A little while ago Ghostcrawler gave us something you don’t usually see coming from the game developers. The exact formula for calculating Armor Penetration. And with it, some new light shed on exactly how armor penetration works for us. So the point of this post is to break down that formula so we have a better understanding of what we are looking at, and see if Armor Penetration is any better for us.
The first thing Ghostcrawler talks about is a variable we are going to call “Armor Constant” which will be represented by the letter ‘C.’ We are only going to worry about the effectiveness of Armor Penetration on a raid boss so we are going to calculate everything assuming our target is level 83.
C = 400+85*targetlevel+4.5*85*(targetlevel-59)
So the actual formula with our values inserted looks like this:
C = 400 + 85 * 83 + 4.5 * 85 * (83 -59)
That calculates out to be 16635.
Ghostcrawler also told us that we will never get 100% of our Armor Penetration and that the formula for figuring out exactly how much of our Armor Penetration is being used is:
(Armor + C)/3
We know that all raid bosses as this point in time are believed to have 13083 armor. We haven’t seen anything to the contrary yet so that is the number we use. So assuming we have no other armor debuffs at the moment we calculate our cap for Armor Penetration like so:
(13083 + 16635)/3 = 9906
The game now runs a check to see which value is uses for Armor Penetration. It will either use the boss armor value or use the number we just calculated as our cap for Armor Penetration (9906). It will use the lowest value, therefore we are going to further our calculations using the 9906 number.
Currently I have 12.42% Armor Penetration in my gear. So the next step is to take my current Armor Penetration and multiply it by our lowest value that we determined above. In this case it as follows:
9906 * 12.42% = 1230.32
So we take that number, which is now the actual armor amount that our Armor Penetration is allowing us to ignore and subtract it from the bosses armor value.
13083 – 1230.32 = 11852.68
So by taking that number and dividing it by the original armor value:
11852.68/13083 = .9059
We now see that I only actually was able to get 9.5% Armor Penetration as opposed to the 12.42% that my tooltip indicates I *might* be able to reduce.
So the last calculation we want to do is using the modified armor value from a boss after Sunder Armor and Faerie Fire are applied. Faerie Fire reduces a target’s armor by 5% and 5 stacks of Sunder Armor reduce the target’s armor by 20%, bringing it to a total of 25% reduction which gives us a number of 9812.5 before we calculate our own personal armor penetration.
Our Armor Constant variable still hasn’t changed and remains being C = 16635. But our boss armor value is now dropped to 9812.25 after reducing it by 25%. So now we can re-run the calculations we just did. First we calculate our Armor Penetration cap:
(Armor + C)/3 = (9812.25 + 16635)/3 = 8815.75
The game will once again choose between our armor penetration cap (8815.75) or the actual armor value (9812.25). So at this point our calculated cap is still lower, so we will take that and multiply it by my current personal armor penetration:
8815.75 * 12.42% = 1094.91
We now take our boss armor value (after Sunder Armor and Faerie Fire) and and subtract how much armor we are ignoring to see it’s effectiveness.
9812.5 – 1094.91 = 8717.59
So if we divide 8717.59/9812.5 we see we get a value of 88.84%. That means we got pretty close to using all of by armor penetration since I was able to personally reduce the boss armor by 11.16%, while my maximum is 12.42%.
The trick now is to determine how much Armor Penetration is effective and if it is a worthwhile stat for us to be using. So the first thing is to calculate how much damage the boss is reducing with it’s armor, it’s post-Sunder/Faerie armor, and finally it’s armor after applying our personal Armor Penetration.
The first thing we want to do is verify that the formulas we use to calculate damage reduction is still accurate. The formula on Wowwiki states this is the formula for damage reduction:
%Reduction = (Armor / ([467.5 * Enemy_Level] + Armor – 22167.5)) * 100
Putting in my own personal values shows this to be correct:
41.02 =(10595 / ((467.5 * 80) + 10595 – 22167.5)) * 100
This matches up perfectly with the damage reduction number on my character sheet. So now we can calculate the boss damage reduction with our 9812.5 number (which is the post-Sunder/FF value)
39.17% = (9812.5 / ((467.5 * 80) + 9812.5 – 22167.5)) * 100
So now let’s do that one more time and see what the damage reduction is with my personal armor penetration:
36.39% = (8717.59 / ((467.5 * 80) + 8717.59 – 22167.5)) * 100
So with my personal armor penetration of only 12.42% (but only getting 11.16% of it) I would see a 2.78% increase in my physical DPS. At face value that seems like a decent return considering I have so little armor penetration.
But of all 3 Hunter specs, only one of them is reliant on physical DPS, and that happens to be Beast Mastery. As Survival, Explosive Shot is still comprising >40% of my total DPS, and Black Arrow and Serpent Sting bringing in a combined 12-14% of my total DPS and a *huge* portion is coming from magic damage.
Also take into consideration that Armor Penetration is not transferred to your pet at all so it is a Hunter-only stat.
But that being said, with the 25% boost to the effectiveness of armor penetration, a BM Hunter should heavily consider Armor Penetration with such a large portion of total damage coming from Auto Shot, Steady Shot and Aimed Shot if you chose to spec into that.
Hopefully this has helped shed some light on the beast that is armor penetration calculations. I checked my math and I am pretty confident that my numbers are accurate and formulas are up-to-date, but by all means if you see any glaring errors, please either leave me a comment or post in the forums about any corrections that need to be made.
I know the site is loading a tad slower right now with the new template. I am still working on implementing some mf my existing CSS styles, compressing certain files and just working to help improve load times.
So yeah, questions, comments, etc. Post ‘em!
Drotara (or BehemothDan) considers himself a geek on many levels. A web developer and programmer by trade, he has no shortage of geeky hobbies. Whether it's trying to stay current in World of Warcraft raiding, playing competitively in the WoW TCG, Magic: The Gathering with friends, or a night at the local shop playing DnD, it's all good to him!
instead of looking at physical v magical DPS, you should look at DPS affected by ArPen against DPS not affected by ArPen. In this light, it's still not an attractive stat for any hunter, even BM, since my pet is doing ~50% of my total damage. If it's not good for Surv because it only affects ~50% total damage, then it's not good for BM either. It would be cool, though, if I could talent my pet to gain my armor penetration, or even better, if he just got it like armor et al.
That is a very good way of looking at it Monkey. I think it might be a safe assumption that having ArP affect our pets would be a huge DPS increase for any Hunter spec, especially for Beast Mastery.
Please bear with me while I try to resolve issues already cropping up with IntenseDebate. Sigh.
Drotara, I know that you must have been working on this already, but I’m especially happy that this is up so soon after I made a post asking if you had any more information on it.
I picked up “Rifle of the Platinum Guard” on a run last night so my ArP is just going up. I think that it’s time to play with Shandara’s spreadsheet and see if it’s an improvement, apart from the awesome looks.
This is a great artical, I love the theorycraft of wow.
Many thanks again
/Kord
OK ArP is not THE greatest stat even for BM hunters but then again it is much better than the haste on tier 7 gear. It’s not like your losing AP or Crit you’re just switching ArP for haste wich is a much bigger point for point DPS gain than even for Survival Hunters (not only because it affects Aimed/Multi as well as Auto and Steadyshot damage).
@Kahd That’s sort of my thoughts as well. I have been preferring ArP over haste.
You’ve made a couple of errors in your armor reduction formulas.
Original: 39.17% = (9812.5 / ((467.5 * 80) + 9812.5 – 22167.5)) * 100
Should Be: 37.20% = (9812.5 / ((467.5 * 83) + 9812.5 – 22167.5)) * 100
Original: 36.39% = (8717.59 / ((467.5 * 80) + 8717.59 – 22167.5)) * 100
Should Be: 34.39% = (8717.59 / ((467.5 * 83) + 8717.59 – 22167.5)) * 100
Your “Armor” values are coming from a boss level mob, so “Enemy_level” should be 83 instead of the 80 you have there. Doesn’t really change much (DPS is now +2.81% :/) , but it’s more for clarification
@siny Ahhh, good catch! I’ll fix that. [EDIT: After re-visiting that information, I believe I may have had it right the first time. As when calculating the reduction, using the level 80 in the formula signifies the level of the mob attacking you, not what level you are, and in the case of the boss we are assuming it's point of view. In the first example where I check my own damage reduction we use 80 because our character sheet tooltip specifically states damage reduction against a level 80 attacker.]
Nice post i must say really cleared a few things up for me. lately i changed my mainspec from survival to Marksman just to see if there was any differens in the dps and damage done. now what i found out was that the dps and dmg done is almost idendical if you play the MM spec properly. which leads me towards the conclussions. Looking at the damage meters from entire ulduar raids i found that my autoshot is nr 1 and then chimera, aimed and arcane on the following positions. with this true im actually going to try to switch out my gems and go full out arP to see if my autoshots ect will be higher, as a result of all your mathwork it seems as if it should.
thank you for your work
Do all of these stats work for arms warriors as well?
and do the formulas only apply to armor pen rating from armor? do you apply the armor pen formula to from mace spec(15%) and battle stance(10%)or do you just take them off the total armor like sunder and FF.
The formulas are accurate for other classes as well. To the best of my knowledge the Mace Spec and Battle Stance bonus is treated like having ArP on your gear but I would need to double check that before I said it with 100% certainty.
Thank you. <3
Does explosive shot, serp sting and black arrow ignore a mobs armor? I am not sure how much armor penetration really affects these abilities.
Abilities that do specific magic damage such as Chimera Shot, Explosive Shot, etc ignore armor completely. Abilities like Multi-Shot, Aimed Shot, and Auto Shot are affected by armor.
Chimera shot is physical damage. The sting portion of it is not. And yes I have been raiding MM since 3.1 and autoshot is still #1 dmg ability, followed by chimera/aimed/arcane and then steady. All those shots other than arcane and serpent sting are affected by armor. I’ve definitely noticed the difference with the increase in armor pen from my new Ulduar gear, have been closing in on the warlocks/rogues on meters and pushing over 6k dps on some fights.
Chimera shot is physical damage. The sting portion of it is not.
Unless it’s been changed super recently, all aspects of Chimera Shot deal nature damage, even the 125% weapon damage is considered nature. I tested this myself.
Drotara
I like the way you present ArP Real Value, nice and simple
1 Comment however, with regards to you concluding value of 2.78 dps increase from ArP, this value is actually higher. (I made the same mistake for a while, and was wandering why the ArP value was lower then what I was expecting)
In summary:
Let’s assume you have raw 1000 Physical Dps Output against a 0 Armor Target.
Without ArP or Sunder, taking into account the Boss Armor Reduction
the Dps you are doing to the boss is 1000 – 410.2 (41.02% Red.)=589.98
Now Including Sunder and Fairie Fire
the Dps you are doing to the boss is 1000 – 391.7 (39.17% Red.)=608.30
Your DPS actually is up by 608.30-589.98/589.98 = 3.11 % with Sunder
Now Include your ArP
the Dps you are doing to the boss is 1000 – 363.9 (36.39%% Red.)=636.10
Your DPS actualy is up by 636.10-608.30 /608.30= 4.57 % with your ArP
So the DPS increase from your ArP is 4.57 % and not 2.78
Making ArP a much more interesting Stat
Cheers Mathok
“We know that all raid bosses as this point in time are believed to have 13083 armor.”
That is not longer true. The raid bosses have now 10645 armor.
Since survival is battle with cooldowns and you can put Aimed Shot in talents… While all other shots are on cooldowns you need to spam few steady shots . So my point is to say that ArP is not that bad for Survival hunter neither
i was wondering if its worth getting ArP if you have
http://www.wowhead.com/?talent#jbxGoIIcofMrsoZhgLzZ0xG0z:GphMcV
which for those who don’t want to open the link the stats are:
102crit rating
chance on hit to increase ArP by 665 for 10 seconds
I am a surv hunter but planing on going mm soon
Well your link opened Death Knight talents, but I assume you were trying to link the Mjolnir Runestone? Even with the trinket, if you are going for a full ArP build, you will still need some more ArP on top of the trinket proc. You might be able to skip a few things.
Shmii put up a great list in our forums: http://qqpewpew.com/forums/viewtopic.php?f=11&t=37
oops sorry about that guess i didn’t press c hard enough when i went to copy the link to the runestone, but ty for answering my question.
heres the link i meant to put for those who want to see the trinket
http://www.wowhead.com/?item=45931
As of now Marksman is the best DPS spec with ArP and if u proc a trink such as runestone u spam Steady Shot u also have to regem ArP a little bit