Tuesday, January 22, 2008

Smite versus Fireball


I had originally intended this as a reply to Mera's comment on raiding fire, but as I delved into the matter, I found that I had far too much information to divulge here.
The comment was thus:
"Actually, for base damage per second, smite is the base spell in the game."

Hmm... quite a claim you've made there, Mera.

In my old troll days, I most likely would have replied with "rofl, nub", but I am a respektible blooger now, and I should craft something intelligent to reply with.

So off I go to investigate this, comparing fireball to smite, to find out which of these spells is... I dunno, better I guess.

So. First off, untalented comparison.

SMITE
Rank 10
Smite an enemy for 549 to 616 damage. 2.5 second cast time. Costs 385 mana.

On average, Smite will hit for 582.5 damage every 2.5 seconds.
Therefore, per second, Smite will:
Deal 233 damage every second.
Cost 154 mana every second.
(1.512 damage per point of mana)

Pretty damn mana efficient, if you ask me. Looking at fireball now...

FIREBALL
Rank 13
Deals 633 to 805 damage, and an additional 84 damage over 8 seconds. 3.5 second cast time. Costs 425 mana.

On average, Fireball will hit for 803 (counting the DoT damage) every 3.5 seconds.
Therefore, per second, Fireball will:
Deal 229 damage every second.
Cost 121 mana every second.
(1.892 damage per point of mana)

Le gasp! Smite deals more damage than fireball!

Fireball is more mana efficient, but still...

Ok, let's talent up this biznatches, find out what happens when we "maximize" these two spells against each other.

(Please remember this principle. All talented increases to spell damage come AFTER the caster's bonus spell damage is applied to the spell.)

First, our test beds. We have a priest, specced to maximize his Smite damage. This priest has a spec like 33/28/0, or other some such madness, to get all the talents that make Smite more smitey.
Our mage here is specced the new classic 2/48/11 spec, to maximize his uber leet dee pee ess.
We are going to assume the following.
Both the mage and the priest have unlimited mana.
Both the mage and the priest have untalented 20% critical strike rate.
Both the mage and the priest have 1000 spell damage in their respective school.
Each has 300 spirit, but this is only really important for the priest, thanks to Divine Spirit.

For right now, we're only comparing Fireball versus Smite, and leaving Scorch out of the equation. Meaning the mage's fireballs will hit 15% softer than they would otherwise. We'll get to that later, I promise.

So. First off, let's improve our Smite.

Smite has a 2.5 second cast time (base), meaning it gains 71.42% of our bonus spell damage.
Which means Smite will get an extra 714 damage on top of its tooltip. Now, we're looking at 1263 to 1330 damage per Smite. One fifth of these will critically strike, meaning 150% damage. Smite can critically strike anywhere from 1895 to 1995.
Meaning that Smite, including critical strikes, will do, on average, 1685 damage per cast.

Now let's add in these handy little talents we have...

For Smite, the talents that make it awesome are split between two different trees. We have some in Discipline, some in Holy. We're going to assume that our Priest has talented to get all of them. Meaning, we have the following:

Self buff, Divine Spirit. Increases Spirit by 50 (this will come in handy later).

Force of Will. Increases Spell Damage by 5% and the critical strike chance of offensive spells by 5%. (Smite will now hit for 1299 - 1366 damage, and has a 25% critical strike chance)

Holy Specialization. Increases critical strike chance of Holy spells by 5%. (Smite now has a 30% critical strike chance)

Divine Fury. Reduces the cast time of Smite by 0.5 seconds, among other things, but we're only concerned with Smite. (Smite now has a cast time of 2 seconds)

Searing Light. Increases the damage of Smite by 10% (Smite will now hit for 1429 - 1503 damage)

Spiritual Guidance. Spell damage increased by 25% of the priest's spirit. Our priest, thanks to Divine Spirit, now has 350 spirit. 25% of that would be an extra 88 spell damage.

Surge of Light, just for kicks and giggles. 50% chance on spell critical that the next Smite will be free of cost, but be incapable of critting itself.

So. With all that, our new spell damage value is (1000 + 88)*1.05 = 1142.

Of that 1142, 71.42% of that will apply to Smite. Meaning Smite will gain 816 spell damage on top of the tooltip.
And then from there, Smite will get an extra 10% damage.
Right now, our damage will be 1502 - 1575 per cast.
We also now have a 30% critical strike chance, meaning Surging Light has a 15% chance to proc.
Let's factor these in, then...
Smite will crit for 2253 - 2363 damage. Averaging those in, Smite's relative damage will rise by 692 damage. Average in Surging Light as well, we get an additional 231 damage.

Meaning, fully talented, Smite will do, on average, 2425 - 2498 damage.

Therefore,

SMITE
Rank 10
Smite an enemy for 2425 to 2498 damage. 2.0 second cast time. Costs 385 mana.

On average, Smite will hit for 2462 damage every 2.0 seconds.
Therefore, per second, Smite will:
Deal 1231 damage every second.
Cost 193 mana every second.
(6.378 damage per point of mana)

Whew, that was long. But there ya go.

Now, let's get to fireball before my fingers fall off...


Fireball has a base cast time of 3.5 seconds, which means we gain the full benefit of our spell damage. Meaning our tooltip damage will be 1633 - 1805. Not including the DoT effect.

As to what we're going to do about the DoT effect. The fireball DoT does not stack, but it does "refresh" in the same way any other debuff would. Assuming we're chain casting these, means the DoT will be refreshed every 3 seconds. Meaning that we get 3 seconds of the 84 damage of 8 seconds, meaning we effectively get 32 damage of that in between fireballs. Bonus spell damage does not apply.

So let's look at our talents.

Improved Fireball, reduces cast time by 0.5 seconds (Fireball now has a cast time of 3 seconds)

Ignite. Critical strikes will now deal 40% of their damage as a DoT ability. (Fireball now, effectively, has 210% damage on any critical strike)

Master of Elements. Critical strikes will restore 30% of their base mana cost. (Mathematically, this means Fireball gets cheaper. We'll get to this soon)

Playing With Fire. 3% increase to spell damage caused. (NOTE THIS!! Spell damage CAUSED, not SPELL DAMAGE. This does not change our base spell damage, but changes what our spell actually hits for. Effectively, this means Fireball's damage is increased by 3%)

Critical Mass. Increases critical strike chance of fire spells by 6%. (Fireball now has a 26% chance to criticall strike)

Fire Power. Increases damage dealt by fire spells by 10%. (Another +10% damage for Fireball)

Pyromaniac. Reduces the mana cost of fire spells by 3%, and increases critical strike chance by 3%. (Fireball now has a 29% chance to critically strike, and is 3% cheaper)

Combustion. (Effectively means we get 3 guaranteed critical strikes with fireball every 3 minutes. We will mathematically add this in at the end)

Molten Fury. When the target is below 20% health, you deal 20% more damage. (Effectively meaning you deal 120% damage 20% of the time.)

Empowered Fireball. Fireball gets an additional 15% of your bonus spell damage. (Hurrah!)

Elemental Precision. Reduces mana cost of frost and fire spells by 3% (Fireball now is 6% cheaper to cast.)

Icy Veins. (Mathematically speaking, 20% more fireballs for 20 seconds every 3 minutes)

Now, let's see what all this does to our precious little fireball.

Like the priest, we're going to assume that we are self buffed, meaning we have Arcane Intellect and Molten Armor up, thus increasing our critical strike chance by 3.5%. Meaning our fireball now has a 32.5% chance to criticall strike.

Fireball will gain 1150 spell damage on top of the base value, and then that amount will be increased by 13%.
Meaning, our new fireball will hit for 2015 - 2209 damage, not including crits or any of that juicy stuff.
So let's toss them in.

First off, how to deal with Combustion. Combustion has a cooldown of 3 minutes, meaning we can use it once every 180 seconds. In 180 seconds, we woul cast 60 fireballs. Of those 60, normally 32.5% of them would crit, working out to 19.5 fireballs crit every 3 minutes. Combustion essentiall guarantees 3 critical strikes, so we can safely assume that it would add 1.5 critical strikes where previously it would have been a regular hit.
Thus, effectively giving us 21/60 fireball crits per those 3 minutes, giving us, mathematically, a revised 35% critical strike chance to fireball. Again, this is mathematically speaking.

Fireball will crit for 4232 - 4639 damage (this is already including the ignite damage) 35% of the time thanks to Combustion.
Average that back in to our base spell damage, fireball will now deal, on average, 3567 - 3761 damage every 3 seconds.

Bear with me, we're almost done. We have but two loose ends left to tie, and these are Icy Veins and Molten Fury.

First, Icy Veins. It will boost our fireball's casting speed by 20% every 3 minutes, essentially meaning every 3 minutes we get to deal 20% more damage. So, for 160 seconds we'll be dealing damage normally, and for 20 of those we'll be doing more.
Therefore, .111% of the time, we'll be dealing 20% more damage, which mathematically works out to 0.0222% more damage.
Factor that in, and fireball will now deal, on average, 3646 - 3845 damage every 3 seconds.

And now we get to Molten Fury. 120% damage, 20% of the time. 1.2 * .2 = 0.24, meaning thanks to Molten Fury, fireball will deal 24% more damage.
Factor that in, and fireball will now deal, on average, 4521 - 4768 damage every 3 seconds.

One last thing relating to mana cost. 35% of the time, fireball will be 30% cheaper. Mathematically, thats a 10.5% reduction to the mana cost of fireball.

I hope you stayed with me all this way. Let's see what fireball looks like now.

FIREBALL
Rank 13
Deals 4521 to 4768 damage, and an additional 32 damage over 3 seconds. 3.0 second cast time. Costs 355 mana.

On average, Fireball will hit for 4677 (counting the DoT damage) every 3.0 seconds.
Therefore, per second, Fireball will:
Deal 1559 damage every second.
Cost 118 mana every second.
(13.2 damage per point of mana)


FOR EASY REFERENCE

SMITE : FIREBALL
2462 damage per cast : 4677 damage per cast
1231 damage per second : 1559 damage per second
193 mana per second : 118 mana per second
6.378 damage per point of mana : 13.2 damage per point of mana

In conclusion. Fireball has greater DPS than Smite, and over double the mana efficiency of Smite, when considering talents.

Anyone want to wonder what this looks like if we toss in the Scorch debuff? I know I do. Let's math!

SMITE : FIREBALL (with Scorch debuff)
2462 DPC : 5379 DPC
1231 DPS : 1793 DPS
193 MPS : 118 MPS
6.378 DppM : 15.152 DppM

I think its fairly clear which spell is the better one here.

30 comments:

Hyouzan said...

To much math... Now my head hurts, but thanks for the comparison. Mage > Priest

Euripedes said...

Well, I wouldn't go so far as to say Mage > Priest.

But, fireball > Smite, for sure.

Megan said...

Yes, it is clear which spell is the winner.

Deathcoil.

Zerei said...

Megan, of course, wins.

Not even Sanctity Aura (+10% holy damage for party) and Judgement of the Crusader (+130ish holy damage to target) from a paladin would tip those scales, though.

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Anonymous said...

at the end of your post in your computations for fireball you mentioned molten armour where I think you ment molten fury.

yallazon

Euripedes said...

Ack!

Thanks yallazon-not-anonymous.
Corrected that glaring error.

Gold farmer post with kinky dranei pic deleted.

Jabari said...

Minor math note:

Smite is worse than you're making it here, as Surge of Light procs aren't "free" extra damage - the "free" Smite is instant, but it still costs a GCD... SoL probably reduces "pure" DPS a bit because of that (though it's pretty good for mana efficiency)

For "pure" DPS purposes, speccing Power Infusion might be better, but you can't get all of PI, Force of Will, and Spiritual Guidance (due to PI's totally stupid dependency on Mental Strength *grrrr*).

Brandstone said...

What if you were to throw in Holy Fire every time the DoT ran out? Also, some links to proposed builds would be useful. I'm thinking build such as this would provide close to comparable damage to a similarly geared mage, and have the side benefit of emergency heals, Imp Divine Spirit, Power Infusion, and the situational Pain Suppression.

Euripedes said...

The problem with tossing in Holy Fire and such means that we would essentially be extending this "math" thing into a straight up Smite Priest versus Fire Mage DPS comparison.

Which would, of course, require far more math and theorycrafting than my brain could handle before exploding.
Sadly, there is no Arcane Brilliance buff IRL.

The whole point of this post was to demonstrate Smite versus Fireball.
Maybe I should take the stuff about Scorch out, but I deemed it necessary to demonstrate, a little more realistically, what fireball would ACTUALLY do, DPS wise.

To add in what a Smitey priest would do ACTUALLY, I would have to assume a full spell rotation of things like Holy Fire, Smite, and Shadow Word: Pain.
Therefore requiring GCD, and all that stuff.

Anyone else wanna do it? =D

The base math is here already.

Mera said...

Rofl, and all this came from a passing comment, after remebering that a while ago I saw on wowwiki a table comparing base eg untalented, no +dmg spells.

Euripedes said...

Yeah, it was originally intended as a comment of "No, you're wrong. See?"
Then a little bit of math.

Now it's this huge, cantankerous monstrosity.

Like starting off with a thin guy, saying "Maybe I'll buy a Mars Bar", then transforming into this 900 pound man who regularly eats leftover food he find in his chin.

costas said...

Hi. Thanks for your detailed math analysis. I would also like to make a comment. In you post you mentioned that :

<<...Of those 60, normally 32.5% of them would crit, working out to 19.5 fireballs crit every 3 minutes..>>

However, the total chance to make a critical depends on two parameters : First parameter is knows as 'chance to hit the enemy first' (also known as spell critical hit chance) and then if the spell hits, there is the second parameter known as 'chance to make a critical hit' (also known as spell critical strike).
Therefore, the total chance to make a critical is the product of the two above mentioned parameters. The concequence of this is that the total chance to make a critical is smaller that the spell critical strike which is mainly given through the gear [a minor fraction depends on the character's stats (intellect)] character].
A detailed analysis is given to the following site :

http://www.wowwiki.com/Spell_hit

Also, in order to increase you DPS, only +damage gear is required until your +damage gear reach a value of about 1500 (at the moment, I think this number is impossible to come up !!).Theoretically then, above this value, spell critical strike plays an important role and its contribution is highly appreciated in order to maximise your DPS.
A detailed analysis is also given to the following site :

http://www.wowwiki.com/Stat_comparison

Thanks again for the posts.

Euripedes said...

All well and good data, costas :)
Coming up with raw damage, DPS numbers, whatever, with no base line, that has to be taken into account.

In a comparison like this, however, it really doesn't matter.
When comparing two spells like this, whatever parameter that would effectively lower the crit chance of one spell will also apply to the other.
If the actual critical strike chance of fireball is lower than the tooltip thanks to the spell critical hit chance, smite will be subjectted to the exact same thing.

If you take away X from both sides of the equation, the equation is still exactly the same.

costas said...

Hi again. I have to make one more comment. As it is mentioned in a post earlier on, the equation for the total critical chance is as follows :

total critical chance =

spell strike x critical heat

Thefore, by changing the values of those two parameters in a such way that their product is always equal (e.g. increasing spell strike and decreasing critical heat)the value of the total critical chance is the same.
At a first sight, someone might say : so ? what's the point of this ?

Here is the answer !!

Althought the value of the total critical chance is the same, the DPS value has been changed !!!!!!!

Bear in mind that in an earlier post I mentioned that : to make a critical strike to an enemy is a two way process
First, your spell must hit the enemy and secondly, if your spell hits, there is a chance to make a critical hit.

By choosing to increase one of these two parameters, you MUST increase critical heat first because this is the restriction in order to make the second parameters possible to happen.In addition, an increase in hit rate will usually yield a constant level of damage, whereas a high crit chance gives a more random damage distribution over time.

All other things being equal and without considering talents, an 1% increase in spell crit chance will result in a gain of 0.5% of a spell's base damage, whereas a 1% increase in spell hit chance will give a 1% increase of a spell's base damage.

CONCLUSION :

As long as no other effects come into play, +spell hit rating is more effective than +spell crit rating.

Euripedes said...

Don't forget that is to a point.
Once you are hit capped, any further spell hit rating is utterly worthless.

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