Solving the mathmatical tangles of ArPen
by Mike Schramm 
May 18th 2009 at 3:00PM
Armor penetration is probably one of the most misunderstood stats in the game, for a number of reasons. First of all, it's only become popular lately -- while it's been in the game since 1.10, it's only started showing up regularly on items in Wrath. And even then it's really only a meta-meta stat: the core abilities like Strength and Agility are easy to understand, the next level of abilities are things like hit rating and crit rating, and then armor penetration, you could argue, goes another level after that: it's a stat that affects a stat affected by a stat. It's for that reason, then, that Xanthan argues we need a more elegant solution.Armor penetration basically allows you to hit an opponent as if they're wearing less armor than they really are. That's not to hard to understand -- if you have a certain amount of armor penetration, then the opponent armor number in the equation that determines damage done is lower (edit: by a percentage, not a number) than it would usually be. But the confusion comes in when you see how armor penetration scales. It actually scales exponentially, not linearly -- if you have no ArP and you increase it by a little bit, you only get a little extra damage increase. But if you have a lot, and you add a little more onto that, then you'll get a bigger damage increase, due to the way the math works (I'm bad at math, but Xanthan has an excellent, clear description of the calculations in the forum thread, and we've posted some explanations before as well). Blizzard recently capped ArP at 100% (so you could never get into a place where you're reducing armor below the amount of armor that's there), but it's still possible to have the amount of armor reduced equal the amount of armor on a target, causing the equation of armor vs. armor penetration to divide by 0, and at that point, things get wacky, and terms like "infinite damage" come into play.
So there are a few things Blizzard could do here. I was talking about ArP with Matthew Rossi the other day (he was trying to explain it to me for the Phat Loot Phriday post), and he brought up the idea of Blizzard removing it completely, and just replacing it with a damage boost (which is essentially what it does anyway). Xanthan's solution takes it one better: instead of reducing an opponent's armor (thus creating the issue of what happens when you reduce it up to the extreme limit), he suggests that armor penetration increases an attacker's ability to do damage through armor -- in essence, he says, making it akin to how Haste just "increase your attacks per second rather than reducing your seconds per attack." Very well put.
Odds are that Armor Penetration is in for a change eventually -- at the lowest levels, where it's been in the game for a while, the math is harmless, if a little loopy. But as the stat scales, Blizzard will be dealing with some strange issues, so it might be better to change (or even remove) it now.
Filed under: Items, Analysis / Opinion, Odds and ends, Blizzard, Buffs
Reader Comments (Page 1 of 2)
Gryph667 May 18th 2009 3:13PM
Our dps warriors have been drooling over their spreadsheets, seeing numbers for dps in the trillians. It's silly, really.
slimj091 May 18th 2009 3:17PM
the thing that i think some melee, and hunter's don't like about armor pen is that you can't visibly see how much it is increasing your dps.
with recount you can see how being hit capped increases your dps in numbers, same with expertise, and crit rating. in the character panel you can see how attack power and haste rating increase your dps. but with armor pen you just don't know if the amount you currently have is helping you more than what the same amount of haste, or crit rating would without heading over to EJ's and reading a 20 page long post that reads more like a physic's term paper.
Tickle May 18th 2009 3:21PM
Aren't you the same dumbass who recommended axes for ferals, 2handers and strength for shamans?
I really don't think you should post anymore.
CursedSeishi May 18th 2009 3:35PM
And aren't you the same dumbass who posted that strength is not an important stat for enhance shamans, or that druids should only be stuck to staffs and maces when some axes actually would do great for dps druids?
Yeah, I don't think YOU should post anymore.
slimj091 May 18th 2009 3:47PM
"or that druids should only be stuck to staffs and maces when some axes actually would do great for dps druids?"
great.. that's all i'd need is to add feral druids to the list of classes i have to roll against for my weapons. it's bad enough that i have to explain to my guild that down the road warrior dps will be somewhat good again. now i'd have to share my weapon's with furries? to hell with that.
Ahima May 18th 2009 3:49PM
While I agree that the OP was rude and demeaning in his post, it is not the case that strength is an important stat to Shaman any longer.
It changed when Wrath came out and now only gives 1 AP instead of 2 per point of Str.
Tickle May 18th 2009 4:07PM
Maybe I was a bit too harsh, but sickens me seeing people give out advice when they're clearly clueless.
@ CursedSeishi
Way to go, not only are you unaware of the fact strength is even less useful to enhancement shamans than intellect (1int=1AP, and minimal spellcrit on top), also that druids cannot use 2 handed axes.
So next time before you come act all high and mighty, get your facts straight to avoid humiliating yourself.
CursedSeishi May 18th 2009 4:15PM
True it gives less AP, but an enhance shaman still benefits from it through the 30% ap=sp talent. They only changed it in lich king because of the homoginization of armor, so to make what was normally hunter mail good to them, they nerfed strength and added the 100%int=ap talent to make up for it. I haven't played mine it a bit, but the way I see it it's still a good stat to have. It also scales with Kings. I haven't played my enhance shammy in a while, but last I remember he tore through things pretty easily.
And slim, I'm not sure if 2h axes can be used by druids, but I said some would be good, not all. Staffs and some maces still seem more statted towards a druid. I've only seen a druid use the Staff of Trickery, though a hunter or two have rolled on it before.
CursedSeishi May 18th 2009 4:17PM
I never said a druid can use an axe, I just said some would be good for them, L2R.
Farproc May 18th 2009 3:29PM
I do NOT understand ArPen on a number of levels.
1. Its loopy scaling mean that item budgeting is going to be screwed over for items with it.
2. It doesn't change your chance to proc, miss, parry etc. It just changes the damage. So, why the #$%^ didnt they just put AP in the item. Easier to budget with a nice constant effect.
3. It seems a rather unfair stat in pvp anyway - as it reduces armor, its going to have a bigger effect on targets that start on low armor anyway. ArPen - unless i misunderstand its math - is like an 'extra damage vs cloth' stat, and clothies already take enough damage thank you. what with having virtually no armor to start with.
Ohtar May 18th 2009 3:32PM
I believe it works by lowering a percentage of the targets armor so the reduction at least percent-wise is equal across the board.
Banthis May 18th 2009 3:40PM
Ohtar is correct, it reduces by a percentage, not a set amount, so it's not terribly better against cloth. In fact, someone who has stacked ArPen will see less benefit against cloth than against plate.
As to why they didn't just put it into AP instead, well, it functions very differently. ArPen only affects physical (white) damage. It doesn't do anything for magical effects or poison. This is why, as an SV hunter, it's an OK stat for me but that's it. It doesn't help my Explosive Shot, Black Arrow, or anything else like that. It only helps my Auto Shot.
This is why it can't simply be replaced with AP. AP would boost all of my damage, while ArPen only helps some of it. For classes that depend more on white damage, it's a bigger help. For those who don't care or never see white damage, it's useless. For hybrids it's not bad, but it's not great. Sure, a lot of ArPen would be great, but I'd have to stack it to the expense of things that would give me a bigger boost elsewhere.
It's a neat stat and a neat idea, but it's clunky right now and can lead to some strange situations due to the odd equations it uses. I think Blizzard will clean those up, though, and it'll eventually become another stat that we like but won't be at the top of our list to stack.
CursedSeishi May 18th 2009 3:41PM
Like Ohtar said, it reduces the target's armor by a percentage, not a flat number. So if it reduced it by 10% and you had two targets, one with 1k and one with 100k, that 1k would only lose 100 while the 100k loses 10k.
If I remember, it used to be a flat number, but Blizz changed it in TBC so people with a bit would be hitting clothies like they had none.
Otherwise... yeah, really hate ArPen, all the gear in lich king when you started was loaded with the crap and it annoyed the hell out of me. Still don't really get the math behind it, still don't like it.
slimj091 May 18th 2009 3:42PM
"ts going to have a bigger effect on targets that start on low armor anyway. "
not really. armor pen reduces armor by a percentage now. so say you have (and i'm basing this off of my crappy mage) 1900 armor, and the melee that has you targeted for a trip to the graveyard has 12% armor pen. it reduces your armor by 228. for plate with say (again basing this off my warrior) 14k armor it reduces it by 1680.
while clothies do have much less armor than plate wearer's. keep in mind that they were never intended to go toe to toe with a melee class in melee range. all in all it's fair because everyone regardless what kind of armor they wear gets affected by it equally.
do clothies get hit harder than plate wearer's with it? yes. but they would get hit harder without it also. such is the way of things when trying to protect yourself from harm with silk robes.
farproc May 18th 2009 3:57PM
Ok, its a % so its not so bat.
However, even if it just helps white damage - I still dont understand why we need another "boosts damage" stat.
As a druid, I can, and must, increase my damage by using, +Agility, +Strength, +Attack Power, +Expertise, +Hit Rating, +Crit Rating AND +Armor Pen? WTF! And im sure I've forgotten some other wierd stats.
When you count up all the defensive stats, you realize that WoW has a really crap combat system that seems like it was put together by two kids in a school yard coming up with awesomer and awesomer stats and counter stats.
Zeplar May 18th 2009 6:39PM
People are not remembering, yes it reduces more armor from a high-armor target than a low-armor target, BUT because armor scales inversely, it still affects them similarly.
The last 2000 armor on a 38000 armor tank might only account for 1% damage reduction (made-up number). 2000 armor on a 6000 armor clothie might account for 10% damage reduction.
So it reduces more armor from plate than cloth, but that armor is worth less. Which is why stacking LOTS of arP is what makes it good. Once you have reduced the plate wearer to 6000 armor, every additional point of ArP scales exponentially BECAUSE armor scales inversely.
Amun May 18th 2009 3:40PM
1/0
NO! YOU FOOL! YOU'VE DOOMED US ALL!
Aeryk May 18th 2009 3:46PM
Actually, the way I read it, since its percentage based, you would see more effect from it against targets with higher armor
Robert M May 18th 2009 5:42PM
I think you are partly right.
If a DK has 50% damage reduction from armor, and you have an ArP rating that reduces armor by 4%, then you would be hitting him like he has 48% damage reduction, but if a clothy has 20% reduction, and you have 4% ArP, then you would be hitting them like they have 19.2% reduction. You are taking a bigger chunk or armor away from the DK, but you also are hitting the clothy harder because they aren’t able to mitigate as much damage on the front end.
I think the point, from the article, is that at 4% it’s not that great a stat, but at high numbers where the more and more armor is ignored, ArP allows you to essentially shred through all types of armor because it is percentage based.
Again, I may be a total dumb ass, but that’s the way I have come to understand it on here and a few other sites.
My biggest concern about ArP, is that it’s really a physical stat. Clothies aren’t stacking ArP, but hunters and melee are. It seems like a stat that was intended to help melee fight melee, and somehow has gotten out of control when Blizz decided to make it a more prominent stat on Northrend gear.
Again, I apologize if I'm completely off here.
Arashikou May 18th 2009 6:25PM
It really depends on how you define "effect."