(edited by Blood Red Arachnid.2493)
Finding the Diminishing Returns in Stats
Without any of the messy complications of procs or conditions?
Damage = K * Power * ( 1 + ((Precision – 832) / 2100) * (0.5 + Critdmg)))
d(Damage)/d(Power) = K * ( 1 + ((Precision – 832) / 2100) * (0.5 + Critdmg)))
d(Damage)/d(Precision) = K * Power * (0.5 + Critdmg) / 2100
Precision is more beneficial than Power when d(Damage)/d(Precision) is greater than d(Damage)/d(Power) or:
Power – Precision + 832 > 2100 / (0.5 + Critdmg)
Plot for various values of critdamage to make your plot.
It is funny how the solution becomes so simple once it is found. Now I know my mistake of trying to deriving power to precision instead of deriving damage to power then damage to precision. Still, I was close, even if it only counts in horseshoes.
I do like how precision is represented as a base line where 4% precision is acquired from base stats. Although I do think this represents a slight problem in implementation, though. Base precision is truly 916 with a 4% crit chance, and precision cannot be taken out of this and placed into power instead. Attribute investment must exist above these values, so technically that base 4% critical chance is an additional factor added on to power investment. It is here that things become a bit more complicated… but criticism is worthless if I don’t contribute:
Essentially the damage function would have to be changed to
=K x Power x (1 + (0.04 + (Precision – 916)/2100) x (0.5 + Crit dmg))
Where Power is distributed to the 0.04% crit rate independently of precision, as it is in the game. From here, we can differentiate those two functions to get
d(Dmg)/d(Pow) = K x (1 + (0.04 + (Prec – 916)/2100)(0.5 + Critdmg)
d(Dmg)/d(Prec) = K x Pow x 1/2100 x (0.5 + Critdmg)
And the new ratio is…
Power – Prec + 916 – 84 > 2100 /(0.5 + Critdmg)
Power – Prec + 832 > 2100 / (0.5 + Critdmg)
which is Ironic because it is the exact same ratio, and I just ran a mile in a circle. I guess you can work out that precision part ahead of time and it comes to just the same number. But at least I now proved that it works out.
Anyway, the things like procs and conditions is that they can be factored as a series of uptimes and probabilities that, for any particular build, can be added as an addition to DPS that is based upon precision. It is tedious and has to be done on a build by build basis, but it doesn’t require any calculus. Just some ambiguous terms (I like to set the proc rate at 90% certainty of occurring before then as a baseline).
You should also check out a post I made last October.
https://forum-en.gw2archive.eu/forum/professions/warrior/Toughness-Power-theory-numbers/first#post652269
Came to pretty much the same conclusion as the above link… power > all.
The question you then have to ask is “well I’ve got all the power I can possibly get… do I still want more damage? If so… how much of other areas am I willing to give up?”.
Nowadays the answer to that question is “I am happy to give up my vitality, because I die less” and so power and toughness are your primary efficiency stats.. This is why you see many people rocking knight/cavalier gear in wvw, because it’s a good mix of power, toughness, and prec/crit dmg. In hardcore speedruns people sacrifice the toughness as well for full zerker.
It goes the other way in wvw though, because the amount of damage you need is precisely equal to the amount of damage requires to kill someone. Aka deal more damage than they can heal over time, and prevent them from escaping either by cc or burst. After you hit that number, you tend to increase your survivability. There’s no point killing someone in 2 seconds instead of 20 seconds if you will also be eating mud afterwards. If the kill is coming – be patient and keep yourself healthy for the next one.
In terms of efficiency though, I load up on power, then toughness, then crit & crit dmg. Knight weapons, helm, chest, legs. Zerker shoulders, gloves, boots. Cavalier trinkets with maybe a zerker amulet thrown in (the 8% crit dmg on trinkets is a really efficient use of stats).
To compare whether I’d want more power than precision, I just look at the numbers in terms of % damage increase.
Before adding crit damage, precision increases damage at a flat rate: 21 points = 1% crit chance = 0.5% more damage; hence 42 precision = 1% damage (up to a cap at around 2016 additional precision)
Power on the other hand starts at 9.16 power per 1% damage and doesn’t reach 42 per 1% damage until you already have 4200 power; playing with a build editor I was able to cap out a warrior at 4395 power, with 25 might/bloodlust stacks, food buffs, traits that convert toughness into power, an offhand shield (with the shield grants toughness trait), signet of might, banner of strength, dropping the 6th rune bonus for another strength rune and the second sigil bonus for a crest of the soldier.
Basically, without crit damage it’s a very distant goal to make power worth less than precision for raw damage at any point. 50% crit damage means precision is level with power once you hit 2.1k power, which is attainable, but… there’s no set that gives crit damage without power, so you can never truly make the trade-off of precision for power. To make precision worthwhile, you’re forced to take power anyways. The more valuable you try to make precision, the more power you get as a side effect.
There is a point where things can trade off. It just requires a bit of out-of-the-box thinking.
Basically mix ’n match sets. While it is easiest to go either full zerker or full cavalier or full knight, something else that can be done is changing out pieces of equipment for others once stats become redundant.
Take, for example, critical chance. A very untested threshold I’ve always held for crit chance is 50%. The idea goes like this: technically your chance of getting a critical hit doubles ever so frequently with more and more precision, but at 50% chance that growth is slowed to a crawl. Once you crit on half the hits, no more significant gains can really be made, since if you fully dedicate yourself to getting critical hits the most you could ever do is double your current crit chance. With no crit damage, that is equivalent roughly to going from 1.25 damage boost to 1.5 damage boost, or a further 20% increase from the previous investment of stats. So, once that 50% mark is reached, it is more worthwhile to invest in other stats.
So, if a player has something like full Rampager gear and ends up with an absurd crit chance (the highest I managed to get, boons and traits included, was 96% crit chance on my engineer), then you start swapping out pieces of Rampager gear for either Celestial, Carrion, Cavalier, or something like that. This makes an all-around more efficient build, sacrificing very little strength for much greater utility on return. Though something like a 96% crit chance isn’t readily achievable to every class, I imagine there are many situations where a character’s crit rate grows quite rapidly due to trait abilities and fury uptime.