Guild Wars 2

I need someone better at math than myself to help here. I’ve heard plenty of people say that Power is significantly better than Precision for increasing damage, but my own math says otherwise.
It seems pretty straight forward; 1% total damage is equal to a 1% chance at double damage. ~20 Power grants 1% total damage, and ~21 Precision grants an extra 1% chance to crit.
Let’s take 100 hits for 10 damage as the example.
10×100 = 1000
1000×1.01 = 1010
99×10 = 990 + 20 = 1010

Now understand that the base critical damage is only +50%, not double damage. But +50% critical damage is very easy to achieve. The more you have above that the more the relative value of Precision increases. And on top of that, higher crit chance increases the frequency of triggering various sigils and traits, making it even more valuable.

The Wiki formula for expected average damage with crits supports my conclusion;
“Base damage * (((0.50 + Critical Damage / 100) * (Critical Chance / 100)) + 1) "
Following that, +50% Critical Damage and a 50% Critical Chance results in an overall 50% increase in damage, just as I would expect.

What am I missing here?

because if u calculate power vs precision with 0% critical damage (1.50) power always win, but when u have better crit damage, u can get more damage return from precision

Grimwolf.7163:

What am I missing here?

That you’re fighting with weapons, not with a calculator. Power is guaranteed damage, statistics don’t help with bad luck. And usually, I don’t hit my enemy 100+ times before he’s dead.

Effects on Critical Hits is one thing missing.

Sigils such as Sigil of Flame or Sigil of Lightning basically act as a free hit when they proc on a critical hit every 5 seconds. Sigil of Strength gives you a stack of Might on a Critical hit, where the Superior version can keep roughly a stack of 4 on a person without any Boon Duration increases (140 Power and Condition Dmg there).
Traits also affect how a critical hit behaves. For Mesmers, this means their Clones and Phantasms apply a 5 second Bleed when they crit (and their crit rate is the Mesmer’s crit rate minus things like Sigil of Accuracy).

Now before that makes Precision seem better then Power, Power has its own advantages.

Its a stable damage increase. Something enemies/objects just can’t be hit with criticals, such as Dragons and any destroyable objects Precision (and Condition Dmg to a degree) tend to do rather poorly against these things in comparison to a pure Power focused character. There is nothing “exciting” to add to straight power that Precision can add, BUT its always going to be there.

Glass Cannon Berserker builds get the best of both worlds, at the cost of being … well Glass Cannons.

With 2100 power, 50% critchance and 50 critdamage
you get: 0.5*2100 + 0.5*2100*2 = 3150
add 21 power: 0.5*2121 + 0.5*2121*2 = 3181.5
add 21 precision: 0.49*2100 + 0.51*2100*2 = 3171

The amount of extra damage Power brings is based on Precision and Critical Damage. Similarly the amount of extra damage Precision brings is based on Power and Critical Damage.
If I understood you correctly you are basing your Precision analysis on all three: Power, Precision and Critical Damage (= average damage).
In other words you say that every +1 to CritChance causes +1% more damage. So going from 0% to 100% with steps of 1% would cause 1.01^100 = 2.7 times as much damage, which obviously is not true.

Wethospu.6437:

With 2100 power, 50% critchance and 50 critdamage
you get: 0.5*2100 + 0.5*2100*2 = 3150
add 21 power: 0.5*2121 + 0.5*2121*2 = 3181.5
add 21 precision: 0.49*2100 + 0.51*2100*2 = 3171

The amount of extra damage Power brings is based on Precision and Critical Damage. Similarly the amount of extra damage Precision brings is based on Power and Critical Damage.
If I understood you correctly you are basing your Precision analysis on all three: Power, Precision and Critical Damage (= average damage).
In other words you say that every +1 to CritChance causes +1% more damage. So going from 0% to 100% with steps of 1% would cause 1.01^100 = 2.7 times as much damage, which obviously is not true.

Where would you get that assumption? I said nothing like that. I’ll go straight to the extreme end;
100% crit chance with +100% crit damage would lead to x2.5 overall damage.

The mistake made in the OP is the assumption that 21 power adds 1% damage. It adds more than that. Therefore, power is pretty much the way to go if you want to achieve anything. It increases damage more than precision, unless you build super glassy with maxed crit damage.
IMO, the devs could buff the precision stat a little bit. Even with all the sigils procs and stuff, power seems to be more efficient than precision in creating DPS.

How do you know it adds more than 1% per 20 points? I tested it on several different Thief attacks and they all scaled by almost exactly that amount.

So very confused what you did there. I lost you at “99×10 = 990 + 20 = 1010”. No idea where those numbers came from and also we are dealing with average damage here. The formula you gave out is the critical damage average formula which is different than the average damage formula. This means that you need to take into account the damage when your attack does not crit which Wethospu.6437 has pointed out in his formula. I’ll assign labels to his numbers so you know what is going on. Also, note that since power has a linear relationship with % damage, we will assume 1 power = 1 damage in this case.

With 2100 power, 50% critchance and +50% critdamage (note that 50% is base so +100% in total)
you get:
Expected Damage without Critical + Expected Damage with Critical =
(Prob. of non-crit x Damage without Crit) + (Prob. of crit x Damage with Crit)=
(0.5 × 2100) + (0.5 x (2100*2)) = 3150
add 21 power: 0.5*2121 + 0.5*2121*2 = 3181.5
add 21 precision: 0.49*2100 + 0.51*2100*2 = 3171

Notice that when you add precision, you are also lowering the expected damage of a non-critical because you lowered the prob. of a non-critical.

I don’t see where you’re going with this.
First, that formula I gave which you didn’t understand was the result of dealing 99 regular hits and a single crit with +50% critical damage.
Second, the formula I took from the wiki is not simply for finding out the average damage of a critical hit. If it were, it would have no use for critical chance, and would have to include additional math for the damage variances. I assume I must have misunderstood what you mean here, because it just makes far too little sense.
The formula I used does take non-crits into account, because it simply averages the critical damage. 4x damage every other hit is equal to 2x damage on every hit.
Finally, that formula you showed supports exactly what I’ve been saying all along. The two grant extremely similar amounts of extra damage at that level of critical damage, and with at least around 53% critical damage Precision would always come out ahead. Exactly as I’ve been saying.
In PvE/WvW it isn’t difficult to get 100% critical damage, at which point Precision would grant FAR more damage than Power.

… the formula you gave IS the average damage of a critical hit. What you have there is Prob of crit x Crit Dmg Factor x Base damage which is the “expected damage with critical” in the formula in my post.

Also, I see what you are trying to get at. The critical value will come out ahead if you have a high enough critical dmg BUT you need to take a look at the crit dmg % that items give you as well. Most items give you around 1% crit dmg for 9 power sacrificed and some are even higher. Because of this limitation, the TOTAL crit dmg you gain for the power sacrificed actually results in a lower average damage. You can do this on a spreadsheet with actual ingame ascended/exotic item numbers. In general, 1% crit dmg for less than 7 power or precision is good to average. Sacrificing anymore than this will result in a lower average damage (though a lot of people do this more for the burst damage cause that is what matters the most in PvP).

EDIT: I’m not sure what skills you guys got as a thief. But on a Guardian, Power > Pre >Crit dmg at all times since we cannot actually reach such a high enough number.

But if you’re stacking both Precision and Critical Damage, then you’re not sacrificing damage on either end. They both pull ahead of Power. On Trinkets, which average as you said 1% Critical Damage for 9 of another attribute (in this case let’s say Power, even though the two are not in direct competition).
9 Power would grant around 0.45% damage. 1% Critical Damage then would be better with at least 46% Critical Chance.
And with Trinkets alone you can easily get enough Critical Damage for Precision to pull ahead, so you don’t even need to take the less efficient armor values into account.

MLieBennett.9031:

Glass Cannon Berserker builds get the best of both worlds, at the cost of being … well Glass Cannons.

And why they love their protection…

They don’t pull ahead given the amount of limited stats; I have them on a spread sheet. If you don’t believe me, input the real numbers yourself on a spread sheet cause it seems nothing else will convince you.

Tinboy.7954:

EDIT: I’m not sure what skills you guys got as a thief. But on a Guardian, Power > Pre >Crit dmg at all times since we cannot actually reach such a high enough number.

I disagree.
In most situations Power dominates, but in group enviroment high stacks of might can easily make precision more useful than power damage wise (when you had a lot of critical damage, which is not unusual to have on a cookie cutter guardian build).

Vargamonth.2047:

Tinboy.7954:

EDIT: I’m not sure what skills you guys got as a thief. But on a Guardian, Power > Pre >Crit dmg at all times since we cannot actually reach such a high enough number.

I disagree.
In most situations Power dominates, but in group enviroment high stacks of might can easily make precision more useful than power damage wise (when you had a lot of critical damage, which is not unusual to have on a cookie cutter guardian build).

Yep, you are correct. I had a bad choice of words. But yea, you would literally need to keep 20+ stacks of might at all times for it to be better in the long run.

Tinboy.7954:

They don’t pull ahead given the amount of limited stats; I have them on a spread sheet. If you don’t believe me, input the real numbers yourself on a spread sheet cause it seems nothing else will convince you.

I just did; as a Thief with literally nothing more than 20 points in Critical Strikes and all Ascended Berserker Trinkets, Precision and Critical Damage are both high enough to put each other above Power.

Grimwolf.7163:

Where would you get that assumption? I said nothing like that. I’ll go straight to the extreme end;
100% crit chance with +100% crit damage would lead to x2.5 overall damage.

Yes, you are correct. 100% CritChance and +100% CritDamage adds more damage than 20 Power.

However, what you need to understand is a difference between non-critting damage, critting damage and average damage (which includes crits). Critical Hits add damage equal to difference between non-critting and critting damage.
On your example your non-critting damage = average damage which means you assume 0% CritChance.

My example in that case is:
With 2100 power, 0% CritChance and 50 CritDamage
you get: 2100 = 2100
add 21 Power: 2121 = 2121
add 21 Precision: 0.99*2100 + 0.01*2100*2 = 2121

As you can see, same result as you got. But 0% CritChance is not realistic.

You’re taking that example too literally, it was just meant to be simple. I understand that you’d still have a chance to crit even if you are taking Power instead, but the scaling should be the same regardless. 1% crit chance adds 1% damage with +50% crit damage whether you’re going from 0% to 1% or 79% to 80%, and 20 Power adds 1% damage whether you have a 0% crit chance or 100%.
Yeah it’ll grant more actual damage since the numbers being put out are larger, but the percent is the same, and both Power and Precision are working on percents.

The main reason for criticals is procs, not so much raw damage. Depending on traits and sigils they can be far more valuable. Flamethrower hits 10 times in 2 seconds, at least two of those will be crits. Depending on gear/traits you could procc up to 4 buffs and conditions per hit.

Absolute damage calculations become very fuzzy because condition damage becomes a parameter too, as do fury/weakness durations.

Grimwolf.7163:

You’re taking that example too literally, it was just meant to be simple. I understand that you’d still have a chance to crit even if you are taking Power instead, but the scaling should be the same regardless. 1% crit chance adds 1% damage with +50% crit damage whether you’re going from 0% to 1% or 79% to 80%, and 20 Power adds 1% damage whether you have a 0% crit chance or 100%.
Yeah it’ll grant more actual damage since the numbers being put out are larger, but the percent is the same, and both Power and Precision are working on percents.

I have to take it literally. You are basing your theory on one result (only one it’s working on).

Damage added by critical hit is: damage of crit – damage of non-crit. This is X*Power*(CritDamage – 1). X is constant (weapon, target armor, etc) so I leave it out for simplicity. Power is similarly a constant too but I will include it for clarity (so base damage (non-critting) is equal to Power).

Effect to average damage is 0.01 * Power * (CritDamage – 1), because extra damage applies only 1% of time.

This added damage is 1% more damage if: added (average) damage / original (average) damage = 0.01

This is:
0.01 * Power * (CritDamage – 1) / (Power (1 – CritChance) + Power * CritChance * CritDamage) = 0.01
Multiple by 100 and move average damage to otherside so:
Power * (CritDamage – 1) = Power (1 – CritChance) + Power * CritChance * CritDamage
Divide by Power (this is why it could have been left out in the beginning too):
CritDamage – 1 = 1 – CritChance + CritChance * CritDamage
Move stuff around:
CritChance * (CritDamage – 1) + 2 – CritDamage = 0

With 50% extra CritDamage total CritDamage becomes 2 so:
CritChance * 2 + 2 – 2 = 0
CritChance = 0

So with 50% extra CritDamage only way to get 1% more damage with 1% extra CritChance is if original CritChance is 0.

However, if you look at added average damage with 50% extra CritDamage it becomes 0.01 * Power. Which means with 50% extra CritDamage damage added is always equal to 1% of BASE damage (non-critting).

Hopefully this cleared it out. If not, please ask.

I’m having difficulty following your math, so decided to do some practical testing in the Mists with the testing weapons.
I was able confirm with certainty that Precision or Critical Damage can surpass Power once you have an achievably high level in the other, but I don’t know exactly what amount. It seemed higher than my math previously led me to believe.
Without any Sigils, Runes or Major Traits, 300 Power with 150 Precision and 15% Critical Damage did drastically more damage than taking 300 Precision and 30% Critical Damage with no Power.
But when I took Sigils and Runes to boost Precision and Critical Damage as much as I could, then those two setups began to do relatively equal amounts of damage. In fact I think Power was already pulling ever so slightly behind. And this was without an on-crit sigil.

I can try to explain and clarify it bit more.

Extra damage caused by a critical hit is damage difference between a critical hit and a normal hit.
If a normal hit does X damage that means a critical hit will do (1.5 + CriticalDamage / 100) * X damage.
Difference is (1.5 + CriticalDamage / 100) * X – X which is X * (0.5 + Critical Damage / 100).
21 Precision (1%-point more CritChance) means on average every 100th hit will do extra damage so effect to average damage is 0.01 * X * (0.5 + Critical Damage / 100).

Wiki refers average damage as expected damage which is:
Base damage * (((0.50 + Critical Damage / 100) * (Critical Chance / 100)) + 1).

Now you said that 21 Precision will increase damage by 1%. This means: added damage / original damage = 0.01
So:
added damage = 0.01 * original damage
So:
0.01 * X * (0.5 + Critical Damage / 100) = 0.01 * X * (((0.50 + Critical Damage / 100) * (Critical Chance / 100)) + 1)
0.5 + Critical Damage / 100 = ((0.50 + Critical Damage / 100) * (Critical Chance / 100)) + 1
Critical Damage / 100 = (0.50 + Critical Damage / 100) * (Critical Chance / 100) + 0.5
Critical Damage = (50 + Critical Damage) * Critical Chance / 100 + 50

Now if Critical Damage = 50 then
50 = (50 + 50) * Critical Chance / 100 + 50
0 = 100 * Critical Chance / 100
0 = Critical Chance

If you wonder why it looks bit different from my original calculation that’s because wiki uses “in-game” values. Critical Chance is a value from 0 to 100 so they divide it by 100. Critical Damage is extra Critical Damage so they divide it by 100 and add 1.5 (default damage multiplier for a critical hits).
I like to keep things simple and use Critical Damage simply as a damage multiplier for a critical hit and Critical Hit as a chance to hit a critical hit.

Not really sure if this helps at all so if you could point out which part causes issues so I can try to clear that up.

I decided to use GW2buildcraft.com and test 30 power vs 30 precision straight up . ( No armor, weapons etc )

with 30 trait points in power
Power 1216
Precision 916
Effective Power 1364.35
Critical Chance 4%
Damage 10%
Condition Duration 30%

with 30 in precision

Power 916
Precision 1216
Effective Power 1195.3
Critical Chance 23.29%
Damage 10%

this pretty much tells me that you have to seriously gear into Precision to beat power since those 30 trait points only give you a 23.29% chance to crit and thats what your banking on with precision more than anything else .

Wethospu.6437:

If a normal hit does X damage that means a critical hit will do (1.5 + CriticalDamage / 100) * X damage.
Difference is (1.5 + CriticalDamage / 100) * X – X which is X * (0.5 + Critical Damage / 100).
21 Precision (1%-point more CritChance) means on average every 100th hit will do extra damage so effect to average damage is 0.01 * X * (0.5 + Critical Damage / 100).

I think I see the issue here. It would seem that I somehow completely misunderstood exactly what that wiki formula was supposed to be doing, and didn’t even follow it exactly. Pretty ridiculous on my part.
I’ve been using a formula like;
((0.5 + Critical Damage / 100) * (Critical Chance / 100) + 1) = Percent Increase
So for example;
((0.5 + 50 / 100) * (50 / 100) + 1) = x1.5 total damage
It still seems sound to me though, because logically a 50% chance at double damage should result in an overall 50% increase compared to a 0% chance or damage, in the same way that a 100% chance at double damage would result in double the overall damage.
Based on the other formulas though, I doubt it’s that simple. I just have no idea why.

Let’s say we compare two builds with base stats plus a certain amount added.
Base Critical Chance of 4%, base Critical Damage of 50%.
Power build = +1400 Power, + 300 Precision, +30% Critical Damage.
1400 Power = +70% Damage, + 5% Sigil of Force = 75%
300 Precision = 14% Critical Chance, +4% base = 17%
30% Critical Damage = 30%, +50% base = 80%
Criticals = +13.6% Damage
88.6% total damage increase over base.

Critical build = +500 Power, +800 Precision, +70% Critical Damage
500 Power = 25% Damage
800 Precision = 38% Critical Chance, +4% base, +5% Sigil of Accuracy = 47%
Critical Damage = 70%, +50% = 120%]
Criticals = 56.4%
81.14% total damage increase over base.

This is the kind of math I’ve been using.

Now, on a more practical level, here are two build links. They both have very similar attributes, except the first has Rune/Sigil choices which favor Precision, and the second has Rune/Sigil choices which favor Power.
http://gw2buildcraft.com/calculator/thief/?7.0|8.1g.h1.0.0.0|8.1g.h17.0.0.0|1n.7h.1n.7h.1n.7h.1n.7h.1n.7h.1n.7h|2s.0.2s.0.3s.0.2s.0.3s.0.2s.0|0.k00.u000.k00.0|0.0|0.0.0.0.0|e
This build, by my math, deals 124.2% damage over base.

http://gw2buildcraft.com/calculator/thief/?7.0|8.1g.h2.a.0.0|8.1g.h17.a.0.0|1n.7b.1n.7b.1n.7b.1n.7b.1n.7b.1n.7b|2s.0.2s.0.3s.0.2s.0.3s.0.2s.0|0.k00.u000.k00.0|0.0|0.0.0.0.0|e
This build, by my math, deals 118.45% damage over base.

Grimwolf.7163:

—
It still seems sound to me though, because logically a 50% chance at double damage should result in an overall 50% increase compared to a 0% chance or damage, in the same way that a 100% chance at double damage would result in double the overall damage.
Based on the other formulas though, I doubt it’s that simple. I just have no idea why.
—

Yes, this is correct but as I said it only works if your original chance was 0%. The way stats work is that more you focus on one stat more effective others become. If in your example critical chance is ridiculous low it will win.
Point I’m trying to get across is that going from 50% critical chance to 100% critical chance won’t increase damage by 50%.
Let’s say with 0% critical chance you deal X damage. At 50% critical chance you would do 1.5X damage. At 100% critical chance you would do 2.0X damage.
As you can see going from 50% to100% increases damage by 0.5X which is 0.5X/1.5X = 1/3 = 33% increase.

Doesn’t that mean though that Power would scale in the same manner? Whether you have enough Power to take you from 1500 to 2000 average damage or Precision or Critical Damage, the increase between those two points is still ~33%
I’m not seeing where this causes a lower stat to start scaling better.

the problem is your trying to work out % damage increases, unless your taking one damage amount as base and referring your % damage increase against that every time it is all diminishing in terms of % gain.

Taking Weths example, if your base damage is 1.0X with the 50% crit rate your damage is 1.5X thats a 50% increase, if you then go to 100% crit rate and not have 2.0X damage thats a 100% damage increase against your base damage of 1.0X but not a 50% increase from the 1.5X.

Yes this also works for power, if you have 2100 power, 21 more power will then give you 1% damage, however if you add another 21 to that 2121 it will give less than 1% increase to the damage you where doing but if your working with 2100 power damage being your base at all times it comes out as 2% more damage than that base.

So if your trying to work out % increases in a non diminishing way you have to choose a specific damage as base and refer to that constantly or realize that you need to work on actual damage gain rather than , if your set on working with stating % damage increases I’d recommend using the complete base stats of 916 power, 916 precision and 50 critical damage as at 80 you cannot go lower than that, if using those as base 9.16 power = 1% increase over that base damage.

Let’s say you have 1200 Power (+14.2%), enough Precision for 50% Crit Chance and 100% Crit Damage.
A particular attack has a base damage of 2000.
With your Power factored in, it becomes 2284.
With your criticals factored in and averaged, the damage becomes 3997.
With 20 more Power, the damage becomes 4032.
The increase in damage is 0.875%.

Now let’s cut out crits completely and take enough Power for that alone to put the damage at 3997. That would be 2913. 1997 over base.
Add another 20 Power to that, and the damage goes from 3997 to 4017
…and if that was accurate, it would seem what you’re saying is correct. Definite reduced impact…
I’m still not sure why the math is working out this way, which makes me really curious.
I understand why the higher the damage is, the less percent increase there would be from one step to the next. But not why the value of each individual attribute affects it differently depending on it’s own size.
I kinda feel like an idiot right now for not being able to understand it. I’ll have to think about this.

Something crucial that I originally overlooked is that I was not taking this into consideration when I did my original testing of damage granted by Power. So Power likely does grant only slightly more than 1% damage for every 20 points. Like maybe 18 or 19 points. I’ll have to test it again.

If other stats stay same (like Power and CritDamage) then every point of Precision adds same amount of raw damage. However, if you increase (decrease) Power or CritDamage raw damage added by Precision changes. This also works for Power and CritDamage.

That’s why if you deeply invest in one stat other stats get better returns.