Guild Wars 2

If so, why?

What is the value of one power versus one ferocity point?

Expected damage:
Damage of basic hit without critical * chance to have non-critical hit + damage of critical hit * chance to have critical hit.

Power is very likely better than critical damage, because it affects both critical and non-critical hits and scales with critical damage anyway. If you want to know the exact details, I’d check wiki for formulas.

Actually this calculation is rather simple. We can use Power in place of damage because damage is just some multiplication of Power. I’ll use my Ranger’s stats as an example.

2587 power,
1960 precision ((1960-895)/21 = 50.714% critical chance)
1060 ferocity (1.50 + 1060/15 * 0.01 = 220.667% critical damage)
Expected damage:
2587 * (1-0.50714) + 2587 * 0.50714 * 2.20667 = 4170.12

if we add one point of power we get:
2588 * (1-0.50714) + 2588 * 0.50714 * 2.20667 = 4171.73

if we add one point of ferocity instead we get:
2587 * (1-0.50714) + 2587 * 0.50714 * 2.20733 = 4170.98

adding one point of precision shifts the focus a bit:
2587 * (1-0.50762) + 2587 * 0.50762 * 2.20667 = 4171.61

So Power>Precision>Ferocity as far as DPS goes. There are traits that benefit from critical hits though so those have to be taken into account too.

So that means that Ferocity must have a value of 1/1500 versus power having a value of 1/1000. Interesting. That does make sense though. More testing! Wondrous. Your rangers numbers are just what I needed though I admit I’ll be setting your critical chance to 100% for this.

Really interesting question would be to find out if there’s any point at which the power/precision/ferocity dynamic changes and plot a graph of it. Based on my example we know only that at that specific point increasing power would be the best thing, but it may not be so depending on what critical chance we get.

Well that is somewhat what I am trying to figure out.

A quick explanation of what I am doing is trying to test (and prove) that the veracity of a stat is equivalent to it’s weight and that there is a simple and easy to understand way for everyone to be able to calculate their effectiveness without fear of being severely crippled through their game choices.

It’s been an interesting process but Ferocity has me tripped up. It’s importance fluctuates too much and innate doubling doesn’t work on it either.

To compare power vs. ferocity write it out like this:
(2587+x) * (1-0.50714) + (2587 + x) * 0.50714 * 2.20667 > 2587 * (1-0.50714) + 2587 * 0.50714 * [1.50 + (1060+x)/15 * 0.01]

Is this true for all values of x?

I already know the answer to that question, it’s no, but the nature of the question is whether it is ever true for the pool of options set before us (A.K.A. “Max Stats”). Because there is a limited number of options for choosing between precision and ferocity, such as Sigil of Bloodlust vs. Sigil of Cruely, food items, and runes those are the only testable values.

Fundamentally can you ever have enough power for 15 power to be worth less than 15 ferocity and where is that? And that’s where the doubling problem comes in; ferocity is both significantly better and significantly worse than power depending on the model; if you consider the base 150% and say “That 50% is ferocity. Doubling thereforce takes 1,500” you have a weight of 1/1500 which will catch up somewhere around 10,000 or something iirc from mental math but if you say, “That 50% is not ferocity, it is innate, and therefore doubling only requires 750” obviously 1/750 is significantly better than 1/1000.

I could try writing an equivalency but I am not sure it would mean what I thought it meant even if it is all turned into ferocity because base damage itself would greatly effect the outcome. Maybe this particular stat is just not workable because there are multiple elements that go into it. Hm.

Hm…

As it happens, this question is a very old one.

In that thread years ago, I was trying to figure out when it is that power became better than precision. This was before ferocity was a “thing”, and crit damage was just itself. Also, my calculus skills have improved since then.

But, you can do similar calculations today:

Damage = K x Power x (1 + (Precision – 916) / 2100) x (0.5 + Ferocity / 1500)

DDamage/DPower = K x (1 + (Precision – 916) / 2100) x (0.5 + Ferocity / 1500)
DDamage/DPrecision = K x Power x ( (0.5 + Ferocity / 1500)
DDamage/DFerocity = K x Power x (1 + (Precision – 916)/2100 x (751/1500)

That is, DDamage/Dpower is the change in damage as power changes. DDamage/DPrecision is the change in damage as how precision changes. DDamage/DFerocity is the change in damage as how ferocity changes. The breakpoints are where one is equivalent to another.

That is… a bit hard to deal with overall, as we’re talking about 3 separate variables that all multiply each other. Also, it is a bit hard to deal with, due to how frivolous it all is. The fact is, you choose stat sets, not arbitrary stats. What arrangements of stats you can have are already preset in stone.

So instead, most theorycrafters look at assassin vs. berserker, and which rune set gives more bang for its buck on which class. The general trend for how damage goes is this:

Power is the most efficient stat, starting out. 1000 power doubles the damage you do from base stats, and there is no cap on this growth. When compared to precision, you’d need 2100 points of precision just to do 50% more damage. Precision and Ferocity can be seen as modifiers to power.

Precision is the second most efficient stat, as it increases the chance you’ll do critical damage. With base crit chance, the breakpoint between power and precision is at

Power > 2100 / (0.5 + Ferocity/1500) + Precision – 916

Or when you have 4,284 power. You may have immediately noticed, but there’s no way to get 4,284 power. So when building, you opt for “as much as possible”.

Ferocity is the worst scaling stat, because it is the most dependent. Precision can function without ferocity, but not the reverse. If you put 1000 points into Ferocity with no precision, you get a 5.7% extra damage out of the whole things. It is a total waste, until you already have a lot of precision and a lot of power.

So, in short, power first, precision second, ferocity third. Don’t bother with skipping steps.

Zenith.6403:

To compare power vs. ferocity write it out like this:
(2587+x) * (1-0.50714) + (2587 + x) * 0.50714 * 2.20667 > 2587 * (1-0.50714) + 2587 * 0.50714 * [1.50 + (1060+x)/15 * 0.01]

Is this true for all values of x?

I just put this into WolframAlpha and got the result x > -0.006. The breakpoint is right here! If I had one less power and ferocity, then ferocity would be better than power? Maybe I made a mistake or I’m not understanding this correctly. I double-checked and power seems still better than ferocity with values 1 lower

-1 power, -1 ferocity
2586 * (1-0.50714) + 2586 * 0.50714 * 2.206 = 4167.63

add 1 ferocity:
2586 * (1-0.50714) + 2586 * 0.50714 * 2.20667 = 4168.50

add 1 power instead:
2587 * (1-0.50714) + 2587 * 0.50714 * 2.206 = 4169.24

I took the effort to plot Power vs Ferocity in Wolfram Mathematica. The short answer is that Ferocity scales better than Power for ascended attribute numbers.

You can find a PDF of my results here: Power vs Ferocity

Some explanation:
I assumed a Weapon strength (ws in the pdf) of 1000 and a full set of ascended equipment with power (P), precision ( R) and Ferocity(F) attributes only. I did not include damage multipliers from allies, boons or traits. The formula for R is dependent on the number of stats not in power or ferocity and then the standard formula for Crit Chance with a maximum at 100%. Damage(d) is then calculated by the well known formula with an assumed Heavy armor Target (2600 armor and 0 toughness) and skill specific coefficient of 1. Wolfram Mathematica can generate 3d plots which are unable to be rotated in a PDF so I included six different views of the data. It can be seen that the slope of Ferocity is much greater than the slope for Power. However, Ferocity starts at a lower number (0 minimum possible Ferocity) than Power (1000 minimum). So Power is better than Ferocity at lower attribute levels and Crit chances. But, Power Damage is overtaken rapidly as your attributes increase causing your crit chance and crit damage to increase. Finally, I created a table interchanging Power and Ferocity between major and minor attributes of the equipment. In other words, a table showing the interchange of one Power for one Ferocity. Instead of listing a table of 422 numbers, I then listplotted the table to show that damage increased as power decreased and ferocity increased. The final plot clearly shows that your overall damage increases as you interchange Power for Ferocity.

This makes sense. Damage scales additively with Power, but multiplicatively with Ferocity. I did not find the exact attribute point where Ferocity overtakes Power, but it is clearly somewhere below ascended attribute totals; thus, unimportant for min-maxing in raids or other high damage needed areas. Finally if a Ferocity/Power/Precision(F,P,R) armor were to be added, it would deal more damage and replace Berserker’s(P,R,F) for Power Builds.

A lot of people have differing opinions on the matter.

I sat with myself for a while on this and it’s just not working out for me. The question “How much better or worse than than power is ferocity?” is dependent on two distinct variables: The Weapon Strength and The Skill Coefficient. Solving the unifying equation is not proving to be easy, that is, where you can plug in both a designated Weapon Strength and Skill Coefficient to see which works out better.

Basically I need to solve for the skill coefficient and weapon power in which power and ferocity have equivalent weight considering Power Major and Power Minor. I think. I am not actually sure since plugging the values in here and there may or may not produce the same effects.

As for it being an “old question”, it isn’t, this has nothing to do with precision.

As for the breakpoint being negative doesn’t that suggest that this is a logarithm? Or an exponent depending on how you want to frame it? That does make sense but the scaling is so heavily dependent on coefficient and weapon power.

As for the slope point the problem is that a coefficient of 1 is high in this game. Setting it to 1 does make sense (terminate the variable) but it’s higher than most of the game’s actual coefficients. I’ll just have to make a table for every weapon and every coefficient in steps of .01 up to 1.

More testing. More testing!

When is 15 power worth 15 ferocity?

Blood Red Arachnid.2493:

Damage = K x Power x (1 + (Precision – 916) / 2100) x (0.5 + Ferocity / 1500)

This is plain wrong. Since it implies that while having 916 precison (zero crit chance) implies improved damage by crit damage. The real damage formula is:

Damage = K x Power x (1 + (Precision – 916) / 2100 x (0.5 + Ferocity / 1500))

Now on to my own result I’m going to describe the relations between the different stats : K x Power x (1 + (Precision – 916) / 2100 x (0.5 + Ferocity / 1500))

Let’s start with the easiest pair to compare Precision and Ferocity . So assume power unchanging we see that the only thing that can be influenced by either Precision or Ferocity is

(Precision – 916) / 2100 x (0.5 + Ferocity / 1500) which we want to maximize.

Since we have a limited amount of stat points for these stats combined (nl.O with O>=1000) we can write the formula to:

(Precision – 916) / 2100 x (0.5 + (O- Precision)/ 1500) = (Precision – 916) / 2100 x (750 + O- Precision)/ 1500

Since this is a second degree function we can find the top of this function at a Precision of:
-(916+O+750)/2(-1)= 833+O/2

Ferocity is O/2-833. Thus it is better to invest in Precision until the difference between the 2 becomes 1666.

Since we now can describe Precision and Ferocity in the term O we can now describe the damage formula as:

Damage = K x Power x (1 + (833+O/2- 916) / 2100 x (0.5 +( O/2-833 )/ 1500))

What we want to maximize in this case is:
Power x (1 + (833+O/2- 916) / 2100 x (0.5+(O/2-833)/1500))
Since we have a limited amount of stats (nl 5303 ) we can now rewrite the formula to:
(5303-O) x (1 + (833+O/2- 916)/2100 x (0.5+(O/2-833 )/1500))
Now try to maximize the formula and you’l see it will be when O = 0.

So power is in gw2 terms always best, but since we have to place stats in precision and ferocity we then have to place in precision until precision becomes 1666 higher.

To everyone in this topic… make sure to include traits and BUFFS in your calculations, as they skew the balance.

I just use a spreadsheet.

Tim.6450:

Blood Red Arachnid.2493:

Damage = K x Power x (1 + (Precision – 916) / 2100) x (0.5 + Ferocity / 1500)

This is plain wrong. Since it implies that while having 916 precison (zero crit chance) implies improved damage by crit damage. The real damage formula is:

Damage = K x Power x (1 + (Precision – 916) / 2100 x (0.5 + Ferocity / 1500))

So basically I misplaced a parenthesis.

reikken.4961:

To everyone in this topic… make sure to include traits and BUFFS in your calculations, as they skew the balance.

I just use a spreadsheet.

Traits and buffs only matter if they’re 100% uptime, or near enough to 100% that the difference is negligible.

As for whether power+prec or prec+ferocity (you cannot simply assume a single stat for this, as precision is essentially the determining factor) being better, it depends at which point you have enough precision to have a substantial critical rate, and then enough power to ferocity to make the most of said critical rate.

IMO, once you’re able to maintain a ~75% or higher critical rate, I’d start looking at more ferocity over power as you’ve got a substantially higher ability to inflict damage from using ferocity. Though, the balance probably starts to tip once you’re at 51% or higher critical rate.

Aidan Savage.2078:

Traits and buffs only matter if they’re 100% uptime, or near enough to 100% that the difference is negligible.

many traits and buffs are indeed near 100% uptime. like fury
but anything above like 30% uptime is going to have an impact. you just calculate it as such. don’t pretend it’s always there if it isn’t, but do consider it.

Fury isnt 100% uptime unless your trait/skill cooldown is the same or lesser than the duration of the fury buff. Frankly anything with a low uptime of 30% is irrelevant to the point of insignificance as far as which is better. Take the critical traits from engi’s Firearm line. +10% vs <240 range and/or bleeding targets. Both are conditionals that are never going to have substantial uptime until long after the start of a fight.

It’s really easy to factor in traits and buffs. Just translate it to its respective stat (power, precision, ferocity), then multiply its effectiveness by its uptime.

For example, take No Scope from the Firearms line of an engineer. If we ignore the crit rate for now, we can assume that it’ll proc every 10 seconds or so. This means that you’ll get 40% fury uptime, with fury equivalent to 420 precision. Overall this will result in a scaled increase of 168 precision.

Keep in mind that buffs and traits only matter if they are affecting only one of the stats. If it is a trait that just affects damage overall, then it doesn’t do anything to the ratio between the stats.

You make the mistake of translating Fury into a precision increase. It is not, and should not be considered one. It’s an “after math” increase wholly independent from precision. This is even more true when stats are downscaled, as fury’s one of the few buffs that down get downscaled as well.

yeah I just estimate my fury uptime and add an appropriate amount of crit chance when calculating my stats. Or if it’s for a raid, I might assume maxed boons and also banners and the +150 of [stat] party buff traits.

and the nice thing about spreadsheets is you can very easily swap back and forth between different buffs being on or off and see what difference it makes

and btw, a lot of classes can easily get 100% fury uptime even solo
rev, ele, and thief come to mind

also… at lv 80, +420 precision and +fury are functionally identical as far as I’m aware. assuming the precision is added after any traits that calculate off of precision

I solved it.

With a weapon power of any value ferocity equals power at 1500 ( which means that’s the weight of one point in ferocity) rounded to a while number.

Ferocity is always a better choice with a skill coefficient of 6% or greater at the base of 1550. I found this by finding when 15 pts in ferocity equaled 15 in power while reducing both by the skill coefficient at every step.

Ferocity scales better after 1550 power. Now to test runes, food, and sigils for BiS.

Fascinating!

Thank you for all of your help.

FYI: This was tested presuming 100% precision. However after reading the above i decided to test for 4 additional points, 75%, 50%, 25% and 4% crit.

75% and 50% retain 1550 across the board considering a skill coefficient of 6%.

Ferocity does better at all skills with a coefficient of 23% or more with 1550 power.

Ferocity does better with a 4% chance at a coefficient of 1.57 but this is “on average” and thus highly unstable (and ill-advised) using the same base power.

All of the weapon numbers were 1 to terminate the variable. Any weapon of any power should augment these results heavily in favor of Ferocity.

DGraves.3720:

I solved it.

With a weapon power of any value ferocity equals power at 1500 ( which means that’s the weight of one point in ferocity) rounded to a while number.

Ferocity is always a better choice with a skill coefficient of 6% or greater at the base of 1550. I found this by finding when 15 pts in ferocity equaled 15 in power while reducing both by the skill coefficient at every step.

Ferocity scales better after 1550 power. Now to test runes, food, and sigils for BiS.

Fascinating!

Thank you for all of your help.

FYI: This was tested presuming 100% precision. However after reading the above i decided to test for 4 additional points, 75%, 50%, 25% and 4% crit.

75% and 50% retain 1550 across the board considering a skill coefficient of 6%.

Ferocity does better at all skills with a coefficient of 23% or more with 1550 power.

Ferocity does better with a 4% chance at a coefficient of 1.57 but this is “on average” and thus highly unstable (and ill-advised) using the same base power.

All of the weapon numbers were 1 to terminate the variable. Any weapon of any power should augment these results heavily in favor of Ferocity.

i dont understand how you concluded this because the difference between 100% and 50% crit rate will literally weaken ferocity by a factor of 2 when compared to power.

you must be doing something wrong.

I’ve setup an Excel sheet that calculates a “perfect” (trying to maximize effective power) combination of ascended gear pieces according to predefined stat minima (e.g. at least 20k health and 2k6 armor). It’s still a bit clunky but it works, if anyone is interested pm me. It would be good if you’ve used Excel before though^^

insanemaniac.2456:

i dont understand how you concluded this because the difference between 100% and 50% crit rate will literally weaken ferocity by a factor of 2 when compared to power.

you must be doing something wrong.

This is the primary problem with how people calculate things; ferocity is ferocity, it is not effected in any way by precision, and thus it suffers no reduction. You can claim that ferocity and it’s being engaged is less and then average that out but you fall into the trap of averaging behavior which tends to fail in short-engagements. Since all attacks are independent events every event has a chance of 50% with no guarantee of order therefore it is unreliable to calculate this using “conversion methods” and also just a bad idea.

That aside the secondary problem is the understanding of the base and what it actually means. If the weapon power is 1 and the skill coefficient is 6% then at 50% critical chance 15 ferocity still outpaces 15 power because of how coefficients work. 6% of 15 is .9 added to the base is 60.9 while 1% of the adjusted base of 60 ( 6% of 1000 ) is still 6 making 66. It’s Net vs. Gross. Even if you did divide the 1% in half you’d still get 63.

DGraves.3720:

insanemaniac.2456:

i dont understand how you concluded this because the difference between 100% and 50% crit rate will literally weaken ferocity by a factor of 2 when compared to power.

you must be doing something wrong.

This is the primary problem with how people calculate things; ferocity is ferocity, it is not effected in any way by precision, and thus it suffers no reduction. You can claim that ferocity and it’s being engaged is less and then average that out but you fall into the trap of averaging behavior which tends to fail in short-engagements. Since all attacks are independent events every event has a chance of 50% with no guarantee of order therefore it is unreliable to calculate this using “conversion methods” and also just a bad idea.

That aside the secondary problem is the understanding of the base and what it actually means. If the weapon power is 1 and the skill coefficient is 6% then at 50% critical chance 15 ferocity still outpaces 15 power because of how coefficients work. 6% of 15 is .9 added to the base is 60.9 while 1% of the adjusted base of 60 ( 6% of 1000 ) is still 6 making 66. It’s Net vs. Gross. Even if you did divide the 1% in half you’d still get 63.

what did i just read =/

if you arent working in terms of expected values (averages) then why are you doing calculations instead of empirical testing?

Aidan Savage.2078:

You make the mistake of translating Fury into a precision increase. It is not, and should not be considered one. It’s an “after math” increase wholly independent from precision. This is even more true when stats are downscaled, as fury’s one of the few buffs that down get downscaled as well.

Except that it is, for all intents and purposes, a precision increase. The effective of fury is dependent upon the amount of precision that already exists, and the more precision one has, the less of an effect on overall damage that fury will have.

insanemaniac.2456:

DGraves.3720:

insanemaniac.2456:

i dont understand how you concluded this because the difference between 100% and 50% crit rate will literally weaken ferocity by a factor of 2 when compared to power.

you must be doing something wrong.

This is the primary problem with how people calculate things; ferocity is ferocity, it is not effected in any way by precision, and thus it suffers no reduction. You can claim that ferocity and it’s being engaged is less and then average that out but you fall into the trap of averaging behavior which tends to fail in short-engagements. Since all attacks are independent events every event has a chance of 50% with no guarantee of order therefore it is unreliable to calculate this using “conversion methods” and also just a bad idea.

That aside the secondary problem is the understanding of the base and what it actually means. If the weapon power is 1 and the skill coefficient is 6% then at 50% critical chance 15 ferocity still outpaces 15 power because of how coefficients work. 6% of 15 is .9 added to the base is 60.9 while 1% of the adjusted base of 60 ( 6% of 1000 ) is still 6 making 66. It’s Net vs. Gross. Even if you did divide the 1% in half you’d still get 63.

what did i just read =/

if you arent working in terms of expected values (averages) then why are you doing calculations instead of empirical testing?

Actually averaging is only one form of modeling. I strongly suggest against it since logically and “empirically” there are too few iterations per sortie to actually achieve an averaged outcome. For instance if you have a critical of 95% during most of your sorties you will have more than 95% critical rate. Since all of the events are calculated independently the odds of failing to get the result are exponential, not linear, which changes how we view things. For instance the odds over 20 strikes to get 20 in a row at a 95% chance would be .95^20 which is .3585 or 36%. This is a far cry from the 19/20 one would presume if averaging.

Let’s just say I use a different method and it seems to work a lot better.

Math™ by DGraves.

It isn’t iterations per single sortie. It is iterations per every sortie, ever.

Blood Red Arachnid.2493:

It isn’t iterations per single sortie. It is iterations per every sortie, ever.

Which is useless. How much can we possibly even begin to care about sorties we’ve completed let alone sorties we’ve yet to face? We care about the sortie we are in now. If your 5% chance to not get a crit pronounces itself multiple times in a row you think “that sucks” not “Finally, I am seeing justice done for having too many critical strikes against that other enemy over there who is dead now.”

People who use averaging tend to skew their own DPS (if it even must be used … I shudder) and often against themselves because as I said probability of singular events is exponential, not linear, so they presume they need more of a stat than they really do. The difference between 80% and 90% precision is far greater than the difference between 90% and 100%.

But this is not the time nor the place to discuss this. I could not care less for unrealistic “expectations” due to the misuse and misunderstanding of averaging and it’s immediacy.

Well, the whole point of theorycrafting is to create a better build for the future, so technically all we can ever care about are the undetermined sorties of the future. It’s not that hard. Just find the limit of f(x) as x approaches infinity.

ok this thread was extremely distressing to me so i dug up this table which i saw a week or 2 ago in a reddit thread that had better math.

the way to read this is as follows:

• row corresponds to precision / crit rate.
• column corresponds to ferocity.
• in each cell is a number. this number is the power you would need to attain before 1 more precision or ferocity gives more overall dps than 1 power.
• the green (and blue) means get 1 ferocity and not 1 precision (blue is when you have fury).
• the white is when to get 1 precision instead of 1 ferocity.

i cannot verify the numbers and do not wish to take the effort to, but when you consider the source its unlikely to be significantly wrong.

Blood Red Arachnid.2493:

Well, the whole point of theorycrafting is to create a better build for the future, so technically all we can ever care about are the undetermined sorties of the future. It’s not that hard. Just find the limit of f(x) as x approaches infinity.

Actually the entire point of theorycrafting is to find the most efficient way to do something. It’s regressive. Theorycrafting can help build future builds but generally speaking future builds are just reiterations of older builds with modified mechanics to keep up with the modifications of the developer. They are not actually “new”.

As a matter of fact most theorycrafting is so regressive that it doesn’t even start “from scratch”; many of the elements in theorycrafting are taken from other games in which certain things did not apply such as active dodging versus mathematical dodge chance.

This question is proof. The scaling of ferocity is 1/1500 and the scaling of power is 1/1000 but since all three elements (weapon strength, power itself, coefficient) are multiplied each can just be converted into power as a singular value and so long as that equates greater than 1,500 ferocity will win. It requires 1,550 to round up to the next whole number.

Number of people who immediately answered that? 1

Number of people who actually said the opposite? 3.

This if what it means to “start from scratch”. The presumption that power was the best option … was just a presumption.

Nope. Power wasn’t presumed best. It was tested and found to be best. Besides, your whole point is bunk anyway because PVP build making is dynamic and built to fight what other players theorizes other’s builds will be, so its all future there.

DGraves.3720:

This if what it means to “start from scratch”. The presumption that power was the best option … was just a presumption.

well… its not just a presumption. have a look at that table i linked. the guess that any of power, precision, or ferocity could be the best under certain conditions underpins the entire exercise in making a table like that.