Guild Wars 2

If I have 40 percent damage reduction from armor and toughness, and I use signet of judgement for the 10 percent damage reduction… Will I take 50 damage from a 100 damage hit (the reductions stacked) or will I take 54 damage (first the armor/toughness reduction brought it down to 60, then signet took another 10 percent off)?

And how does protection figure into all this?

Thanks <3

FAQ 30 partially answers this.

Damage reduction modifiers like Judgement and Protection are applied after Direct Damage is calculated ( Direct Damage being skill co-efficient multiplied by power and other modifiers and divided by the target’s armor ).
In your example Signet of Judgement will be a 10% reduction on 60% of the base damage. ( so 54 damage).

Fortunately Protection and Judgement are stacked additively, so it will be a 43% reduction of 60% ( 34.2 damage )

I have a short video clip which illustrates the damage reduction of these effects and how they stack which I can post if you like

If you have 40% dmg reduction plus protection and the signet, that would be almost 100% dmg reduction.

Thanks for the answers. I will watch the video when I get home from work also.
I have calculated that for a full valor / soldier guardian with the 150 toughness and 90 toughness traits using a shield has almost 50 percent damage reduction compared to a light armored char, and that the signet provides the effective hp equivalent of over a few hundred toughness. When combined with protection it increases to having the equivalent of nearly 900 more toughness, and over a thousand if traited.

A very good investment for a tanky guard, thanks!

here’s an old thread I’ve referenced in the past which has some numbers on the subject at Guildwars2 Guru

You can’t really put an exact number equivalent of toughness against a percentage defence modifier because the former is applied before damage modifiers ( like crit ) whilst the latter is calculated after – but you can certainly use them as ball-park estimates.

Funny you should link that thread. I’m actually Lilitu from GW2 guru, so a portion of the math is actually mine throughout the thread. Small world

This is how I put a rough number on the percent modifier:

If the output of the damage formula is 2,127,000 and you have the base 916 toughness and 1211 (2127 defense) then you will take 1,000 damage from this attack.
If I manage to get 1418 toughness from gear, valor, traits, shield etc (okay that’s a stretch, but I’m making the numbers simple) then my overall defense is 916+1418+1211 = 3545.

The damage formula changes to 2,127,000 / 3545 = 600 damage taken. All that toughness reduced my damage taken by 40%.
Now add the signet and it drops to 540. Alright, but how much toughness was that worth?
You can find out by switching the formula above to fit the 540 number:
x (toughness) = 2,127,000 / 540
x = 3939. An increase in toughness of 394. The signet was worth 394 toughness.
My effective hp shot from (assuming 1000hp for relative terms) 1000/600 = 1.666 to 1000/540 = 1.85.

Comparatively the formula would have looked like this if the signet was before the damage formula rather than after (which is why I was asking):
x (toughness) = 2,127,000 / 500 (pre-existing 40% dmg reduction as shown above plus 10% from the signet)
x = 4254. An increase in toughness of 709.
My effective hp shot from (assuming 1000hp for relative terms) 1000/600 = 1.666 to 1000/500 = 2.

You can see why I was kind of hoping it was additive with the damage reduction from armor/toughness I guess it was too good to be true, but this is equally as tasty.

If you keep going down this road you’ll find that this signet and protection actually get better and better in both effective hp terms and toughness equivalence terms as you get higher and higher toughness. The numbers also start inflating if you use light armor rather numbers rather than heavy (in the very first example I have 3545 defense and 40% damage reduction compared to if I had nothing except my base stats… it’s probably closer to 50% damage reduction if you compare it to an ele/mesmer/necro. So it’s actually worth even more toughness and effective hp if you take a lightly armored class as the baseline, since toughness is worth ever so slightly less on heavy armor.