Comparing damage reduction from armor to avoidance
Moderators: Fridmarr, Worldie, Aergis, theckhd
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Comparing damage reduction from armor to avoidance
Since Theck mentioned that he hasn't run the numbers to compare the damage reduction of avoidance to armor in the 'Armor vs HP Math Help' thread (that thing is way to long now) and since I had figured out a rough way of doing this using data from his agil vs dodge thread, I figured I'd share. Unlike most of the math Theck uses, this isn't actually very complicated and only uses division, subtraction, and some basic algebra. Note: I am completely ignoring the EH benefit of armor, only comparing the damage reduction. Stam vs armor discussion not welcome.
Ok so let's review some data from Theck's agil vs. dodge thread:
the DR from the 10 dodge gem was .2196%.
the DR from 22 armor (the agil gem) was … oh wait, Theck didn't give that in a matching form. He gave us 99.9541%. Simple enough to convert it though: 100%99.9541%= .0459%, or if you do the math from when he gives the DR from armor %'s earlier, carrying more significant figures, .04606%.
Ok so now that we have a quantity of itemization and a given % DR, we can set those two to be equal…
10 dodge rating = .2196% damage reduction
22 armor = .04606% damage reduction
Now, we can divide the left sides and the right sides together, and still have a valid equation (I can edit in a proof if people need it)…
10dodge rating / 22 armor = .2196% DR / .04606% DR
%DR cancels, multiply both sides by 22 armor, divide both sides by 10.
1 dodge rating = [22*.2196/(.04606*10)] armor
1 dodge rating = 10.489 armor
Now, just apply dimensional analysis and you can convert dodge rating <> armor based on their damage reduction values. Of course, this an estimate, and due to scaling the conversion rate could be off by a sizable margin for various current armor/avoidance levels. (look at the scaling graph for base armor in the agil vs dodge thread, and consider that the part from armor goes down 9% from 107 to almost 98%, when it was added on from 83%. That's going from contributing 24% to 15%.) I also kinda assumed that Theck has his avoidance levels fairly well balanced as far as diminishing returns go, so 1 dodge rating would = 1 parry = 1 def. rating etc, as far as DR goes.
However, the fact that with this conversion our eversofavorite armor trinket, the glyph of indomitability, would be equivalent 170.85 dodge rating, compared to 126 on the equivalent ilvl Eitrigg's Oath or Fervor of the Frostborn (heroic mode 10 AC), it shows that it certainly is possible that armor could be better than avoidance for damage reduction for some people. This is relevant for pieces that trade avoidance rating for armor, like bonus armor pieces, (not like trinkets where it's either all a or all b plus x special effect) and certainly could reaffirm the choice to get a bonus armor piece. I'm sure it would be possible to come up with an function of sorts with inputs x base armor, y dodge, z parry etc, that would spit out a conversion rate for you.
tl;dr version:
the damage reduction from armor can be competitive, if not better than the damage reduction from avoidance. I suck at maths so go ask Theck to help you out if you want a more detailed analysis and graphs etc.
Ok so let's review some data from Theck's agil vs. dodge thread:
the DR from the 10 dodge gem was .2196%.
the DR from 22 armor (the agil gem) was … oh wait, Theck didn't give that in a matching form. He gave us 99.9541%. Simple enough to convert it though: 100%99.9541%= .0459%, or if you do the math from when he gives the DR from armor %'s earlier, carrying more significant figures, .04606%.
Ok so now that we have a quantity of itemization and a given % DR, we can set those two to be equal…
10 dodge rating = .2196% damage reduction
22 armor = .04606% damage reduction
Now, we can divide the left sides and the right sides together, and still have a valid equation (I can edit in a proof if people need it)…
10dodge rating / 22 armor = .2196% DR / .04606% DR
%DR cancels, multiply both sides by 22 armor, divide both sides by 10.
1 dodge rating = [22*.2196/(.04606*10)] armor
1 dodge rating = 10.489 armor
Now, just apply dimensional analysis and you can convert dodge rating <> armor based on their damage reduction values. Of course, this an estimate, and due to scaling the conversion rate could be off by a sizable margin for various current armor/avoidance levels. (look at the scaling graph for base armor in the agil vs dodge thread, and consider that the part from armor goes down 9% from 107 to almost 98%, when it was added on from 83%. That's going from contributing 24% to 15%.) I also kinda assumed that Theck has his avoidance levels fairly well balanced as far as diminishing returns go, so 1 dodge rating would = 1 parry = 1 def. rating etc, as far as DR goes.
However, the fact that with this conversion our eversofavorite armor trinket, the glyph of indomitability, would be equivalent 170.85 dodge rating, compared to 126 on the equivalent ilvl Eitrigg's Oath or Fervor of the Frostborn (heroic mode 10 AC), it shows that it certainly is possible that armor could be better than avoidance for damage reduction for some people. This is relevant for pieces that trade avoidance rating for armor, like bonus armor pieces, (not like trinkets where it's either all a or all b plus x special effect) and certainly could reaffirm the choice to get a bonus armor piece. I'm sure it would be possible to come up with an function of sorts with inputs x base armor, y dodge, z parry etc, that would spit out a conversion rate for you.
tl;dr version:
the damage reduction from armor can be competitive, if not better than the damage reduction from avoidance. I suck at maths so go ask Theck to help you out if you want a more detailed analysis and graphs etc.
 gerbi7
 Posts: 9
 Joined: Fri Feb 22, 2008 3:55 pm
Re: Comparing damage reduction from armor to avoidance
What practical applications do you have in mind for this study, gerbi7? I'm just curious about the big picture.
Havard, 80 Blood Elf Paladin, US Moon Guard
Håvard, 60 Human Paladin, US Moon Guard
Håvard, 60 Human Paladin, US Moon Guard
 Håvard
 Posts: 37
 Joined: Tue Sep 16, 2008 8:51 pm
Re: Comparing damage reduction from armor to avoidance
Part of the reason I didn't bother with the math for it rests on the nature of avoidance and armor. Even if avoidance did reduce total damage intake by more over the course of a fight, it's not a reliable way to prevent damage. With armor, it's guaranteed mitigation on every hit. That reliability has a good deal of value in and of itself.
So even if avoidance was twice as good as armor at reducing total damage taken, I think most tanks would take the armor. I can see a few gimmick situations where it would go the other way, but with diminishing returns on avoidance now I doubt they'd still be feasible.
So even if avoidance was twice as good as armor at reducing total damage taken, I think most tanks would take the armor. I can see a few gimmick situations where it would go the other way, but with diminishing returns on avoidance now I doubt they'd still be feasible.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Call to Arms 5.x, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
MATLAB 5.x, Call to Arms 5.x, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 7655
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Comparing damage reduction from armor to avoidance
I generally think avoidance is undervalued, not in the damage that it prevents, but in the burst that it prevents. Dangerous burst types of damage are often in the form of multiple hits. Avoidance can drastically cut into the frequency of strings of hits, reducing the number of times you are "at risk" in an encounter significantly. Icecrown Radiance really hurts avoidance though, for instance if you went from 65% avoidance down to 45%, you'd see in increase in 3 hit chains by 400%.
You can probably come up with some sort of comparison vs armor in terms of damage reduction, but I doubt it's a static number because of how avoidance stacks, and it would always need the caveat of reaching certain EH levels first before you'd consider giving up armor for it.
You can probably come up with some sort of comparison vs armor in terms of damage reduction, but I doubt it's a static number because of how avoidance stacks, and it would always need the caveat of reaching certain EH levels first before you'd consider giving up armor for it.
 Fridmarr
 Global Mod
 Posts: 9639
 Joined: Sun Apr 08, 2007 1:03 am
Re: Comparing damage reduction from armor to avoidance
Fridmarr wrote:I generally think avoidance is undervalued, not in the damage that it prevents, but in the burst that it prevents. Dangerous burst types of damage are often in the form of multiple hits.
^ I like this but I also try and be rounded out and not that guy who stacks one certain way. I have yet to die to a "tank death" it's always been the other tank that gets wtfpwnd
I refuse to go down easy

kysu  Posts: 154
 Joined: Fri Sep 19, 2008 10:21 am
Re: Comparing damage reduction from armor to avoidance
Fridmarr wrote:I generally think avoidance is undervalued, not in the damage that it prevents, but in the burst that it prevents.
It's really not. In BC we stacked and gemmed avoidance whenever possible because the effective health we were giving up for it was nowhere near the relative gains in avoidance. It almost literally became a scenario of asking yourself, "can I take one hit? OK! Gem avoidance now!" Nowadays with diminishing returns and the Icecrown Radiance debuff, you're giving up quite a bit of both armor and stamina to achieve results far below where we were in BC. Figure, the best avoidance pieces are the three way splits with def/dodge/parry and not the ones with armor/def/dodge or something. You have to swap out your stamina and armor trinkets for Corpse Tongue Coin or the Onyxia Blood Talisman. I've been trying to assemble a BiS avoidance set just to see what I can do with it, but I'm not sure if it will play out in raids to any significant advantage, if it's not actually a detriment.
That said, avoidance is an extremely powerful tool. It's just less powerful the less you have of it, and so that's where we're at now.
 JamesVZ
 Posts: 28
 Joined: Mon Jan 25, 2010 10:38 am
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