Guild Wars 2

After spending an hour playing with the numbers, I have found myself way too out of practice to come to a solution to a problem.

This problem, of course, is exactly when it is that overall damage output would be better increased by investing into precision than into power, and then at what point precision becomes inefficient against power once again. Much similar calculations can be used to come up with a most efficient survivability by comparing offensive and defensive stats, which only share the relationship that one multiplies the other in the end.

In short, basically it is this: When you add 916 power, you double your damage output. When you add 916 more, you increase your damage output by another 50%. When you add 916 more, you increase your damage output by 33%. Add 916 more for 25% and so on and so fourth. There will come a point where, investing points into precision will give more offensive output than investing into power. This can also be true for survivability, where eventually investing into more HP and/or toughness will result in the player living longer than if they just made the enemy die faster.

But alas, it seems that every turn I have taken has lead me to a dead end. I’m fairly certain that the problem can’t just be solved algebraically, since that method can’t break the limit of a linear interpretation of the data. Logarithms and exponents being used to express similar behavior, but alas the critical points aren’t exponents. I’ve tried basic derivation (infinitesimal change in power vs. infinitesimal change in precision), but I keep hitting methodological blocks with that operation. Considering I haven’t had to derive any function in years, I’ve found myself out of practice and unable to remember all of the tricks of the trade, let alone remember what can be compared to something else without being total nonsense.

I’ve heard of the existence of a chart somewhere that has already solved this issu e.. However, I cannot find hide nor hair of this chart other than mention of its existence. Of course, I would have to check my math against it and use basic logic to see if it makes sense.

Right now, I’ve found myself lost at the moment. I’m sure there is some handy equation somewhere that can solve this problem in five minutes, but hell if I know what it is. Does anyone have any idea what the solution to this problem might be? As much as I’d love to continue on with this problem, it has devolved into me wandering around aimlessly while playing with numbers, not sure if they mean what I think they mean.

EDIT: Forgot to put up what I had done so far. So using some basic logic, I came up with the following:

Power: increases by 1/916% for every point.

Precision: grants an amount of power equal to

Power x (0.5 + Crit Damage) (1/2100)

So divide that by 916 to get the total percentage increase. Note, the critical damage given as a function of the original 4% crit rate is not factored in since that is not a function of precision (this makes things a bit more complicated, but I’ll get there once I solve the bloody thing). So, it should be simple to solve where

1/916 < Power / 916 x (0.5 + Crit Damage) x (1/2100)

Reduced down simply, it comes to

2100 / (0.5 + Crit Damage) < Power

Which comes to the threshold precision would outpace power. With no additional crit damage, it would take 4200 Power before precision would become more potent. With 100% crit damage, it would take 1400 Power for Precision to become more potent.

But all that… just doesn’t seem right. Mostly because it also doesn’t factor in the same diminishing return system that power is being subject to. Eventually (I assume around the 50% mark), crit rate will cease being valuable and then power will become the default investing stat.

Take a look at this post.

https://forum-en.gw2archive.eu/forum/game/players/Damage-Power-Precision-and-Golden-Ratios/first#post1743110

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.