Roywyn

As requested, I'll do a repost if this for patch 2.4.
That means I'll adapt most things to sunwell gear level, and use OOCmp5 = 5*0.009327*sqrt(int)*spi for the new spirit regeneration.


"But there is no mana issue!" - Well, there is, but in a more subtle way. Can you spec out of all mana talents, use flame caps, destruction potions, molten armour, no evocation and still last through a fight? Maybe with a very good shadow priest on a short fight.
But what if you don't get one, or if the fight is rather lenghty?

There are quite a few means of recovering mana, but which one to chose in which situation?
Let's take the following scenario:

A deep fire spec as base, Icy Veins, no Clearcasting, Fireball spam, Sunwell gear.
1650 spell damage, 300 spell crit, hit capped, 350 haste, 650 intellect, 330 spirit, with AI, GotW, BoK,Wrath of Air totem, flask, food, weapon oil. No racials, no Divine Spirit.

This setup (which is about the best you can get from gear seen so far) gives a bit more than 22% haste. With Icy Veins and 1 Bloodlust over 6 minutes, we have 2.33s average cast time. Or 2.15 Fireballs every 5 seconds.

That makes our regeneration while not casting 1.19*spirit per 5 seconds.
Including BoK, every point of intellect increases our regeneration while not casting by 0.352 mp5.

So, that's 392 mp5 while not casting, 65 mp5 more with Divine Spirit. 10% more for humans, 2.5% more for gnomes.

This setup has 11700 base mana. Switching from Sunflare/Heart (20+21int) to a Golden Staff (54+3*10+30int) adds 73*15*1.1 = 1205 mana, making 5 ticks of Evocation return 9679 mana.


I take a 6 minute boss fight, uninterrupted casting. That way, you can use your 2m CDs 3 times, or 3m CDs 2 times. That fight length is a multiple of these cooldowns, so nothing can get a benefit from cooldown coming up early.
The actual length of the fight shouldn't matter too much to the model, but I think that one is a pretty decent model.


How much is spell hit worth?

With Sunwell gear, you'll end up below the hit cap. You'll gem some hit or dmg/hit gems in yellow slots, and gem for damage or haste in the remaining sockets.
Since damage and haste gems are roughly equal there, I'll just assume that every +hit you get from talents will make you drop +5 hit on a gem for +6 damage on a gem. So, every free +1 hit rating is worth +1.2 damage that you can by regemming.

Thus, 1% hit ~ 12.6 hit rating ~ 15.1 damage equivalent.


How much are other stats worth?

On average, one Fireball costs 350 mana with Elemental Precision, Pyromaniac, Master of Elements. No Clearcasting.

According to Vontre's sheet, 1 crit rating ~ 0.86 damage, and it adds 0.124 mp5 from MoE.
Also, 1 haste rating ~ 1.12 damage while costing -0.37 mp5.

That means socketing 5 crit over 5 haste gives you 2.47 mp5 at the cost of 1.3 damage.

1 intellect ~ 1.1*22.08/80 crit (with BoK) ~ 0.3036 crit ~ 0.26 damage and +0.0376 mp5 just from the crit.
With BoK, we also get 16.5 mana, or 0.2292 mp5 from the initial mana pool. Evocation adds another 0.1719 mp5.
It also adds 0.352 mp5 while not casting.

1 spirit grants 1.309 mp5 while not casting. And 0.11 damage with improved divine spirit.


Regarding talents and talent choices

Taking Arcane Meditations means you lose Elemental Precision, Arcane Concentration means you lose Icy Veins. A fire spec needs 42 points to maximise PWF, Critical Mass, Fire Power, Pyromaniac, Combustion, Molten Fury, Empowered Fireball.

To get Clearcasting and Icy Veins, one would lose more in fire talents than the Tri-Spec gains.



Talents

Elemental Precision
3% hit translates to 37.8 hit rating or 1.2*37.8 = 45 damage. 3% cost reduction is 12.75 mana less per cast, or +27.5mp5.

Icy Veins
20% haste for 20s every 180s => 2.2% haste averaged. With +22% base haste, we go from 122% speed to 1.022*122% = 124.684% speed, 2.684% haste more, or ~42 haste rating.
Thus, Icy Veins ~ 47 damage and -15.5 mp5.

Arcane Concentration (Clearcasting)
Saves ~40 mana per cast, or +86 mp5.

Arcane Meditation
Returns 30% * 392 mp5 = +118 mp5 while casting.

Master of Elements
Assuming 40% crit chance, it saves 425*30%*35% = 51 mana per cast, or +110 mp5.


Armour/Evocation

Mage Armour returns 30% * 392 mp5 = +118 mp5 while casting.

Molten Armour gives 3% crit ~= 68 crit rating ~ 58.5 damage and +8.4 mp5 from Master of Elements.

Evocation with 2T6 gives you 75%*12905 = 9679 mana at the expense of 10s cast time. That means a 9679mana/6min = +134 mp5 at the cost of 10s/6min = -2.77% haste ~ -43.6 haste rating ~ -49 damage, +16 mp5.

So, using Evocation is a +150 mp5, -49 damage change.

Note that these numbers do not change with more passive haste rating on gear. Passive haste will speed up your evocation and your spells in the same manner, and you still lose 10s of your hasted effective 360s*122% (haste) cast time.

You can use Evocation in the last moment of Heroism or Icy Veins, to reduce the channeling time, and cheat some more duration out of your Heroism/Icy Veins buff.
This is in most cases not practical to do. In a 6 minute fight, you can use your Icy Veins twice. Once very early in the fight and then when the mob hits 20%. You want to use Evocation (if at all) around 50%-25% though, to make sure you have full mana in the execute phase. It just doesn't seem to match into a time frame.

Same with Heroism, which should be used under 20%. You don't want to waste that time on Evocation.


Consumables

Mana Potions return +100 mp5, or +140mp5 with the Alchemist's Stone (few mages are alchemists though).
Destruction Potions give 120 damage and 2% crit for 15 seconds on a 120 second cooldown. That's +19 damage and +0.5mp5 from Master of Elements.

Mana Gems return +100 mp5, or +125 mp5 with the Serpent-Coil Braid.
Flame Caps give 80 fire damage for 1 minute on a 3 minute cooldown, or +26.6 fire damage average.

This does however change when you use those comsumables with your other cooldowns.
Heroism, Icy Veins, Combustion, Molten Fury, Skull/Hex make up for 14% of our damage.
At 40% crit rate, Combustion adds on average 1.23 crits per use.


Stacked Cooldowns

Stacking a Destruction Potions with Icy Veins and Combustion and Skull looks like as follows.
+20% haste, +12.3% crit damage (+15.5% crit), +9.1% Skull haste.
Stacking those and reducing it by 14% (the use of cooldowns averaged) yields a +29% increase over averaged out use.

Stacking Molten Fury and Bloodlust in addition (the value of Combustion goes down to +9.5% due to more haste), the value of a Destruction Potion is increased by +96% over averaged use.


Stacking Flame Caps with Icy Veins, Combustion and Skull looks like as follows.
+20% haste, +10.1% crit damage (+12.6% crit), +9.1% Skull damage for 20 seconds.
Stacking those is a +44.14% increase. Averaging it out over 1 minute isn't much better than the averaged numbers over the whole fight. Hm, differences are too small there to compare them properly.
Meh, would have to redo about every calculation to fix that, can't be bothered. I'd estimate a ~10% benefit from stacking Flame Caps with Icy Veins, Combustion and Skull.

Stacking Molten Fury and Bloodlust in addition (the value of Combustion goes down to +7.8% due to more haste), the value of a Flame Cap is increased by +120% for 20 seconds, then +56% for 20 seconds (Molten Fury and Bloodlust) and +20% for the last 20 seconds (Molten Fury).
Averaged over 1 minute, it's +65.3% from Flame Caps, or +45% over the averaged use.



Elixirs and Flasks

A Flask of Pure Death adds +80 fire/frost damage, a Flask of Supreme Power adds +70 damage.


An Elixir of Major Fire/Frost Power adds +55 fire/frost power.
An Adept's Elixir adds +24 damage and crit, or +44.6 damage and +3 mp5.

So, at 0.29 mp5/dmg, Adept's Elixir is cheap to make but not worth it for pure power. Might be useful for AE spam with TLC and AToI when hovering at the AoE damage cap.


An Elixir or Major Mageblood adds +16 mp5.
An Elixir of Draenic Wisdom adds +30 intellect and spirit. Thats +7.8 damage (and another +3.3 damage with Improved Divine Spirit) and +8 mp5 from crit and the mana pool, +5.2 mp5 if you use Evocation. It also adds +50 mp5 while not casting, or +15 mp5 with Mage Armour.

So, Draenic Wisdom beats Mageblood when using Evocation and Mage Armour, a Flask will beat Elixirs when not using Evocation or Mage Armour.
Elixir of Draenic Wisom and Major Fire/Frost Power when using Evocation and Mage Armour yield +28 mp5 at the cost of -17.2 damage, or -12.9 damage with Improved Divine Spirit.


Trinkets

Icon of the Silver Crescent averages at +69 damage, Hex-Shrunken Head at +88 damage, an ideal DM:Crusade is +80 damage.
Thus, I'll just assume a static +80 damage trinket to compare the other two mana trinkets to.

The value of the stone and braid very much depends on the other trinkets you have, so take the comparison to a +80 damage trinket just as a rough guideline.


Serpent-Coil Braid gives 30 crit rating, 12 hit rating, 25mp5 and 225 damage for 15 seconds every 2 minutes.
12 hit ~ 14.4 damage, 30 crit ~ 25.8 dmg, +3.7 mp5.
This adds up as +68 damage and +29 mp5 in total.

The braid does have one significant disadvantage though.
Flame Caps have a 3 minute cooldown, so they will be paired with Combustion/Icy Veins. Mana Gems have a 2 minute cooldown, so the braid proc will usually not be synchronised.

You also can't use your mana gem right at the start, so the braid can be quite a bit harder to handle when it comes to proper cooldown management. And will most likely lose damage from not stacking cooldowns.


The normal Alchemist's Stone gives +15 to all stats and 40mp5. That's +4 damage from intellect, +1.6 damage from spirit if you have IDS, 248 raw mana, 434 mana with evocation (6.03 mp5 averaged), and +0.5mp5 from crit.
It also adds +25 mp5 while not casting.

Seeing that it's will only be useful when you run OOM with all other mana sources used, the best use of the trinket will total +5.6 damage and +54 mp5 while casting with mage armour.

The Redeemer's Alchemist's Stone is a +40 damage, +40 mp5 trinket.

The Sorcerer's Alchemist's Stone is a +63 damage, +40 mp5 trinket.


Blessings

Blessing of Wisdom gives you +41mp5 or +49.2mp5 if talented.

Blessing of Kings gives you ~30 spirit and ~60 intellect.
The intellect adds +15.6 damage, +2.26 mp5 from crit, 900 mana, or 1575 mana with Evocation (+22 mp5)(and some spirit ticks), +24mp5 total.
The increased stats also add +52.6 mp5 while not casting, or +15.8 mp5 while casting with mage armour.


Downranking

Downranking Fireball from rank 13 to rank 12 reduces its mana cost by 15.
With 40% crit, we get 12% mana back on average, talents reduce the cost by an additional 6%.
That makes it 12.3 less mana, at 2.15 casts per 5 seconds that's 26.45 mp5.

The base damage loss per cast is 2 for one DoT tick and 41.5 for one cast, which equals 43.5/1.15 = 37.83 less +damage.
I expected it to be a pretty bad trade-off, but wanted to check the number for sake of completion.

Further downranking, and also upranking to the datamined rank 14 Fireball (which does not exist) provides very similar damage/mana trade-off.


Wanding

What does the situation look like when you're totally out of mana and can only stand there and wand for a half a minute before your cooldowns come up again and you can continue casting?

Fireball has 735+21 base damage. At 1650 spell damage, not casting means you lose 2307 spell damage.

For wands, since shadow wands are a big taboo, the best choice seems to be an arena wand.
A season 3 wand does 189.5 fire DPS, 1.9s shoot timer. Taking spell hit and crit into consideration, the damage equivalent of wanding is:
189.5/1.15*(1+0.53*0.3)/(1+0.4*1.163)*0.97/1.15*5/2.15 = 255.68
(Fire Power + 4T6, crit adjustment, hit adjustment, scaling, shoot/cast time factor).

As for mana 749 mp5 from not casting fireballs, and recover 459 mp5 from spirit while not casting.

So, without Judgement of Wisdom, this would be a trade of 1208 mp5 for 2051 dmg, or 0.589 mp5/dmg.

With Judgement of Wisdom up, the mana recovered increases by 0.5*74*(5/1.9*0.96-2.15*0.99) = 14.72, the ratio increases to 0.596 mp5/dmg.

Changing the wand to the Sporeggar wand with 96.9 fire DPS, 1.3s shoot timer, the numbers change as follows. The damage equivalent is 96.9/1.15*(1+0.53*0.3)/(1+0.4*1.163)*0.97/1.15*5/2.15 = 130.74, the mana recovered by Judgement of Wisdom increases by 0.5*74*(5/1.3*0.96-2.15*0.99) = 57.86.

The mana recovered changes to 1266 mp5 for 2177 damage, or 0.582 mp5/dmg.


So, trying to switch to a faster wand for Judgement of Wisdom is actually a very minor loss to total damage given the huge gap of quality between fast and slow non-shadow based wands.


How does that look like at very low gear levels?
Let's assume 500 spell damage, no haste at all, the Sporeggar wand and 330 mp5 while not casting.

The damage loss from not casting is 1157.39, wanding makes up for 130.74, so we're facing a -1027 damage loss.
You gain 5/3*348.5 = 581 mp5 from not casting Fireball, and 330 mp5 from spirit, for 911 mp5 total, making it a ratio of 0.89 mp5/dmg.



Scorch

Scorch is cheap and does low damage. I still want to check how Scorch compares to other alternatives for mana saving.
I'll assume that you can fit two Scorches into one Fireball cast. There's issues with cast delay and you'll run into troubles when your Scorch cast time drops below 1 second, but I'll just assume the best case scenario here.

Scorch does 305-361 fre damage (333 average) for 180 mana. For detail on the calculation, check the Fire Blast section below.
For two Scorch casts and accouning for the crit difference and 4T6, we get
2*(333+1.5/3.5*dmg)*1.0317499*0.9565217 = 657.2695 + 0.8459067*dmg damage.
One Fireball would do (735+1.15*dmg)+21/(1.4652) = 749.3325 + 1.15*dmg damage.

The equivalent spell damage loss would then be the difference (92.063 + 0.3040933*dmg)/1.15 = 80.0548 + 0.2644*dmg.
So, at 500 spell damage you'd lose -212 dmg, at 1650 spell damage you'd lose -516 dmg.

For the mana conservation with 40% crit, one Fireball costs 425*(1-0.03-0.03-0.4*0.3) = 348.5 mana, two Scorches cost 2*180*(1-0.03-0.03-0.44*0.3) = 290.88 mana.
With 2.15 Fireballs every 5 seconds you'd save 123.883 mp5. At low gear levels with no haste at all, you'd save 5/3*(348.5-290.88) = 96 mp5.

That's a conversion of 0.45 mp5/dmg at 500 spell damage, and 0.24 mp5/dmg at 1650 spell damage.

So, you're far better off running out of mana and wanding than using Scorch at any gear level.
About time that the "Scorch is good DPM" myth got finally busted.



Fire Blast

Fire Blast is an instant spell with a very high base damage. It can be used between Fireballs to increase damage. It is very expensive on mana, so it comes with a drawback.

Fire Blast scales a lot worse than Fireball though. At 2336 spell damage and above, it is stricly a DPS loss compared to Fireball. Until then, it might provide a DPS gain

Also, using Fire Blast has two major disadvantages.

First, it is an instant spell, which makes it twice as susceptible to cast delays than Fireball.

Second, there is an issue with Ignites overwriting. If both, Fireball and the following Fire Blast crit, it is very likely that the Ignite damage of one of your crits will be overwritten, causing you to lose damage.
I haven't heard whether this issue still persists or not, but that's mostly because with the currently available gear Fireball is a minimal possible gain in the best case which comes a huge mana, positioning and talent point cost.

Also, once your global cooldown drops under 1 second, Fire Blast does not benefit from further haste, while Fireball still does.


Let us assume the best case.
Fire Blast does 664-786 fire damage (725 average) for 465 mana, with a cooldown of at least 6.5 seconds.
Fireball does 649-821 + 21 fire damage (735+21 average) for 425 mana with a 3 second cast time.

A 2*Fiba/FiBla rotation takes 7.5 seconds and can be kept with up to +15% haste, or 2.6 second Fireballs.
After that, a 3*Fiba/FiBla can be used until you pass +50% where the global cooldown reached 1.0 seconds.

Bear in mind that with a 4% higher crit rate and 40% base fire crit, Fire Blast will do (1+0.44*1.163)/(1+0.4*1.163) = 103.17499% damage compared to fireball, but gets another 1.1/1.15 = 0.9565217 multiplier because 4T6 doesn't affect it.

Since haste won't affect the damage/mana trade-off ratio, I'll assume a 2:1 rotation at 7 seconds for simplicity. Compared to pure Fireball spam, this trades half a Fireball for one Fire Blast and one more Fireball DoT tick.
So, we gain (725+1.5/3.5*dmg)*1.0317499*0.9565217+21/(1.4652) = 729.8286 + 0.42295*dmg and lose half a Fireball which is 0.5*((735+1.15*dmg)+21/(1.4652)) = 374.6663 + 0.575*dmg.
This results in (355.1623 - 0.15205*dmg) more damage before multipliers over this duration.

That means that Fire Blast always is a strict DPS loss beyond 2336 spell damage.

Keep in mind that 1 point of spell damage would add 2.5*1.15 = 2.875 damage over the course of 2.5 Fireballs.
Which means that Fire Blasts is the equivalent of gaining (124.62 - 0.052887*dmg) spell damage.

That is +124 damage at 0 dmg, +98 damage at 500 dmg, +72 damage at 1000 dmg and +37 damage at 1650 spell damage in our example.


As for the mana, half a fireball costs 0.5*425*(1-0.03-0.03-0.4*0.3) = 174.25 mana.
A Fire Blast costs 435*(1-0.03-0.03-0.44*0.3) = 351.48 mana.
Assuming an average 7 second cycle, that is an increase of 127 mp5.


This all assumes perfect conditions without delay, perfect positioning and no Ignite overwriting issues.
Until it is confirmed that Ignite never bugs out any more, I strongly recommend not to use Fire Blast in your regular cycles.




Summary/Comparison

This is a list of choices you can make to maintain your mana.
It's ordered by efficiency, by the amount of mp5 you gain per point of sacrificed damage.

1) 5.27 mp5/dmg - Chaining Mana Potions over Destruction Potions gives you +99.5 mp5 at the cost of -19 damage.
(Drops down to 4.09 mp5/dmg with Combustion, Icy Veins, Skull, 2.69 mp5/dmg with Bloodlust, Molten Fury on top.)

2) 3.70 mp5/dmg - Chaining Mana Gems over Flame Caps gives you +100 mp5 at the cost of -27 damage.
(Drops down to 2.55 mp5/dmg with Combustion, Icy Veins, Skull, Bloodlust, Molten Fury.)

--) 3.39 mp5/dmg - Not using Fire Blast at top end gear levels gives you +127 mp5 at the cost of -37 damage.

3) 3.06 mp5/dmg - Evocation gives you +150 mp5 at the cost of -49 damage.

*) 2.69 mp5/dmg - Using a Mana Potion over Destruction Potion with Combustion, Icy Veins, Skull, Bloodlust, Molten Fury yields +33 mp5 at the cost of -12.3 damage.
*) 2.55 mp5/dmg - Using a Mana Gem over a Flame Cap with Combustion, Icy Veins, Skull, Bloodlust, Molten Fury gives you +33 mp5 at the cost of -13 damage.

*) 2.41 mp5/dmg - Serpent-Coil Braid gives you +29 mp5 at the cost of about -12 damage. (Additional damage loss from cooldown desynch.)
7) 2.35 mp5/dmg - The Sorcerer's Alchemist's Stone gives you +40 mp5 at the cost of -17 damage.

8) 2.17 mp5/dmg - Arcane Concentration instead of Icy Veins yields +102mp5 at the cost -47 damage.
9) 2.02 mp5/dmg - Arcane Meditation instead of Elemental Precision yields +91 mp5 at the cost of -45 damage.
10) 1.89 mp5/dmg - Mage Armour gives you +110 mp5 at the cost of -58 damage.
11) 1.90 mp5/dmg - Socketing Potent Pyrestones over Reckless Pyrestones (crit over haste) yields +2.47 mp5 at the cost of -1.3 damage per gem.

12) 1.63 mp5/dmg - Elixir of Draenic Wisdom and Major Fire Power offer +28 mp5 at the cost of -17 damage when using Evocation and Mage Armour.

--) 1.29 mp5/dmg - Not using Fire Blast at low blue gear levels gives you +127 mp5 at the cost of -98 damage.
13) 1.27 mp5/dmg - Using Drums of Restoration over Drums of Battle gives you 142 mp5 at the cost of 112 damage.

14) 1.00 mp5/dmg - The Redeemer's Alchemist's Stone gives you +40 mp5 at the cost of -40 damage.

--) 0.89 mp5/dmg - Wanding at low blue gear levels when out of mana give you +911 mp5 at the cost of -1027 spell damage.

15) 0.72 mp5/dmg - The Alchemist's Stone gives you +54 mp5 at the cost of -74.4 damage with mage armour.
16) 0.70 mp5/dmg - Downranking to rank 12 Fireball gives +26 mp5 at the cost of -38 damage
17) 0.64 mp5/dmg - Talented Blessing of Wisdom over Blessing of Kings with mage armour gives you +10 mp5 at the cost of -15.6 damage.
--) 0.59 mp5/dmg - Wanding at top-end gear levels when out of mana gives you +1208 mp5 at the cost of -2051 spell damage.

--) 0.45 mp5/dmg - Using Scorch at low blue gear levels when out of mana gives you +96 mp5 at the cost of -212 spell damage.
--) 0.24 mp5/dmg - Using Scorch at top-end gear levels when out of mana gives you +124 mp5 at the cost of -516 spell damage.


This means if you're min-maxing to the extreme, you'd chain mana potions as first priority, and mana gems as second priority.
Using Evocation is a clear third priority, using mage armour or respeccing to 10 or 18 arcane are next best choices afterwards.
The Serpent-Coil Braid and Sorcerer's Alchemist's Stone are in that league as well. They depend on your other trinkets, your hit on gear and your stackable cooldowns.

Redeemer's Alchemist's Stone, the normal Alchemist's Stone and choosing BoW over BoK are poor choices for mana regeneration.
They are only just barely better than running out of mana and having to wand.

Spamming Scorch is very, it's the only thing that is even worse than running out of mana and having to wand.


Changes since 2.3.2

So, what's different now?

Spirit regeneration was buffed by around 50%, making mage armour and arcane meditation better.
The abundant spell haste increases overall mana consumption, but also amplifies the benefits of cost reduction talents.
The lack of spell hit on gear increases the value of spell hit talents, and hit on some special items of interest.

I re-read everything again and corrected some typos, and it should be mostly correct now.


[Edit]:
Your mana consumption of fireball spam is 148 mana per second, or 740 mp5.
That means you'll run out of mana without any regenereation in 80 seconds.

For a 6 minutes fight, your initial mana pool can be represented by 162 mp5 (11700 mana spread over 6 minutes).
If you can get a shadow priest (375 mp5 at 1500 DPS), then potting and gemming will get you through the fight (737 mp5 totaled).
Without one, you can use evocation and mage armour for 260 mp5, leaving you 115 mp5 short, or 8280 mana.


[Edit]:
04/20/08 Added wanding and scorch.
04/19/08 Added fire blast and downranking.
04/02/08 Added crit gems vs. haste gems.
03/02/08 Added elixirs vs. flasks.
03/02/08 Added cooldown stacking for potions/caps.