Lately I have noticed people trying to compare different talents in nearly every thread in the mage forums. In order to consolidate these discussions, and provide some mathematical data behind them I set out to do a little bit of work with some of the core discussions.

The following is some math behind the more controversial talents. I can add more if people have questions about the benefit of other talents.

I assumed a ttw/fire spec for most of the math, although it would be easy to make changes towards another spec.
The following stats were used in my calculations, they are approximate BiS statistics, and the "Relative value of Crit Rating" was just me sidestepping the work to turn crit into DPS. DPS is calculated in an infinite mana situation.
Int: 1400
Spirit: 900
Haste rating: 420
Crit rating: 500
Spell Power: 3000 (whenever this number is of significance I will show alternates with more moderate amounts of spell power)
Relative value of Crit Rating: 1.64
4P T8 is being worn (This effects the percent of spells which are fireball)

Here is the Excel File with my math. It is hosted on GoogleDocs, you can't edit it, but you can export it as a .xls file.

Arcane Concentration (~33.7mp5 per point)
- With this talent all 5 points are equal.
- Calculated with 58% fireballs (620 mana) and 42% LB/Pyroblast (718 mana).
- Each talent point is providing you with about 33.7mp5.

cast time - fireball	2.48
chance of fireball	58%
cost of fireball	620
cast time - LB/Pyro	1.24
chance of LB/Pyro	42%
cost of LB/Pyro	718
average cast time	1.96
average cost of spell	661
period of 2% proc	98.0
equiv mp5	33.7

Magic Absorption (4.5-5.5% magic damage mitigation per point)
- The talent points give the same amount of resistance, but are not equal.
- The following table is calculated with P(x) = 0.5 - 2.5*|x - AR| (see this thread for the reasoning behind the math)

Source	Resist	Mean	0%	10%	20%	30%	40%
Nothing	0	0.0250	0.5000	0.2500	-	-	-
1pt MA	40	0.0795	0.3182	0.4318	0.1818	-	-
2pt MA	80	0.1356	0.1610	0.4110	0.3390	0.0890	-
motw	76	0.1297	0.1758	0.4258	0.3242	0.0742	-
motw+1pt MA	116	0.1853	0.0367	0.2867	0.4633	0.2133	-
motw+2pt MA	156	0.2342	-	0.1644	0.4144	0.3356	0.0856
aura/totem	130	0.2031	-	0.2422	0.4922	0.2578	0.0078
aura/totem+1pt MA	170	0.2500	-	0.1250	0.3750	0.3750	0.1250
aura/totem+2pt MA	210	0.2917	-	0.0208	0.2708	0.4792	0.2292

	Benefit of 1st point	Benefit of 2nd point
Nothing	5.45%	5.60%
W/MOTW	5.56%	4.89%
W/Totems	4.69%	4.17%

Student of the Mind (1st point: 23mp5/32dps, 2nd & 3rd point: 17mp5/24dps)
- The talent points are clearly not equal, the first point gives more spirit than the other two.
- The first point gives you ~23mp5, the other two give you ~17mp5

Base mana regen	563	Change
mana regen 1pt	586	23
mana regen 2pt	603	17
mana regen 3pt	620	17

- With Glyph of Molten Armor. The first point gives you ~20 crit rating, the other two give you ~15 crit rating.
- Neglecting the non-damage benefits of the crit attained via increases spirit (mana regen from extra master of elements procs is immaterial)
- The first point gives you ~32dps while the other two give you ~24dps

	W/ glyph of MA	W/o glyph of MA
crit rate from first point	20	13
crit rate from other points	15	9
dps from first point	32	21
dps from other points	24	15

Arcane Meditation (1st & 3rd point: 96mp5 per 17% regen, 2nd point: 90mp5 per 16% regen)
- All points are not equal
- Same regen formula as earlier.
- 563mp5 base
- 90/96mp5 per point

Base mana regen	563
Mana regen per 17%	96
Mana regen per 16%	90

Master of Elements (~110mp5 per point)
- Each talent point is equal
- This talent is not effected by changes in mana cost of a spell (i.e. Clearcasting). See Enthorn's post for an explanation.
- Assuming constant casting, benefit diminishes proportional to diminishing dps time.
- Using the same proportion of casts as in the Arcane Concentration discussion, 58% fireballs (620 mana) and 42% LB/Pyroblast (718 mana).
- With glyph of molten armor each point gives ~110mp5

	W/ glyph of MA	W/o glyph of MA
cast time - fireball	2.48	2.48
cost of fireball	620	620
chance of fireball	58%	58%
crit chance of fireball	66.07%	62.15%
cast time - LB/Pyro	1.24	1.24
cost of LB/Pyro	718	718
chance of LB/Pyro	42%	42%
crit chance of LB/Pyro	64.07%	60.15%
Average mana regain per cast	43.08	40.49
average cast time	1.96	1.96
Mp5	110	103

Combustion
- I am not even going to get into this talent.
- The math for it is not fun, and a large amount of its benefit is player based, not math based.
- For what it's worth, I personally don’t take it, I find it too clumsy.

Frost Warding
THIS IS NOT WORKING, MY SPELL POWER COEFFICIENT WAS INCORRECT AND THE WORK TO FIX IT WILL TAKE SOME TIME
SEE THIS POST FOR AN EXPLANATION OF THE PROBLEM
- This part is still in the excel file, and you can play with it at the proper coefficient level.

While this Master of Elements is generally worse than Arcane Meditation, it does have the benefit of scaling with mana usage. You are going to consume more mana when you crit a lot, as a result of increased Hot Streak procs. However, you are going to regen more mana from Master of Elements at the same time. Arcane Meditation stabilizes mana regeneration, while the mana regeneration from Master of Elements will vary proportionately to mana consumption. As a result, the decision still is a hard one to make.

Nice work. I'd love to see something similar for Arcane with relation to Arcane Stability, Student of the Mind and Incanter's Absorption, and perhaps even Frost Warding and Magic Absorption as mp5 talents in specific AoE heavy encounters.

I'm leaning toward dropping Ice Shards for Frost Warding due the the relatively small amount of AoE required for Ulduar, and 2/2 Magic Absorption for 2/3 points in Incanter's Absorption for conjunction with Frost Warding and Frost/Fire Wards along with priest shielding. I'd love to see the maths behind the benefit of these talents rather than subjective experiences gained from players with similar specs for fights like Mimiron and Hodir.

Arcane Stability is a talent that is largely situational, it is hard to quantify.

SotM in an arcane spec could be taken from my spreadsheet.
Your Int would change (Arcane Mind).
Your crit would likely change due to different gearing.
Your Relative value of Crit Rating would change, I got my number from rawr.

Incanter's absorption is very doable, although I would have to research the average +dam as a result of the talent (which would vary based on the fight and your health). I would also probably end up using Relative value of Spell Power.

Frost Warding, done.

Keep in mind, I am not particularly adept at Arcane or Frost specs.

you can type
[ table ] name | name
data | data [ / table ]

name	name
data	data

to display the above instead of using screenshots.

Tables changed, thanks for the tip Manly.

In other news, I saw you attached a spreadsheet for the Frostfire thread. I'd like to do the same for the spreadsheet I used here, do I need special abilities to do that?

Yeah the spreadsheet has only been there for about a year. I could be wrong but I was under the impression that anyone could attach any attachment to any post. Although now that you mention it, it would explain why I seldom never saw anyone do it yet had the ability all along to do so and didn't even noticed it. If I were to make a guess, its due to my TTT status that I have rights to put up attachments -- if not, probably because of guild member. I can't really change anyones access although I doubt it would be a huge deal if it is linked rather than just directly embedded.

Is this list exhaustive in your scope or would you consider looking at a talent such as flame throwing? Might be a bit difficult as it would depend strongly on the fight, but it's often a point that is considered expendable in the fire tree, perhaps for additional points in magic absorption or some of the other points you listed.

You will be refunded 30% of the spell's base cost regardless of how much the spell cost you:

0:00'38.969 Enthorn gains Clearcasting.
0:00'39.109 Enthorn Clearcasting was removed from Enthorn.
0:00'42.828 Kologarn is afflicted by Pyroblast. #152983
0:00'42.844 Enthorn Pyroblast hits Kologarn for 10296 Fire. (Critical) #152984
0:00'44.078 Enthorn gains 215 Mana from Master of Elements.

It's actually really hard to find examples of this... Clearcasting is removed when the spell finishes its cast. Therefore, in the logs, sometimes you'll see nearly back to back, within the same second, application and removal of Clearcasting. This is because a spell landed, you gained Clearcasting, and a spell finished, and consumed it.

0:04'31.844 Enthorn Fireball hits Heart of the Deconstructor for 12720 Fire. #98989
0:04'31.954 Enthorn gains Clearcasting. #99008
0:04'31.954 Enthorn Clearcasting was removed from Enthorn. #99014
0:04'33.860 Enthorn Fireball hits Heart of the Deconstructor for 10048 Fire. (1112 Resisted)

Here's an easy example of what we're looking for though:

0:04'51.625 Enthorn gains Clearcasting.
0:04'52.594 Enthorn Clearcasting was removed from Enthorn. #102138
0:04'52.844 XT-002 Deconstructor is afflicted by Living Bomb.
0:05'04.797 Enthorn Living Bomb was removed from XT-002 Deconstructor. #104351
0:05'05.266 Enthorn Living Bomb hits XT-002 Deconstructor for 3763 Fire. (Critical) #104426
0:05'06.438 Enthorn gains 215 Mana from Master of Elements.

Because Frost/Fire Ward gets little to no love (Frost Warding talent, Molten Shields talent, minor glyphs), I decided to do some basic math. For the most part, the Wards only serve the purpose of taking some of the brute force out of a targeted strike...which isn't too horribly GCD efficient in raid situations. So I figured I'd look at the Sapphiron fight and use of Frost Ward, specifically by the use of Frost Warding talent. So then I figured, what the hell, look at base mitigation, Frost Warding mitigation and mana returns, and Frost Warding + Molten Shields for a Frostfire spec...and got semi-lazy. I've only run the 25-man comparison, and only at 0 resistance. It's not too hard to extrapolate from there.

According to WoWhead and WoWWiki, Sapphiron ticks the raid for 1200-tick every 2s in 10 man and 1600/2s in 25 man, the wards have a base 1950 absorb at max rank, and I did the math for both a 33.333% coefficient and the standard 42.86% coefficient for instant casts...I have not been able to find any hard confirmation of which coefficient is accurate, but plan on testing with a fellow mage soon(ish)[tm]. I'm ignoring applications of Sapphiron's Blizzard ability for the moment. Assuming a base of 2k spellpower because it is easy and reasonable...also, there is no lower bound on the spellpower. The base on the Ward value is enough to take two hits to cause an absorb check, even if you have zero resistance. The upper bound to begin creating extra checks is nearly 4k spellpower. By that point, you are likely not worried about mana efficiency on Sapphiron [or gear from said beastie]. For simplicity, this is also an achievement run where no one has any frost resistance, as I'd need to double-check whether resists are checked before or after wards anyway.

So, one cast of the ward lasts 30s (it’s not going to last that long), and can only be cast every 30s. 1.5s/30s assuming keeping the ward ‘permanently’ up is a full 5% of casting time during the fight. I’m treating more than five absorbs as six absorbs…five or more absorbs only comes up ~1.8% of the time. This is simple spreadsheet math, as I don’t feel like doing calculus just now. The least amount of decimals involved is four [two past being percent], so I’m going to go out of 10,000 casts to average mana return. Each absorb returns 1600 mana to the mage. Although nearly half the casts will not return any mana [42.25% will double fail, 3200 overcomes the ward], the number of absorbs over 10,000 casts is actually shown to be 10,860. This means that taking the course of the fight, each ward cast returns 1737.6 mana, over 30s between ward casts. Since each ward costs 523 (522.88) mana, the return for your investment is a full 1214 or 1215 mana per 30s. Therefore the MP5 gained by having two points in Frost Warding on the Sapph-25 fight [0 resistance] is 202.45 MP5, for 1 GCD every 30s. 101/102 Mp5 per talent point isn’t bad, it’s a shame it’s so fight specific! Lazy-man's spreadsheet included.

It's worth noting casting a ward doesn't always result in a loss of dps time. On Sapphiron I'd cast a ward when running to/from an iceblock or when running to avoid a Blizzard. On Ignis I'd cast it just before Flame Vents when you can't cast anyway without getting spell locked. On Razorscale I'd cast it when the adds were down and we were waiting for a new pack.

It's not always the case that you'll lose a full 5% dps time. For the same reason I'd cast Evocation while behind an iceblock during Sapphiron.

The spell coefficient for Fire/Frost ward appears to be 0.30 from both a post by Faxmonkey a few years ago and from the source code of the DrDamage addon.

Talents such as this and MA are normally taken to simply reduce raid-wide damage (which is typically magical in nature) on the mage themselves. Any mana gains are a bonus rather than the prime motivator for taking them.

Seronid, thanks for the coefficient, I'll redo the post with regards to that.

As for the reason for taking it, you are correct for MA, although Frost Warding doesn't change incoming damage.

Frost Warding talents has a 30% chance to negate all the damage from an incoming spell , so if for example a 20k frostbolt is thrown at you, you have 30% chance to prevent all the damage and get 20k mana back so it does reduce incoming damage (without the talents only small part of the 20k would be prevented).

Or am i totaly wrong?

It has a 30% change to negate the warded damage if you have the appropriate ward up at the time.
The classic example is if you are lucky at Razorscale and not only negate the 12K fireball but get 12K mana for it as well.

These mp5 calculations do not take into account big mana return hits like the one Seonid mentioned, Frost Warding can return so much more mana on certain fights that it feels wrong to simplify it like that.

I'm not convinced that they should really, the example I gave illustrates what the talent is capable of, but it's still an edge case scenario that you can't really model in any meaningful form.

The base mana regen used in the Arcane Meditation calculations seems off.

Wearing BiS Ulduar gear from Enthorn's thread, I see a base regen of 625 in Rawr 2.2.6 with 1/3 Student of the Mind and Wisdom/Judgements/Replenish disabled.

Wait, the 30% chance to restore mana also gives a 30% chance to not count against the ward's remaining absorption amount?

I'll redo the math to reflect that, ugh.

I'm not sure what to tell you. His spirit/int might be different, I'm not using his gear, but using the base mana regen formula isn't hard. The issue does not lie in my math, but somewhere else.

There is no way to theorycraft incoming damage outliers. My new numbers will only deal with periodic constant damage.

My guess would be that formula is pre-3.1. From the 3.1 patch notes:

"Mana Regeneration: The amount of mana regeneration derived from intellect and spirit has been reduced by 40%; however, talents that allow for mana regeneration while in combat have been increased. As a result, in-combat regeneration for classes with those talents will stay the same, while out-of-combat regeneration will be lower."

Yes, on any given incoming damage of the appropriate type, you have a 70% chance of the ward absorbing damage normally and not returning mana, and a 30% chance that the hit is converted to mana restoration without reducing the remaining absorption on the ward. Mana return doesn't happen unless the talent procs, in which case it absorbs the *entire* hit, even if larger than the current remaining potency of the ward.

That's the real value of the talent. It's decent for cases where there is constant incoming damage in small ticks, like Sapphiron, but it shines in cases where the incoming damage is in bursts that are larger than the ward can normally absorb, like Razorscale, since it then results in both a large amount of mana restoration and a larger reduction in incoming damage than otherwise possible. Your math only really covers the first case, where no incoming damage event ever exceeds the size of the ward.

Confirmed. I just did the math on my own character sheet, and using the 0.005575 base_regen value gives me 502mp5, but my character sheet says 301mp5, 60% of that. The patch 3.1+ base_regen value for level 80 is 0.003345.