[Druid] The threat value of arpen

UPDATED: thanks to Ciopo I went and redid a bit of the math here; sunder and FF stack multiplicatively, the armor for a boss was reduced (from 13083 to 10643, per experimentation) and the math was redone. Turns out arpen is even better than I originally calculated. And thanks to Ramenchef at EJ, I've updated again.

In an earlier post I mentioned the value of threat for every 100 points of itemization for a bear...and kind of glossed over one specific value, that of armor penetration. Here's what I said about it back in the day:

Now, this definitely doesn't do a good job of modeling armor pen, and I didn't want to go into the insanity of that; it's quite complex. It does do a decent job of it given that in general, bears aren't going to have a ton of armor pen.

That's all true, but it doesn't really help a lot. The real trick though is that bears are going to be likely swimming in armor pen by the time they're geared out to the gills; every single tier piece has it, all the offtier pieces have it (at least from icecrown directly), and even some of the weapons have it.

So what's the actual value of arpen on threat? How good is it? The TL:DR version: Armor Penetration is the best threat stat for bears after hit and expertise.

First, we have to go back and revise some of our assumptions. We'll start with the boss base armor: that's 10643 (corrected from 13083), from experimental testing. That's kind of the assumed number. It might be off; anecdotally people have indicated that (as an example) the Mimiron tank and Vezax both had higher armor than this, but we'll go with that since its' the accepted value.

We'll assume sunder and faerie fire are both up on the target. Before anything else, these take off 24% of the armor since they multiply. (this doesn't stack the way you'd think with armor pen). So that's 10643 *.8*.95 = 8088.68.

Next we get into an odd thing, which is that armor pen can only affect some of the armor on the target. There's a lengthy explanation over at wowwiki about this from ghostcrawler and an even lengthier conversation from EJ about how he's slightly wrong, but the long and short of it is that the formula for determining the affectable armor by armor pen by a lvl 80 mob (it was thought to be towards a level 83 mob, but it's attacker level that matters) is:

(935/6)*80 + armor/3 - (44335/6)

Which ends up being the magical number of 7773.727 for a boss. That's the maximum armor that armor pen could remove, and the percentage that it goes against. So for example: if you had 700 armor pen, you would have 'removes up to 50% of armor'. The target's armor after sunder and faerie fire is 8088.68. You can remove half of the minimum of (8088,7773.727) which is 7773.727.

(7773.727*.5) = 3886.8635. This is the total armor that can be removed, leaving 4201.8165 left.

Now to figure out what that actually does, we go to the armor formula, which tells you the damage reduction by armor. That is:

(armor / (armor +(467.5*80 - 22167.5))) for a level 80 attacker and a level 83 mob.

For 4201.8165 armor, that ends up giving 21.6% damage reduction. Not bad, given that before this the armor reduction was almost 35%.

Okay, okay - enough about the math. Let's see what the threat values are. Again, this is a mangle/ff/lacerate/swipe rotation, assumes lacerates don't fall off, and doesn't take into account any T10 bonuses.

We'll start with the basic idea that you're expertise soft capped on dodge (132 expertise) and have 100 hit. You have 10k AP and a 40% crit rate. For a 3 mangle/3lacerate/3 swipe/3 FF rotation, your base TPS is 5131.187 with 0 armor pen. And here's how we scale with 100 armor pen:

armor pen	TPS	difference
0	5412
100	5517	105
200	5626	109
300	5741	115
400	5863	122
500	5992	129
600	6128	136
700	6272	144
800	6425	153
900	6588	163
1000	6762	174
1100	6948	186
1200	7146	198
1300	7360	214
1400	7586	226

Yep, that's right - at the highest level of arpen arpen gives 226 total threat per 100 points of it, which is huge! Before you look back at that prior article note that this is relative; at that same level of arpen expertise is worth 220 TPS per 100 rating, and hit is worth 240. All the stats go up in value as arpen improves. And this is with some fairly vanilla stats (no haste for instance); numbers will change some.

Still, even at lower levels it's worth a lot more than I had anticipated. It's certainly worth more than 100 haste or 200 AP, as an example.

Why is that? Well, part of it is simply that bears have big, meaty attacks that do a lot of damage. Maul and Mangle are good, and swipe is up there too. Only FF and the lacerate bleed don't benefit from it. Also, the benefit is fairly high on a per-point basis. I'm a bit more surprised that the static threat values from maul don't overwhelm this, but apparently not.

And part of it is the scaling nature itself.

Now, what level of arpen are we looking at? Just based on my prior list for 264 gear, you have something like this:

Frostbitten Fur Boots - 64 arpen

Sanctified Lasherweave Handgrips - 80 arpen

Sanctified Lasherweave Headguard - 92 arpen

Sanctified Lasherweave Legguards - 108 arpen

Sanctified Lasherweave Shoulderpads - 72 arpen

Ikfirus's Sack of Wonder - 0 arpen

Vengeful Noose - 80 arpen

Toskk's Maximized Wristguards - 60 arpen

For a total of 496 arpen! Yikes. At that level, here are the values of stats per 100 rating (assuming 100 hit and 132 expertise):

hit: 185 TPS

expertise: 168

arpen: 129

haste: 86

AP: 76

crit: 69

In this situation, arpen becomes the next best threat stat after hit and expertise, and it's almost competitive. At higher rates it does become competitive with expertise - but hopefully as a bear you're not quite at the point where you're trying to reach the hard cap of armor pen.

I'll go back and amend the previous values. I may end up changing the weighings for itemization, but I suspect it won't matter that much one way or another.

ETA: you can check my spreadsheet out over at google. It's a bit messy, but it does have the various numbers and formulae.