Armor Math: +9/-2, or +10

Hi guys, just got a unfortunate drop, a +9vDemons/-2while Ench Amber Aegis

I've been told by those who are no doubt right about it that the one extra armor from a green is better than the +9/-2 combo....

Just interested in the math behind it; Assume the -2/+9 are always met, same with the +10. Looked at wiki, and either I'm misreading the tables or I don't understand what I should be looking at.

Thanks for the insight

I will assume you were looking here: http://wiki.guildwars.com/wiki/Armor_rating

The trick is to find the amount of damage where these two situations negate the same amount of damage (the resulting damages are equal).

-9/-2: Armor based damage is reduced to 85.56% then reduced by 2
-10: Armor based damage is reduced to 84.09%

Let x = incoming damage
Let y = resulting damage

y(-9/-2) = .8556x - 2 = y(-10) = .8409x
x = 136.05

If x < 136 you would want the shield with the -2, if x > 136 the other is preferred. Then again, there is also the +30HP to consider, which outweighs the slight difference in damage.

Note that between these two scenarios, it takes an incredible amount of incoming damage to make a difference with these two equations. For example, for the discrepancy to equal 10:

(.8556x -2) = (.8409x) + 10
x = 816.33

You can see there that you are much, much better off with the shield with a Fortitude mod.

Keep in mind that the -2dmg mod will only work while enchanted (duh) but will, more importantly, also only work against physical damage.

Basically this is a good shield if you use enchantments and are facing demons, other wise your not going to get much more then the base armor on that sheild.

Don't let people put you down, that is an awesome shield, and I know a couple people that might want to buy it.

Now to answer your question. The difference between a +10 and a +9 armor mod is ~1,47%. This means that if you take 100 damage without the redux, you will take 1,47 damage more with the +9 shield.

Put otherwise, that one armor doesn't change a thing, and the only thing the +10 does is look prettier.

Also, @ the nice calculation above, I beg to differ. When tanking DoA, most of your incoming damage will be physical, because you will have Shadow form up, and the only thing casters can do is wand you. This leaves you with Rangers, Paragons, Warriors and Dervishes trying to pound your head in with all their might. The only moment a +30hp mod will be better is when you are hit less than 15 times. Other than that, the -2 redux will have vastly outdone the +30hp mod. My +10vDemons -2ench Outcast shield has saved my ass countless times when tanking, when things where getting a bit too sketchy.

You did your calculation wrong in such a way that you took a +9/-2 and a +10 monomod, without the -2. So actually you get:

y(9/-2) = .8556x - 2 = y(10/-2) = .8409x - 2
Which is of course never the case, but we can calculate the difference in damage you take nonetheless.
So, let's say a Margonite Anur Vu is on your tail, swinging his hammer at you, and he hits you for 100 damage.
You have the following:
Blessed armor, Shadow Form, Shroud of Distress, +9/-2 or +10/-2 shield, no bonds.
First of all, the -2 negates your damage to 98. Furthermore, Shadow Form and Shroud reduce this to 88 damage. Then you have either +98 or +97 armor depending on which shield you are wielding.
With the +9/-2 shield, this damage will be reduced to: 88 . .5267 = 46,3 = 46 damage.
With the +10/-2 it will be: 88 . .5176 = 45,5 = 45 damage.

Because of how damage is calculated in Guild Wars, in many occasions, it will be rounded off to the same numeric number. As such you will take the same damage using a +9 or a +10 shield. It does not make a significant difference.

I am not a 100% sure as to whether or not the order in which my calculations took place are correct, if I am not, please point it out, and I will update this.

Nah, they were comparing the +9/-2 to +10/30, because the OP said:Meaning the Aegis of Aargh/Terror.


I doesn't have to be calculated that a +10/-2 is better than a +9/-2.


Also, forgive me for being annoyingly pedantic:
Actually, that is not how you interpret the multiplier difference of 0.147. You have to compare the 0.8556 (+9 armor) to the 0.8409 (+10 armor).

The 9 armor compared to the 10 armor will take 0.8556/0.8409 x 100% = 101.75% damage, or +1.75% damage.

You can also read this in the table at the -1 armor multiplier value.

Physical attacks do not always deal physical damage. Guild Wars defines physical damage as Piercing, Slashing, and Blunt only, so the shield will not reduce wand damage. Also, Ensign put together a good explanation of how damage works that can be found here.

I should note that I would probably use the Amber since the skin is amazing. That kind of stat disparity hardly matters except in a competitive setting.

Ok, so my calculations might not have been perfect, I had this feeling when typing them down, but the bottom line is still that the -2 WILL be better, because as a quite experienced DoA tank, the only ones that will do any damage with wanding is the Fury group, because for some reason, their wands do retarded damage (ranging from 20-40 sometimes). All the others deal straight up 0's with their silly wands, so the only thing that will damage you is actually physical. The places you get hit the most with physical damage is when doing Gloom Cave prep, first ball in city (without bonds you need to be fast before your energy runs out and you get mashed to bits), doing full trench and when doing Big Room in Foundry.
At the Gloom prep, I've had quite some occasions where I saw my health drop to ~50 because of the Sanity's and the Spirits hitting me whilst burning. I can safely say that the total damage my -2 mod had absorbed was far more than 80 damage, so I might've died with the DoA green.
At big ball you can have occasions where your Emo drops your bonds because either he wasn't paying attention and ran out of your range, or for some reason his energy drained (the latter shouldn't happen, so if it happens you were either being too fast or he was being too slow). At this moment what you need to do is survive long enough for the Emo to bond up the other tank and die afterwards. The only reason surviving there is hard is because you don't have balth spirit, and the Margonites scream FEAR ME very loud. So you will die due to lack of energy. Now, in this situation you will have quite some foes hitting you. These range from Hammer Warriors to Dervishes, to Rangers, all dealing physical damage. The damage my shield reduces there goes in the range of about ~300-1000 damage depending on how long I stay there. Shroud of Distress is the big savior there, because it will regen as well, so with the DoA green you will survive about equally long as someone with a -2 shield.
Not much to say about first ball, the only reason you could die there is due to a slow team.
Now, in trench, I can also safely say that my shield has saved my ass there multiple times, because the only things you will have hitting you, or the main things are Fiends, Earth/Flesh Tormentors, Sanity's, Spirit Tormentors and Stygian Brutes, Horrors and Golems. All of which deal physical damage. The difference between taking 2 damage and 0 damage is quite big and quite vital when doing trench, so also there, a -2 shield will vastly outdo your +30hp shield.

Don't let anyone ever tell you a +30hp shield is better than a -2 shield in DoA. I'm not saying that without a -2 shield you'll die, or with it you will be a better tank, but it is vastly better, whether you want to admit it or not.

The OP never specified what he would be running while using the shield. If he is part of a speed clear team and is one of the tanks, I agree with your assessment since the HP is mostly irrelevant due to Protective Bond. While running without it (or versus demons anywhere else) the health is generally better.

Well, using the shield anywhere other than in DoASC on a tank is quite silly, because in DwG it's pretty useless, and running balanced, you will not be under an enchant 100% of the time.

I prefer +45hp for trenches. The only time you will die is when pulling mesmer lord, and here you take damage only from flesh/earth/sanity tormentors.

Earth tormentors do earth damage with their attacks, so the -2 won't trigger.
When you pull you should have everything running after you until the point where you stop to shadow step. Here you take 1 hit from the earth, 1 from the flesh and 1 from the sanity. Then you keep running, and the sanity will hit you maybe 3-4 more times before you cancel stance out. So in total the -2 shield is going to save you like 15hp or something.

True, but the Sanity does the most damage by burning you. Also, you get hit more than once usually, but the mesmer lord isn't the pull where the -2 saves the most damage, it's at the ele pull. Also, a nice trick is to dc to something the second before you stance out, that helps out a lot.
I seem to find that fiends don't hit for an aweful lot, I get like 95% of their hits as 0's, the rest are 3-5 damage, so my guess is the -2 makes a couple 1 and 2 damage hits to be 0. When you pull the patrol that's moving up to the ele, the only thing from that patrol that should ever hit you is a Sanity or a Spirit tormentor, the rest shouldn't even reach you. When you dc into the fiend group and jezus pull them all the way up the empty trench, you will get hit by the fiends like 10-15 times. Also, there is usually also a flesh tormentor in that group, which will hit you once or twice. The fiend damage is usually 0, the Flesh hits you for like 20's. Now, imagine all those fiend hits were instead 2 damage, you would take more damage (nothing special, but still) and you will lose more health than without the -2 mod. This does NOT imply that without the -2 shield you would've died, but it still states that the -2 shield is superior.

But agreed, the mod doesn't do an awe full lot, it's just a cool shield to have imo.

Something like a year ago I went through and tested the damage order of a bunch of stuff, the notable discovery in this case is that insignias and inscriptions are applied after armor, making them even more effective.

If you are curious, here's what I have recorded for my findings (and was too lazy to ever put up on the wiki). Skills on lines with a bunch of slashes basically take effect in whatever order they were cast. A couple of the comments are obviously outdated (old Aura of Holy Might and old Mysticism). This was before the Shadow Form change, but my guess is it's damage reduction would go on the same line as Shield Stance.
It occurs to me that if SF would reduce your damage to 0 (or 1) without a -2 shield mod, that shield mod would be doing nothing (or only -1) for you in those cases.

Fiends do 0 dmg even without a -2 shield. Also, we obviously do something different because I don't bring dc for trench.