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Armor Penetration - When does it make sense to use it?


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#1
TheThirdRace

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-- Original post --
It came to my attention recently that Armor Penetration could be much better than what I thought. (Thanks yarpenthemad21)
 
I just got the Hakkon dagger and I really don't know if I should go for Attack or Armor Penetration.
 
My question is at what point does Armor Penetration becomes better than Attack for Perilous and Nightmare?
 
Any numbers would be greatly appreciated, all I have right now is Goxhen guide and I know it's far from being entirely accurate...

He does list DPS stats in this order for "most damage" to "less damage":
3% Flanking Dmg > 1.75% Attack > 3% Armor Pen > 1.75% Crit Chance = 1.75 Dexterity (rogue) >1.75 Willpower > 1.75 Magic (mage) = 1.75 Strength (warrior) > > 1.75 Cunning > 3% Crit Dmg > 3% Barrier Dmg > 3% Guard Dmg

Anyone has any idea?

-- Current results --
*** Edit #3 ***
After a lot of feedback, here are what we learned...

Your amount of %Attack before crafting a Tier3 weapon upgrade has a huge impact on the results. My first calculation were with 0% Attack before any Tier3 weapon upgrade and the results was 62+ Armor (see Edit #1). After including my 40% Attack before crafting, the Armor target was reduced to 40 (see Edit #2). Shaving 1/3 Armor is already huge, but it plays even better with the second thing we learned in this thread...

Enemy levels increase each zone, meaning their health and armor increase too. For example, a Perilous Venatori footsoldier could have 30 Armor on area 1, but might have 35 on area 2 or even 50 on area 5. We still don't have the exact numbers for every units (all numbers in the previous example are fictive), but the fact that Armor increase each zones makes a target of "40+ Armor" even easier to reach.

Thus, we can draw these conclusions:

  • The lower your weapon damage is (not DPS, I really mean damage), the faster Armor Penetration will become better than Attack
  • The more %Attack you have before crafting a T3 weapon upgrade, the faster Armor Penetration will become better than %Attack
  • As a general rule, you'll reach that Armor "target" somewhere in Perilous (area 1 to 5). You'll still need to calculate the numbers for your exact situation, but I think it's safe to say that it will become better to use Armor Penetration for any T3 upgrade whenever you play Perilous, unless you always die on first zone...

*** CAREFUL ***
Armor Penetration has no effect whatsoever on magical attacks. This means it's not worth a damn on Mages. Most, if not all Avvar abilities are Elemental damage, thus it also doesn't help him the slightest unless you auto-attack a lot.

-- Previous results --
Edit #1: My first attempt at finding out

Spoiler

Edit #2: My second attempt at finding out
Spoiler


Edited by TheThirdRace, 16 July 2015 - 09:28 PM.

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#2
K_A_Rnage

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Having watched a lot from the fade I noticed that Templars have around 80 armour. I also noticed that when it was sundered it was quite often 0.
However using rings; arm pen 20% of 80 = +16 base damage vs att+10% base hit (330 - 80 = 250) giving you +25 base dmg. I have used the Maul but obviously this scales, especially with staves so Armour pen may well be better on mages.
Personally I would like to know if 20% Sunder on Hit stacks??

#3
Piffle

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In NM armour pen is better.

 

E.g. Dragon has 99 armour in NM. It effectively halves your base damage.

 

Oh where's kmeeg? He's way better at articulating this stuff than me.


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#4
yarpenthemad21

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It's possible to make some sort of spreadsheet for it, all you need is base damage, armor value and armor penetration value.

Still basic idea is quite simple I would say.

final_damage = (base_damage * rand(0.95 to 1.05) - armor * (1 - armor_penetration))
* (ability_multiplier)
* (1 + critical_damage_bonus + flanking_bonus)
* (1 + attack_bonus + damage_multiplier + type_bonus)
* (1 - magic_resistance)

Our well known damage formula.
As we see armor is subtracted from base damage value. Also armor is reduced in additive way by armor_penetration. Armor penetration stacks like crit chance pretty much, it's capped at 100% and can reduce armor to 0.

Still base damage is main value in formula, other multipliers (ability, attack, crit) are based around it. So math here is very simple.
10% less base damage = 10% less damage. 10% more base damage = 10% more damage.


Enemy armor directly reduce base damage.

Each 1 point of enemy armor reduce damage by: 100%/base_damage - example with 150 base damage = 0.(6)%. So 20 armor would reduce by 13.(3)

Calculation how much armor penetration gives could look like that.
You take base_damage - enemy armor. Using previous example 150 - 20 = 130.
Penetrated 1 point of armor (so for armor value 20 it would be 5% armor pen) would give as 100%/(base dam - armor) dam increase so on example = 0.769....%
Armor pen of 100% would reduce 20 armor so would increase damage relatively by in example by 0.769% * 20 =15.3846%

Now it's obvious that value of armor penetration depends of enemy armor and base damage of weapon.
From what I've observed from fade (and I'm looking for info maybe from other ppl, it would help a lot):

1. Only few enemies does not have armor. For sure it is: wraith, DD, venatori mages, undead skeletons.
2. Perilous values starts at 19 (shades and probably archers) and end at 65-70 (templar knights). Highest armor is on red templars (I think 30 is lowest there). NM values are even higher, even 105 for templar knight. I would love to see full list of health and armor values.
3. 2h warriors with huge base damage get lowest benefit from armor pen. I still don't know if Avvar elemental attack ignore armor. Damage from korth might is very inconsistent, basic "version" tend to deal more damage sometimes on non resisted targets, cold tend to deal lowest damage etc.

Higly promoted rogue players should consider using armor upgrades with sunder effect (instead of willpower I think, leg part from what I know), it stacks with other similar effects and should with quite low cost boost the effectiveness.
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#5
yarpenthemad21

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Having watched a lot from the fade I noticed that Templars have around 80 armour. I also noticed that when it was sundered it was quite often 0.
However using rings; arm pen 20% of 80 = +16 base damage vs att+10% base hit (330 - 80 = 250) giving you +25 base dmg. I have used the Maul but obviously this scales, especially with staves so Armour pen may well be better on mages.
Personally I would like to know if 20% Sunder on Hit stacks??


Why idea that attack ring boost directly base damage?
It's just a attack stat, works like 20 willpower pretty much.

Sunder of any sort stacks. There are few 40% versions.

#6
K_A_Rnage

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Why idea that attack ring boost directly base damage?
It's just a attack stat, works like 20 willpower pretty much.

Sunder of any sort stacks. There are few 40% versions.


Re attack; probably just my wording. Your formula is far more comprehensive.

Re sunder stacking; thanks for this. I will definitely be looking at my Armour Upgrades :D

#7
Drasca

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Short answer:

I put on T3 Single Dagger upgrade 6 Offense Metal Dawnstone and 3 Offense Leather Craggy Skin on my Hakkon's Dagger. That one's a no brainer.

AP if you want to play NM and above instead of Attack

Not on Magic weapons / attacks

 

Longer answer:

Other weapons and equipment:

Requires lots of math work comparing other upgrades such as critical bonus damage, crit chance, ability to crit, etc. As Yarpen mentioned,  I really need to do a spreadsheet.

 

Also, comparing whether other teammates have reduced enemy armor or not, so the damage isn't obvious with all these variables in play.



#8
yarpenthemad21

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Short answer:
I put on T3 Single Dagger upgrade 6 Offense Metal Dawnstone and 3 Offense Leather Craggy Skin on my Hakkon's Dagger. That one's a no brainer.
AP if you want to play NM and above instead of Attack
Not on Magic weapons / attacks
 
Longer answer:
Other weapons and equipment:
Requires lots of math work comparing other upgrades such as critical bonus damage, crit chance, ability to crit, etc. As Yarpen mentioned,  I really need to do a spreadsheet.
 
Also, comparing whether other teammates have reduced enemy armor or not, so the damage isn't obvious with all these variables in play.


I have an idea for making spreedsheet for few armor values (0,20,40,60,80,100 or whatever you choose) and get damage gained for each of it. After that compare it to different stat (attack/crit whatever)
After that looked from which point armor pen gives more damage increase. The less value of this armor there the more useful it is.

A lot of depends on build choose and sometimes even kit.
In general rogue benefits more from armor pen, still

1) Assassin has passive cold ambush - 50% armor pen after stealth for couple of seconds. Next is cheap shot so sunder effect and next is sunder effect on upgraded twin fangs which is 40% armor pen. So on her armor pen is pretty much enough from just passives and abilities.
2) Alchemist - similar, ambush, twin fangs, gasp in the armor
3) Archer - sunder from cheap shot and gaps in the armor.
4) Hunter - only throwing blades and cheap shots in that line, so it forces a build in some way.
5) Duelist - nothing. Best place to use either armor penetration on weapon and/or add sunder to armor in my opinion.
Last weekend could show the damage difference, because undead skeletons got 0 armor and templar got the highest from all factions (horror got around 65 on perilous). Bolt damage difference is quite significant without any armor pen. Sunder effect would help with bolt but for higher punch on anything else build in armor pen is needed.

Warriors, here most benefit would be on NM+. I've seen many units having 80 or 100 armor there, taking dragon maul 330 damage and 100 armor it's a massive 30% damage reduction.
Reaver - sunder from shield breaker which I think isn't a common choice.
Katari - piercing blows and shield breaker, fairly easy to get.
Avvar - nothing, still don't know how his hits works with armor.
Lego - shield breaker - easy to get.

Next question I have is:
Is sunder effect considered status effect and give some bonus XP?

#9
Angelus_de_Mortiel

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Next question I have is:
Is sunder effect considered status effect and give some bonus XP?

 

My answer: Potentially yes and no. I tested is and all other status effects when making my Beginner's Guide. It is considered, by definition, to be a status effect. However, it did not grant any support XP during my testing.

 

Disclaimer on that: That was a few months ago, and as such that may no longer be true. However I have seen no patches denoting it was changed.



#10
Texasmotiv

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To state it simply, because arPen is a % and not a static value it becomes more valuable as Armor values rise as you gain more benefit from 25% of 100 armor than 25% of 50 armor.

Also since armor directly subtracts from your base damage the gain is multiplied by the rest of the formula. The difference between getting that extra 25 damage is like going from the hossberg twainer to the skywatcher axe on the dragon for example.

#11
yarpenthemad21

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List of enemies health and armor per difficulty would be some much useful now really.
I wonder why on ME3MP this kind of thing existed and here it's all about what you see from fade.
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#12
capn233

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List of enemies health and armor per difficulty would be some much useful now really.
I wonder why on ME3MP this kind of thing existed and here it's all about what you see from fade.

 

Because nobody has bothered to compile a list of it for DAI.



#13
KalGerion_Beast

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Are you a Geth Infiltrator using a Javelin?  If so, it makes sense.  


Edited by KalGerion_Beast, 14 July 2015 - 03:37 PM.

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#14
yarpenthemad21

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Because nobody has bothered to compile a list of it for DAI.


I'm pretty sure that ME3MP data was extracted not from gameplay itself but either from memory or files. From what I remember you can't even see in game health values of enemies, just a "healthbar".

#15
capn233

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He does list DPS stats in this order for "most damage" to "less damage":
3% Flanking Dmg > 1.75% Attack > 3% Armor Pen > 1.75% Crit Chance = 1.75 Dexterity (rogue) >1.75 Willpower > 1.75 Magic (mage) = 1.75 Strength (warrior) > > 1.75 Cunning > 3% Crit Dmg > 3% Barrier Dmg > 3% Guard Dmg
 

 

Forgot to mention earlier, the assumptions here were weapon base of 150 and enemy armor of 50, with 10% attack, 0% AP, 40%CDB, 25% FDB, 10% Crit Chance.

 

Also not entirely clear to me from the thread if the correct damage formula was used, since the posted one is not consistent with the one aznricepuff has since posted, read directly from scripts.  Not to take anything away from GhoXen's effort, since it is not particularly easy to derive a formula like this directly from in game testing.  If you read through the test section, there seemed to be sections going back and forth whether armor was subtracted "before" or "after" other bonuses.



#16
SkillSpray

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Allright, Math inc.

 

Disclaimer:

 

I'm guiding myself based on http://dragonage.wik...s_(Inquisition).

I'm not a math genius, so if I get something wrong, feel free to correct me.

 

Abbreviations:

 

ChC: Critical Hit Chance

ChD: Critical Hit Damage

ArPen: Armor Penetration

 

I'll be comparing ChD vs ArPen. (ChD would be the obvious choice for a decent amount of ChC to increase damage)

 

Assumptions: 

 

  • 100% ChCit's tricky to factor in ChC, as there are multiple talents modifying it (e.g. : added ChC when flanking, Izzy's upgrade on Bolt, etc). This simplifies calculations, as I'm considering the best case scenario for ChD compared to ArPen. If ChC is <100%, the value of ChD decreases.
  • Skill multiplier of 200% weapon damage: Dragon Rage taken as default, for obvious reasons. Reaver is FotM.
  • 50% Attack: either from Willpower or weapons, this is a fairly easy value to get, averaging 25% from willpower and 25% from weapon.
  • Variable weapon damage/Armor values of enemies:  I'll perform calculations on various base weapon damages vs various values of enemy armor. ArPen is much more valuable against enemies with high armor, and less valuable for higher base weapon damage.
  • Not Flanking: again, simplifies calculations; afaik bows/Izzy's bolt do not benefit from flanking (projectiles in general), though Hall has a talent that increases his damage by 25% when flanking. Flanking damage has the same value as ChD, as it's factored in the final damage at the same stage as ChD in the damage calculations formula
  • No extra damage reduction on the enemies: RT/Venatori Shieldbearers have a 50% damage reduction if not flanking applied at the end of the formula, meaning the damage is reduced by a flat 50% after the damage is calculated. Again, too many complications for napkin math. Elemental resistances are not factored in as well, as armor has no effect on elemental damage. I'm doing calculations for physical damage.
  • No extra damage multipliers from the talent trees: stated above, every character has several or no extra damage multipliers, with/without certain conditions to meet for the damage bonus to be applied.
  • Not factoring sunder. Highly variable, target not always sundered for the same amount, IF sundered.

Introduction: 

 

Quoting Wiki:

 

 

 

damage = (random between 0.95 and 1.05) * damage

if physical and not rune
effectiveArmor = armor * (1 - armorPenetration)
damage = damage - effectiveArmor
if critical
damage = max(2, damage)
else
damage = max(1, damage)

isMeleeRange = distance less than 3 meters
if flanking
if not isMeleeRange
flankingBonus = max(0, flankingBonus - 25%)
else
flankingBonus = 0

damage = damage * (1 + abilityBonus)
damage = damage * (1 + damageMultiplier + typeBonus + attackBonus)
damage = damage * (1 + criticalBonus + flankingBonus)
damage = damage * (1 - resistance)

if physical and isMeleeRange
defense = defenseMelee
else if physical and not isMeleeRange
defense = defenseRanged
else
defense = defenseMagic

damage = damage * (1 - defense)

if shielded and not flanking
damage = damage * 0.5

 

The base ChD is +40% (a skill/attack does 140% damage when it is a critical strike). Calculations will be done with 2x20% ChD rings vs 2x20% ArPen rings - 180% total ChD and 0 ArPen and 140% total ChD and 40% ArPen.

 

The damage values are calculated using the formula:

 

 

 

final_damage = (base_damage * rand(0.95 to 1.05) - armor * (1 - armor_penetration))
* (ability_multiplier)
* (1 + critical_damage_bonus + flanking_bonus)
* (1 + attack_bonus + damage_multiplier + type_bonus)
* (1 - magic_resistance)

 

Ignored the randomizing, flanking bonus, damage multiplier, type bonus and magic resistance, as stated in the assumptions.

 

Green=ArPen better; Red (pink-ish) = ChD better.

 

NG7u16d.png


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#17
capn233

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I'm pretty sure that ME3MP data was extracted not from gameplay itself but either from memory or files. From what I remember you can't even see in game health values of enemies, just a "healthbar".

 

In ME3 there was no listing of enemy HP values in game, that is correct.  Initially much of the mechanics work was done with in game testing using memory tools.  Use a test target, see how known damage amount alters target values (more or less).  Later, the HP was simply taken from game files.  Also could be compared with the multiplayer balance change thread when applicable.

 

For DAI, there are numerous ways to compile such data, but I guess it just hasn't been done.  Or I missed that spreadsheet.



#18
Drasca

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Allright, Math inc.

 

Disclaimer:

 

I'm guiding myself based on http://dragonage.wik...s_(Inquisition).

I'm not a math genius, so if I get something wrong, feel free to correct me.

 

Try using the formula here instead:

http://forum.bioware...mbat-mechanics/

 

Disclaimer:
Some of the variables involved are actually simplifications summarizing all around. We don't know what part of the formula damage passives from MP are placed in the SP formula. .

 

I am reaaally reaaally hate spreadsheets, otherwise I would be using them.



#19
SkillSpray

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@ Drasca

 

The formula derived from that wiki page comes out exactly the same. Your link is simply more easily understood and accessible.

Thanks for the tip though.

 

As it looks right now, ArPen is only worth it on daggers/bows for high armor enemies, which is to be expected. Working on Hakkon weapons atm.

 

Edit: Woops, got the base crit multi wrong. assumed it's 100%, while your link says it's 40%. Correcting.



#20
TheThirdRace

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Ok, I've applied the damage formula and it seems Armor Penetration becomes better than Attack when enemies have 62+ armor.

Here's how I came to the 62 armor value...

Damage formula
final_damage = (base_damage * rand(0.95 to 1.05) - armor * (1 - armor_penetration))
* (ability_multiplier)
* (1 + critical_damage_bonus + flanking_bonus)
* (1 + attack_bonus + damage_multiplier + type_bonus)
* (1 - magic_resistance)


Assumptions
Weapon damage      -> 167 (Hakkon dagger)
Armor Penetration  -> 18% (6x Dawnstone for Tier3 dagger grip)
Attack             -> 10.5% (6x Everite for Tier3 dagger grip)
Rand(0.95 to 1.05) -> 1 (Normalized value for simplicity)
Any "text" value   -> 0


Case #1 - 60 Armor
0% AP, 0% ATT
final_damage = (167 * 1 - 60 * (1 - 0))
* (ability_multiplier)
* (1 + critical_damage_bonus + flanking_bonus)
* (1 + attack_bonus + damage_multiplier + type_bonus)
* (1 - magic_resistance) = 107 damage


18% AP, 0% ATT
final_damage = (167 * 1 - 60 * (1 - 0.18))
* (ability_multiplier)
* (1 + critical_damage_bonus + flanking_bonus)
* (1 + attack_bonus + damage_multiplier + type_bonus)
* (1 - magic_resistance) = 117.8 damage


0% AP, 10.5% ATT
final_damage = (167 * 1 - 60 * (1 - 0))
* (ability_multiplier)
* (1 + critical_damage_bonus + flanking_bonus)
* (1 + 0.105 + damage_multiplier + type_bonus)
* (1 - magic_resistance) = 118.235 damage


Conclusion: 10.5% ATT is better than 18% AP at 60 Armor

Case #2 - 61 Armor
For easier reading, I simplified the formula by removing unused values

0% AP, 0% ATT
final_damage = (167 - 61 * (1 - 0))
* (1 + attack_bonus) = 106 damage

18% AP, 0% ATT
final_damage = (167 - 61 * (1 - 0.18))
* (1 + attack_bonus) = 116.98 damage

0% AP, 10.5% ATT
final_damage = (167 - 61 * (1 - 0))
* (1 + 0.105) = 117.13 damage


Conclusion: 10.5% ATT is slightly better than 18% AP at 61 Armor

Case #3 - 62 Armor
For easier reading, I simplified the formula by removing unused values

0% AP, 0% ATT
final_damage = (167 - 62 * (1 - 0))
* (1 + attack_bonus) = 105 damage


18% AP, 0% ATT
final_damage = (167 - 62 * (1 - 0.18))
* (1 + attack_bonus) = 116.16 damage


0% AP, 10.5% ATT
final_damage = (167 - 62 * (1 - 0))
* (1 + 0.105) = 116.025 damage


Conclusion: 18% AP is slightly better than 10.5% ATT at 62 Armor

Case #4 - 99 Armor (Nightmare dragon)
For easier reading, I simplified the formula by removing unused values

0% AP, 0% ATT
final_damage = (167 - 99 * (1 - 0))
* (1 + attack_bonus) = 68 damage


18% AP, 0% ATT
final_damage = (167 - 99 * (1 - 0.18))
* (1 + attack_bonus) = 85.82 damage

0% AP, 10.5% ATT
final_damage = (167 - 99 * (1 - 0))
* (1 + 0.105) = 75.14 damage


Conclusion: 18% AP is much better than 10.5% ATT at 99 Armor

Conclusion
With those results, I conclude 62 armor is where 18% Armor Penetration becomes better than 10.5% Attack.

From that conclusion, 2 questions arise:
1- Did I made a mistake while calculating that?
2- How many enemies have 62+ armor? (is there any spreadsheet with those values like there was in ME3?)


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#21
LearnedHand

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Keep in mind the opportunity ost of going with armor penetration. I mean not just going for armor penetration on weapon versus attack % or crit damage but also maybe boosting your damage against high armor targets but decreasing it against all other enemies. I would have a hard time ever going with armor penetration on the weapon. I like the idea of using armor upgrades for sunder or grabbing the stray passives that give armor penetration. In short, options that have little opportunity cost.

 

By opportunity cost I mean not just going for armor penetration on weapon versus attack % or crit damage but also maybe boosting your damage against high armor targets but decreasing ​it against all other enemies. 



#22
TheThirdRace

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Allright, Math inc.

 

Disclaimer:

 

I'm guiding myself based on http://dragonage.wik...s_(Inquisition).

I'm not a math genius, so if I get something wrong, feel free to correct me.

 

Abbreviations:

 

ChC: Critical Hit Chance

ChD: Critical Hit Damage

ArPen: Armor Penetration

 

I'll be comparing ChD vs ArPen. (ChD would be the obvious choice for a decent amount of ChC to increase damage)

 

Technically, I asked for Armor Penetration VS Attack, not VS Critical Damage... I don't see how this could help me with that in mind :)

 

I do appreciate the effort though!



#23
TheThirdRace

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To state it simply, because arPen is a % and not a static value it becomes more valuable as Armor values rise as you gain more benefit from 25% of 100 armor than 25% of 50 armor.

Also since armor directly subtracts from your base damage the gain is multiplied by the rest of the formula. The difference between getting that extra 25 damage is like going from the hossberg twainer to the skywatcher axe on the dragon for example.

 

This is true, but without any indication on how much Armor enemies have, it can become a very moot point.

 

It doesn't matter if Armor Penetration is 100% when Armor is at 10, but it would be incredibly powerful if Armor was at 1000.

 

Without those Armor numbers, it's actually impossible to determine the actual moment where the formula switch from "more beneficial going for Attack" to "more beneficial going for Armor Penetration".

 

My guess is that Armor Penetration could be very powerful, but unless you play only Nightmare/Heartbreaker, it ain't gonna matter.



#24
Luke Barrett

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This is true, but without any indication on how much Armor enemies have, it can become a very moot point.

 

If you're in Fade Mode you can see enemy Armor Ratings when you inspect them.



#25
TormDK

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Luke - You strike me as a math guy. could you comment on why Bioware so far has chosen not to release the math behind the multiplayer game from a design perspective?

 

We sit and do math that might not even be true, so you would save everyone alot of mental energy if you simply had a sticky thread with all the math included.

 

It's not like we don't already have discussions regarding which classes are "better" from a purely theoretical perspective, so I don't assume thats why?


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