Damage tax

The damage tax refers to an old side-effect of the Improved Fireball and Improved Frostbolt talents for the mage class. The damage tax lowered the amount of spell damage that effected Fireball and Frostbolt by 2% per point in the respective talents. The damage tax was introduced in patch 2.0.6 and removed in patch 2.3.

Each of these talents reduces the casting time of the associated spell by 0.1 second per point. This effectively increased the damage per second of those spells, making them must-have talents, as Fireball and Frostbolt are primary damage spells (depending on talent build). Blizzard developers may have felt that mages were doing too much damage compared to other classes, thus the damage tax was introduced to lower overall damage output. With the damage tax, the Improved Fireball and Improved Frostbolt talents still increased damage per second, but not by nearly as much as without it. As another side effect, the damage tax lowered damage per mana or Fireball and Frostbolt, making the talent a tradeoff between damage output and efficiency. For example, each talented Fireball would deal less damage than an untalented Fireball, but more could be cast over a period of time, yet the mana cost remained unchanged.

Formulas
Frostbolt's spell damage coefficient is normally 81.4% of total Frost spell damage, while Fireball's spell damage coefficient is normally 100% of total Fire spell damage. The spell damage penalty from the damage tax is multiplicative, and is applied after the additive spell damage bonus of "Empowered" talents, Empowered Fireball and Empowered Frostbolt.

With 5 points in Improved Frostbolt, the coefficient is (81.4% * 90%), or 73.3%. The following formula will compute the spell damage coefficient for Frostbolt with points in both talents, where X is the number of points in Improved Frostbolt and Y is the number of points in Empowered Frostbolt:

(1 - .02X)[(.95(3/3.5)) + 0.2Y]

The following formula will compute the spell damage coefficient for Fireball with points in both talents, where X is the number of points in Improved Fireball and Y is the number of points in Empowered Fireball:

((3.5/3.5) + .03Y)(1 - .02X)

Note that the cast time reduction does not affect the base damage coefficients, Fireball it is still based on a cast time of 3.5 seconds and Frostbolt is still based on a cast time of 3.0 seconds.

Using Improved Fireball as an example, and ignoring Empowered Fireball for now, taking into account only spell damage, the following equation computes the DPS of Fireball. In this equation, d is the amount of Fire spell damage, B is the base Fireball damage, and X is the number of points in Improved Fireball.

((3.5/3.5)(1.0-0.02X)*d + B)/(3.5 - 0.1*X)

Solving this equation for zero points and five points in the talent gives:

0.2857*d + (B/3.5) @ 0/5 Imp. Fireball 0.3000*d + (B/3.0) @ 5/5 Imp. Fireball

These two examples illustrate that before talents, each point of spell damage adds 0.2857 DPS to Fireball, while after talents each point adds 0.3000 DPS, meaning that Improved Fireball with the damage tax is an overall DPS improvement regardless of the spell damage penalty. The same calculation for Improved Frostbolt shows the same result:

(.95(3.0/3.5)(1.0-0.02X)*d + B)/(3.0 - 0.1*X) 0.2714*d + (B/3.0) @ 0/5 Imp. Frostbolt 0.2931*d + (B/2.5) @ 5/5 Imp. Frostbolt

With the damage tax removed, the equation for Fireball DPS becomes:

((3.5/3.5)*d + B)/(3.5 - 0.1*X) 0.2857*d + (B/3.5) @ 0/5 Imp. Fireball 0.3333*d + (B/3.0) @ 5/5 Imp. Fireball

A mage gains 0.3333 DPS per point of fire spell damage, compared to only 0.3000 DPS with the damage tax in place. For Frostbolt without the damage tax:

(.95(3.0/3.5)*d + B)/(3.0 - 0.1*X) 0.2714*d + (B/3.0) @ 0/5 Imp. Frostbolt 0.3257*d + (B/2.5) @ 5/5 Imp. Frostbolt

A mage gains 0.3257 DPS per point of frost spell damage, compared to only 0.2931 DPS with the damage tax in place.

In conclusion, the damage tax lowered DPS but never lowered it compared to not taking the "Improved" talents at all.