Monday, April 28, 2008

Spell Damage Vs Spell Crit (for Moonkin)

Note: This guide was written well before WotLK as released. The information and modeling done here is based completely on a BC version of WoW. While I thing this information is still generally correct, It does not apply direct any more. I do plan on writting a new guide and will post on my blog when it is done.

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 550 and 646. It is increased by 10% because of Moonfury, so the average base spell damage for Starfire is 657.8. 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

10 comments:

Anonymous said...

Very nice writeup.

Note that Wrath-spam never benefits from Nature's Grace (unless you don't have the talent for 1.5s Wrath).

If you have the Haste to lower the global cooldown, the haste will lower the cast time of non-NG Wrath by the same amount.

For SF, you can, in principle get to the point where a point of crit is better than a point of spell. I'm going to change your SF formula slightly to

(658+(55+spell*1.2)*1.1)*(1+1.09*crit)/(3-.5*crit)

Changes from your formula:
1) Moonfury gives slightly more than 10% to base damage (look at your tooltip, or Efejel's spreadsheet).

2) I included the SF idol.

3) I included CSD, giving 209% damage to crits (reported by Elitist Jerks). They get this from:
150% normal crits.
154.5% from the CSD 3% boost.
209% because Vengeance doubles the 54.5% "bonus" damage.

Using my formula, 20% SF crit (that means 9% crit in caster before CSD, low I know) CR = +spell at 1523 buffed +spell.

I will also mention that for MF spam (Dueling a rogue?) crit can win because the MF direct damage has a very low (15% before talents) spell coefficient.

- Erdluf

Cdin said...

@Erdluf

Thanks for checking out my blog and pointing out the errors in my post. I will reconfigure the numbers and edit the post to make it correct, but first a couple of comments.

1. Now that you mention it I do vaguely remember hearing aobut the base damage being higher than what is in Wowhead. I built this analysis using WoWhead Info and should have checked the game first. Thanks for catching it.

2. I didn't include any of the idols into the equation because which one you use really depends on the situation. I would also argue that from a raiding stand point the Starfire Idol is probably the third choice. With the internal cooldown removed you will get more damage from the Moonfire idol on average and your raid will get more benifit out of Idol of the Raven Goddess with its recent buff. However, you are correct that the Starfire Idol improves the value of crit.

3. I swear that someone could earn a Ph.D. trying to figure out and explain Blizzard Math. Thanks for pointing out how the bonus damage is calculated from the CSD. I had not seen it before.

However, if you look at the math under realistic conditions, it doesn't really change my point. You are right that crit will equal SD in value on a point for point bases at 1523 total spell damage, a 20% crit rate, and the starfire idol equiped. Unfortunately that is a very unlikely set of circumstances.

It is not difficult to reach 1523 spell damage fully buffed with consumables and a wrath of air totem. I am primarily T5 geared and am very close to that level. However, It is very unlikely that you will get to that level of SD with only 20% crit. Fully raid buffed I have around 28%. So using your formula and a more reasonable crit rate of 27% I found the break even point to be 1626. This level of spell damage is only reasonable for the highest tier of raiders who would have an even higher base level of crit thus reducing the value of an additional point of crit. Last time I looked Gifted from Death and Taxes had a 35% crit rate on Starfire pushing the break even point to 1740 SD. This level of SD cannot be reached with the gear currently available.

Therefore, since Spell Crit is virtually unavoidable as you increase your Spell Damage, it is highly unlikely that a moonkin will ever reach a level of Spell damage and Spell Crit where Spell Crit is more valuable on a point for point basis.

Though I must say it makes this gem goddly. I need to go back and see if it is worth wearing my T4 helm again just so I can socket this gem.

4. My blog is written almost exclusively from a raiding stand point and from my understanding moonfire spam isn't a great tactic even in PvP. You are right. My math showed that the Direct Damage portion of MF does benifit significantly more from spell crit than spell damage. So, I agree that on the rare occation that you moonfire spam crit is better than Spell damage. However, that shold be the exception and not the rule.

Thanks again for reading.

Anonymous said...

um....

you divided 1 crit rating by 2206 but it should be 22.06 which gives 1 crit rating equal to 0.0453 % chance to crit, which makes all your math after that point off by multiple of 100.

Cdin said...

@Anonymous #2

I think if you review the math you will realize that my math is correct.

You are correct 22.06 points does equal a 1% chance to crit, so 1 point of crit does equal a 0.0453% chance to crit.

What you are missing is that 0.000453 is the mathamatical equivalent to 0.0453%.

Artorin said...

I just recently hit 1100 spell dmg unbuffed on my druid but my spell crit is pretty low. I'm not sure if the crit % you are talking about in the comments is your crit for all spells or talented for starfire/wrath. My base crit while in moonkin is only 19.6% So with my current spell dmg should I continue with points in SD or try and focus on crit? I don't get to raid really but I still like to max out my potential with my gear.

Cdin said...

@Artorin

My analysis includes the crit you get from talents so you would have a crit rate of 23.6%.

At this point you should still be focusing on Spell Damage especially if you don't raid much. There are very few moonkin that will ever get to a point where Crit is better then Damage. The only way to do it is to have the best possible gear or to have really high Damage(1500+) and really low crit (15% or lower. The first possiblity would be awesome. The second means you geared incorrectly.

I ran some quick numbers for you. Unbuffed and without the meta gem one point of crit is worth about 0.71 Spell damage for you. With normal raid buffs (flask, food, oils, and such), the value of one crit increases to around 0.80. If you have a wrath of air totem it increases even more to about 0.85.

If you do have the meta gems all of these values increase by around 0.05.

As you can see, Crit is starting to became a very nice stat for you but doesn't pass damage. I wouldn't actively stack it but I think you will find that you get quite a bit of it just by improving your gear to get more spell damage.

Artorin said...

Thanks for responding! Stacking SD seems to be the way to go and is what i've been doing its just hard when you see those big crits to not want to see more of them. I picked up the 2.4 badge chest which has a fair amount of spell crit and a little more spell dmg.

The meta I'm using is the spell dmg + 2%(I think) Int gem. I use it since it increases my spell dmg mana regen and crit by a slight amount but after reading your post should I switch to the 3% increase crit dmg? Since my focus is more on spell dmg vs crit I'm not sure what gives me the most increase.

Cdin said...

The Chaotic Skyfire Diamond is by far the best meta gem for PvE Moonkin. Its not even close. Here is why.

The gem you are using gives you 14 damage and 2% to Int. Assuming your are about my level you have around 500 Int fully raid buffed. That means the Gem give you an extra 10 int. That isn't much. If you translate it into other stats that 10 int gives you 2.5 Damage, 2.8 crit, 1 Mp5 from Dreamstate, maybe .1 Mp5 from Intensity, and 150 mana.

The Chaotic Skyfire Diamond other hand gives you 4.5% extra damage on your crits due to the way blizzard does math. I can't remember the numbers off the top of my head, but this translates to at least 20 spell damage for your average moonkin. Plus you get 12 crit on top of that. The more yoru gear improves the more this gem will do for you. For me, I think the gem would translate into 43 spell damage fully raid buffed, and doesn't include the 12 crit.

The added int from your current gem does a lot of little things for you, but they don't add up to the shear power of the Chaotic skyfire.

Hope this helps.

Anonymous said...

Very nice to see this dialogue. But, a few things don't match my real experiences. I have a 70 Moonkin, 600+dmg, 22Crit. My SF crits for 3K sometimes, and my Wrath for 2K often. Also, Wrath DOES take advantage of NG, as I am often spamming 1sec 2K Wraths. My DPS is definitely higher with IS,MF,Wrath. SF is more mana efficient in the long run for raids, but wrath rules in PVE and PVP.

Why am I seeing people say that NG doesn't work with Wrath?

Why do your crits seem so low?

Cdin said...

@ Anonymous (comment #9)

It's funny you should ask this because I just put up an analysis comparing Starfire to Wrath. It's funny how these things come togeather some time.

I'm going to try and take your comment in secions.

"Why am I seeing people say that NG doesn't work with Wrath?"

NG does affect the Cast time of Wrath but it DOES NOT affect the global cooldown. NG will allow you to cast 1 second Wraths but the global cooldown will still be 1.5 seconds. Therefore after you cast your 1 second Wrath you will still have to wait half a second to cast another spell. Therefore the cast time of Wrath is still affectively 1.5 seconds for DPS purposes. On a side note NG does reduce the Global Cooldown in the current WotLK Beta.

"Why do your crits seem so low?"

My damage numbers are per cast averages. With a 25% chance to crit your going to crit once ever 4 casts on average. So if your spell hits for 1k normally you would have three casts that hit for 1k and one that would hit for 2k. Summed togeather that is 5k. If you divide that by 4 casts then each cast hits for 1.25k on average.

"My DPS is definitely higher with IS,MF,Wrath. SF is more mana efficient in the long run for raids, but wrath rules in PVE and PVP."

You also stated that you have 600+ spell damage. For this reason I assume that you are still in Karahzan. In a 10 raid your much less likely to have Curse of Elements up on the boss, therefore you probably are getting more DPS out of Wrath. However, You are sacrificing a lot of mana for the added DPS, and will go OOM on some of the longer fights. At a 25man level the buffs bring Wrath and Starfire very close togeather in terms of DPS and there for the mana benifits of Starfire clearly out way Wrath.