Mage theorycraft

Mages debate heavily about talent selection, or spec (from the term specialization). Mages can select talents from three schools of magic: Arcane, Fire, and Frost, and when you see three numbers divided by slashes, as in 18/0/43, the numbers indicate talent points spent in each of the three talent trees in that same order. Generally speaking, players choose to specialize in one school or another.

Note   Mage specs, or builds, are also discussed in the topic Mage builds.

Each spec benefits a mage differently and feeds different aptitudes. Most mages place the highest importance on one of these categories:


 * Damage per second (DPS)
 * Battle control
 * Survivability
 * PvP
 * Control of DPS and damage per mana (DPM)

Ultimately, it is a matter of play style: what casting fits the player's style better, allowing the maximal performance.

In a raid in Burning Crusade, the mage's role is generally accepted as primarily to provide DPS, along with crowd control (CC) of humanoid and beasts and removing of curses.

Often the discussion on what talent selections are best depends on the player's belief about issues that are not quantifiable, such as survivability.


 * For raid DPS at level 70, the 51/10/0 Arcane Barrage Ignite build is theoretically the highest single-target caster DPS build in-game as of patch 3.0.2 according to SimulationCraft


 * Deep Fire builds also provide competitive PvE single target DPS and very powerful AoE DPS
 * While Frost mages used to be unique in having Ice Block as a tool for dropping aggro temporarily and removing debuffs, now all mages have Ice Block and Frost mages were given another talent, Icy Veins. While they have traditionally been viewed to be worse for raid DPS than Fire mages, Icy Veins changed that image. They also have a significant burst DPS and mana recovery utility ability granted them by the Water elemental. It is without question that a deep Frost mage has the best (solo PvE) AoE ability with the slowing talents for Blizzard and the target-able Frost Nova a Water Elemental gives. Frost mages are also considered superior in PvP. The 51 point talent Deep Freeze was given the ability to cause significant damage to any enemy that could not be snared or stunned (effectively, most bosses) in the 3.3 patch, which when combined with the Fingers of Frost talent gave a powerful burst damage ability.


 * Arcane/Frost builds, specifically 40/0/21 produced great DPS in high-end (T6+) raids before 3.0.2, but Blizzard removed such ability by increasing the mana penalty for spamming Arcane Blast.

Arcane
Arcane is a DPS and utility tree. Multiple different spell rotations were used in the arcane tree historically, from Arcane Missile spam when Lightning Capacitor did not have an internal cooldown to AB, AB, AM or even AB-spam as typical high DPS rotations until Arcane Blast was nerfed in 3.0.2. After patch 3.0.2 high DPS arcane spell rotations are centred around the new 51-point talent [Arcane Barrage]. Typically in a 51/10/0 build the rotation is an iteration of Arcane Barrage and Fireball with Arcane Missiles replacing Fireball when [Missile Barrage] talent procs.

As the AB debuff is 8 seconds, it was possible to squeeze in a Scorch (or Fire Blast if close enough) after the AM, and still have the next rotations AB start with the "old" debuff up, but land after it fades. Meaning that the AB will have the short cast time, but still only the low mana cost. (AM takes 5 secs, Scorch 1.5 and AB 1.83 when 2 debuffs are stacked. Which means the AB will land 0.33 secs after the old one faded. It would be exactly when it fades with a 3rd AB). This bug was fixed in 3.0.2.

Arcane was only a viable spec in end game raiding if the user posses 2 pieces of Tier 5. Another must have for arcane was the Serpent-Coiled Braid off of Morogrim Tidewalker in SSC (for the 25% additional mana from using emeralds as well as the bonus to damage when a gem is used). The added 20% damage to Arcane Blast was the only viable option that made Arcane a possibility to come out with a large amount of DPS. Most T6 mages kept T5 shoulders and gloves all the way into the Sunwell. Arcane was the hardest spec for a mage to undergo in raids due to the constant need for attention to the Arcane Blast stacking debuff and mana. Arcane mages in high level stacked groups (with a shadow priest and a restoration shaman) could spam Arcane Blast for most of the fight attaining huge DPS. If properly executed an arcane mage could annihilate 2/48/11 or 0/40/21 mages without any problems at all. When speced properly Arcane Mages only needed 76 Spell hit meaning that there was far more room for stacking damage or haste.

As Blizzard did not intend Arcane Blast to be the main nuke of the Arcane tree and did not want Arcane mage to feel compelled to carry 2 pieces of T5 deep into Wrath of the Lich King expansion, the DPS rotation of Arcane was completely refactored with new talents in patch 3.0.2 - 2 piece T5 bonus was lowered to 5% (down from 20%) and Arcane Blast debuff damage bonus was greatly lowered while also greatly increasing the mana cost penalty. These changes made Arcane Barrage - the new 51-point Arcane talent, the new main nuke on the Arcane mages.

Assumptions
Arcane Barrage and Arcane Missiles (with Missile Barrage) are the major nukes used in all Arcane builds.

---Not updated for 3.0.2 below this line---

Fire
Deep Fire is the spec of choice for maximum DPS, without regard to DPM, burst damage, or snaring/kiting a mob.

Assumptions

 * The classic Deep Fire build is a 10/48/3 build similar to this one.
 * As of 2.3, with the introduction of Icy Veins and the much improved Mana Emerald and Evocation, 2/48/11 has become a more popular build.
 * The rotation the mage will be using is as follows: 5 Scorches, 7 Fireballs, 1 Scorch (to renew the debuff), 7 Fireballs, etc.
 * A Fireblast may be interspersed every 2 fireballs for higher DPS and lower DPM.

Calculations
PvE direct damage component formula taken from Spell DPS

To make the math feasible, we will make the following (admittedly unrealistic) assumptions: The target is a level 73 raid boss with 0 spell resistance and 0 resilience No special trinkets/gems/set bonus/weapon/item procs (these will be handled separately, at a later date) An infinitely long battle Infinite mana You never die You are never interrupted

2/48/11 spec
For this spec, the +critical damage % is .90.

Fireball Damage = Hit*(815 + 1.15*P*3.5/3.5)*(1 + .03*S + .17)*(1 + .9 * Crit Chance) ** this ignores the DoT component of the fireball which is relatively insignificant (and makes these formulas even less pretty) Fireblast Damage = Hit*(725 +     P*1.5/3.5)*(1 + .03*S + .17)*(1 + .9*(Crit Chance+.04)) Scorch Damage = Hit*(333 +     P*1.5/3.5)*(1 + .03*S + .17)*(1 + .9 * Crit Chance)

Where the .17 comes from the Playing with Fire(3%), Firepower(10%) and Molten Fury (20%*20%=4%) talents.

Since the battle is infinitely long, using the "ideal" rotation of 2 fireballs and 1 fireblast, while keeping scorch up (lets assume 1 cast every 3 rotations just to be "safe"), you get a long rotation of 6 fireballs, 3 fireblasts and 1 scorch for a total damage per long cycle of:

6*Hit Chance*(815 + 1.15*Plus Damage*3.5/3.5)*(1 + .03*5 + .17)*(1 + .9*Crit Chance) + 3*Hit Chance*(725 + Plus Damage*1.5/3.5)*(1 + .03*5 + .17)*(1 + .9*(Crit Chance+.04)) + 1*Hit Chance*(333 + Plus Damage*1.5/3.5)*(1 + .03*5 + .17)*(1 + .9*Crit Chance) = Hit Chance*1.32 * ( (4890 + 1.9*Plus Damage)*(1+.9*Crit Chance) + (2175 + Plus Damage*9/7)*(1.036+.9Crit Chance) + (333 + Plus Damage*3/7)*(1+.9*Crit Chance) )

Over a total time of:

(6*3+(3+1)*1.5)/(1+Haste%) = 24/(1+Haste%) seconds.

Example
Malula is a 2/48/11 specced fire mage with 1000 +damage, 100 hit rating, 25% crit rating (including talents) and 50 spell haste.

Hit Chance = (.83+100/12.615) = .9393 Plus Damage = 1000 Crit Chance = .25 Haste% = 50/1570 = .0428

Malula's DPS = .9393 * 1.32 * ( (4890 + 1000*1.9)*(1+.9*.25) + (2175 + 1000*9/7)*(1.036+.9*.25) + (333 + 1000*3/7)*(1+.9*.25) ) / (24/(1.0428)) = 733.46

Results
To be found.

Frost
---Updated for 3.0.2 below this line---

The Frost tree is notable for being the most recognized Mage PvP tree due to its combination of high survivability, derived from such talents as Ice Barrier and Cold Snap, and powerful control tools such as Summon Water Elemental and its many amplifiable snares. This notion is often accompanied by the idea that Frost builds are inferior in PvE by a large margin compared to other trees' high-DPS options.

In past times, this would be incorrect. A Frost DPS-oriented build did have lower sustained DPS than a Fire or Arcane DPS-oriented build, but historically this inferiority was around a measly few percent and was compensated by the tree's ability to provide high sustained burst through cooldown stacking of damage trinkets, the Water Elemental and its recently added Icy Veins ability, which was useful in burst-based fights like The Curator and shorter than average fights like in Zul'Aman chest runs.

Frost Mages are also at an advantage in longer than average fights or when there is no mana support due to their high DPM, which also allows them to use Molten Armor where other Mages might need Mage Armor.

In Patch 3.0.2, however, Frost DPS builds lag behind by around 10% overall damage relative to Fire and Frostfire (the most accepted raiding builds), a margin so large burst DPS, mana efficiency and survivability simply do not suffice to make Frost accepted in raids. Balance steps taken in this patch boosted Frost's AoE capability beyond that of all other Mage specs (by giving Blizzard the ability to critically strike), and gave it raid utility in the form of the revamped Winter's Chill utility. Fire however received the same utility in the form of Improved Scorch, and it is doubtful whether Frost Mages will be seen with frequency in raids in the upcoming expansion.

Raiding as Frost
For those who wish to raid Frost, the current optimized WotLK raid DPS build is as follows: (19/0/52).

To work optimally with this build the following steps are to be taken:
 * Frostbolt is the main nuke and will be used at all times when not casting Ice Lance or Fireball. It composes the vast majority of your DPS.
 * Focus Magic must be cast before the fight begins on any caster (as it only works with spells) preferably with high critical strike rate;
 * Water Elemental must be used early at all cooldowns, stacked with Damage trinkets;
 * Icy Veins must be used early at all cooldowns, stacked with Damage trinkets;
 * Cold Snap will be used early to allow it time to become available again near the end of the fight
 * The above is to be ignored if it interferes with raid cooldown stacking at ~35% boss health (high-DPS timezone due to Death's Embrace, Molten Fury (mage talent), Execute, etc.), as Heroism/Bloodlust and Drums are often up at this time. Icy Veins, Water Elemental and Cold Snap MUST be available then to maximize DPS. Make sure you cast Water Elemental before Heroism/Bloodlust is cast so your pet will benefit from the buff as well.
 * Ice Lance is to be cast on the second charge of Fingers of Frost, since it will have triple damage (quadruple with Glyph of Ice Lance) plus a high chance to critically hit thanks to Shatter and its crits are further boosted by Ice Shards. The first charge will be consumed by a Frostbolt, since you will be chaincasting Frostbolts whenever possible and interrupting the Frostbolt to cast an Ice Lance (or any other spell for that matter) is always a DPS loss.
 * Deep Freeze should be cast instead of Ice Lance if it's Cooldown it's ready.
 * Fireball must be cast only and as soon as you get the Brain Freeze proc, if you keep casting Frostbolts you risk wasting more Brain Freeze procs, as it will only get refreshed, it is not stackable.
 * You will not attempt to squeeze an Ice Lance into a ghost "third charge" of Fingers of Frost. The spell's low coefficient makes it a DPS loss to have it cast at modest levels of spell power, and 60% of a Frostbolt is a better DPS/DPM investment of the 1.5 seconds Ice Lance's GCD utilizes.
 * Ice Barrier has to be used smartly. Losing 1.5 seconds of GCD to cast a barrier that will not be absorbing it's a waste of DPS, however, casting it a moment right before the boss uses his aoe nukes will relief the pressure on the healers and maybe even save your life. Try to use it every time you have to move around during a fight.
 * Mana Gems should be used as soon as the cd is ready. With Precision (mage talent) and Frost Channeling you will have little use for Evocation and can spend those 8 seconds DPSing instead.
 * The talent point into Improved Blizzard is to allow Fingers of Frost and Brain Freeze to proc.

General
When evaluating Trinkets, it's often beneficial to compare the average gains of the Trinket as a whole. For On-Use Trinkets, such as Icon of the Silver Crescent, it is, generally, sufficient to determine the effective +damage of the Trinket as follows: D = n + (b * (d / c)) Where... D = Expected bonus n = Constant bonus b = Temporary Buff bonus d = Duration c = Cooldown So, for example, the following data exists for Icon of the Silver Crescent: n = 43 b = 155 d = 20 c = 120 Allowing the following value to be calculated: D = n + (b * (d / c)) D = 43 + (155 * (20 / 120)) D = 43 + (155 * 1 / 6) D = 43 + (155 / 6) D = 43 + 25.833 D = 68.8333 An important thing to note, however, is that this is merely an averaged expected +damage, and a much more accurate model of effective +damage can only be obtained by taking into account other variables such as Cooldown Stacking.

The same formula also applies for On-Use Trinkets which grant other attributes as well, such as Hex Shrunken Head

For On-Proc Trinkets, the working is different, and the effective gain from the On-Proc effect can be obtained as follows: D = n + (b * (d / (t / z + c))) Where... D = Expected bonus n = Constant bonus b = Temporary Buff bonus d = Duration t = Spell Cast Time z = Proc Chance c = Internal Cooldown For example, we have the following information on Quagmirran's Eye: n = 0 (As it has +0 Haste, yet +37 Damage) b = 320 d = 6 z = 10% c = 45 For the sake of example, we will consider the case of a talented 3.0s cast Fireball, with t = 3.0 Using this information we can obtain: D = n + (b * (d / (t / z + c))) D = 0 + (320 * (6 / ((3.0 / 0.1) + 45)))) D = (320 * (6 / (30 + 45))) D = (320 * (6 / 75)) Similar formulas can also be used in evaluating trinkets such as Eye of Magtheridon, however the constant z, that is, the proc chance, is simply substituted for the relevant variable, in the case of Eye of Magtheridon, this is your chance to not hit.

Shiffar's Nexus Horn
Shiffar's Nexus-Horn

Forum Link to Discussion

Model written out by Murphrid.

Assumptions

 * Common assumption is that Shiffar's procs 20% of the time on a crit.
 * Tooltip has been observed to be incorrect, it lasts 15 seconds instead of 10. The duration has been fixed to last the correct 10 seconds.
 * Assume a hidden cooldown of 45 seconds. (From the WoWhead page)

Results

 * For a casting time of t and a crit chance of c, it will, on average, take t/(.2*c) seconds to proc the trinket (for 1.5 second Scorches and a crit rate of 30%, that's 25 seconds).
 * From the hidden CD, 70 second cycles.
 * You get 225 spell damage 10/70 of the time, or 21% of the time, equivalent to 225*10/70 = 32.1 +damage all the time.
 * This analysis neglects the 30 crit rating.
 * The full formula for calculating the average +damage given by Shiffar's Nexus Horn is -

E = 225 * 10 / (45 + (t / (0.2 * c))) Where... E = effective +damage t = cast Time c = critical strike chance

For a simpler understanding of this; The higher your crit is, the more this becomes usable. But, if you have less crit, it's definitely not worth your time. It is also important to note the usefulness of this trinket decreases with longer cast times - for example, if you consider this spell used with Fireball(3s) as opposed to Scorch(1.5s) it adds 23.7 +damage at 30% crit, as opposed to 32.1 +damage; a quite substantial loss of 12.7 +damage total. A good amount of crit to aim for to make this trinket viable in raids is 30% unbuffed.

N.B. - with the duration now being fixed to 10s instead of 15s, the value of this trinket is somewhat diminished.

Fall of the Lich King
As of Patch 3.3, this page seems to be rather lagging and very messy. The four main Mage specs as of 3.3 are as follows, ranked in order of overall DPS. (Writer's Note: I'm writing these as I go, so they will come in piecemeal as I have time).

Arcane
There are several different variations of this spec, depending on gear and raid composition. The base spec that I will discuss is a cookie cutter spec for beginners. This is especially good for a Mage who has just hit 80, and as such is not hit capped. The talent tree can be found *here. This talent tree maximizes your chances to hit with Precision and Arcane Focus. The 3 points in Arcane Stability bank mainly on a Paladin in your raid having up Concentration Aura. If you know for a fact that there will not be Conc Aura, you should move 2 points from Arcane Concentration to Arcane Stability. If you have a well geared tank who knows what they are doing, you can move one point from Arcane Subtlety to Arcane Concentration. If you have a Shadow Priest or a Balance Druid specced into Imp. Faery Fire, that will remove 3% of the hit rating you need, and if you also have a Draenae in your group, that will give you another 1%. The chance to hit on a Level 80 Raid Boss for a level 80 caster is 83%. So, with this spec, our chance to MISS is 11%. With a Shadow Priest or Balance Druid, it becomes 9%, and with a Draenae in our group, it becomes a 8% chance to miss. 26.2 hit rating gives us 1% chance to hit, so with optimal raid composition and the base spec listed here, we need at least 210 hit rating. If you are far enough over that, I HIGHLY suggest moving points from Arcane Focus to Incanter's Absorbtion, as this can greatly increase your DPS. If you have points in Incanter's Absorbtion, you will also want to move 2 points in the Frost tree from Ice Shards to Frost Warding. Make sure that you are using your Wards during raids, and make sure to use the right one. Don't use a Flame Ward on Sindragosa, who deals mainly Frost damage.

Rotation
The rotation for this, and indeed for all Arcane Specs, is as follows. Arcane BlastX4, Arcane Missiles. Note that if you have low mana, or low mp5, you should reduce it to Arcane BlastX3, Arcane Missiles. The reason that an Arcane Mage uses this rotation is because of the Talent Missile Barrage. This gives a 40% chance for your Arcane Blast to proc a buff that will cut the casting time (but not the overall damage) in half. In order to calculate the odds of reaching a full stack of Arcane Blast (the damage buff that it gives can't go over 4 stacks) without a Missile Barrage proc, we take 60%, the chance for the proc to NOT occur, and X, the number of times we cast Arcane Blast. 0.6^4 = 12.96% 0.6^3 = 21.6% 0.6^2 = 36% 0.6^1 = 60%

So, in all likelyhood, every seventh or eighth rotation you will get to a full stack of Arcane Blast without a Missile Barrage proc. If you are using this spec, you most likely don't have much mana, so I would highly suggest that if this occurs, you simply terminate the stacks with an Arcane Barrage. Note: DO NOT allow the stack to simply fall off. This will lose you about 50% of your DPS.

Glyphs
The best Glyphs to use for this spec are Molten Armor, Arcane Missiles, and Arcane Blast in the Major slots, and Frost/Fire ward in 2 of your minor slots. For the 3rd minor, you should probably use Glyph of Slowfall, for any raid in which you get shot up into the air.

(Writer's Note: I'm going to stop here for now. Feel free to add on)