Spellpower increasing spell DPS

Spellpower's effect on DPS is very simplistic in nature. All it does is increase the average damage of a spell by a proportion, which is nothing more than the coefficient. Say you are a mage and your Fireball does 100 damage. Since Fireball has a base cast time of 3.5 seconds, it has a 100% spellpower coefficient. Therefore if you have 100 spellpower, your Fireball will now do 200 damage instead of 100. In this respects, spellpower is very binary.

The mistake that many players make is assuming that higher coefficients equate to higher spellpower scaling. This is not true. All spell coefficients are completely normalized so that each and every spell in the game scales from spellpower at exactly the same ratio. To view a spell's actual spellpower scaling, however, you do not look at the coefficient but rather at spellpower per second (or SPS). Determining a spell's SPS consists of a very simple function: divide the spell's coefficient by its cast time. For example, Wrath has a base cast time of 2 seconds, giving it a coefficient of 57.14%. Lightning Bolt has a base cast time of 2.5 seconds, giving it a coefficient of 71.43%. Fireball has a base cast time of 3.5 seconds, giving it a coefficient of 100%. Although their coefficients are different, all three spells scale exactly the same based from spellpower. For all of these spells, their SPS is 28.57%. (Note that if you divide each of the numbers provided, you may notice some slight inconsistencies after the fourth decimal point. This is merely an account of rounding. When using unrounded variables, the numbers are exactly the same; however, Blizzard rounds everything to the nearest fourth significant digit.)

It has been noted across several expansions by several classes that their spells simply do not scale well enough with spellpower. If all spells scale by exactly the same value (since all coefficients are normalized), how is this possible? The short answer is talents. Although talents such as Wrath of Cenarius or Empowered Fire cause some of the scaling issues, they are rarely the true culprit. As they are the easiest example of this phenomenon, let's look at balance druids who use Wrath and Starfire. As mentioned, Wrath has a coefficient of 57.14% and Starfire has a coefficient of 100%. The Wrath of Cenarius talent boosts Wrath's coefficient to 67.14% and Starfire's to 120%. Using base cast times (2 seconds and 3.5 seconds, respectively), Wrath has an SPS of 33.57% and Starfire has an SPS of 34.28%. From this, it is easy to assume that Starfire has better spellpower scaling than Wrath.

There is, however, one other thing that impacts spellpower scaling: haste. Although haste is an entirely different topic that will be covered later, I will note that haste is an entirely normalized stat. No matter what the cast time of your spell, haste affects the scale of each and every spell in the game in exactly the same way. As with everything else in the game, there are a few exceptions to the rule. In these cases, the exception plays the part of talents that reduce base cast time. A vast majority of talent trees within the game have a talent within them that reduces the base cast of a spell by a flat value. In most cases, this value is .5 seconds (again, there are exceptions). In the case of balance druids, both Wrath and Starfire have their cast times reduced by .5 seconds via the Starlight Wrath talent. This is important because shaving .5 seconds off of a 2-second spell requires more haste than taking .5 seconds off of a 3.5-second spell. Since these talents alter base cast times of spells and therefore do not impact haste scaling in anyway, the only thing they alter is spellpower scaling. In the case of balance druids, the Starlight Wrath talent in conjunction with Wrath of Cenarius gives Wrath an SPS value of 44.76 and Starfire an SPS value of 40.

Due to the combination of different scaling values of talents such as Wrath of Cenarius and the impact on spell cast times from talents such as Starlight Wrath, it is entirely possible for a spell to have lower spellpower scaling than other spells, despite spellpower being equalized from a base level.

SPS is a theoretical value of scaling. While very useful for determining how spells scale with gear and as a tool for game balancing, it might not be exactly what you need. If you merely wish to see how much damage a spell is capable of doing at a given level of spellpower, then there is a simple formula to do that. The formula is mere Base Spell Damage + (Spellpower * Coefficient) = Spell Damage. Base Spell Damage is merely the damage a spell does as listed in the tooltip. For a spell such as Fireball, the base damage would be 888 to 1,132 damage. Since base damage for spells is usually a range of some form, using the range's mean (calculated as ((Highest Damage Point - Lowest Damage Point) / 2) + Lowest Damage Point) is the most accepted practice. Spellpower is whatever spellpower level you wish to use, and Coefficient is the coefficient of the spell in question.

Spellpower increasing rotational DPS

It is a fact of life (or rather, WoW) that players do not use only a single spell within their rotations. Instead, players often use multiple spells in order to achieve the highest level of DPS. Due to this, knowing the spellpower scaling of a specific spell is rather meaningless. There are some practical implications, sure, but the really important bit is knowing how spellpower affects a rotation as a whole. Here is the part where the theorycrafting takes a really sharp turn in becoming much more complex.

Configuring the effects of spellpower on a rotation is not something that can be done sitting at a desk with a pen and some paper. While the calculations themselves are certainly possible to do using this method, there is no way of getting the required data without actually going into the game. This is because calculating rotational DPS requires one additional piece of information: the overall damage breakdown of each ability.

Within a rotation, each spell used is going to account for a specific percentage of the total damage done. For example, a mage who casts three Fireballs that deal 100 damage each and then one Fire Blast that deals 100 damage would get 75% of his damage from Fireball and 25% of his damage from Fire Blast. Figuring out the actual damage breakdown for each class or spec in the game is impossible to do without logging into the game and finding out the data yourself. It also requires the use of an addon such as Recount or Skada, which will break down all of this information for you automatically in an easy-to-read format.

I should note that there is a method for getting this data without going into the game itself; however, doing so is either going to be very time-consuming or require the use of a simulator. In order to get this data without going into the game, you have to artificially construct a damage rotation by hand. This means writing out each ability cast within the rotation, running calculations to determine the damage caused by each spell, running calculations to determine the damage caused by the rotation as a whole, and then dividing each individual spell's damage by the total damage done within the rotation. Since a lot of rotations within the game rely on factors of RNG, any hand-written rotation is generally going to have to cover a time frame of at least five minutes of casting in order to be accurate. For some classes, this is going to add up to several hundred spell casts. That is a lot of additional math, and merely logging into the game to free cast a rotation at a target dummy is much, much simpler.

Once you have the damage breakdown of your specific rotation, you can then begin calculate the rotational scaling of spellpower. The formula for determining spellpower's effect on a rotation is simply (Spell A's SPS * Spell A's Damage Percentage) + (Spell B's SPS * Spell B's Damage Percentage), repeating the process for each spell involved. Again using a balance druid, say that 56% of his rotational damage is from Starfire and 44% of his rotational damage is from Wrath. Talented, Wrath has an SPS of 44.76, and Starfire has an SPS of 40. The formula is set up like this: (44.76 * .44) + (40 * .56), which results in a rotational SPS of 42.09. This means that a balance druid's rotation gains 42.09% of his spellpower value every second.