Spell Damage Vs Spell Crit (for Moonkin)

If you have done any reading on moonkin DPS then you have probably seen the basic hierarchy of DPS stats. Spell Hit > Spell Damage > Spell Crit. You may have also seen the generally accepted relative values of each of those stats. Spell Hit is considered to be worth 1.2 Spell Damage until the hit cap. Spell Crit is considered to be worth 0.7 Spell Damage. These numbers are a good general guideline for your average raiding moonkin but they are way to static to really be accurate. In this post I would like to lay out the math and show why Spell Damage is always better than Spell Crit on a point for point basis.

Assumptions/Disclaimers:
1. A spell’s chance to hit is unaffected by its chance to Crit or by how much Spell Damage a caster has. Therefore it affects both Spell Damage and Spell Crit equally and will not be included in this analysis.

2. Spell Haste does not impact the amount of damage caused by Spell Damage or Spell Crit. It only affects the speed at which the damage occurs. Therefore it affects both Spell Damage and Spell Crit equally and will not be included in this analysis.

3. I have tried to structure the analysis in such a way to favor Spell Crit and give it every benefit of the doubt. Therefore I will be focusing on Starfire Since it gets the most benefit from Spell Crit.

4. I have excluded the affects of any of the moonkin idols from the calculations since which one you use really depends on the situation. However, the [Ivory Idol of the Moongoddess] and the [Idol of the Unseen Moon] will will increase the value of Spell Crit a little since they increase the damage of your Spellfire before crit. On the other hand [Idol of the Raven Goddess] will reduce the value of an additional point of crit since it increases your base chance to crit.

Talents Affecting Starfire DPS:
Starlight Wrath – Reduces casting time by 0.5 seconds.
Focused Starlight – Increases Crit rate by 4%.
Vengeance – Increases the crit bonus damage by 100%.
Nature’s Grace – Reduces the cast time of your next spell by 0.5 sec after a crit.
Moonfury – Increases damage by 10%.
Moonkin Form – Increases Crit rate by 5%.
Wrath of Cenarius – Increases Spell Damage Coefficient for Starfire by 0.2.

The Math:
There are a couple of important things to remember when comparing Spell Damage and Spell Crit. The first is that they are interrelated. So we have to determine how an additional point of Spell Damage is affected by your current level of Crit and how an additional point of Crit is affected by your current level of Spell Damage.
Also, due to Nature’s Grace, crit not only determines how much damage is dealt but how quickly it is dealt. So with regard to Starfire, the numbers will be converted to DPS.

How much additional DPS will you receive from an additional point of Spell Damage?

Moonfury, Wrath of Cenarius and your Crit rate all affect Spell Damage. Starfire has a base Spell Damage Coefficient of 1, and let X equal your Crit rate for Starfire. So the additional DPS from one point of Spell damage is:

DPS = (((1 + 0.2)*1.1)*(1 + X))/(3 - 0.5(X))

So if your crit rate is 25%, Then
DPS = (((1 + 0.2)*1.1)*(1 + 0.25))/(3 - 0.5(0.25))
DPS = (1.32*1.25)/(3.00 - 0.125)
DPS = 1.65/2.875 = 0.5739 DPS per point of Spell Damage at a 25% Crit rate.

How much additional DPS will you receive from an additional point of Spell Crit?

First we need to figure out how much damage Starfire does. It has two components, base spell damage and bonus spell damage. Base spell damage is the damage that comes with the trainable spell with no bonus from gear. A max rank Starfire can hit for between 540 and 636. It is increased by 10% because of Moonfury, so the average base spell damage for Starfire is 646.8. Bonus spell damage is what you receive from gear and is calculated on your character screen. It is modified based upon the base casting time of the spell and talents. Starfire has a Spell Damage Coefficient of 1, and it is modified by Wrath of Cenarius and Moonfury as I said before. So the damage of your average non-crit Starfire is equal to:

Damage = 657.8 + (Spell Damage)*(1 + 0.2)*(1.1)
Damage = 657.8 + (1000)*(1 + 0.2)*(1.1) = 1977.8, If you have 1000 Spell Damage

To get the damage of your average Starfire you have to include crit. To do that, multiply the entire equation by one plus your crit rate:

Damage = (657.8 + (Spell Damage)*(1 + 0.2)*(1.1))*(1 + Crit Rate)
Damage = (657.8 + (1000)*(1 + 0.2)*(1.1))*(1 + 0.25) = 2472.3, If you have 1000 Spell Damage and a 25% crit rate.

To get your average DPS for Starfire you have to divide by your average cast time.

Damage = ((657.8 + (Spell Damage)*(1 + 0.2)*(1.1))*(1 + Crit Rate))/( 3 - 0.5(Crit Rate))
Damage = ((657.8 + (1000)*(1 + 0.2)*(1.1))*(1 + 0.25))/(3 – 0.5(0.25)) = 859.91304, If you have 1000 Spell Damage and a 25% crit rate.

Now, if we had one point of crit rating to the percentage then we change the out come in a couple of ways. First, you will crit more often therefore increasing your damage. Second, criting more often will decrease your average cast time due to Nature’s Grace, thus increasing your DPS. To increase your Crit rating by 1% you need 22.06 points in crit rating, so one point of crit rating increases your chance to crit by 1/2206 or 0.00045331%. If you slip this into the equation you get the following results:

Damage = ((657.8 + (Spell Damage)*(1 + 0.2)*(1.1))*(1 + Crit Rate + 0.00045331))/( 3 - 0.5(Crit Rate + 0.00045331))
Damage = ((657.8 + (1000)*(1 + 0.2)*(1.1))*(1 + 0.25045331))/(3 – 0.5(0.25045331)) = 860.29271, If you have 1000 Spell Damage and a 25% base crit rate plus one more point of Spell Crit.

So from one point of Spell Crit you gain 0.37967 DPS with 1000 Spell Damage and 25% base Crit rate. Lets compare this value to the DPS value I calculated for one additional point of Spell Damage.

0.37967/0.5739 = 0.66156.

So, at 1000 Spell Damage and 25% crit rate, one additional point of Spell Crit is worth 0.66156 points of Spell Damage.

I have calculated this value for several levels of Spell Damage and Spell Crit. Here is a graph that shows the results.

There is one way to significantly improve the value of your Crit rating. It is the [Chaotic Skyfire Diamond]. How this gem impacts your critical strikes is a little more complicated than it sounds. Due to some strange math from blizzard your critical strikes will hit for 209% of your normal spell cast. Having this gem socketed will increase the value of spell crit rating by 4% to 5%. Here is another graph that shows the impact of having this gem socketed.

Conclusions:
1. My results do confirm the relative value of one Spell Crit to be worth about 0.7 Spell Damage for your average raiding Moonkin with about 1000 to 1100 Spell damage. However, it also shows that that value changes significantly depending on your level of Spell Damage. The rule of thumb I would use is 0.7 if geared from T4 content, 0.8 from T5 content, and 0.9 from T6 content.

2. It is also often suggested that at some level of Spell Damage, Spell Crit becomes more valuable than Spell Damage on a point for point basis. While this is true in theory it is really not practical in the game because of how gear is itemized, and I am not convinced that it is possible at all.
Spell crit is unavoidable as you progress through raid content. As you pick up more Spell Damage gear you will also get quite a bit of Spell crit. I tried to take a look at the best gear available from Sunwell and T6 content. I found that it is possible to get to 1450 -1475 spell damage. thise means that you could get to 1750 - 1800 Spell Damage fully raid buffed. However, at the same time you would be pushing your crit level to 35% or more, thus reducing the marginal value of Crit rating.
Needless to say, while the highest tier of hardcore raiders may get close or even cross this barrier, the average moonkin raider has no hope of ever reaching this point if they make the correct gear choices.

Additions:
I did do an analysis of the other three Druid DPS spells. Most of the information would be very similar in structure to what I have posted above and wouldn’t change the conclusions in any significantly. In fact, they only make Spell Crit look worse. However, I would like to give a quick summary how each spell looked with regard to the Spell Damage vs Spell Crit comparison.

Wrath – Wrath looks very similar to Starfire, but a little worse. The reason is that Wrath does not benefit from Nature’s Grace due to the global cooldown.

Moonfire – The initial burst of damage from Moonfire can crit but the DoT cannot. Thus, a significant portion of Moonfire’s damage is unaffected by Spell Crit. According to my analysis one point of Spell Crit is worth between 0.30 and 0.35 points of Spell Damage for most reasonable levels of Spell Damage.

Insect Swarm – Insect Swarm cannot crit and therefore is completely unaffected by Spell Crit.

Acknowledgements:
I owe thanks to Phaelia over at Resto4Life for giving me the idea for this post with her Versus posts. She was also kind enough to look over my post before it was published and give me a few pointers. Unfortunately due to my lack of blogging/HTML knowledge I was not able to implement some of her great ideas. Hopefully someday I will figure this stuff out had have a blog that looks half as good as hers.
I also owe thanks to Erdluf from the comments section for pointing out a couple of mistakes in my analysis.

Toon Update
Graylo - Not much here. I ran Kara with him on Friday night and picked up 22 badges but that is about it.

Graypal - Didn't play him a whole lot over the weekend but I am working towards getting him the spell strike set and the Belt of Blasting. I farmed a whole lot of Primal Fire over the weekend with graylo. Still need to pick up about 15 more primal fires but it wasn't all that hard.

Grayfel - Didn't work on him as much as I wanted to. He is almost level 43 but I had some issues with spawns and such and didn't get him up