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Currently I have a slow attack speed weapon for my Barb in D3. It has a socket. Should I add a Ruby or Emerald?

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One way to find out would be to socket the ruby, and see how much it increases your damage stat. Then multiply the crit hit damage bonus of the emerald by your crit rate to calculate its average damage increase, and compare. –  Wikwocket Jun 5 '12 at 18:15
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I thought I had read somewhere that dps in your character screen includes crit. Not sure where though... –  Aaron Jensen Jun 6 '12 at 3:54
    
@bwarner and others: Does anyone know what the "new behavior" of rubies in 1.0.7 actually is? From what I can tell from this thread, it sounds like the developers changed the calculation from 50 to 90, + 20 to 70 to 110 and don't realize that these two are mathematically equivalent (thus the formulas below would be unchanged.. though the new damage buffs would require a change to the charts). There must be more to it than that?? –  BlueRaja - Danny Pflughoeft Feb 14 '13 at 19:07
    
If nothing else, there are some new levels of gem with significantly different values, so it would be worthwhile to make sure those behave similarly. In addition the change to rubies is that the min and max damage are applied completely independent of each other, where previously min damage could end up boosting max damage as well. Maybe you didn't account for that before, in which case it won't have an effect. –  bwarner Feb 14 '13 at 19:17
    
@bwarner: It doesn't matter if I accounted for it or not; as long as the expected damage-per-attack added by a ruby (RubyDamage below) is correct, regardless of how it's calculated, the equations below will be correct. So, the equations are still correct; all that needs to be changed are the charts, due to the more expensive gems being buffed. I'll see if I can get to that this week. –  BlueRaja - Danny Pflughoeft Feb 14 '13 at 19:55
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7 Answers

Update for 1.07

The folks over at Teamliquid did the number crunching already.

Basically, the ruby is better than an emerald only if it adds a significant % of your overall weapon damage. The more significant it is, the better off you are with the ruby. Also it takes into account of how much your crit/crit damage is.

Here is the relevant chart from that link, for a bigger version click on the above link:

enter image description here

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There is no way I can compete with the #1 answer.

However, I'll provide some intuition.

Critical Damage improvement is obviously proportional to Critical Hit Chance.

Increase Weapon Damage is proportional to attack speed.

Critical damage is proportional to attack speed but that is already taken into account for DPS. If 2 weapon have the same DPS, and same critical chance, critical damage will improve the 2 weapons at the same rate. However, increase weapon damage will improve the faster weapons more.

So high attack speed low critical hit chance, ruby.

Low attack speed, high critical hit chance, emerald.

Intuitively this is as far as most readers will understand anyway. Ruby increase DPS by the square of attack speed. A weapon with 2 attack per second benefit from ruby twice than a weapon with 1 attack per second if DPS is the same.

Not so from Emerald. It simply add a percentage to your DPS and proportional with critical hit chance.

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C'mon? Negative vote? I updated the answer again. –  Jim Thio Oct 15 '12 at 0:46
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Critical damage is also proportional to attack speed, isn't it? If each attack has a chance to crit, then it doesn't matter whether you're attacking quickly or slowly; your average-crit-damage-per-hit is the same, and your DPS will scale up or down with the attack speed. –  Paul Marshall Feb 14 '13 at 18:20
    
Critical damage is proportional to attack speed but that is already taken into account for DPS. If 2 weapon have the same DPS, and same critical chance, critical damage will improve the 2 weapons at the same rate. However, increase weapon damage will improve the faster weapons more. –  Jim Thio Feb 15 '13 at 3:44
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Look at your Damage.

General rule: Low Crit%/CritDmg% -> Ruby, otherwise Emerald.

You don't see lvl 60 Players with rubies in their weaponsockets for a reason :)

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That reason is that the synergy between Crit Chance and Crit Damage blows away any slight amount of straight up damage that rubies provide. –  Frank Nov 25 '12 at 22:35
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Time for a bit of math. Let's define the following:

  • RubyDamage: The damage-per-attack added by imbuing a ruby
  • EmeraldCritDamage: The percentage of damage-increase due to a critical hit added by imbuing an emerald
  • AttackSpeed: Your attacks-per-second
  • WeaponDamage: Your current damage-per-attack (including bonuses, like from your primary stat)
  • CritChance: Your current percentage (from 0 to 1) per hit of getting a critical-hit.
  • CritDamage: Percentage of damage-increase due to a critical hit

Using a ruby will add

RubyDamage * AttackSpeed * (1 + CritChance*CritDamage)

to your total expected DPS, while using an emerald will add

WeaponDamage * AttackSpeed * (CritChance)(EmeraldCritDamage)

to it. You only want to use a Ruby if the first expression is larger than the second expression; that is,

(first expression) > (second expression)
RubyDamage*AttackSpeed*(1 + CritChance*CritDamage) > WeaponDamage*AttackSpeed*(CritChance)(EmeraldCritDamage)
RubyDamage*(1 + CritChance*CritDamage)/(CritChance*EmeraldCritDamage) > WeaponDamage

Thus you only want to imbue a ruby if the expression

RubyDamage*(1 + CritChance*CritDamage)/(CritChance*EmeraldCritDamage)

is greater than your weapon damage+bonuses. Note that this damage will increase as your primary stat goes up, so in general the emerald is the better choice for the long-run. Notice also this equation does not depend on your attack speed at all.



[Edit] To make this easier to make sense of, I've created a graph:

Flawless Square

How to read this graph:

First, find your critical-hit damage% and critical-hit chance% (as shown on your detail tab in-game). Find that value on the above chart, and get its approximate value.

Next, take your damage (as shown on your character sheet) and divide by your attacks per second (as shown in the "details" tab).

If your damage (divided by attack rate) is larger than the graph-number, use an Emerald. But if the damage is smaller than the graph-number, use a Ruby. If they are approximately the same, you could use either, but I would recommend an Emerald, since it will scale better as your damage goes up.

The above chart is for Flawless Square gems. The other gems are largely similar:

So, in general, if you have low damage and low crit-chance, use a ruby; if you have high damage or high crit-chance, use an emerald (though if you have high crit-chance but low damage, you might want to double-check here).

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What about items that boost crit damage? –  Alok Jun 5 '12 at 21:29
    
@Alok: I just realized my previous comment is wrong; it does depend on crit damage. Please see edit for corrected formula. –  BlueRaja - Danny Pflughoeft Jun 5 '12 at 22:00
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Awesome, more math! I am just using ruby out of laziness, but will plug in the numbers now that I have a reference, thanks. –  Alok Jun 5 '12 at 23:15
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@BlueRaja-DannyPflughoeft This edit makes this one of the most researched posts I've ever seen in Arqade - nicely done! –  Dave McClelland Jun 13 '12 at 21:39
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TL;DR for those that don't want to do the math: Use a Ruby at low levels, switch to an Emerald sometime in late nightmare/hell. Even with no crit or crit damage gear, your Damage/Attacks will break 2k easily in the 40's or 50's with up to date gear, and an Emerald will only get marginally better from there. –  LessPop_MoreFizz Jun 14 '12 at 4:17
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A Ruby is a flat increase while Emerald is percentage based. Additionally, Emerald is dependent on gear or skills to boost crit chance to perform better. As the base weapon damage rises, at some point the %age based calculations should favor emeralds.

You need to post the weapons or atleast their approximate iLevels so the question is answerable imho. I generally put in a ruby because I haven't gone for a crit build on any of my characters, though at higher levels it might be that Emerald has better results even without a lot of crit bonus.

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ruby increases your weps damage, which is affected by attack speed and your primary attribute. I know what your saying, but as you level your primary attribute tends to go with it, unless your going a specific build, like me with my monk, the benefit from the base damage of your wep, also increases. –  Dave Jun 5 '12 at 18:40
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Faster attack speed & attributes should benefit crits as well so that should be a non-factor –  Alok Jun 5 '12 at 18:41
    
yah, but I'm pretty sure he's not 60 yet. Honestly their comes a point for every character where crit bonus damage, even if you have the base 5%, will out benefit flat damage, as a statistical dps. From rough fast calculations, it seems that you need at least 20k, for this to be true. Of course this assuming some things, roughly a value of 1300 for a base attribute stat, but even if you swing as fast as 2 attacks per second and have 5% chance to crit, you'll be getting a tiny bit more from the emerald. –  Dave Jun 5 '12 at 19:19
    
No it's not. Imagine if you have a weapon with 50% damage but 200% attack speed. Then ruby will improve your DPS by about twice. Read my answer. Emerald will improve those weapon damage equally. –  Jim Thio Oct 15 '12 at 0:47
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If you have a high-attack speed weapon, you want a Ruby in your socket. If you have a slower attack speed weapon, or if you are going a crit-heavy build, you want an Emerald in your weapon. I found a pretty good blog post explaining the differences here and in their video:

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Good summary in the linked post/video! –  Wikwocket Jun 5 '12 at 18:19
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The attack speed should affect both ruby and emeralds equally, so this answer cannot be correct. See my answer. –  BlueRaja - Danny Pflughoeft Jun 5 '12 at 21:36
    
@BlueRaja-DannyPflughoeft Attack speed has a bit of a non-standard effect on the ruby because the bonus provided by the ruby changes based on attack speed. LessPop has an answer somewhere around here that talks about that. (Though I suppose as long as you get RubyBonus correct, it's moot) –  Raven Dreamer Jun 5 '12 at 22:47
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@Raven: I think you're referring to this answer. It is currently being debated on that thread whether or not the effect actually exists. However, even if it is true, since LessPop is claiming that Rubies become less effective for high-attack-speed weapons, that would make Cloud9's answer even more incorrect! –  BlueRaja - Danny Pflughoeft Jun 6 '12 at 19:11
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Depends if you're stacking crit chance. If you have a decent chance to crit, of at least 15% (really hard to say since so many things affect your damage, but remember the emerald only does anything if and when you crit) it would probably be worth it, otherwise you won't be critting enough for it to pay off.

I watched the video above, and even still if your not going crit I'd throw in a ruby for 2 handers. He's right in the video about the faster weapons gaining more of a benefit from the ruby, but it doesn't make it worthless for 2 handers.

In my opinion it all comes down to what your crit % is right now. If you have over 10%, give it a shot it might pay off, but otherwise I'd stick to straight damage and let your damage modifiers do their job.

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