[Armor Penetration] Theorycrafting

Chulak · 01/03/08, 11:30 AM

With the introduction of Armor Penetration as a much more available stat on the badge rewards that came with 2.3, I have seen much discussion regarding the DPS value of armor pen without a lot of hard numbers. I've seen some math floating around regarding what armor penetration should do, but up to this point I have not seen any hard numbers on what it does do, even under controlled circumstances. Much of the discussion has surrounded the proc rate dependent Executioner enchant, and not the value of static armor penetration in general.

It occurred to me the other day that there may be a readily available method for testing the value of static armor penetration, as I still have four pieces of Beast Lord armor sitting in the bank. Before going through the trouble I'd like to get feedback on my concept to make sure my theory is sound. Perhaps the idea will be shot down, and if so then so be it.

The 4 piece Beast Lord set bonus is 600 armor penetration for 15 seconds on use of Kill Command. Even swapping four pieces of gear out to get the 4 piece set bonus back, I should easily be able to keep that proc up 100% of the time for purposes of testing. I know from experience that it will simply refresh, and that there is no hidden cooldown.

The 4-set proc should allow me to select a fast spawning elite mob (perhaps one of the mini bosses at the forge camps in Nagrand), kill him repeatedly in the same gear both with and without use of Kill Command, and compare DPS. Since it is easy enough to pull pet DPS out of my DPS, and there would be no difference in my stats, I believe this would provide a quantifiable reference on the specific value of the Armor Penetration provided by the buff; and thus the value of armor penetration in general. I would use a standard 1:1 shot rotation of only Steady Shot/Auto Shot to remove the magic damage from Arcane Shot from the picture, as that should not be mitigated by armor and would only skew results.

This is where my ability to theorycraft breaks down a bit, however, and why I would like some feedback from the community here. The questions that immediately come to mind are below.

1) Is it fair to stipulate that an elite world mob at level 68-70 has 10000 armor like a boss does? I would need a 10000 armor mob for the test to recreate a boss fight scenario, but would like a readily available mob as opposed to an instance boss that requires a reset/reclear.

2) I believe that %DPS increase would be an effective number for evaluating armor penetration, as well as being easily extractable from the test proposed above, producing a result of 600 Armor Pen = X.XX% DPS increase. Does this sound valuable?

3) What factors am I failing to account for?

Hanos · 01/03/08, 11:41 AM

Originally Posted by Chulak

With the introduction of Armor Penetration as a much more available stat on the badge rewards that came with 2.3, I have seen much discussion regarding the DPS value of armor pen without a lot of hard numbers. I've seen some math floating around regarding what armor penetration should do, but up to this point I have not seen any hard number on what it does do, even under controlled circumstances. Much of the discussion has surrounded the proc rate dependent Executioner enchant, and not the value of static armor penetration in general.

You didn't look around enough (not to mention this is in the wrong forum). The formula for armor mitigation is known, and list on these forums, based off that information and the list of boss armor values, you can figure out the exact value of armor penetration gear.

1) Is it fair to stipulate that an elite world mob at level 68-70 has 10000 armor like a boss does? I would need a 10000 armor mob for the test to recreate a boss fight scenario, but would like a readily available mob as opposed to an instance boss that requires a reset/reclear.

No, it isn't fair to stipulate that, in fact that is grossly wrong in every situation. No known raid mob in the game has 10,000 armor.

2) I believe that %DPS increase would be an effective number for evaluating armor penetration, as well as being easily extractable from the test proposed above, producing a result of 600 Armor Pen = X.XX% DPS increase. Does this sound valuable?

This is a flawed testing method, don't waste your time

3) What factors am I failing to account for?

Too many to list in a timely manner.

Here is the post I put up on my guild forum, while I don't think it is 100% accurate, as it is a napkin math in large, it gives you the general idea:

The key to this is the Armor Mitigation Formula:

Damage Reduction % = Armor / (Armor + 400 + 85*(5.5*Level-265.5)

For a lv 70 mob:
Damage Reduction % = Armor / (Armor + 10,557.5)

For a lv 73 mob (boss)
Damage Reduction % = Armor / Armor + 11,960)

Using the values for a boss we get the following relative mitigation percentages:

7000: 36.92%
6000: 33.41% (3.51%)
5000: 29.48% (3.93%)
4000: 25.06% (4.42%)
3000: 20.05% (5.01%)
2000: 14.33% (5.73%)
1000: 7.72% (6.61%)
0: 0% (7.72%)

What you see is going from 7000 to 0 AC each 1000 AC reduction is worth more

If you assume a 1000 damage unmitigated hit:
0 AC - 1000
1000 - 923
2000 - 857
3000 - 799
4000 - 749
5000 - 705
6000 - 666
7000 - 630

Now Raid Bosses have the following approximate Armor Values (Lurker has 7685 so 7700 vs 7685... not material)
Serpentshrine Cavern:
Hydross the Unstable: 7700
The Lurker Below: 7700
Leotheras the Blind: 7700
Fathom-Lord Karathress 6200
Morogrim Tidewalker: 7700
Lady Vashj: 6200

Tempest Keep:
Void Reaver: 8800
High Astromancer Solarian: 6200
Al'ar: 7700
Kael'thas Sunstrider: 6200

Hyjal Summit:
Rage Winterchill: 6200
Anetheron: 6200
Kaz'rogal: 6200
Azgalor: 6200
Archimonde: 6200

Black Temple:
High Warlord Naj'entus: 7700
Supremus: 7700
Shade of Akama: 7700
Teron Gorefiend: 6200
Gurtogg Bloodboil: 7700
Reliquary of Souls:
- Essence of Suffering: 0
- Essence of Desire: 7700
- Essence of Anger: 7700
Mother Shahraz: 6200
Illidari Council:
- Gathios the Shatterer: 6200
Illidan Stormrage: 7700

So taking the majority of raid bosses that have 7700, we apply raid buffs:
-Sunder - 2600
-Faerie Fire - 610
-CoR - 800

Which gives us a total of 4010, taking boss AC down to 3690, which is 23.58% mitigation.

Now if you take your T6 set for rogues, which has -350 armor on it (Gloves + Shoulders), you get to 21.83% mitigation.

So, if we start at 21.83% mitigation which is where most T6 rogues will end up, an additional 175 Armor Penetration takes that down to 20.93, which is a .9% decrease in mitigation. This means that if you have a Sinister Strike the would hit for 1000 unmitigated:
21.83% - 781.7
20.93% - 790.7

790.7 - 781.7 = 9 Damage = 1.15% increase

If you take the same rogue, but Hemo Spec, you gain 560 armor penetration from Serrated Blades, so you now have base armor of 2780 with 18.86% mitigation, if you add the same 175 Armor Penetration you get 2605 armor with 17.89% mitigation.
18.86% - 811.4
17.89% - 821.1

821.4 - 811.4 = 10 Damage = 1.20% increase

While not significant in and of itself, what happens when you stack it becomes far more impressive. With an ideal gear set, a Hemo rogue can get 728 Passive -Armor, with -1000 from Warp Spring on Proc, -300 from Madness on Proc, and - 840 from Executioner on proc.

When you look at the debuffed AC of 3690, take out 728 from gear, 560 from talents you are at 2402, if all procs happen at the same time you can get the boss down to 462 (could wear the -armor legs/neck to get to 112 AC). Now 462 + 175 = 637

637 - 5.06%
462 - 3.72%

You get a 1.4% increase from the same 175 -Armor if it is the last 175 -Armor, which means that Armor Penetration stacking can increase the value of the same amount of -armor by up to 22%. If you compare it to a boss with no debuffs compared to one full debuffed the value is up to 56% more.

Now you may be wonder, how this compares to other sources of damage increases:
Based on what I have seen and read, 175 Armor Penetration costs the same as 17-27 of one other stat (most of the -armor items tend to be poorly itemized) so if you assume you could get 20 Agi, Hit, Crit etc.

20 Hit (Generally the most valuable DPS Stat) is 20/15.8 =1.27% increase to hit, which is a 1.27% increase to white damage which is about a .8% increase in total damage done, compared to 175 -Armor increasing DPS 0.9% on a undebuffed mob.

NOTE - Percentage Gains from Armor Penetration should all be multiplied by ~.9 as ~10% of Boss DPS is from Rupture and Deadly Poison which is not mitigated by armor.

Chulak · 01/03/08, 11:50 AM

Alright, in that case I apologize for making a useless post, please move this thread to the Dung Heap where it belongs.

Cheeky · 01/03/08, 11:59 AM

Originally Posted by Chulak

Alright, in that case I apologize for making a useless post, please move this thread to the Dung Heap where it belongs.

As an aside, the Hunter DPS spreadsheet handles Armor Penetration just fine, even the 4-piece Beast Lord proc.

Fiola · 01/03/08, 1:26 PM

Originally Posted by Chulak

2) I believe that %DPS increase would be an effective number for evaluating armor penetration, as well as being easily extractable from the test proposed above, producing a result of 600 Armor Pen = X.XX% DPS increase. Does this sound valuable?

I think the easiest way to look at Armor Penetration is to use a chart All the formulas are known - it's the individual math calculations that are messy. But for rough calculations, a chart does the job.

Here's something I tossed together a while ago:

AC\AP	100	200	300	400	500	600	700	800	900	1000
1000	0.87%	1.76%	2.67%	3.59%	4.52%	5.48%	6.45%	7.44%	8.45%	9.47%
2000	0.80%	1.62%	2.45%	3.29%	4.15%	5.02%	5.90%	6.80%	7.72%	8.65%
3000	0.74%	1.50%	2.26%	3.04%	3.83%	4.63%	5.44%	6.27%	7.11%	7.96%
4000	0.69%	1.39%	2.10%	2.83%	3.56%	4.30%	5.05%	5.82%	6.59%	7.38%
5000	0.65%	1.30%	1.97%	2.64%	3.32%	4.01%	4.71%	5.42%	6.14%	6.87%
6000	0.61%	1.22%	1.85%	2.48%	3.11%	3.76%	4.41%	5.08%	5.75%	6.43%
7000	0.57%	1.15%	1.74%	2.33%	2.93%	3.54%	4.15%	4.77%	5.40%	6.04%
8000	0.54%	1.09%	1.64%	2.20%	2.77%	3.34%	3.92%	4.51%	5.10%	5.70%
9000	0.51%	1.03%	1.56%	2.09%	2.62%	3.17%	3.71%	4.27%	4.82%	5.39%
10000	0.49%	0.98%	1.48%	1.98%	2.49%	3.01%	3.53%	4.05%	4.58%	5.11%

Say you want to figure out how much the executioner Proc is worth - it's roughly -800 AP, so you look at that column. Against someone with 8k AC (high-end of raid bosses), it's around +4.51% physical damage while Executioner is active. If that mob instead has 4k AC, the proc is worth +5.82% physical damage.

DKP-Borgar · 01/03/08, 1:46 PM

Even if it is a death topic. We know the values of certain mobs and how armor penetration works with it.
But does anybody has an addon, that uses this knowlegde? I mean it would be really nice, to know how much dmg am I doing, when working on certain mobs/bosses

For example, I use mobinfo to gather hp values of bosses and so on.
But does anyone has an addon that displays:

a) armor value (even if guessed) of the mob (decreasing with sunder armor, curse, etc.)
b) current armor penetration (+ executioner proc) of the player

This way a comparison between useful stats and armor penetration would be possible.

world · 01/03/08, 11:43 PM

It would definitely be possible, albeit slightly fiddely.

What you would need to do is set up a way of tracking a _set_ physical damage ability done to a mob. The easiest ones I can think of are Hamstring and Thunderclap. By knowing the amount of damage that should be done, and comparing it to the actual damage done, its a simple calculation to work out the % damage reduction, and hence the AC of the mob.

However, now for the tricky part. Things that can mess up the results / need to be considered are - different ranks of Hamstring / Thunderclap, Defensive stance, % damage modifiers (either on the player or on the mob, such as Enrage), and existing armor debuffs on the mob.

This can then be compiled into a database (either as an addition to something like Mobinfo, or a separate mod).

DKP-Borgar · 01/04/08, 5:41 AM

The problem I see is, that the value of armor penetration for your personal gerar can only be assumed.
At certain high armor bosses, there might be a chance that regular stats as crit,str,haste might have a greater influence on the damage then armor reduction.

As for now it's mostly a guessing game, since you would have to recount all armor modifiers applied to a mob/boss to evaluate your gear.

Machinator · 01/04/08, 5:44 AM

Originally Posted by DKP-Borgar

The problem I see is, that the value of armor penetration for your personal gerar can only be assumed.
At certain high armor bosses, there might be a chance that regular stats as crit,str,haste might have a greater influence on the damage then armor reduction.

As for now it's mostly a guessing game, since you would have to recount all armor modifiers applied to a mob/boss to evaluate your gear.

This is something that is true for every stat in the game.

Anyway, since there is already threads on this topic could we migrate to one of them where half of this has already been discussed?

PSGarak · 01/04/08, 1:17 PM

I think the point of the OP is to verify that armor penetration is working as predicted, which is something that can't be verified with pure theorycrafting. This can probably be merged into the raid boss armor thread in any case.

Victory Rush and Bloodthirst, I believe, also do a constant damage, and are much higher numbers so it's easier to see fractions of a percent difference. The best way to test this is probably strip proc gear off your armor, equip a warpspring coil, and meticulously watch buffs/debuffs for some boss on farm status, or to swap in a weapon with armor penetration since bloodthirst is not weapon dependent.

koaschten · 01/04/08, 3:20 PM

Just asa sidenote, [Warp-Spring Coil] and Bloodthirst/Victory Rush don't mix

Cireena · 01/04/08, 3:59 PM

Originally Posted by koaschten

Just asa sidenote, [Warp-Spring Coil] and Bloodthirst/Victory Rush don't mix

While this is true you can get an [Icon of Unyielding Courage] and use it to test with. It is a smaller amount of armor penetration, but it is available to everyone and to people that are not/no longer in T5 can still get this and test with it.

Tyrana · 01/04/08, 4:15 PM

Originally Posted by Hanos

The key to this is the Armor Mitigation Formula:

Damage Reduction % = Armor / (Armor + 400 + 85*(5.5*Level-265.5)

For a lv 70 mob:
Damage Reduction % = Armor / (Armor + 10,557.5)

For a lv 73 mob (boss)
Damage Reduction % = Armor / Armor + 11,960)

Using the values for a boss we get the following relative mitigation percentages:

7000: 36.92%
6000: 33.41% (3.51%)
5000: 29.48% (3.93%)
4000: 25.06% (4.42%)
3000: 20.05% (5.01%)
2000: 14.33% (5.73%)
1000: 7.72% (6.61%)
0: 0% (7.72%)

This is wrong, the level of the attacked doesn't matter, the level of the attacker does. Thus for a level 70 player a mob with 7000 Armor should have 39,87% damage reduction.

Nezralix · 01/04/08, 4:18 PM

I'm not trying to be rude, but shouldn't this be in the theorycrafting forum?

Grayson Carlyle · 01/04/08, 7:34 PM

Originally Posted by Tyrana

This is wrong, the level of the attacked doesn't matter, the level of the attacker does. Thus for a level 70 player a mob with 7000 Armor should have 39,87% damage reduction.

Actually, he had it right. You do not do less damage to mobs as you level up.