So I was running some numbers while talking with my guild's mages about specs and efficiency. The results I came up with surprised me a bit, but can't really see any error in my math...though it's 3am and I'm not a complete math whiz or anything. If anybody could doublecheck or comment on this, it would be very much appreciated. Here's the copy/paste of my forum post:

Assumptions:
1) Specced for full dps (fire power for fire, arcane instab/piercing ice for frost)
2) Debuffs up (fire vuln, winter's chill. Didn't count CoE).
3) Not counting resists (I'm not sure on the math for how fire resists work, and I suspect this is a large part of my results, since no partial resists are factored in. If anybody corrects this, please assume elemental precision in all builds).
4) Not counting rolling ignites, calculating for fire giving 210% crit damage (150% + 40% of that) and frost giving 200%.
5) Assuming 15% natural crit rate and 500 spell damage.

Scorch: Base 150 mana, 284 average damage. With spell damage, 499. With fire power, 549. With fire vuln, 627. Factor in 25% crit rate (15% base, 4% incinerate, 6% critical mass) and every scorch you cast will average 792 damage. You will crit 25% of the time and regain 45 mana each time you do, meaning each scorch costs on average 139 mana. That's 5.7 damage per mana, and 528 dps.

Fireball: Base 410 mana, 745 average damage. With spell damage, 1245. With fire power, 1370. With fire vuln, 1575. 21% crit rate (no incinerate), that gives 1922 average. You will crit 21% of the time and regain 123 mana each time you do, meaning each fireball costs on average 384 mana. That's 5 damage per mana, and 641 dps.

Frostbolt: Base 290 mana, 535 average damage. With spell damage, 965. With piercing ice, 1022. With arcane instability, 1053. 28% crit rate (15% base + 3% for arcane instability + 10% for winter's chill) gives 1348 average damage. Adjusted mana cost for frost channeling is 247. That's 5.46 damage per mana, 539 dps.

So...scorch looks to be more efficient, and just barely behind in dps. Fireball is about 10% less efficient, and almost 20% more dps. That really surprised me, and I'm thinking I made a mistake somewhere (such as partial resists). If anybody can check/help me with this or direct me to a post where it's listed more accurately, I would be very grateful.

Edit: Mana restores on scorch/fireball are for master of elements.

Not sure but I think talents like piercing ice and fire power only works on base spell damage. Also you seem to have missed Judgement of Wisdom on frostbolt

The mana restoration wasn't based on judgment of wisdom, but master of elements (restores 30% of the mana cost of the spell upon a crit, fire talent). I didn't factor JoW because it's not up on all fights. Assuming it was, though, it would only serve to make scorch even more efficient than frostbolt.

I didn't know that about piercing ice/fire power. But...it shouldn't matter which order you multiply in, should it? 1 x 3 x 5 is always 15, regardless of the order. Or do you mean that the bonuses from fire power and, say, spell damage are mutually exclusive...what's the term? Additive rather than multiplicative?

That's not Judgement of Wisdom but Master of Elements which he is using for the mana regen. Which isn't included in a 28/0/23 build as it is somewhere in Fire. And ofcourse, Judgement of Wisdom is as of now Alliance only, which isn't handy for those calculations.

As for the other, let's do some theorycraft. Say you have + 540 damage. I'm taking Frostbolt as an example here. Frostbolt with + 540 dmg hits for (535 + (540*0.814) = 974.56, or 975 for short. Then we add Piercing Ice for another 6 %, so 975 * 1.06 = 1033. If it were before gear, it would be: 567 + (540 * 0.814) = 1006 average. Add a + 20 and - 20 damage on each side to have the high/low end dmg. And I'm fairly sure that my old Frostbolts with Piercing Ice and + 545 Frost damage did not go under 1k damage, however low end the hit was. Can't paste a combatlog or anything as I'm fire now, but this would seem to imply that it would scale with gear. And I can hardly see a reason why it would be different for Fire.

Fire Power, Piercing Ice, Arcane Instability etc are added AFTER +DMG from gear. The only talent that is added before gear is Moonfury (Druid Balance Tree). I think all +Heal talents are added pre gear as well.

Can't have Arcane Instability and Winter's Chill on one Mage.

I think he's assuming that these mages will be leeching Winter's Chill (and maybe Improved Scorch) from other mages.

If you're interested in all the little calculations and statistics behind various spells, I highly recommend a mod called Theorycraft. It has more options than you could probably ever want as it can basically tell you anything about a spell. Check it out, and see if its math matches yours.

Also remember that, due to lag making spells take .1 to .4 seconds longer to cast, any DPS calculation you make will be slightly higher than what you will actually see in-game.

If you look at some of the stuff I've done here:

http://forums.elitistjerks.com/viewtopic.php?id=6825
http://forums.elitistjerks.com/viewtopic.php?id=6819

It's generally to address the same questions.

These are good discussions but the complexity is deceiving. I'm not honestly sure that you can really predict dps and damage output without working up at least a quick simulation of what you want to test. The biggest issues are the interaction of lag and casting time plus the rolling ignite mechanics of course but there are other subtle issues as well, including mods like fastcast and cancellation issues that can result. I would also add that fireblast needs to be considered as a viable option for use in a fire mage's rotation as well. It does effectively have the same casting time as scorch but the next spell is essentially lag-free and the higher base damage can make it useful.

The biggest hurdle to accurate mathematical analysis that I see is the synergy between multiple fire mages and combustion/ignites. While one or two WC Mages with the rest 28/23 is fairly straightforward, the changes between 3 and 5 fire mages are a little harder to predict. For now I am pretty much content to conclude (as backed by my own parses) that multiple fire-mage raids will have higher mage efficiency and damage than their counterpart frost mage raids. It is interesting to persue the idea of a single fire mage also having better dps and dpm of course.

you need to factor partial resists for fire, since lvl63 have 15-20 that can not be removed but can be from binary spells.
secondly, you need to include coe. Ignite gains the benefit from coe+fire vulv+PI (but not firepower). So with coe+vuln fire actually does 225% dmg on a crit. More with PI.
third it is technically impossible to cast spells at their exact cast time. theorycast is actually very flawed in this regard. Even with fastcast you can't chain cast spells without at least a .2s delay no matter how fast you hit the keys. .2s added to a 1.5s scorch is a lot more lost dps then .2s added to a 2.5s frostbolt. As the time between spells going up, scorch loses even more vs frostbolt.
fourth i'm not sure if you included the frostbolt penalty to+dmg. Frostbolt receives .814 bonus from +dmg, not .857 as it should. However, frostbolt is calculated as a 3s spell but with talents is 2.5s so it actually gains significantly more from +dmg then scorch does as +dmg goes higher.

Allright...seems like I've made a few errors.

1) I added .85 of spell damage to frostbolt instead of .81. This of course favors fire even more.
2) I wasn't really able to account for the delays between casts. Maybe I should add .25 seconds onto each spell?
3) Ignites are pretty tricky to account for, with multiple fire mages etc. I did this to give a rough idea, and I was expecting to see that fire was more dps but frost was more efficient, with the dps order going fireball > frostbolt > scorch. I wasn't really expecting scorch to be matching frostbolt's dps and efficiency and that's what really surprised me and sent me scurrying to these forums to look for help.

Thanks very much for all the responses so far, I really appreciate it.

Properly, one should look at +damage/unit time. Frostbolt in 2.5 seconds get 81.4% but over a standard 3.0 seconds it gets 97.7%. Because it benefits more than a fireball from the casting time reduction, it actually performs very closely in terms of applying +damage. Scorch is poorer in that application initially but scales brilliantly through crit talents, firepower and the ignite mechanics.