UPDATE: Due to recent Armor Penetration changes, some formulas in this post are no longer correct. For the latest information on Armor Penetration, please visit my new post located here.
Welcome back everyone. I hope all those who had nice, long holiday weekends were safe and enjoyed themselves in whatever they did. Let’s dive right into some math for all you junkies out there!
One of the most popular posts I had on the site, behind the Dummies Guide to Shot Rotations and the list of Shot Rotation Macros, was the Armor Penetration post. And given we are in a new raiding ballgame, I felt it is worth covering again to help determine if Armor Penetration is still such an awesome stat to stack.
Of course Elitist Jerks has been on top of digging up some specific numbers for us, and Lactose, the helpful co-creator of the original Cheeky’s Spreadsheet, informs us that Maexxna has 13083 armor, which is the same in both the 10 man and 25 man versions. Elitist Jerks is reporting that all bosses in 10 and 25 man versions have the same armor value as Maexxna. While they are still collecting data, their initial testing is indicating that this is true. One comment made a great point about all these bosses having the same armor value.
For a casters, nothing is dumber than tossing some random resistance on a boss. It’s “respec or sit”.
Same for melee and armour. Imagine DPS was finally balanced, and then you add another new boss.
If it’s armour is lower than normal, you stack melee. If it’s higher, you stack casters.
So our magic number is 13083. What this also does is give Armor Penetration in PvE a universal value. Regardless of the boss you know it will have the same effect. In BC, on fights such as Teron Gorefiend who had lower armor than other bosses, sometimes it was more beneficial to swap out ArP for other stats. Well given the new Armor Penetration Rating and universal armor values this is no longer the case.
So the first thing we need to figure out is how much damage reduction a raid boss is getting from 13083 armor. When I made the previous thread we had some numbers already laid out for us, including formulas to determine damage reduction. Well the formulas are still technically the same. We just need to fill in some blanks. Previousl the formula for damage reduction calculations was [%Reduction for 70 = (Armor / (Armor + 10557.3)) * 100]. However the number of 10557.3 is no longer correct. But the formula used to derive that number should still be true (We hope). That formula looks like this: %Reduction = (Armor / ([467.5 * Enemy_Level] + Armor – 22167.5)) * 100
Putting this formulate into Excel and replacing Enemy_Level with 80 and Armor with 13083, we see this:
46.20438= (13083/((467.5 * 80) + 13083 – 22167.5)) * 100
So if all these numbers and formulas are still accurate, we see that raid bosses have a 46.2% damage reduction from physical attacks. We can double check this formula again to make sure it is accurate by comparing it to know damage reduction values. As I did in the previous post, let’s use my armor value and adjust the numbers. We leave Enemy_level at 80 (since the Armory calculates my damage reduction off of same level attackers) and replace 13083 with 8489, which is my current armor. That formula now looks like this:
35.7861 = (8489 / ((467.5 * 80) + 8489 – 22167.5)) * 100
And to confirm that, we can use the Armory tooltip to show that I do indeed have a 35.79% damage reduction. So we know that the formula is at least still accurate. Now that we have verified our numbers we can try to determine how effective Armor Penetration is going to be. Let’s simply our formula first for easier number testing before we move on though. We know that the 467.5*80 isn’t changing, so we can make that a static number, which is 37400. The formula is now:
46.20438= (13083/(37400 + 13083 – 22167.5)) * 100
And since we all know our order of operations and that the addition and subtraction order doesn’t matter, we can simply even further by subtracting 37400-22167.5 so the formula looks like this:
46.20438 = (13083/(15232.6 + 13083)) * 100
We know have a formula similar to what we had in BC. Looking back at some old links, this calculator for damage reduction is still accurate as well, by putting in level 80 and 13083 it returns a 46.204% damage reduction. Hooray for correct numbers!
The Armory still isn’t displaying Armor Penetration values yet, so we will have to do some manual addition, but given the numbers we crunched already this will be easy enough. I only have 94 Armor Penetration Rating at the moment, with 35 coming from my Emblem belt and 59 coming from the crafted leggings. We know from the Combat Ratings post that 15.39 Armor Penetration rating is equal to 1% armor reduction (which is a number also supported by the smart folks at Elitist Jerks). So [94/15.39] = 6.1% armor reduction. How much of a DPS increase is that?
If a boss is reducing our physical damage by 46.2% we can obviously assume we are doing 53.8% of our possible DPS. Pretty simple. But we can use that number to figure out our damage increase through Armor Penetration. With my 6.1% armor reduction, we can calculate that it is equal to 798.06 armor ignored, essentially lowering the boss armor value to 12284.937. Let’s recalculate the damage reduction now.
44.64403 = (12284.937 / (15232.6 + 12284.937)) * 100
So with the boss only reducing our damage by 44.64%, we can now figure we are doing 55.35% of our total possible DPS. To figure our DPS gain, we calculate it like this:
55.35/53.8 = 1.0288
So with 94 Armor Penetration Rating, our damage is increased by 2.88%. The two items I chose specifically for their Armor Penetration are providing me with a 2.88% damage increase. So take this into consideration, Piercing Shots, with 3 points increases our armor penetration by 6%. Without any other Armor Penetration we could figure that this talent would only provide us with about the same damage increase since that is just about what my 94 ArP is providing. Which in hindsight seems to be not as strong as similar DPS increasing talents, especially when you can get that from a points in Focused Fired, Improved Tracking, or Ranged Weapon Specialization for example.
But we do have to be fair to Armor Penetration here and remember that we are not the only method of armor ignore on a boss. We can still consider Sunder Armor and other similar buffs/debuffs. A 5-stack of Sunder Armor will reduce a boss’ armor by 3925. Let’s figure out how much damage reduction a boss mob has with only Sunder Armor and then determine how effective that 94 Armor Penetration Rating is. 13083 – 3925 is 9158 so our formula looks like this:
37.547 = (9158/(15232.6 + 9158)) * 100
This means we are doing 62.453% of our total possible DPS before we calculate our personal Armor Penetration. That 6.1% Armor Reduction is now ignoring 558.638 armor, as opposed to the original 798. So while it’s ignoring less armor, what does it do for out DPS? The boss now has 8599.362 Armor. So our formula is now this:
36.08 = (8599.362/(15232.6 + 8599.362)) * 100
Which means we are now doing 63.92% of our total possible DPS. Using the same calculations from above, we can calculate our DPS gain like this:
63.92/62.453 = 1.02348
So by adding in Sunder Armor, our 6.1% Armor Penetration only adds 2.35% damage increase on top of that. Essentially Sunder Armor made our Armor Penetration even less effective, by about half a percent. It’s important to remember that the Warrior is actually reducing the boss armor, so when you fire each shot your armor penetration is calculating it’s value based off the boss’ current armor value, which in this case was 9158. If you were running without a Warrior or they let Sunder Armor fall off the boss, your shots would then calculate based off the original value, or however many Sunders were applied.
So in the end, the real question is going to be what stats do you give up in order to grab that Armor Penetration? The switch to the combat rating system has definitely weakened armor penetration by making it percentage based rather than a flat number. While in Burning Crusade 500 Armor Penetration was always ignoring 500 armor, my 94 ArP rating is not always ignoring the same amount of armor. It definitely shows that Piercing Shots seems to be not worth its points when it is so easy to pick up other talents that increase DPS by flat amounts for fewer points.
I have to admit that sitting down and looking at these numbers has opened my eyes on rethinking the value of armor penetration. The question that is in my head right now is how much haste rating is required to provide a similar DPS increase? We see haste everywhere so has it become a better stat to stack? Or given the choice between armor penetration or haste, which one is more valuable?
So let me mention some non-post related stuff real quick. We are 12 days away from Less QQ, More Pewpew 1 year anniversary! Holy cow! It’s been quite a journey but I will save my musings for that day rather than now. But you can expect another contest with some more in-game give-aways! So keep reading.
Thoughts, comments, mathematical corrections, or need clarification where I might not have been clear, etc etc, leave a comment! And thanks for all your continued reading!
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!
Hey Dro, on the Haste to ArPen conversion, i think that we will see that haste beats ArPen into the ground until you Cap your GCD, after that Haste "Should" take a 40-60% nose dive in effectiveness due to Steady shot no longer being effected. But i have been seeing a few weird things on WWS, something along the lines of Quick Shots allowing you to fire faster than the GCD. Something worth Investigating.
That's what I kind of thought. It's effectiveness should see greatly diminished effects at that point. Anyone know of a mod that will just tell you what your GCD is at? Not a cast bar, but just something that says "Hey, you're at 1.3 seconds" or something? :)
Good post, but there's one thing that's bugging me. When you determine the increase in damage by the percent amount, I think you're confusing the numbers a little.
Take this: 63.92/62.453 = 1.02348, for example.
You state this reveals an increase of 1.02%. However, I would interpret it to reveal an increase of 2.348%.
Imagine if you had a crap ton of armor pen and the first number jumped to say: 85. By your formula, that would be 85/62.453 = 1.36, or a 1.36% increase. Clearly, it's more than a 1.36% increase, in fact a 36% increase, where the difference 85-62.453 = 22.5 is the same as 36% of 62.453 (62.453 * 0.36 = 22.5).
What this appears to mean is that you're rating armor pen lower than you ought to be.
As my main is a Rogue, I thought it might also be useful to mention that by changing the way armor penetration works from a flat value to a percentage (although some things like Sunder Armor and Serrated Blades still use flat values, which makes determining the true value of Armor Pen a little tricky) the effective value of Armor Penetration for Rogues has tanked, less then half what it used to be.
It seems a lot of people feel that way too. Even for Hunters. A lot of the folks over at EJ really don't like the Piercing Shots talent and aren't exactly going out of their way to stack ArP anymore.
Since any BM Hunter with 5/5 Serpent's Swiftness is already soft-capped on their haste, haste is less valuable. Now that haste is less valuable it's also contending for the bottom of the barrel stat with ArP.
Which one is worth more dps, and to what extent is what I'm curious to know.
I know what you mean. I am not sure how to calculate the overall affect of haste but I am looking into it.
I'm happy with the changes in regards to PvP, but the fact of the matter is it holds the same weight and rules in PvE, your going to need more to make it worthwhile. That being said, with current gear, it's pretty crappy stat, and I can see it being better in the latter tiers of raiding again.
Just like it was for Kara versus BT, granted ArP was harder to come by then, but the stats now don't appear to bountiful either. It's being looked down upon at the moment, but I can see it coming back in the future, it still exponentially increases in value, despite the way it's being calculated.
Little redundant, but meh. If the amount of haste keeps rising on raiding gear. I would expect MM to pull ahead of BM, right now they tend to do similar digits from personal experience, obviously some fights better than others (Melee get out of the whirlwind! Okay come back in… NO WAIT! GET OUT! >.<). But with MM being haste capped, larger mana pool and more efficient attacks, with a crit rate that rivals SV at entry raiding levels, I can see it being a beast. It'll just require the gear to back it up.
Only thing I can think of for your addon dilemma as well is that Quartz will show the total cast time, though it -is- a cast bar mod. That or manually calculating it:
You need 1.333… total haste to reach GCD capped, as far as I know, haste effects are multiplicative, while haste rating is cumulative. Thus as BM with Serpents Swiftness, you only need 11% haste excluding quiver, with a 15% quiver your at 38% haste. 2 / 1.38 = 1.449275… cast time on steady shot. Throw in a small 6% haste from haste rating and you should be at 1.36724… cast time with 46.28% total haste.
Unfortunately doing it by hand is the best I know, while it's common sense to some, just some examples for others. That and a personal hope for confirmation to the theories being right. >.>
My 2 copper.
The whirlwind thing is so true. :) I did heroic Vault last night and beat the next closest DPS by 900, but the confident Warrior blamed it on moving out of clouds and spikes. :)
I agree though, it might just be best to hand calculate all of this anyways. :)
You are correct. I skipped a step in my calculations. Editing now. I did it right in the original post thanks to some clarification from readers but somehow missed it here.
Should be fixed now. Thanks for pointing that out. I was afraid I would do that with some of the math. :)
The level 80 number is the level of the attacker, not the defender.
I just did a quick extrapolation based on your formulas by doubling your 94 ArP to 188, which resulted a dps increase from 2.88% to 5.94%, or 2.35% to 4.80% with sunder armor. This goes to show that ArP is still the only stat that gives an increasing return. A quick look through maxdps.com shows that the max ArP a hunter can stack from available gear in game is 481 (leather gear included, no trinkets and gems), or 31.3% ignore armor, and 16.91% increase in dps.
For a rough and simplified comparison among combat ratings:
At 15.39 ratings for every 1% ArP, the first %point in dps gain costs about 35 ratings and the cost decreases as you stack more (28 ratings if you're already at 500) .
At 32.79 ratings for every 1% haste, the first %point in dps gain costs about 65 ratings. This results from a very rough estimate based on the assumptions that, a) as bm, I am shooting steady shot on every gcd, so haste only affects my white dmg (and pet orange dmg), which at the moment makes up for 50% of my total dps and b) haste does not affect the gcd, and I did a quick Google search to find no proof that it does. The cost for dps gain also decreases as you stack more, because white dmg would constitute a increasing proportion of your total dps.
At 45.91ratings for every 1% crit, the first %point in dps gain costs about 46 ratings and the cost remains constant until cap.
At 32.77 ratings for every !% hit, the first %point in dps gain costs about 32 ratings (starting with no hit and 9% miss chance against boss) and the cost increases (very) slightly until cap.
As a jewelcrafter I want to know how I can maximize my dps for each gem slot. With gems giving equal amounts of ratings of all types, it seems that once hitcapped, ArP is the way to go.
This is my very first attempt at theorycrafting and I know my numbers are not precise. Any criticism is appreciated.
As a side note on hit cap, I noticed that Focused Aim does not affect the hit chance of my pet. With the pet outdpsing me on certain boss fights, should I spend those points somewhere else and just go for the hard hit cap?
That is actually very interesting. What might be interesting to do, if someone hasn't done is extrapolate all the way down to 0 armor on a boss. Because unless mitigation has changed the way it functions, the damage reduction provided through armor is on a curve, with it rising quickly and then tapering off once you reach the 75% mitigation cap. However since bosses only have 13083 armor, they are far away from what the mitigation cap so it might be more difficult to see the effects of this curve.
The problem I foresee is that our armor penetration is based off the boss' current armor level. So if for some reason a boss was reduced to 100 Armor through other sources, as our shots are calculated with, let's say 30% armor ignore, it would only ignore 30 armor, this providing a much smaller benefit than if it was being calculated off of 13000 armor or so. And I think that's the reason people have found Armor Penetration to have taken a hit in its effectiveness. The less armor the boss has, the less armor your ArP is actually ignoring.
At least this is my understanding.
I actually read about that last night as well. I think if you are easily able to reach the hit cap without Focused Aim or with reduced points, so be it. You can then spend those points in other DPS talents. But if you have to stretch to reach the cap and end up giving up other large amounts of other DPS stats, it would still be beneficial to spec into Focused Aim.
Shouldn't the bosses be lvl 83 for their calculations? (not 80?)
I have Focused Aim right now. I was going to keep it, and when I gear up, I can put more gems into DPS increase instead of hit. Then, if my gear takes me up to the hard hit cap, I could respec.
Which works too. I think one of the biggest factors in +hit from gear rather than talents, at the moment at least, is that Focused Aim doesn't count towards your pet's chance to hit which is kind of a bummer.
This post is old and not so accurate so i will try to clear some things:
with the lately updates :
1% enemy armor reduced = 12.31 armor penetration rating and not 15.39 which means more % reduction of the target’s armor.
secondly i don’t get why we put into the game the level of the target or even my level…
We know or we assume that all bosses got 13038 so if someone got 500 armor penetration rating for example the reduction would be :
%armor reduction=(500/12.39)
%armor reduction= 40.35
Which means that if my target has 13038 armor i will “see” him like he has 7778
( armor of my target after reduction= (13038×0.4035) -13038 ) )
Armor of my target after reduction = 7778
Now to see how much damage we get increase at physical attacks:
If the target has 13038 armor the damage reduction of physical attack would be
51.98% meaning we will be doing a damage of 48.02% of our base damage.
E.g : let’s say we have standard 1400 damage at our character sheet, the boss will take 674.8 WHITE damage.
But after reduction the boss has 7778 as we said meaning the armor reduction of physical attacks would be 31% allowing us doing 69% of our damage
e.g: let’s say we have 1400 standard damage at our sheet, the boss will take
966 WHITE damage.
And all those without the reduction debuffs on the target such us Faerie Fire (5% armor reduction), Curse of Weakness(5% armor reduction) and -3925 armor from sunder armor.
let’s see again with the reducing armor effects, we got a 10% armor reduciton from 2 spells:
Armor of the boss before the debuffs: 13038
armor of the boss reduced by 10%: 11734
armor reduced by 10% and 3925: 7809
So we got a target of 7809 armor to apply our 500 armor penetration rating, meaning:
That if my target has 7809 armor i will “see” him like he has 4659
( armor of my target after reduction= (7809×0.4035) -7809 ) )
Armor of my target after reduction (including sunder armor, faerie fire and curse of weakness)= 4659
Now to see how much damage we get increase at physical attacks:
If the target has 4659 armor the damage reduction of physical attack would be
24.18% meaning we will be doing a damage of 71.82% of our base damage.
E.g : let’s say we have standard 1400 damage at our character sheet, the boss will take 1005 WHITE damage.
This is it… simple as that. hope this will help some ppl.
@Alandriel Thanks for the comment. Indeed the information here is outdated. I plan on writing a new ArP post in the near future. Great comment by the way. Nice to see people posting such detailed responses.