Guild Wars 2

Recently, I was wondering about the relationship between crit damage/precision and how to budget them.

To put it simply, let’s say you already have x amount of crit chance, and y amount of crit damage (whatever they may be). You now have the choice to add a Cavalier (Power Toughness Critdmg) or Knight (Power Toughness Precision) piece. How do you know which one gives more damage? (just assume you are doing WvW so toughness is a must-have stat).

Obviously, to get crit damage you have to sacrifice precision, and vice versa.

The formula for crit chance from the wiki is: crit chance=(p-822)/21 where ‘p’ is precision.

Using a random exotic piece of cavalier jewelry I have, to get 3% crit damage, you have to sacrifice 40 of some other stat. In this case it is precision.

If ‘T’ is the total budget of stats allocated to precision+crit damage, then you have T-p stats left for crit damage. The bonus crit damage you can get will be (T-p)(3/40)*.

Therefore, the crit multiplier is 50% + bonus crit damage, which is:

1.5+(3/4000)(T-p) (not as a percentage)

The average damage multiplier from crit chance (CC) and crit damage (CD) will be:

damage = (CC x CM)+(1-CC)

If you expand this out, it’s a quadratic equation. But we don’t really care what the equation is, only at which point it reaches its’ peak. Therefore, I differentiated with respect to ‘p’ and set this equal to 0

d[damage]/dp = d [(CC x CM)+(1-CC)]/dp = 0

After a lot of number wrangling and calculator mashing (which you may want to check yourself because it might have a mistake inside) this simplifies itself to:

3T-6p= -4466

We don’t care what ‘T’ is so I put the crit damage equation back in to show that instead. It gives:

Crit Damage = [(1534+3p)/4000 -1.5] * 100

In other words, this is a graph of the ‘optimal’ amount of crit damage which you should have for the precision that you have. Go above it and you should trade crit damage for precision, and vice-versa for going below.

Now I haven’t done math in a loooong time so would like to ask if it’s correct, and if not, why it isn’t. If it is correct, what would you do with this information?

Edit: Fixed the mistake

Well, the first flaw that comes to mind is that the amount of stats that you have to trade for crit damage% differs based on which piece we’re talking about. So you’re off to a very bad start there.

And honestly, I am pretty sure someone already did this math. I’ve seen it around.

Yes, afterwards I will run the numbers for the different pieces, but for now I’m focusing on seeing if it makes sense first.

Sunflowers.1729:

Yes, afterwards I will run the numbers for the different pieces, but for now I’m focusing on seeing if it makes sense first.

Well personally, I don’t think that your math makes sense, if you consider the gear choices with crit damage%.

Your math assumes that the amount of Power you have doesn’t change. You’re also talking about trading Precision for Crit damage%. These parameters exist in exactly two comparisons: Valkyrie vs Berserker and Cavalier vs Knight.

Well, if you’re willing to forego that flaw, you’re still running into the issue with difference types of equipment yielding different amounts of crit damage% per precision.

Also, your math does not take into account any amount of base crit % that you might have, such as Fury or the 4% that you start with (which turns into 5% after just 11 points of Precision). And of course, there are playstyles and traits which kinda make the math moot. For example, Thieves have Hidden Killer and Warriors have high uptime of Fury and Unsuspecting Foe.

And honestly, we already have the average damage increase charted, so honestly I don’t see a point in doing the math. Personally, if I was deciding on gear, I would first optimize the crit damage% with this chart and then move around pieces according to the damage chart.

Okay, so I tried to improve the calculation a bit:

http://www.reddit.com/r/Guildwars2/comments/12dmi5/tip_stat_optimization_with_crit_damage/
The ratios for crit damage tradeoff are from 1:12 to 1:16 (not including traits/runes).

First, the base 4% crit chance is included because the formula on http://wiki.guildwars2.com/wiki/Precision accounts for this.

Second, for fury, all you have to do is to move the graph 20 to the left because it is just a free 20% crit chance.

I actually did this because while the charts that you linked tell you which gear pieces are the best for getting crit damage, it doesn’t tell you at which point you should stop getting crit damage (and get precision instead). Also, the graph at :

http://wiki.guildwars2.com/wiki/Critical_hit#Average_damage_increase

Isn’t very useful since getting 5% crit chance and getting 5% crit damage (moving one space sideways or one space down) isn’t the same – it’s a lot easier to get 5% crit damage.

In the attached graph the blue+red lines are without fury (based off the ratio which varies from 12 to 16), and other two with fury. What it shows is that until you reach 46%ish crit chance, you are better off getting critical chance instead of crit damage. (and 26% if you have fury).

Some people get cavalier gear instead of knights while their crit chance is still very low. The graph shows this is a loss of damage and also when exchanging to cavalier gear is better

Obviously it doesn’t account for things like procs or Hidden Killer, but factoring something like that in is really difficult. You have to adjust for these according to your build. In short, this isn’t meant to be something that you follow to the letter, but as an approximation.

For the graph, the x-axis is the crit chance, and the y-axis is the bonus crit damage.