Wednesday, January 13, 2010

[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















































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:

Vengeful Noose - 80 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.


Anonymous said...

I was under the impression that we received the most threat benefit from first capping hit (263) then expertise (132).

Your assumption is 100 hit. Did I miss the reason why this was the baseline?

Hit is a commodity in ICC gear. I am planning a set around the cap, but if there is a reason we only need 100, I'd love to hear it.

Kalon said...

Anon - you do get the most benefit from hit and then expertise - though if you're below the expertise dodge cap, expertise is almost double the value of hit.

I chose 100 hit because as you say - it's a rare commodity in 264 gear and I wanted to assume some base gear before evaluating. You don't 'only' need 100 hit; the more the merrier, at least for threat. It was an arbitrary choice.

Anonymous said...

I appreciate the speedy response.

I am planning on the following off pieces to supplement our T10 hit problem.

Noose of Malachite - 52 hit
Royal Crimson Cloak - 44 hit
Harbinger's Bone Band - 38 hit
Ickfirus's Sack of Wonder - 114

Assuming heroic pieces, this yields 248 hit with only four pieces of gear.

I will likely hold on to my Belt of the Merciless Killer (68 hit) for quite some time in order to maintain the cap as I gear up.

danimal said...

Hello, I am just curious about something about tanks. With ICC gear it is possible to be melee hit caped and expertise hard caped. My question; Is it worth going for the expertise hard cap? Will that affect the value of arpen?

Meka said...

Expertise is very valuable for your threat generation, but as you get more of it the benefit drops out.

The thing to be aware of is that expertise is very valuable to us, but, as you get more of it it will go from being a threat stat to a survivability stat!

Hard capping expertise won't net you that much more threat, but it will increase your survivability as you negate the chances of being parrygibbed!

TL;DR expertise quickly loses it's value when you pass the soft cap

Adam said...

Awesome post Kalon, keep up the good work! I love reading your blog.

Kalon said...

Anon - I'm personally not that worried about getting hit for my gear. That might have more to do with my role in the raid, but it's still not a huge concern. Those pieces are good though if you can get them.

Danimal, I don't think it's worth going for the parry cap for expertise under most circumstances. You could do it, but you'd lose out on a lot of extra armor and possibly stamina or other cool things. That being said, getting more expertise will improve the value of everything. This makes sense; if before you were hitting 80% of the time, arpen only applies to 80% of your hits. If you hit 81% of the time, it applies that much more. But it does so linearly, so while it's improved it's not so special that it changes the ratios. As always, the rule is simple: get expertise dodge capped (26 expertise skill /132 rating with PP), then go for hit, then go for expertise.

Meka - that's a bit misleading. Expertise's value doesn't decrease until you hit the parry cap, which is at 54 skill. That's quite a bit of expertise to get. Before then, every point is as valuable as the next - and every point is more valuable than anything else you could get save hit (if you're not hit capped).

It loses some value, but it's still one of the two best threat stats a bear can get before the cap.

Thanks, Adam :)

Cainman said...

Excellent explanation of the way Sunder, Faerie Fire, and ArP work together. It's a bit misleading that the tooltip for ArP states you ignore X% of the targets armor when in reality it's a percentage of only a portion of the armor.

ciopo said...

ot my knoweledge sunder armor and faerie fire stack multiplicatively between each other, not additively, meaning them combined are 24% less armor, not 25%. (1*0.8*0.95 -> 076)

This is confirmed from EJ and durid wiki too, iirc.

Kalon said...

That's possible, ciopo. Like I said, I was going from what I read at wowwiki; I didn't remember reading anything definitive from EJ, and it's notoriously hard to test precisely.

It doesn't change a whole lot, mind you; the base armor goes from 9812 to 9943, and the base value at 500 arpen changes from 129 to 124. But I'd be happy to change this if you can find me a link showing otherwise :)

Anonymous said...

Good to see all that Armor pen on tier gear is going to be useful to bears. I am a huge fan of expertise and my threat has taken a very nice jump since picking up the Tier legs and a 251 cloak from Marrow. Interesting that Armor pen is better than haste, I would have thought more Mauls would have been better.

The lack of hit rating on our teir gear is a whole other issue and I am dying to get my hands on the sack of wonder.

ciopo said...

the discussion about how sunder armor and faerie fire stacked was somewhere on this post @ EJ

other than that, it was confirmed on multiple occasion in the durid wiki, at the toskk discusison page.

Kalon said...

Thanks, Ciopo. I'll update the article and the numbers.