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.