Currently I have a slow attack speed weapon for my Barb in D3. It has a socket. Should I add a Ruby or Emerald?
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:
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:
- Flawless Square
- Perfect Square
- Radiant Square
- Flawless Star
- Perfect Star
- Radiant Star
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).
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:
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:
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.
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.
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.