Combat Ratings at level 80 - Page 19

Mavanas · 04/29/09, 2:47 PM

Originally Posted by Slafsinator

A peculiar effect of stacking Armor Penetration to the point of negative armor is that the closer the base/debuffed armor of the target is to the so-called Armor Penetration cap (see Ghostcrawler's post), the more effective Armor Penetration is. Using Shattered Throw to reduce the target's debuffed armor further than with Sunder/Faerie Fire can decrease the DPS of those having above 100% Armor Penetration.

To simplify it -- in one case you debuff someone to 3000 armor and you get 200% Armor Penetration. You end up at -3000 armor on the target -- great. In the other case you debuff the target to 8000 armor and you still have that juicy, tasty 200% Armor Penetration. Result: -8000 armor on the mob.

There is an interesting implication of this observation that is within reasonably attainable armor penetration values. Suppose a rogue has 100 armor penetration from gear, and mjolnir runestone and grim toll proc at the same time, for a total 1324 armor pen rating or 108% armor penetration. Then there is a breakeven value of reduced boss armor at which the rogue will start doing LESS damage with shattering throw. This value is 7779 (assuming shattering throw stacks multiplicatively with other debuffs). Any value below that will make the rogue do less damage when ST is used. For reference, the reduced armor with 5 sunders and faerie fire is 8088.68 and if the rogue has serrated blades, the reduced armor is 7450, so in that case shattering throw starts hurting the rogue's dps. I know it's still not a very common situation, but with further gear changes, armor penetration can go up and the threshold of reduced armor will go up as well.

a civilian · 05/01/09, 3:24 AM

A few comments on properties of this armor penetration system:

Let A be the armor value before armor penetration, but after debuffs. This would be the armor value the target sees on their character pane. A' is the effective armor value after armor penetration. I will denote by x the fraction of damage taken from an armor mitigated attack (1-damage reduction). C is the armor constant, 15232.5 for level 80 attacker. k is the nominal armor penetration fraction.

We know
$1-x = \frac{A'}{A'+C}$
and
$A' = A-k(A+C)/3$ .

Thus,
$x = \frac{C}{(A+C)(1-k/3)}$ .

Some implications of this:

This expression asymptotes at k = 3, so that if you could obtain 300% armor penetration, you'd do infinite damage (assuming there's no cap). Not realistic? You can actually get surprisingly close -- [Grim Toll], [Mjolnir Runestone], [The Dusk Blade], and executioner yield 151% armor penetration; another 25% can be obtained from mace specialization and battle stance, so that you "only" need 124% passive armor penetration from gear. This is little over 1500 armor penetration rating -- still not realistic.
It's actually not possible to obtain enough armor penetration that an armor debuff would cause you to do less damage.
$\frac{\partial x}{\partial A} = \frac{-C}{(A+C)^{2}(1-k/3)}$ ,
which is always negative (for k < 3). That is, an increase in armor (before armor penetration) always yields a reduction in damage.
The equation
$\frac{\partial x}{\partial k} = \frac{C/3}{(A+C)(1-k/3)^{2}}$
for the absolute effect of a change in armor penetration, quantifies the increasing returns of armor penetration. In particular, armor penetration is
$\left(\frac{1-k/3}{1-k'/3}\right)^{2}$
as valuable at armor penetration k' as at armor penetration k (if other stats are held constant).

Edit: indeed, these are only valid for A > C/2. I had forgotten there was a minimum function involved.

Mavanas · 05/01/09, 12:07 PM

You cannot ignore the minimum function in the cap formula.

The exact formula for effective armor is

$A' = A-k*min(A, (A+C)/3)$

For high values of armor debuffs, A becomes smaller than (A+C)/3, and the formula simplifies to

$A' = A(1-k)$

and armor mitigation formula becomes

$x = \frac{C}{A(1-k)+C}$

The breakeven value of A is C/2, which can occur any time you have sunders and shattering throw up, or if you have faerie fire, sunders and serrated blades.

This changes your analysis somewhat, in particular for A < C/2, you will do infinite damage if k=C/A+1, which given the restriction on A is at least 3. So the magic value k=3 remains unchanged.

However the partial with respect to A becomes:

$\frac{\partial x}{\partial A} = \frac{-C(1-k)}{(A(1-k)+C)^{2}}$

which is positive for k>1 (easily obtainable, see for example my previous post). This means that a decrease in armor decreases damage.

The partial with respect to k changes to:

$\frac{\partial x}{\partial k} = \frac{C/A}{(A(1-k)+C)^{2}}$

which is always positive.

Mavanas · 05/03/09, 6:40 PM

I have done additional testing of spell crit reduction against boss-level target dummy. There have been some extensive tests of physical crit reduction against bosses, but very little testing of spell crit reduction. Dontmindme has shared with me the results of his previous tests. He found 1 crit in 1060 successful wound poison applications at 2.2% spell crit, and 2 crits in 3667 applications at 2.16% crit. He was under the impression that both tests seem to indicate a 2.1% spell crit reduction.

My tests:

Obs	Rating	Perc Crit		Crits	Observed	Reduction
3722	96	2,0912%		0	0,0000%	2,0912%
3330	97	2,1130%		0	0,0000%	2,1130%
739	97	2,1130%		0	0,0000%	2,1130%
3724	98	2,1348%		1	0,0269%	2,1079%
1912	98	2,1348%		1	0,0523%	2,0825%

Here are some conclusions:
- Spell crit reduction against boss-level targets is no more than 2.1348%.
- I have not been able to disprove a hypothesis that spell crit reduction is at least 2.1130%.
- There is a 17% chance that spell reduction is 2.08% and there were no crits in tests 1-3 by random chance
- There is a 37% chance that spell reduction is 2.09% and there were no crits in tests 1-3 by random chance
- There is a 59% chance that spell reduction is 2.10% and there were no crits in tests 2 and 3 by random chance

So while 2.1% appears to be a likely round number for spell crit reduction, more tests with higher number of observations are needed to pinpoint the exact number.

Here is backup for key tests: 1 crit out 3724 observations with 2.1348% crit and no crits out of 3330 observations with 2.1130% crit

In same tests, I have observed white damage crit reduction:

Obs	Theory	Observed	Reduction	CI low	CI high
12210	21,45%	17,23%	4,22%	3,55%	4,89%
13420	20,70%	16,14%	4,56%	3,94%	5,18%
4396	19,41%	14,83%	4,58%	3,53%	5,63%
2024	17,39%	13,04%	4,34%	2,88%	5,81%
8824	18,60%	14,36%	4,24%	3,51%	4,97%
8382	19,81%	14,83%	4,98%	4,20%	5,74%
12210	6,51%	1,83%	4,68%	4,43%	4,91%
11242	14,07%	9,21%	4,87%	4,31%	5,39%
					
Conversion		4,56%	4,43%	4,89%

Thus while this does not disprove the hypothesis of 4.8% crit reduction for white damage crits for rogues, 4.5% seems like a more likely number.

• Vulajin · 05/03/09, 6:53 PM

Originally Posted by Mavanas

Thus while this does not disprove the hypothesis of 4.8% crit reduction for white damage crits for rogues, 4.5% seems like a more likely number.

Unless the mechanics changed at some point, the 12037 attacks I performed when we originally tested this with 4.79% tooltip crit without experiencing a single crit disprove any possibility of a 4.5% reduction for rogues.

Also from the PTR: Retesting hit table assumptions

Roywyn · 05/07/09, 1:55 PM

Originally Posted by Mavanas

There have been some extensive tests of physical crit reduction against bosses, but very little testing of spell crit reduction.

Those results of spell crit for rogues also match the results of spell crit for mages, if I'm not mistaken.

However spell crit reduction for mages is completely different from your results. Which makes it likely that it's also different for other pure caster classes.
Melee mechanics are also different for mages, so there's a precedent of split mechanics (a weapon skill capped mages will almost only get glancing blows against raid and boss mobs, not just the usual 24%, unless they recently changed it).

Mages below 2.1% or even below 2.0% spell crit (that's as low as you can get due to your base intellect) will easily get a crit or two when testing for short amounts of time. Some more thorough tests suggested that the spell crit reduction is a lot lower than 2% without gear, but slowly increases up to around 3% when you get crit and intellect from gear and buff.

There has been no real conclusion that is universally agreed upon for mages since the things are pretty obscure.

Mavanas · 05/09/09, 2:00 AM

Originally Posted by Roywyn

Those results of spell crit for rogues also match the results of spell crit for mages, if I'm not mistaken.

However spell crit reduction for mages is completely different from your results. Which makes it likely that it's also different for other pure caster classes.
Melee mechanics are also different for mages, so there's a precedent of split mechanics (a weapon skill capped mages will almost only get glancing blows against raid and boss mobs, not just the usual 24%, unless they recently changed it).

Mages below 2.1% or even below 2.0% spell crit (that's as low as you can get due to your base intellect) will easily get a crit or two when testing for short amounts of time. Some more thorough tests suggested that the spell crit reduction is a lot lower than 2% without gear, but slowly increases up to around 3% when you get crit and intellect from gear and buff.

There has been no real conclusion that is universally agreed upon for mages since the things are pretty obscure.

I noticed that phenomenon with poisons too, in two cases, when I put on more crit gear and calculated the crit reduction, I ended up with 2.4-2.5% crit reduction, however the confidence intervals still included 2.1%. It may well be that the reduction formula is more complicated, it could be in relative terms.

• landsoul · 05/12/09, 3:08 PM

With sunders and fearie fire only, it seems that the intersection is at 1530 penetration rating. Anything more than 1530 rating will decrease your effective dps if shattering throw is applied to the target. Here's some graphs to show.

x is armor penetration rating, y is percent damage done /100

sunders, faerie fire

sunders, faerie fire, shattering throw

intersection point

As said before, if you have too much ArP, a shattering throw will be bad for you specifically, probably not for the rest of the raid at that given time though. Further evidence that shattering throw and the new armor penetration system is terrible design. Shattering throw is especially terrible for the warrior casting it, especially if they have a high amount of ArP (which is what best possible gearing leans towards)

Slafsinator · 05/12/09, 5:19 PM

I honestly have no idea how you came to that conclusion, Landsoul. According to my tinkering, the point where using Shattering Throw potentially reduces your DPS does not have any relation to the player's ArPen at all (barring really extreme, ludicrous amounts of it).

Instead, only the target's debuffed armor matters, and the optimal amount of armor for a target to have for your 100%+ ArPen character is: 7616,25 (=15232,5/2). Anything more will initiate the ArPen "cap", and anything less will yield a lesser effect on ArPen, crossing over into negative values.

What you can do though, is conjure a graph on how much armor reduction you need from debuffs to make the target stick at 7616,25 with different base armors, but it's really not that interesting thanks to the amount of useful armor values for raiding and DPS. Against a boss you want 28,38% armor reduction from debuffs, which is just more than FF + sunders, and quite a bit less than FF + sunders + shattering throw.

I'm coming to these figures through my spreadsheet, feel free to poke around and see if I made any mistakes.

suicuique · 05/13/09, 5:57 AM

Originally Posted by Slafsinator

I honestly have no idea how you came to that conclusion, Landsoul. According to my tinkering, the point where using Shattering Throw potentially reduces your DPS does not have any relation to the player's ArPen at all (barring really extreme, ludicrous amounts of it).

I'm speculating here.

Assuming shattering throw is similiar to sunder/FF mechanics (i.e. it is applied as a debuff on the mob and then ArP comes into play), we get following standard scenario:

1) without shattering throw
ca 8089 = boss armor post sunder/ff
ca 7774 = amount of armor which is base to the ArP calculations

2) with shattering throw
ca 8089*0.8 = 6471 debuffed boss armor = amount of armor on which ArP calculations are based (because it is < 7616)

The implications of this would be:
100% ArP is enough in 2) to get boss to 0 armor, while in case 1) you'd need ca 104%.
The point is, that in case 1) the armor value affected by ArP is higher while at the same time more armor has to be offset tto reach zero, while in case 2) ArP is less effective once you reach negative armor regions.

Rough calculations point me to 1527 being the lower bound for ArP when case 1) starts becoming more effective (read: reaches higher negative armor values) than case 2).

Lollersk8er · 05/19/09, 8:35 AM

Is the new 100% cap applied before or after the 8,1% effectiveness 'cap'?

kalbear · 05/19/09, 11:48 AM

They haven't actually announced that they're going to do a 100% cap yet. No one knows what the mechanics are.

• Aldriana · 05/20/09, 5:43 AM

Brief testing on target dummies tonight indicates that ArPen is indeed capped, and at 100% (not 0 armor).

hellord · 05/20/09, 11:01 AM

I just did few tests and can confirm that battlestance is just reducing the cap by 10%. I have to guess mace stance does the same so reducing the gear cap to 75%.

• landsoul · 05/21/09, 12:45 AM

I just confirmed tonite with accuracy of 99.98 percent that you cannot remove more armor than the effectiveness cap.

I did one test:

Sunder x5, target dummy, 4037 AP with battlestance, 1216 penetration rating with grim toll proc.

Bloodthirst multiplier: 0.5 (ap scalar) * 1.1 (unending fury) * 1.06 (2H spec) = .583 dmg per ap

4037 attack power strike yields 2353.57 expected damage, I did 2265 damage.

2265/2353.57 = 96.2367398% damage applied.

effectiveness cap with 5 sunders = (10643*.8+15232.5)/3 = 7915.63333

1216/12.3216 + 10%= 108.7314403% armor removed (clearly over 100%)

The boss debuffed, has 10643*0.8 = 8514.4 armor. Assuming the entire effectiveness cap of armor was removed, the boss is left with 8514.4-7915.633 = 598.7666 armor.

Damage applied with 598.766 armor = 15232.5/(15232.5+598.766) = 96.2178221% which exactly matches the actual bloodthrist damage I dealt.

Conclusion
You can only remove armor up to the armor penetration effectiveness cap of (debuffed armor + 15232.5)/3 and any penetration after 100% tooltip is ineffective.

Prinsesa · 05/25/09, 4:36 AM

Conclusion
You can only remove armor up to the armor penetration effectiveness cap of (debuffed armor + 15232.5)/3 and any penetration after 100% tooltip is ineffective.

Raid boss armor = 10,643

Debuffed armor = 10,643 * (1 - (Sunder + Faerie Fire))
Debuffed armor = 10,643 * (0.75)
Debuffed armor = 7982.25

Effectiveness Cap = (debuffed armor + 15232.5) / 3
Effectiveness Cap = (7982.25 + 15232.5) / 3
Effectiveness Cap = 7738.25

Minimum Armor = debuffed armor - effectiveness cap
Minimum Armor = 7982.25 - 7738.25
Minimum Armor = 244, which is 1.58% DR against a level 80 attacker

Am I doing this correctly?

hellord · 05/25/09, 5:32 AM

Originally Posted by Prinsesa

Raid boss armor = 10,643

Debuffed armor = 10,643 * (1 - Sunder) * (1- Faerie Fire)
Debuffed armor = 10,643 * (0.76)
Debuffed armor = 8088,68

Effectiveness Cap = (debuffed armor + 15232.5) / 3
Effectiveness Cap = (8088,68 + 15232.5) / 3
Effectiveness Cap = 7773,727

Minimum Armor = debuffed armor - effectiveness cap
Minimum Armor = 8089 - 7774
Minimum Armor = 315, which is 2.026% DR against a level 80 attacker

Am I doing this correctly?

Sunder and FF stack multiplicatively.

MasterMace101 · 05/25/09, 7:48 PM

Originally Posted by Prinsesa

Originally Posted by Prinsesa View Post
Raid boss armor = 10,643

Debuffed armor = 10,643 * (1 - Sunder) * (1- Faerie Fire)
Debuffed armor = 10,643 * (0.76)
Debuffed armor = 8088,68

Effectiveness Cap = (debuffed armor + 15232.5) / 3
Effectiveness Cap = (8088,68 + 15232.5) / 3
Effectiveness Cap = 7773,727

Minimum Armor = debuffed armor - effectiveness cap
Minimum Armor = 8089 - 7774
Minimum Armor = 315, which is 2.026% DR against a level 80 attacker

Am I doing this correctly?

So by your Math

Armor Reduction Cap = 100 - 2.026 = 97.974%
Armor Penetration Rating Cap = 97.974 * 12.3216 = 1207.196

hellord · 05/26/09, 6:18 AM

Originally Posted by MasterMace101

So by your Math

Armor Reduction Cap = 100 - 2.026 = 97.974%
Armor Penetration Rating Cap = 97.974 * 12.3216 = 1207.196

No.
Armor Penetration Rating Cap = 100% = 1232
Armor reduction cap at 100% ArP = 7774 vs 8089

Glory · 05/27/09, 6:25 AM

Did somebody a test with 100% Arp and 5x SA + FF + Shattering Throw. Armor should go negative again, if possible.

Arp Effectivness Cap will be
(10643*0.8*0.8*0.95+15232.5)/3=7234.5

Boss Armor is 6470.9

Armor after Arp 6470.9-7234.5=-763.6

Maybe the easiest way to test this on a priest.
~2k armor
~5k effectivness
~3k negative Armor after Arp

a civilian · 05/27/09, 7:13 AM

The the arp effectiveness cap is min(armor, (armor+C)/3), not just (armor+C)/3, so armor will never go negative.

• landsoul · 05/27/09, 8:35 AM

Hey guys guess what? Blizzard nerfed rage generation some time ago without telling us, and here's the new formula in game:

$\text{Rage} = \frac{3}{8}(fs+\frac{7.5d}{c})$
f=1.75,3.5,7 for offhand hit, offhand crit/main hand hit, main hand crit
s=base weapon speed
c=320.6
d=damage done

This is a nerf from what we thought it was:
$\text{Rage} = \frac{1}{2}(fs+\frac{7.5d}{c})$

I'm not sure if this is also true for druids, but yeah, sucks =(

Prinsesa · 05/27/09, 10:11 AM

Originally Posted by MasterMace101

So by your Math

Armor Reduction Cap = 100 - 2.026 = 97.974%
Armor Penetration Rating Cap = 97.974 * 12.3216 = 1207.196

Nope. Armor Penetration stops when your tooltip reads 100%, even if the DR on the effect means it's not actually 100% and there's still some armor left over. The calculations I made was trying to find out just how much armor left over that actually is, which turned out to be 315 armor for a Sundered-and-FF'd raid boss.

The Armor Penetration cap is still 1232 rating.

Thanks to hellord as well for the earlier correction.

By the by, the OP should be updated to reflect 3.1's buff to armor penetration by dividing the old conversion ratios by 1.25

• landsoul · 05/30/09, 8:01 PM

The actual rage generation formula is this: as posted by Bornakk:

minimum of
$\text{rage}=\frac{1}{2}(fs+\frac{7.5d}{c})$
and
$\text{rage}=2(\frac{7.5d}{c})$

c is 453.3
f is hit factor, as we know as 1.75, 3.5, 7
s is base weapon speed
d is damage dealt

For low damage hits, the second equation usually applies.

• GravityDK · 06/05/09, 1:46 PM

Hi all,
I have written a user guide for TankPoints which you all may find helpful for educating non-serious-theorycrafters. The guide should help a person with decisions like which enchant is better for you, what damage reduction you get in Frost resist gear and more.

To save multiple original posts, I am going to maintain this page with the latest version of the file.

I am notifying here because this is the authoritive thread on combat ratings. I have PM'd Whitetooth about this too.