Thief, FFXI, and other unimportant matters

Shamaya, Asura

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Diablo 3 Crit Gem & DW Testing
Mamimi
shamayaasura
~ Video ~

I heard a little bit about some concerns that crit gems on offhands were working counterintuitively, or at least not in line with the consensual thinking; that both crit gems in both hands were affecting your overall dps, which in other words is tantamount to marginally increasing the dps of both the hand that the gem is in, as well as the other hand; that CHD from the gem would be as if CHD from anywhere else on your character's equipment.

I'm always striving to make sure I'm playing at my best, and whether or not gems work like this or in another way has a kind of big effect on optimizing a characters. So I decided to test and confirm how crit gems were working when dual wielding. Feel free to skip to the TLDR.

Possibilities
Let's look at some theoretical possibilities for how CHD gems could be behaving. I consider (1) to be the general understanding of how they are intended to work. And that it is working as intended is what I hope to verify.

Let's say you have 50 natural, base CHD. You have 50CHD from paragon. You have no CHD in gear and you have 2 130CHD gems.

Possibility (1): Total multiplier; 360CHD applied to both hands;
Possibility (2): Gems total divided; 360CHD, but 100"natural"(base, passive, and gear?) is added to both hands, and 260 CHD is divided between 2 hands; IE 230/hand
Possibility (3): All CHD divided; 360CHD is 180/hand.
Possibility (4): Gems buff separately; One hand is 100+130=230CHD; same for the other hand.

If (1), second sample will be buffed by NewCHD/OldCHD, or 360/230; if (2), our first sample (single wield) will have 230CHD, and in our second sample it will have (100 + 260/2) or 230 still; if (3), NewCHD/OldCHD will be (360/2)/230, or an actual damage loss; if (4)the offhand gem will have no theoretical effect on the main hand, so mainhand would still have 230CHD.

I suppose there could be more possibilities (5^n), that the gem in the mainhand only effects its hand, and a gem in the offhand has its effect split between the two weapons, or that the reverse is true, or other imaginative ways that damage could be divied up, multiplied, or added in different ways. But outside of looking at the game code, a little testing is really all that can be done.

Testing
For this test I fought Ghom in my normal gear using a Mara's Kaleidescope to heal myself from the poison, so that I could test this on a high difficulty and comfortably get sufficient sample sizes. I used entangling shot for no particular reason other than that it does not pierce and only hits one target. I didn't have on Cull the Weak, but it wouldn't matter anyway. My total dex, elemental damage, bonus to elites, passives are of no consequence because they are straight multipliers to the formula, and I am only comparing min/max damage as shown on my weapons. I'm not wearing any rings/ammies or gear that would otherwise raise my min/max damage. If I had I would have that accounted for. No archery as well (wouldn't have screwed anything up). No calamity or mark. No pets. Area damage should be a non-issue, as it supposedly does not group a procced on-screen area damage number with the damage number of the attack that procced it. And additionally, the main target does not get affected by area damage; only additional targets. There also were no additional targets (the way I pulled him, he didn't spawn any leeches for some reason).

Single-Wield Sample
Mainhand is Nat's with dmg range 1255-2149, a max/min of 2149/1255 or ~1.71. Observed lowest min and highest max: 1,344,223 & 2,285,372, ratio of 1.70. Not a 100% thorough sample, but 70/71 or 98.5% sufficient so can most likely work with it safely.

Dual-Wield Sample
Added an offhand Denettas with similar dmg range (important thing is we're comparing max crit dmg observed, and its max is significantly lower than my mainhand Nat's). It has the same CHD gem in it (130%), and 656 dex. After adding it, I remove the 655dex points that I'd had in paragon. To make sure the sample is sufficient, we should try to get as close as possible to the new max/min ratio. This will be the higher of the two max's of either weapon being dual-wielded, divided by the lower of the two mins. My ratio will be 2149/1166, or 1.84. This is my Nat's max divided by my Denetta's min.
Observed lowest min and highest max: 1,565,187 & 2,845,425. The observed ratio is ~1.828, or ~98.6% sufficient, similar with the single-wield sample size.

The Results
Now we'll divide the highest observed max from the dual-wield sample, by that of the single-wield. The ratio we get is 2,845,425/2,285,372, or ~1.245.

Let's go back again to our theoretical possibilities about the various ways that the effect of gems can have when dual wielding.
If proposition (1) mentioned earlier is true, our damage will go up. If (2) is true, we will get no damage increase if we use the same gem, and damage would go down if we used no gem or an inferior gem. If (3) is true, we'll still get a damage loss. And if (4) is true, we'll have no damage increase, and a damage decrease for the offhand specifically with no gem or an inferior gem.

An interesting thing to note is that out of all of the four propositions (excluding 5+), if we get any bit of higher damage at all, then we should know that (1) is true, and we really needn't further scrutinize the second sample. But in the name of thoroughness, I'll do that.

Our highest max ratio of 1.245 between the two samples comes from the 130% CHD gem in the offhand. This put me at +544%CHD (644% Dmg) for the second sample, with +414%CHD (514% Dmg) for the first. Our ratio would be 644/514, or ~1.253, aka ~25.3% increased damage. This is incredibly close to the observed ratio we got of ~1.245, from a ~98.5% sufficient sample size.

The fact that the observed damage and theoretical damage are so close is pretty convincing for verifying that CHD gems are working as intended and as is commonly thought that they do. Especially the fact that propositions (2)-(4) would not even increase our damage at all, or less likely propositions (5n) would pretty much not even be close to the huge increase in damage that we get from proposition (1) being true.

TLDR; CHD gems are working as intended. Your on-sheet CHD is affecting both weapons fully. In other words, a dual-wielded gem's contribution to your CHD is treated and calculated the same as is CHD anywhere else on your character (or from any other source for that matter, I would imagine).

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