Guild Wars 2

I was always interested in finding the optimal combination of Power+Precision+Ferocity for a given amount of stats. Unfortunately, I have not yet been able to find something of significant relevance or interest on the web, and I myself am not able to calculate something like that.
GW2 formula for Damage, where X = Power, Y = Precision, Z = Ferocity, A = Various damage multipliers active at the time(Such as having +10% damage and +5% damage bonuses would mean that A is 1.1 × 1.05…)(Restrictions: X > 916, Y > 916, Z > 0)
X × (1 – (Y – 842) / 2100) + X × (Y – 842) / 2100 × (1.5 + Z / 1500) × A × Weapon Damage × Skill Coefficient ÷ Target’s Armor
Only the XYZ part is relevant for the sake of stat optimization, since the rest cannot be affected.
(This looks unnecessarily complicated, but can actually be applied for GW2 buildcrafting. Basically, I’m asking the question of how to “spread” my stat points over power/precision/ferocity. For example, let’s say I have 5,000 stat points and want to get an optimal combination of damage. How should I “put” my points?)

I just swing my sword.
Then i swing my sword again. And again.
Then i win.

Wanze.8410:

I just swing my sword.
Then i swing my sword again. And again.
Then i win.

Have you never, ever lost to some Dark Overlords in WvW who came, killed you and were gone like a scary nightmare?
Well, it can be that they just know the secret of this formula… and that gives them the power…

https://forum-en.gw2archive.eu/forum/game/players/Damage-Power-Precision-and-Golden-Ratios/first#post1734821

Torsailr.8456:

https://forum-en.gw2archive.eu/forum/game/players/Damage-Power-Precision-and-Golden-Ratios/first#post1734821

This is extremely relevant… But, he’s not at the level of Dark Overlords yet:
Unfortunately, the math he provides only does work with 2 variables given a constant critical damage… Which means that he is just showing a ratio of Power to Precision given Certain Ferocity, not optimizing all 3 variables in tandem with each other…
And he also draws a very incorrect conclusion of power being more important than precision at all times when you have less than 35% bonus critical damage.
I can just slap three numbers: 1000 precision, 10000 power and 1.8 critical damage(which is only 30% bonus critical damage). At this point, getting 100 points of precision will be better than 100 points of power(In fact, it’ll be still better when you have 2900 power to 1000 precision, which is a little bit realistic already)

https://forum-en.gw2archive.eu/forum/game/gw2/Finding-the-Diminishing-Returns-in-Stats/

I had the same musings awhile ago. That was back when crit% was still just crit %. So, the updated formulas for today would be

Damage = K*Power*( 1 + ((Precision – 832)/2100)*(0.5 + Ferocity/1500)))

Applying calculus and derivating those values

d(damage)/d(power) = K*( 1 + ((Precision – 832)/2100) * (0.5 + Ferocity/1500)))
d(damage)/d(precision) = K*Power*(0.5 + Ferocity/1500)/2100
d(damage)/d(ferocity)= K*Power*(1 + ((Precision – 832)/2100))/1500

I am really hoping I got that last formula right, since again I haven’t had to use calculus in years. Anyway, the idea is that by setting these formula against each other, we can come up with a series of equations to find where each stat becomes the most efficient. In particular, when the change in power is equal to the change in precision, which is equal to the change in ferocity. Power is equivalent to precision in growth when:

Power = 2100/(0.5 + Ferocity/1500) + Precision – 832

and Power is equivalent to ferocity in growth when… gonna have to work out the math on this one.

Let U = (Precision – 832)/2100

1 + U(0.5 + Ferocity/1500) = Power/1500 * (1 + U)

1500 + U(750 + Ferocity) = Power (1 + U)

Power = (1500 + U(750+ Ferocity)) / (1 + U)

Substituting back in…

Power = (1500 + ((Precision – 832)/2100) * (750 + Ferocity)) / (1 + ((Precision – 832)/2100))

Which is.. really messy. Someone should probably check my math and methods on this. This messy equation is why most people try to go with benchmarks, and just calculate the power to precision ratio from there.

As to finding an equivalence point for when the change in damage is the same across all three? I’d say good luck with that. I can barely handle the algebra at this time. But I hope what I have provided helps.

EDIT: I kitten ed. Ferocity is expressed as a percentage point, and not a solid number. It is /1500 instead of /15, and I was just doing the conversion in my head automatically.

This should do (assumes fury) https://www.wolframalpha.com/input/?i=maximize+%28916%2Bx%29+*+%281+%2B+%2824.5+%2B+y%2F21%29%2F100+*+%280.5+%2B+z%2F1500%29%29%2C+x%2By%2Bz%3D5000

However, optimizing damage formula doesn’t give you the highest damage. Pretty much every build has buffs or critical hit based effects (which make precision more important) so truly optimal attribute allocation varies from build to build.

Evalia.7103:

Wanze.8410:

I just swing my sword.
Then i swing my sword again. And again.
Then i win.

Have you never, ever lost to some Dark Overlords in WvW who came, killed you and were gone like a scary nightmare?
Well, it can be that they just know the secret of this formula… and that gives them the power…

I am a fast runner.

I don’t see how you could possible determine optimal stat allocation except on a skill by skill basis since each skill has two DPS components~

base damage x crit chance x crit magnitude
scaling coefficient x power x crit chance x crit magnitude

As the ratio of base:scaler varies from skill to skill the sweet spot is also going to vary from skill to skill (thought you could do an aggregate value for a whole weapon tray 1-5 with weighted ratios for auto-attack vs directed skills driven by cooldowns…)

It CAN be solved, but the solution is going to be about three dimensions deeper than what’s been shown here so far and it will be unique to each possible weapon set up for each profession including do you have cooldown reduction traited (and even that being a best approximation vs. the actual frequency of use of skills in combat).

And yeah… all that before factoring buffs and the hard cap on crit chance/leaving sufficient room in you build for Fury if you expect to have decent fury uptime. Some of those rat-tail curves are abruptly clamped .

To add to the fun while best output ratios between crit chance and crit magnitude are easy enough to calculate (at least below 75% crit chance – see clamping above) several professions have auto-crit mechanics that could radically shift that ratio in some use cases… If you have 5 auto-crits coming and can consistently accomplish the task you have set yourself in those five hits, do you need stat-based crit chance at all?

And finally you have the weighting issue that affects many of my builds: proc on crit effects. While a pure DPS evaluation is simpler, if you are running crit proc sigils or any of the 38 traits that proc on crit you might want to give that some consideration when spreading your stat points around.

Evalia.7103:

I was always interested in finding the optimal combination of Power+Precision+Ferocity

Zerker.

Evalia.7103:

I was always interested in finding the optimal combination of Power+Precision+Ferocity for a given amount of stats. Unfortunately, I have not yet been able to find something of significant relevance or interest on the web, and I myself am not able to calculate something like that.
GW2 formula for Damage, where X = Power, Y = Precision, Z = Ferocity, A = Various damage multipliers active at the time(Such as having +10% damage and +5% damage bonuses would mean that A is 1.1 × 1.05…)(Restrictions: X > 916, Y > 916, Z > 0)
X × (1 – (Y – 842) / 2100) + X × (Y – 842) / 2100 × (1.5 + Z / 1500) × A × Weapon Damage × Skill Coefficient ÷ Target’s Armor
Only the XYZ part is relevant for the sake of stat optimization, since the rest cannot be affected.
(This looks unnecessarily complicated, but can actually be applied for GW2 buildcrafting. Basically, I’m asking the question of how to “spread” my stat points over power/precision/ferocity. For example, let’s say I have 5,000 stat points and want to get an optimal combination of damage. How should I “put” my points?)

You have 5000 stat points but the problem is you don’t count extra buffs, so it all depends on your profession and regular party set-up. I see your question as “Berserker, Assassin, and how many pieces of each”

Fury: 20%
Banner of Discipline: 8%
Spotter: 7%
Signet of <Precision>: 8.5%
Sigil of Accuracy: 7%

And then you have traits that increase critical chance too, so it’s not just a matter of stat allocation. In my opinion going above 70% critical chance isn’t worth it at all, because Fury + Banner or Spotter will get you above 100% and you will waste precision

Full Ascended Assassin + max points in the precision trait line = 70% critical chance.
Full Ascended Berserker gear = 54% critical chance, you can get to 70% using a combination of critical chance traits, the sigil and the precision signet. So the question between Assassin and Berserker is really, if I don’t use crit trait/sigil/signet, will my other choices give me more damage?

While pretty simplified this chart on the wiki may also help in some broad speculations.

“Average damage increase” at https://wiki.guildwars2.com/wiki/Critical_hit

Though not ideal because it takes 15 ferocity to increase crit damage, while 21 precision to increase crit chance, so you can’t just look to see which next step is higher.

Also, on top of that do you want to consider all of the extra stuff that can be added by crit hitting? Traits that proc on crit, constant sigils vs. proc on crit sigils, etc. I think these will always make precision more valuable than ferocity even if only slightly.

On top of all that your boons and traits will also play a valuable roll in your optimal traits. If you get 80-100% uptime on fury you can ignore a lot more precision, if you have a trait or two (like the necro and reaper) where you can get 100% (situational) crit chance with 0 precision that will change your numbers also dramatically.

http://dtguilds.com/forum/m/6563292/viewthread/19418960-math-balancing-power-precision-ferocity-based-on-ep

We solved this one a while back.

There are other aspects to consider, though, such as on crit procs which are likely more valuable than straight dps.

Some additional reading and extreme min.max discussion if this sort of thing interests you: http://dtguilds.com/forum/m/6563292/viewthread/18718546-post-patch-assassin-mix-ep-evaluation