all that math done up there isn't theorycrafting then what exactly is? I assume a spreadsheet was cooked up during the process as well.
There's also the fact that this post is from APRIL. Things have obviously changed since then (including the amount of ArP ppl can find on gears these days), and will again with the upcoming nerf.
They should alleviate that kind of confusion by labeling these patch/time sensitive posts.