Tuesday, March 2, 2010

Spell Power Coefficients & The Irrelevance of Base Spells

For casters damage in the end game is largely governed by the invisible hand of spell power coefficients, and these coefficients have a number of major problems. In this first post on what is wrong with spell power coefficients, I'll talk about how spell power coefficients overwhelm and trivialize base spells.

Here is a sketch of the argument
  1. Most of your damage comes from spell power rather than base spells
  2. The relative strength of base spells rarely affects the relative spell power coefficients
  3. Talents and multipliers that affect spell power are what truly determine spell damage
  4. As a result it is the form rather than the content of base spells that determine their effectiveness
Spell Power coefficients come from an old standard default value of casting time divided by three and a half, or duration divided by fifteen for DoTs. AoE spells are penalized as are spells that have other effects (such as a snare). Basically, you should be able to add 2/7 of your spell power to the damage you do every second if you stand and chain cast nukes based on this formula.

At higher level the amount of a spell's damage derived from spell power overtakes the base spell damage dramatically. To use the example of Arcane Blast, the base damage of this spell is 1185 to 1377 for an average of 1281. The coefficient, with the increase from the Arcane Empowerment talent is 80.43%. For a well geared mage with 4000 spell power, this means the spell power component of this spell is 3217. Both the base damage and the spell power component are multiplied by various effects, but the ratio between them doesn't change. The pre-multipler damage of the spell is 4498, 28.4% of that is the base spell, and the remainder comes from spell power. Now 28.4% of your damage is certainly relevant, and you don't want to lose that, but certainly the substantial majority of your damage comes from spell power, not from the base spell.

While there are a few counterexamples, most spells follow the default coefficient as described above. So lets compare two other mage spells to consider their function and how spell power tends to wash out the design of the base spell. Levelling up as a mage, most players would be familiar with Fire Blast as a high damage quick burst they can use to finish an enemy off, or to pump in extra damage at higher mana cost. Comparing the base spell to a fire mage's main nuke, Fireball, Fire Blast is exactly that: quick high damage at a higher cost. The base damage of Fire Blast is 1010, it costs 21% base mana and it is an instant. The base damage of Fireball is also 1010, it costs 19% base mana and takes 3.5 seconds to cast. Since instants use up 1.5 seconds of your time, Fire Blast deals 673 dps while Fireball deals 288. The dps of Fire Blast on the base spell is two and and a third times that of Fireball. And when you are levelling the way you attack your enemies reflects this. You cast Fireballs on them and use Fire Blast when you can to kill them faster. If Fire Blast didn't have a cooldown you'd just spam it, and you'd be pretty great until you got up a few levels and spell power (and talents) started shifting the balance. Why wouldn't you pay 10% more mana per damage to do 133% more damage per time?

The talents that boost Fireball are more numerous and powerful than those that boost Fire Blast, so it is no wonder Fire Blast falls behind. But let's look at the untalented spells to get an idea of what spell power is doing to them. With 4000 spell power, both spells gain 1143 dps. That means Fire Blast deals 1815 dps while Fireball deals 1431. Now Fire Blast only deals 27% more damage than Fireball per time instead of 133% more. Would you pay 10% more mana for that? Of course you would, and you would continue casting Fire Blast, all other things being equal (which in reality they are obviously not) through to very high levels of spell power. But of course the total damage of the Fire Blast is 2724 while Fireball does 5010, so the mana per damage on Fire Blast is now 96% higher. Mana is hardly a thing, so mages would still do that, but if mana were a thing they'd really have to think twice. Spell power radically alters the relationship between these spells. The spell power coefficient increases the dps of each spell equally rather than increasing the dps of the spell with higher dps by more.

The problem is also very evident for shadow priests and in the relationship between Mind Blast and Mind Flay. If we had no spell power, Mind Flay would deal 196 damage per second while Mind Blast would deal 680 dps. Because of the 8 second cooldown, we can get 8 Mind Flay ticks for each Mind Blast. That means 272.4 dps overall from those two spells. By taking Improved Mind Blast we can drop the cooldown to 5.5 seconds. Idealizing this so that we can actually put 5.5 ticks between the Mind Blasts (which would be possible with the right level of haste, I'm just abstracting away the granularity) the dps would become 299.7. That's a 10% dps increase for five talent points. I'd take those talent points. The reality is that spell power inflates the damage of both spells to very high levels and makes the percentage difference between them very small. My actual average non-crit Mind Flay tick was 2584 in a recent raid while my average non-crit Mind Blast was 4847. Instead of Mind Blast dealing over three and a half times the damage of Mind Flay per second cast, it deals only about 25% more per second cast. Where does that leave the Improved Mind Blast talent? My own spreadsheets and Simulation Craft agree that the talent ends up giving you around 6 to 8 dps per point, probably closer to a .1% dps increase per point than a .2% increase per point, and that's in an ideal situation. If you are moving around, dotting multiple creatures, or doing other things with the time that Mind Blast is cooling down, it could be even less or nothing at all. Most shadow priests still take this talent, maybe in part because people will take talents that increase their dps in favour of talents that give some other kind of utility no matter how small the dps increase. But I think the main reason why people take this talent is because it intuitively seems like a useful thing. Looking at the two spells, Mind Blast does big damage and Mind Flay does small damage. You want to spend more of your time doing big damage, so the talent is appealing. In reality because the majority of the damage you do comes from spell power, both do medium damage. All spells do medium damage.

But of course some spells are much better to cast than others. Which of these spells would you rather have: A spell called Fireball that deals 1010 damage or a spell called Fireball that deals 0 damage but also deals 50% more damage. The second spell looks pretty stupid because 50% of 0 is still 0. In reality, with 4k spell power, every mage would prefer the second spell, and it might be enough to make mages all raid as fire instead of arcane.

So what do we look for to determine which spells are best? a) talents that increase the output of that particular spell and not other spells - so that the spell becomes relatively more powerful; and b) elements of the base spell that increase the base spells damage - spell that deal increased percentage damage under certain circumstances, effectively giving them a much higher spell power coefficient. It is the form of the spell, not the content that determines its worth.

What could be done to remedy this situation? More variance in spell power coefficients to bring them closer into line with the intended power of the spell is the answer. Of course that is going to take a bit of thinking. I don't think Fire Blast doing triple the dps of Fireball is a good model to go with, or similarly, Mind Blast doing triple the dps of Mind Flay. This would undoubtedly create burst damage problems in PvP. It would be nice, though, if reading spells gave us an idea of what they did and in what circumstances they were useful. Talents can obviously alter this, but some of the base spell should manage to shine through the talents and not be washed out under spell power coefficients that account for the vast majority of our damage.

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