Tuesday, August 12, 2008

Starfire vs Wrath

Note: This article was written several months ago before WotLK was released. While some of the general information is still correct, a lot of the specifics behind it have changed and Wrath is a much improved spell. I do plan on writting a new guide eventually, but haven't had a chance yet. I will make this one brief comment though regarding SF vs W. Starfire is still better DPM and does significant damage. Wrath on the other hand does do better DPS, but will chew through your mana quickly.

Some of you may ask what is the point of writing this article. Most moonkin know that Starfire is the better raiding spell and with all of the changes coming out in WotLK this analysis may be obsolete fairly shortly. Well, I’m writing it for a couple of reasons. First, I still see a lot of people insist that Wrath is a better spell DPS wise before you get the T5 and T6 set bonuses. Second, who knows what is going to go live in WotLK. There are a lot of changes that improve Wrath’s viability in raid, but until it is finalized we don’t know how to evaluate them. Anyway, here is the reasons why Starfire is the better then Wrath in a raid situation.

Assumptions/Disclaimers:
1. This analysis assumes a standard moonkin spec that buffs both Wrath and Starfire to their fullest potential.

2. This analysis is most relevant for a 25 man raid with all possible buffs. This will be less relevant to 10 raids, and much less relevant to 5 man instances.

3. Stormstrike will be ignored for most of the analysis. Due to its nature it is a hard buff to quantify and assume that it will be available. However, I will try and include it at the end of the analysis.

4. I ignore the resistance debuff from CoE because there is some argument if boss resistances can be lowered.

5. The T5 and T6 4 piece set bonuses clearly favor Starfire, but I will ignore those buffs since they are not necessarily available to all moonkin.

6. Crit damage is ignored since it affects both Wrath and Starfire equally. However, Crit is used to determine average casting time for part of the analysis.

7. All equations assume 1200 Spell Damage, Zero haste, and 25% crit unless otherwise noted.

Talents and Buffs Affecting Starfire or Wrath but not both:
Nature’s Grace – Talent - All spell criticals grace you with a blessing of nature, reducing the casting time of your next spell by 0.5 sec. Note: It currently does not reduce the GCD, so Wrath receives no DPS benefit.

Curse of Elements – Debuff – Curses the target for 5 min, reducing Arcane, Fire, Frost, and Shadow resistances by 88 and increasing Arcane, Fire, Frost, and Shadow damage taken by 10%.

Malediction – Talent – Increases the damage bonus effect of your Curse of the Elements spell by an additional 3%.

Stormstrike – Debuff – The next 2 sources of Nature damage dealt to the target are increased by 20%. Cooldown 10 sec.

Evaluation Criteria:
There are really only two ways to evaluate these spells. Damage per second (DPS) and Damage per Mana (DPM). The argument as to which spell is better really comes down to the priority you attribute to these criteria. The standard argument is that Wrath is better for DPS and that Starfire is better for DPM. I will argue that Starfire is better for both criteria.

Damage per Mana:
First we need to calculate the damage of each spell.

Starfire Damage = 657.8 + (Spell Damage)*(1 + 0.2)*(1.1)
Wrath Damage = 445.5 + (Spell Damage)*(0.5714 + 0.1)*(1.1)


So assuming we have 1200 Spell damage these spells will on average deal the following damage.

Starfire Damage = 657.8 + (1200)*(1 + 0.2)*(1.1) = 2241.8
Wrath Damage = 445.5 + (1200)*(0.5714 + 0.1)*(1.1) = 1331.8

After talents a Starfire will cast 336.7 mana and Wrath will cost 232 mana. So the DPMs of each spell are:

Starfire DPM = (657.8 + (1200)*(1 + 0.2)*(1.1) )/336.7= 2241.8 / 336.7 = 6.658
Wrath DPM = (445.5 + (1200)*(0.5714 + 0.1)*(1.1))/232 = 1331.8 / 232 = 5.739


This clearly shows that Starfire has a higher DPM when comparing unbuffed spells. I have run this analysis for multiple levels of Spell Damage and the disparity only gets bigger as you increase your spell damage. I have also run this analysis with full raid buffs, and the gap is even bigger. This isn’t surprising since a majority of the available buffs are SF only and they clearly out weigh the one and only Wrath buff.

So, to sum it up Starife is better then Wrath from a DPM perspective. Here is a graphical representation of the comparison.


Damage per Second:
We calculated the unbuffed damage of both spells above, and it applies here also. So a non crit cast will have the following DPS.

Starfire Damage = (657.8 + (1200)*(1 + 0.2)*(1.1)) / 3 = 2241.8 / 3 = 747.27

Wrath Damage = (445.5 + (1200)*(0.5714 + 0.1)*(1.1)) / 1.5 = 1331.8 / 1.5 = 887.88

So, at a base level it is clear that Wrath has more DPS then Starfire. The question then is how much can Starfire reduce that gap with the Starfire only buffs that are available?

Including Crit Rate

When a spell crits gets a Nature’s Grace buff that reduces the casting time of your next spell by 0.5 seconds. This buff does not affect Wrath’s DPS at all since it reduces the casting time below the global cooldown. Starfire receives the full benefit since its casting time is well above the global cooldown.
When you factor this in, Starfire’s casting time is now:

Starfire Average Cast Time = (3 – (0.5*Crit rate))
Starfire Average Cast Time = (3 – (0.5*.25)) = 2.875 Seconds with a 25% crit rate.

If we plug this into the equation above it changes the numbers like this:

Starfire Damage = (657.8 + (1200)*(1 + 0.2)*(1.1)) / 2.875 = 2241.8 / 3 = 779.76

Wrath Damage = (445.5 + (1200)*(0.5714 + 0.1)*(1.1)) / 1.5 = 1331.8 / 1.5 = 887.88

It is clear that the numbers still favor Wrath even when you include Crit into the equation.

Including Curse of Elements

First of all, CoE should always be up during a boss fight. If its not your Warlocks and Raid Leaders are epic failures. It may lower personal DPS for the lock but it is a huge bonus for the raid. CoE increases your Starfire’s damage by a minimum of 10%. If the warlock has Malediction then it increases your Starfire by 13%. I will look at it both ways in the next set of equations.

Starfire Damage (w/o Mal) = (657.8 + (1200)*(1 + 0.2)*(1.1))*(1.1) / 2.875 = 857.73
Starfire Damage (w/ Mal) = (657.8 + (1200)*(1 + 0.2)*(1.1))*(1.13) / 2.875 = 881.12

Wrath Damage = (445.5 + (1200)*(0.5714 + 0.1)*(1.1)) / 1.5 = 887.88

So, at this point Wrath and Starfire are becoming very similar in terms of DPS when you include all of the Starfire buffs. This is where most of the debate comes in. Some people will argue that Wrath is the better spell because of this 6.76 DPS despite the benefits of Starfires DPM. They are correct from a pure theoretical view. However, real life doesn’t always perform like the theory says it should, and this brings us to the next adjustment.

Including Spell Lag

This is what most people forget when they evaluate the two spells, and most people don’t know what it is. Spell Lag is the unavoidable time between spell casts. Melee has it easy. They tell blizzard to wack the boss with a sword and blizzard does all the work for them with the auto-swing. Casters don’t have the same ability with their spells. We have to cast each individual one. Since we are human, the time between casts will be longer then the actual cast time even with addons like quartz. We can minimize it but we can’t eliminate it.

So how does this affect the analysis? Lets assume you have an average spell lag of 0.05 seconds. This is a fairly low number. Your Wrath’s cast time is now increased by 0.05 seconds when calculating DPS for a time between casts of 1.55 seconds. Your Starfires cast time would be affected by the same amount of Spell Lag, so there would be 3.05 seconds between each Starfire cast. As you can see Spell Lag affects the faster cast spells much more then the slower spells. In this example Spell lag makes up 3.23% of the time between casts for Wrath but only 1.64% of the time between casts for Starfire. As you can see Spell Lag affects Wrath almost twice as much as Starfire. Lets put into the equation.

Starfire Damage (w/o Mal) = (657.8 + (1200)*(1 + 0.2)*(1.1))*(1.1) / 2.925 = 843.07
Starfire Damage (w/ Mal) = (657.8 + (1200)*(1 + 0.2)*(1.1))*(1.13) / 2.925 = 866.06

Wrath Damage = (445.5 + (1200)*(0.5714 + 0.1)*(1.1)) / 1.55 = 859.24

As you can see Starfire passes Wrath in DPS if you have full raid buffs (excluding Stormstrike) after you include Spell Lag. Even if you don’t have a lock with Malediction in your raid, Starfire is very similar to Wrath in DPS.

Looking at Stormstrike

In this section I will take a look at Stormstrike, listing its problems and showing how it affects the analysis under the best of circumstances.

I really don’t want to include Stormstrike in this analysis at all because it is such a limited buff. However, I’m sure that some readers would discount my analysis if I don’t look at it from all angles.

What is Stormstrike?
It is a debuff placed on the boss by an enhancement shaman where the next 2 sources of Nature damage dealt to the target are increased by 20%. It has a 10 second cooldown before it can be reapplied. Since Wrath is a nature spell it is affected by this Debuff.

Problems with Stormstrike
1. It only affects a finite number of spells. It doesn’t matter how many nature abilities hit the boss in those ten seconds, only the first 2 spells will be buffed. Under the very best of circumstances, only two of your wraths would be affected every 10 seconds.

2. The benefits are not exclusive to Wrath and can be consumed by other players in raid. You will be competing with all Nature Damage dealers for these two procs every ten seconds. However, I do not know if Rogue Poison or Insect Swarm periodic damage ticks consume one of the 2 buffs.

3. When you consume one of the buffs you are preventing another raider from receiving the buff. So, it may increase your DPS but it lowers the DPS of another raid member.

To sum this up, since you can only get 2 buffs every two minutes the average buff will be a maximum of 6.4% since you can cast 6.25 spells per 10 seconds with 0.05 Spell Lag. On top of that, the chances you will get both procs is minimal because the shaman who cast it will take at least one of the procs. If you have an Elemental Shaman in raid you will benefit even less. Finally, to increase your DPS you are lowering the DPS of the shaman who cast it.

So lets say you get one of the two Stormstrike procs. How does it change the numbers? Well you can cast 6.25 spells per 10 seconds with spell lag and no haste. That means you Wrath will get an average increase of 3.2%.

Starfire Damage (w/o Mal) = (657.8 + (1200)*(1 + 0.2)*(1.1))*(1.1) / 2.925 = 843.07
Starfire Damage (w/ Mal) = (657.8 + (1200)*(1 + 0.2)*(1.1))*(1.13) / 2.925 = 866.06

Wrath Damage = ((445.5 + (1200)*(0.5714 + 0.1)*(1.1))*1.032) / 1.55 = 886.73

As you can see Starfire is still very competitive with Wrath in terms of DPS even when Stormstrike is included in the analysis.

Conclusions:
I think this analysis clearly shows that Starfire is clearly the better spell in almost all raid situations. From a DPM stand point Starfire is far superior to Wrath. The DPS view point is a little more complicated. However, with normal raid buffs Starfire is very competitive with Wrath in terms of DPS and even passes it in some cases. When you couple this with the mana efficacy, Starfire is clearly the superior spell of the two.

How this will change in WotLK:

I have run some of the numbers comparing Wrath to Starfire in WotLK. I have often wondered if Starfire would still be the spell of choice in WotLK after Wrath receives buffs from Curse of Elements, Natures Grace, and gets more mana from Moonkin Form. However, with the recent additions of Improved Scorch and Winter’s Chill, the relationship between Wrath and Starfire seems to maintain the status quo.

10 comments:

Horns said...

An excellent analysis, really helpful.

One question: does including Bloodlust in the calculations have any effect?

Cdin said...

If you exclude Spell Lag, all haste effects have no affect on the analysis. This is because they affect the spells in the same manner. The DPS for both spells will increase with Bloodlust, but they will increase at the same rate.

Once you add Spell Lag into the equation there is some impact. The reason is Spell Lag can't be reduced by game stats. It is a user and Latency problem. So lets say you pop bloodlust. Without spell lag your SF cast time would decrease to 2.21 seconds and your Wrath cast time would decrease to 1.15. Since spell lag can't be reduced it affects Wrath much more severly because lag is a much higher portion of the total cast time.

Plac said...

"I have run some of the numbers comparing Wrath to Starfire in WotLK. I have often wondered if Starfire would still be the spell of choice in WotLK after Wrath receives buffs from Curse of Elements,"

I looked up the new ranks of Curse of Elements and I don't see how it buffs the Wrath spell. Is this a typo?

Cdin said...

@Plac

I don't have access to the beta, so my knowledge is second hand. However, I have heard on the forums that it now includes Nature damage, and the tool tip on wowhead WotLK edition says that it does. Here's a Link: http://wotlk.wowhead.com/?spell=47865

"Curse of the Elements Rank 5
10% of base mana 30 yd range
Instant cast
Curses the target for 5 min, reducing Arcane, Fire, Frost, Nature, and Shadow resistances by 165 and increasing Arcane, Fire, Frost, Nature and Shadow damage taken by 10%. Only one Curse per Warlock can be active on any one target. "

Anonymous said...

Natures grace now affects global cooldown, meaning it will have a much greater affect on wrath than on starfire, where as in these calculations you assume it has no affect on wrath. You also dont account for the fact that every time you crit as balance you gain 2% mana back, effectively refunding the entire cost of your wrath, possibly even giving mana back. This will cause both your dmp and dps to favor wrath, a gap that only gets wider with more crit and sd

Cdin said...

@ Anonymous

If you look at the top of the post you will notice that this article was written well before WotLK was released. Also, you will notice that in the first paragraph I said that there are thing coming that increase the utility of wrath, but that they currently weren't in game.

Regarding Nature's Grace, there is quite a bit of debate as to if NG really reduces the GCD or not. Those that say it does point to the patch notes that says it does. Those that say it doesn't point to game longs where they that show little differences in cast times after crits.

I tend to look at it from the tool tip point of view, this is such a big affect of the spell I'm sure it would be listed on tool tip but it isn't.

I tend to side with those that says it isn't in the game bacause I haven't because no one can come up with good evidence to show that it is in the game.

Regarding Mana on Crit. First of Mana on crit has no direct impact on DPS. And it definately doesn't increase the DPS of one spell more then the other. Second, Mana on Crit does improve the DPM of Wrath more then Starfire, but it currently doesn't make Wrath more Mana efficent the Starfire.

Danger said...

New balance moonkin here, after a long stint as a feral tank. I'm reading up on all the different nuisances of moonkins, which there are many. I like your analysis. From a practical standpoint though, I've found that wrath's short cast time makes it extremely useful in movement heavy fights, or to finish dpsing trash, where melee is reducing the health of a mob at steady pace and a long starfire cast leads to a failure (which is frustrating in my opinion). This has little to do with the DPS or DPM, but is an important factor when choosing which spell to cast, and I feel it's worth a mention. Nice writing, and thanks for all the newer articles and analysis. Good luck on getting your Valorous! =)

Danger said...

Oh, but imagine if you could stack enough haste to reduce the casting time of starfire significantly? That would be so lovely!

Anonymous said...

Hey, i'm Delmkin from Area 52 Alliance. I've done just about every wotlk raid so far, and i've come to the conclusion that Wrath scales better. I am currently sitting at about 1790 Spell Power (mostly 25-man gear, with some 10 man pieces), my crit is sitting at about 30.2%, and my haste is sitting at about only 200. My dps is much higher when using wrath. I generally hit about 1800-2000 dps with Starfire in raids (although, it's usually on the lower end of the scale, usually around 1850 or so), and about 2200-2400 with wrath (seems to generally be higher on the scale, usually atleast 2300). This is a very big difference in DPS, starfire was about even with wrath pre-naxx, but now i have come to the conclusion that wrath is an all around more powerful spell.

Boomkins are well off in WOTLK as well which i like, i am usually in the top 3 for dps in 25-mans. I hit about 2300 on single targets, and 3000-4700 with AOE (Hurricane)It can sway alot on AOE, depending on number of mobs during the AOE but i'd say on average i'm at about 3400-3700 with AOE's).

I'm currently working on slightly more crit, but mainly on haste.

Anonymous said...

Oh, and i'm sitting at about 170 Hit atm because of some recent upgrades. For 95+ percent of the raids i was sitting at about 210-230 Hit Rating.