[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.

[Druid] Some sample values of threat per 100 itemization points

UPDATE: I did more math later on, and it looks like armor penetration is much better. I've changed the tables and the conclusions below. The link to that is here.

A lot of folks have been asking about how to have awesome threat, and that their threat is kinda going through the tubes, and what they can do to help it.

Well...here's the bad news. Threat for bears scales very poorly. That early threat bears get is primarily because of frontloaded awesome threat from maul, lacerate and FFF. As we scale with gear...we will not see as high of gains, especially compared to some other classes who don't have these things.

At the same time, there are things you can do. And if you don't read anything else into it, note this: the best threat stats to stack are expertise (until the dodge cap), then hit, then expertise (until the parry cap), then armor pen.

I did a very basic sim to show this. The basic stats starting out are as follows:
10k AP
40% crit
60% armor on the target
0 haste, hit, or expertise to start (other than the 10 expertise skill we get from Primal Precision)

With this value and a rotation of mangle/lacerate/swipe/FFF (a very boring one), we have a threat value of 4473.88 TPS. Yes, this isn't an optimal rotation, and it's assuming no MSS or improved mangle as well.

Here's how adding 100 of any given rating (except AP, since that's 2 AP points for every one rating point) increases that base TPS:
100 expertise (below cap): 296.26
100 hit: +164.32 TPS
100 expertise (after cap): 147.3
100 armor pen: 98.396

100 haste: 68.12
200 AP: 57.5
100 crit: 52.12

Hit and expertise are insanely good here. But what about more realistic numbers? Let's say you're 100 points from the cap on hit and parry-expertise - how do the values fall in then? This means you have 163 hit and 279 expertise rating; in this case, your base TPS is 5418.8.

100 hit: +162.5 TPS
100 expertise (after cap): 147.5
100 armor pen: 98.396

100 haste: 84.5
200 AP: 67.5
100 crit: 63.5

Even here, expertise and hit are far, far better as threat stats. Up until the cap, of course. Then you're hosed.

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. (UPDATED: complexity over here.) And as it turns out, bears are going to likely have a decent amount of armor pen given the leather in T10 - close to 500 with good gear without trying. But really - the most important thing here is that hit and expertise are the only stats that scale with the threat multiplier on bear attacks. That's the key; AP, crit, armor pen, agility - all do not scale.

Haste is an exception, in that it scales with the amount of mauls and thus kind of scales with that threat multiplier. But only barely. Otherwise no dice. And because it doesn't scale with as many attacks as armor pen, you're out of luck.

So if you're having threat problems? Make sure your expertise is above 26 expertise skill. Make sure your hit is reasonable. Then go for more hit and expertise and have fun.

[Druid]My specific goal on armor pen

Really, I think everything should be about armor pen. It's just so fun to talk about. Poorly understood non-linear scaling stats with odd mechanics that are hard to model?

SIGN ME UP.

In the ongoing saga, you should definitely read Runy's take on armor pen, which has loads of good numbers, good suggestions for gearing, and awesome cartoons. As well as showing what you can do if you're going through ToC and have a dream list of awesomesauce.

But here's a more concrete setup: my current gear listing. In case armory isn't working well or isn't current, here's a chardev link too.

And the Rawr report:

Head Conqueror's Nightsong Headguard
Neck Collar of Unending Torment
Shoulders Duskstalker Pauldrons
Chest Vest of Shifting Shadows
Waist Relic Hunter's Cord
Legs Legwraps of the Broken Beast
Feet Runed Ironhide Boots
Wrist Armbands of the Wary Lookout
Hands Sunreaver Assassin's Gloves
Finger1 Dexterous Brightstone Ring
Finger2 Planestalker Band
Trinket1 Darkmoon Card: Greatness
Trinket2 Banner of Victory
Back Shawl of the Shattered Giant
MainHand Anguish
Ranged Idol of Mutilation

And buffed stats:
Attack Power: 11276
Agility: 2333
Strength: 380
Crit Rating: 459
Hit Rating: 241
Expertise Rating: 56
Haste Rating: 202
Armor Penetration Rating: 999
Crit Chance: 58.67081%

Note that unlike Runy's OMG loot list, this isn't close to being optimal. I have a few ToC 10 normal mode pieces (including the weapon), no T9 gear at all, a couple pieces from Ulduar (boots, head, belt), two fairly meh trinkets (and no Runestone), and a really crappy cloak and bracers (at least relatively).

ETA: In case you were specifically curious, the breakdown of that armor pen is as follows:
Gear (including socket bonuses) 677
Food 40
Gems 282

That's just what's dropped for me. I haven't gone out of my way to grab nothing but armor pen gear. I picked up the shoulders because I haven't had a trophy piece yet (and would replace the head first, anyway). I have gotten very lucky on drops in ToC hard 10 man, being the only leather wearer and having almost exactly what I wanted drop.

But still, the important thing: it's gear that you can reasonably expect to obtain in the next month or so. No 258 pieces, no hard mode loot from Ulduar. Only 10-man hard mode gear. No trophy gear either. Hardest pieces come from heroic 10-man, which should be challenging but not insane.

Ironically, the upgrades I do want are going to drop my armor pen a bit. My next piece is going to hopefully be the T9.245 helm simply because with this level of armor pen missing a lot starts to hurt a lot more, and it has loads of expertise. A cloak upgrade would be stellar, but that's more luck than anything else; we're going for the Insanity 10-man tribute this week, so perhaps Cloak of Serrated Blades will drop. And who knows, maybe some day I'll actually get a wrist improvement, though most of them will drop my arpen too. The important thing here is that I'm fine with it dropping; it's not essential that it stays high compared to other stats. And while armor pen is scary good at this level (even after nerf), it's not so good that it will make up for 20 levels of itemization.

One thing that would significantly change my gearing strategy is getting a runestone. Even post-nerf I'm well over the armor pen cap with a runestone, so I'd be going for more agility. But I'm not betting on getting that either, and I'm not going to kill myself if I don't get it.

Anyway, point of all this was to toot my own kitty horn and to also show you that yes, you can get significantly high amounts of armor pen without having stupid gear.

[Druid]Continuing the conversation about arpen

Last week I talked a bit about armor pen mechanics and why it's good (or not), and was helped immensely by Jacemora, Vallen and Alaron. The conversation continued quite a bit, and specifically Alaron put up another great piece on it, using high-geared ferals and calculating their graphs with respect to armor pen and how it improves them - and changed his conclusions to boot.

And like him, I'd like to reiterate something - something that Runy stated recently too: please use brain.

Everyone's gear, playstyle and needs are going to be different. Yes, armor pen is projected by a number of theorycrafters and simulations to be the best stat to stack when you get 'enough', where 'enough' is a wide-ranging number. And yes, I've given a rule of thumb for when you should make the switch. But whether that's best or not for you really depends on...you. There are so many variables that you can't reasonably answer it all, but here are some common ones:

• 10 vs 25? If you're not getting a ton of raid buffs regularly or do smaller raids, chances are armor pen isn't going to be as solid due to not having as much base AP.
• Bear or cat? Armor pen is a good threat stat for bears, but it doesn't hold a candle to agility for overall usefulness. If you're going bear a lot and have a lot of shared gear, don't use arpen in it!
• Hit/expertise? Armor pen tends to do better as you're closer to the hit/exp cap, mostly because it benefits from less spiky behavior - and misses contribute to local spikes.
• Crit rate? If you've got a low crit rate, the chances of getting bad cycles are going to be much higher (where you're missing uptime on rips, etc). If you're not at at least 50% crit rate I'd recommend not bothering with arpen no matter what you can get it to.
• Types of fights? Fights where you can do more burst damage tend to favor agility; if you need to pile in a lot of damage quickly, agility often wins out by sheer luck. Fights with more sustained DPS are wins for arpen. ToC has both at various times; it very much depends on your role.

But the most important one is this: What are you comfortable with? If you like having more CPs and not worrying about things as much, agility is better. If you want smoother cycles, make sure hit/exp are capped. If you want more consistent damage but less spiky good damage, go with arpen. None of these are bad answers, and all will work well. No matter what theory says none of these are so different from each other that you should be mocked for your choice, and the sole arbiter of whether or not you're doing better with it is you.

Honestly, I think Jacemora's going to be disappointed because he simply likes how agility feels better compared to armor pen. It has nothing to do with whether or not arpen theorycrafts better than agility and everything to do with that personal feeling.

That personal feeling is not something you can theorycraft. It's up to you to figure it out.

In any case, both agility and armor pen are very, very good. What I would really recommend is that if you are on the fence, pick one or the other. Don't waffle and hybridize. High crit rates make some really interesting cycles possible; high arpen make some amazing damage possible. A mix of the two makes nothing special.

[Druid] MOAR ARMOR PEN

In case you haven't gotten tired of the various links from Vallen and Jacemora recently, I bring you Alaron of Fluid Druid - and his absolutely excellent, easy to read and understand FAQ on armor pen. It's the best post I've seen on the whole thing so far, and has some really great graphs illustrating how armor pen increases in value as you get more.

Seriously, it puts a lot of the debate to rest and makes it very simple. For now, the rules are easy: if you can get above 600 armor pen, it's the best stat. Otherwise agility is. In 3.2.2, this changes to about 850 armor pen.