Should I socket my weapon with a Ruby or Emerald?
Currently I have a slow attack speed weapon for my Barb in D3. It has a socket. Should I add a Ruby or Emerald?
Solution 1:
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:
- Chipped
- Flawed
- Normal
- Flawless
- Perfect
- Radiant
- Square
- Flawless Square
- Perfect Square
- Radiant Square
- Star
- 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).
Solution 2:
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:
Solution 3:
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:
Solution 4:
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.