Talk:Formulas:Armor penetration

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Shouldn't a decrease from 42.2% to 37% armor mitigation result in a damage increase of 1-((1-37%)/(1-42.2%)) = 9.00%. --bfx 06:33, 16 April 2008 (UTC)

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The article (http://www.parrydodgespin.com/2007/11/10/rogues-and-armor-penetration/) and the thottbot post on serrated blades (http://thottbot.com/s14173) gets its 5% this way:

Ar = Armor reduction as expressed in percent

Ar1 = percent with penetration
Ar2 = percent without penetration

Damage Increase I is:

I = Ar2 - Ar1 # where Ar2 > Ar1, Ar1 > 0, Ar2 > 0, I > 0

I tried to reverse enginner part of how you derived the formula.

Damage expected from armor effects = Full Damage - Damage Reduction. In symbols it would be:

De = 1 - Dr # where Dr is expressed in decimal, Dr > 0, De > 0 Damage Increase, De < Damage Decrease

or

De = 100% - Dr # where Dr is expressed in percent, Dr > 0

De1 = Damage expected with penetration
De2 = Damage expected without penetration

Your forumla and the armor pen calculator damage increase I:

I = 100% - De1/De2 # where I > 0 Damage Increase

or

• I = 100% - (100% - Dr1)/(100% - Dr2) # where Dr1 = damage reduction with armor pen and Dr2 = damage reduction without armor pen

or

• I = 100% - ratio of full damage

But...

• I is damage reduction

Because

100% damage = Damage Reduction + Damage Increase

You know what? Reading the executioner enchant on thottbot (http://thottbot.com/i33307) from the post from Daerien carefully, the I value was meant for damage reduction not damage increase! In your thinking and the calculators thinking (http://rehfeld.us/wow/armor-penetration.html) made the same mistake. Did you write calculator :D.

Lets work the calculation with a Reference damage this time. The math behind this is as follows:

Lets start in the general case and we work with any arbitrary numbers later.

R = Reference Damage
F = Full damage without armor effects = 100%
Ar = Armor Reduction on character sheet

Ar1 = Armor reduction with armor pen
Ar2 = Armor reduction without armor pen

Damage effect as a result of armor for any arbitrary reference damage is:

De = R*(F - Ar1)

Compare the effects with armor pen and without to reference damage

D = (De1 - De2)/R # where De1 = damage effects with armor pen and De2 = damage effects without armor pen

or

D = (R*(F - Ar1) - R*(F - Ar2))/R

or

D = R*((F - Ar1) - (F - Ar2))/R

or

D = (F - Ar1) - (F - Ar2)

or

D = F - Ar1 - F + Ar2

or the real formula for damage increase for any arbitrary reference damage is

• D = Ar2 - Ar1

If D > 0 it is damage increase, D < 0 damage decrease

Lets assume we use R=1000 as our arbitrary reference damage:

So,

D = (1000*(1-0.37) - 1000*(1-0.422)) / 1000 # decimal form

or

D = (1000*(100%-37%) - 1000*(100%-42.2%)) / 1000 # percent form

or

D = 0.63 - 0.578

or

D = 0.052

or

D = 5.2% damage increase

The article (http://www.parrydodgespin.com/2007/11/10/rogues-and-armor-penetration/) just rounded down for the casual reader who isn't really interested in the 0.2%. Since the 9% is suspicious and was ment for "Damage Reduction" I will revert the number back to 5%. Also the calculator wasn't peered reviewed or is not open source so the percentage may be incorrect. The values it outputs has a behavior close to damage increase numbers but may not be correct. I personally use the method of just subtracting the two percentages as well. Trypt0 (talk)