Evocation (formulas)

From WoWWiki

Evocation is a Mage spell that increases the mage's mana by 60% over 8 sec (15% every 2 sec). It can be used in combat. Previously, Evocation functioned by increasing natural (spirit based) mana regeneration. However, in patch 2.3.0 the Evocation ability was changed to instead regenerate 15% of the mages maximum mana every 2 seconds. Since the spell has an 8 second channeling time, that means that a full Evocation will now always restore 60% of the mage's maximum mana, regardless of any other factors.

The information below is maintained for historical purposes, but as of patch 2.3.0 is no longer correct.

Since patch 2.2 a full evocation guarantees four full ticks while channeling. The regeneration tick restarts immediately upon casting, so regeneration from mana per 5 gear and buffs (such as Blessing of Wisdom) can be factored into the equation. Other buffs such as the Arcane Meditation talent or Mage Armor buff have no effect on evocation, because mana regen during evocation is already considered to be "while not casting."

The first step is to calculate the amount of mana that will need to be restored. Total mana is a combination of base mana, mana from intellect, and mana from other sources (such as +150 mana to chest enchant). For example, level 70 mages have base mana of 2241 and receive (280-intellect*15) mana from intellect. For simplicity, the mana enchant should be consideres as part of the mage's base mana, because these equations focus on how stats relate to one another.

I = Total intellect, from gear and buffs.

MP5 = Total mana per 5 from buffs and gear.

M_b = Base mana, based on level.

M_i = Mana due to intellect, (I * 15) - 280

M_t = Total mana, M_i + M_i

M_MP5 = Mana restored from MP/5 over 8 seconds from gear and buffs, MP5*8/5

S = the spirit needed for a full evocation.

To find the required spirit for a full evocation, we need to find the minimum spirit value for which the mana gained from evocation equals total mana, minus the mana restored from mana per 5.

M_b + M_i - M_MP5 = 750 + 15 * S

Solving for S gives the equation:

S = (M_b/15) - (750/15) + (M_i/15) - (M_MP5/15)

Substituting M_i = (I * 15) - 280 and M_MP5 = MP5*8/5into the equation:

S = (M_b/15) - (750/15) + I - (280/15) - (MP5*0.10667)

Note that many parts of the equation are now constants and can be collected. Base mana is only a function of level, so it can be considered part of the constant as well. The constants are collected into a single constant, C:

S = I - (MP5*0.10667) + C

C = (M_b/15) - (750/15) - (280/15) = (M_b/15) - 68.667

For level 70 mages, base mana is 2241 and the constant C is 80.733. This can be thought of as the amount of spirit needed to recover the base mana pool. After that, each additional point of spirit is recovering the mana from one point of intellect. During evocation, every 10 points of MP/5 is worth about one point of spirit. Most mages don't carry much MP/5, and in raid situations will be buffed with Blessing of Wisdom, which can be up to 49.2 MP/5 with the Paladin talent Improved Blessing of Wisdom.

Conclusions

Prior to patch 2.3.0, for an unbuffed level 70 mage with no MP/5 from gear, he will need about 81 more spirit than intellect to recover full mana from 0. For every 10 points of MP/5 subtract one point of spirit, i.e., for a mage buffed with Improved Blessing of Wisdom (49.2 MP/5), he will need about 76 more spirit than intellect.

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