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Nov 03

Theorycrafting basics: Spell Power Coefficients

mop_logo This post was originally written during Mists of Pandaria. Its content may be outdated due to changes that come with expansion packs. Please consider this while reading. 

Questions? Feel free to contact me – contact@sometimesatree.com.

 

I’m keen to finish off my MoP guides (before 5.1!) but since progress is somewhat slowed a bit by exams right now, here’s something to tide you over. Recently I realised that I needed to calculate spell power coefficients to get my approximate stat priorities, and I realised that calculating coefficients is something that I ALWAYS need to go back and re-learn how to calculate.

Why should you, a resto druid, care about spell power coefficients? Because it will tell you how good spell power is relative to your other stats. Did you know that the more spell power you get, the worse it is? That’s because it compounds. More SP is needed to increase your healing by 1% for every point you increase it by (i.e. if you start at 100 and add 1%, you get 101, then if you add another 1% of 101, you get 102.01). But don’t worry – as I’ll demonstrate, the amount of spell power needed before you want to prioritise, say, Mastery over spell power is a number you won’t achieve. And in actuality, you don’t even need to correct the stat weights on a calculator such as Ask Mr Robot – the default values will do just fine for anyone who chooses to use it. The reason you should know it is that it allows you to make estimations for the value of spell power, especially useful for comparison with non-throughput stats (i.e. spirit!) which every healer should have some idea of. It really helps to be able to put a number on how much extra healing you’re giving up for an increase in spirit, especially when it comes to gemming, enchanting and flasking. Before I go off describing things, I’ll give a very brief, very simple description of what Spell Power coefficients actually are:

Your spells are modified by spell power. However, not all spells are affected equally. If they were, then getting more intellect might mean that Rejuvenation ticks (just the ticks, mind you) might eventually rival Healing Touch for their healing done at a certain level of gear. As a result, there could be no spell variety – every ability would have to be the same as another, only scaled down in power and in cast time, or else the game would break.Rejuv would result in the exact same healing every 2.5 seconds as Healing Touch, and therefore, there wouldn’t be any reason to choose to cast different spells. Spell power coefficients are Blizzard’s way to make spells that work differently perform in a balanced, scalable way, by changing their gain from your spell power.

For example, Rejuvenation’s coefficient is .376, which means that 37.6% of your spell power is added to each tick’s base heal, and the result is your actual heal. Healing Touch, on the other hand, currently has a coefficient of approximately 1.34, which means 134% of your spell power is added to the base heal. The difference is put in place because of the difference in cast time – as a HoT, rejuv ticks over a prolonged period of time while being an instant cast, whereas Healing Touch takes 2.5 seconds to cast and heals only once. The goal isn’t that all spells should be the same, but rather, that all spells increase evenly as your amount of spell power increases.

Deriving Spell Power Coefficients

If you want to derive the coefficients yourself, there are two basic formulas. For direct heals, it is

3.5 is the normalised cast time, and the 1.88 applies to healing spells only, althoguh to be honest I don’t understand the full concept behind its inclusion. Note that the base cast time cannot be below 1.5, and cannot be higher than 7 (so if you have an 8 second. Also note that for channeled spells, you simply substitute base cast time with base channel duration.

HoT heals, on the other hand, use a different formula

This time, 15 is the normalised Over-Time duration, 1.88 is adjustment Blizzard added for healing spells (it’s not applied for damage spells), and dividing by number of ticks at the end gives you the per tick. It is especially important to consider the base ticks at the end, because that demonstrates the power of haste! If you have a 6th tick of rejuv, the throughput gain from haste is equal to 2(Coefficient*SP). This formula for Rejuvenation would be [(12/15)*1.88] / 4, which results in .376 or 37.6%. Having a 6th tick of Rejuvenation means that you gain two additional ticks of 37.6% of your SP, which makes 6-tick Rejuvenation about 32% more powerful than 4-tick Rejuvenation.

For AoE heals, you double the normalisation factor (i.e. the denominator of the equation). So for WG, since it is an AoE HoT spell, the formula is Base Hot Duration/30, all multiplied by 1.88 and then divided by the base number of ticks. And from there, things get a bit more difficult. There are a lot of spells in the druid arsenal that have a mixed effect. Unglyphed Regrowth, for example, has a direct heal AND a HoT. Tranquility also has a HoT portion in addition to its channel. Lifebloom has the bloom at the end of the HoT. And the thing about all of these is that no one (at least not that I’ve found) has been able to precisely crack the formulae – Blizzard have done some kind of mixed formula. Some people have come close, and they give very good estimates. After all, though, these coefficients are hidden in the background. But that’s OK, because for practical purposes, you don’t need to know every coefficient to eight decimal places.

Coefficients in Practice: Determining the Value of Spell Power

You may now find yourself in a strange situation. You may be happy that you can calculate the coefficients of some of your abilities. But what does it all mean? How will it help you? Well, let’s start with a comparison to Mastery. By comparing SP to Mastery on a 1:1 ratio, we will see how much better SP is than mastery.

480 Mastery rating gives 1% Mastery, or a 1% increase to healing while Harmony is up (which is in theory a 1% increase to all healing, since it is the acceptable to assume that 100% of spells will benefit from Harmony in a given fight).

So what does an extra 480 spell power mean in terms of additional healing?

With a Flask of the Warm Sun, I sit at precisely 20,000 SP. (I actually got an upgrade that puts me over the flat 20k SP, but I’ve omitted that to keep this simple… but that’s the reason I’m sitting below a haste breakpoint).

To examine the difference based on the coefficients, I’m going to calculate the difference for both Rejuvenation and Healing Touch, two spells that were worked out with completely different formulas, to demonstrate the beauty of this system. We’ll do it based on 20,000SP and 20,480SP. First, we multiply the amount of spell power by the coefficient. Then, we calculate the difference/20,000 (the starting value of SP) to see how much of a boost it is. This table represents this:

Coefficient 20000SP 20480SP Difference Difference/Starting SP
Rejuv 0.376 7520 7700.48 180.48 0.024
HT 1.343 26860 27504.64 644.64 0.024

 As you can see, an additional 480 spell power boosts each of these spells by the exact same amount – 2.4%. This is the purpose of the spell power coefficient. So, we can conclude that 480SP is 2.4 times better than 480 mastery (remember that 480 mastery = 1% increase!). There lies your stat weight. Of course, aside from your weapon, spell power comes from intellect. Something you should also consider is that while yes, 1 Int = 1 SP, 1 Int ALSO provides 0.0008% crit chance. This should also be factored in if you are intent on determining your own stat weights for all stats.

Also, I mentioned that spell power diminishes. Here’s an example to demonstrate – using first 25,000 SP as an example, and then take 48,000 (the point where SP:Mastery = 1:1).

Coefficient 25000SP 25480SP Difference Difference/Starting SP
Rejuv 0.376 9400 9580.48 180.48 0.0192
HT 1.343 33575 34219.64 644.64 0.0192

+480SP @ 25k SP = 1.92% increase

Coefficient 48000SP 48480SP Difference Difference/Starting SP
Rejuv 0.376 18048 18228.48 180.48 0.01
HT 1.343 64464 65108.64 644.64 0.01

+480SP @ 48k SP = 1% increase

Thanks for reading if you made it the whole way. Part 2 (hopefully coming in the next few days) will cover the comparison of SP to Spirit.

Permanent link to this article: http://sometimesatree.com/theorycrafting-basics-spell-power-coefficients/

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