## Spell coefficients

[I get corrections to errors, and I fix.]

Gads, I hate the coefficients. They make the easy figuring… hard. I understand the purpose, though — Blizzard wants bonuses to apply equitably to spells of varying time and effect, and wants high level casters to predominately use high level spells. Your bonuses will be modified to encourage this effect. Still, since we all have small variances in how we play I think it worthwhile to look at them in more depth.

The first “balance” is based on time of casting. The purpose is so the bonus doesn’t have a HUGE effect on throughput – on heals per second. This coefficient is easy to guesstimate, too — it’s based on time of cast /3.5. Where the [add - GLOBAL] cooldown is longer than the spell (usually only instants), the [1.5 second Global] cooldown is used. So the coefficient for both FH and SW:P SW:D is 3.5/1.5 or 42.86%. Now, if you have a channeled spell the final effect uses this same coefficient. That is, if you’re using Mind Flay (2.5 seconds) the coefficient is 3/3.5=85.71%, spread across the ‘ticks’ of the channel. MF, for example, has three ‘ticks’ at one-second intervals, and each tick would get 1/3 of the 85.71% bonus. This is particularly relevant when your spell has differing base damage based on how long the channel goes – starshards being an example. The bonus is spread equally regardless of how the actual effect may be distributed.There are other types of spells, of course, each providing its own coefficient. The one that is somewhat frustrating is the coefficient calculation for Over Time spells. The APPROXIMATE value is to divide the time of application by 15 seconds. However there are several known situations where this is incorrect — SW:P being very applicable to priests. Instead of 120%, SW:P receives a coefficient of 110% — and if we’ve taken two points in Improved SW:P, our bonus coefficient is only 140%.

[added point. The co-efficient does not change when you change cast-time with talents or gear. Greater Heal is 3.0/3.5=85.71% even if you used talents to make it 2.5 seconds of cast time.]

A slight digression comes at this point, when we consider spells that have a direct and over time effect — Holy Fire being an example. For this we determine what proportion of bonus will be applied to each aspect of the spell. We do this by determining what proportion goes to the over-time aspect (by: (Duration/15) / ((duration/15) + (casttime/3.5))=OT proportion), and giving the direct portion the remainder. Then we multiply that proportion times the coefficient for each aspect. Using Holy Fire as our example:

Proportion for OT = (10/15)/((10/15)+(3.5/3.5))=~40%
Proportion for direct=100-40=60%.
coefficient for direct = 3.5/3.5 * 60% = 60%
coefficient for DoT = 10/15 *40% = 26.67%

One more type of spell to go, but not “the end”. We’ve got to plan for AoE – Area of Effect spells. As of Patch 2.1,the coefficient is the cast time / 3.5, divided by 2 — with loopholes. That is, we take our ‘direct spell’ calculation (the one up top) and divide by two to get the coefficient. The biggest loophole is if the number of targets is a known quantity — that is, “heals target and 2 more” (for example). If it’s known, then the amount by which the spell is divided is – yep – the number of targets.

To summarize where we have so far: for most spells, start with cast time/3.5, and divide again for the ability to hit multiple targets. The primary exception is Over Time spells, where we approximate the effect by dividing duration by 15. The resulting number is multiplied times our damage/healing bonus to see what we ACTUALLY get.

But wait, there’s more — if, that is, you downrank. The calculation is (relatively) simple: take the next higher spell’s level learned, add five, and divide the whole by the caster’s level. So if you’re a level 70 casting Flash Heal 4, you use Flash Heal 5 (learned at level 32), add 5 for 37, and divide by 70. (32+5)/70=0.529. This is MULTIPLIED by the cast time coefficient. Since this is flash heal, a 1.5 second spell with .4286 as the coefficient, the final coefficient for level 70 casting FH4 is 0.529*0.4286 = .2267, or 22.67%.

If the spell level to which you’re downranking is less than level 20 (ie you learn it at level 20 or less), it’s got a funky EXTRA coefficient – meaning the coefficient you’re about to use is used WITH (not instead of) the downrank coefficient. It’s 1 – ((20 – spell level) * 0.0375). Again, since this is multiplied by the downrank AND cast-time coefficients, the end result is that for high level players, casting spells of less than level 20 is highly inefficient — most of the time.

Is this right? shrug. It is an attempt by blizzard to discourage casters from using atypical spell patterns because of bonus gear benefits and peculiarities of math. It’s their game. If you don’t want to remember the math, remember the intent:

Blizzard wants the spell bonuses from gear, talents and other benefits to apply equitably to spells of varying time and effect, and wants high level casters to predominately use high level spells. Your bonuses will be modified to encourage this effect.

~ by Kirk on August 27, 2007.