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A Quick Look at Mage Spell Coefficients in Mists of Pandaria

Wednesday, March 28 2012 at 10:30pm CDT

The following numbers are guaranteed to change as beta progresses, but it’s useful to know them while testing and theorycrafting. Knowing mechanics and the numbers that feed into them can help us spot potential problems during beta; for example, in the Cataclysm beta, napkin-math theorycrafting quickly revealed that Frostfire Bolt was powerful enough to bump Frostbolt from the Frost PvE rotation. This was bad for the playstyle, and Blizzard soon made changes to both Fingers of Frost and Brain Freeze to correct the problem.

Most of these numbers were extracted from the spell database using SimulationCraft. Waterbolt was calculated using damage and spell power differences.

Single-Target Spells

This includes spells like Living Bomb that are used in single-target rotation, even though they have an AOE component. Pyroblast’s coefficient includes its DOT, and Living Bomb includes the explosion damage it deals to the primary target. Combustion includes only its instant damage. Ice Lance's Fingers of Frost value includes both the 200% bonus for hitting a frozen target and the 25% bonus specific to Fingers of Frost; it should always have these bonuses active when used in rotation. It is also listed with just the frozen target bonus, for those PvPers who are curious.

SpellCoefficient
Pyroblast4.216
Arcane Missiles (4 charges)3.240
Arcane Missiles (3 charges)2.835
Arcane Blast (4 charges)2.588
Arcane Missiles (2 charges)2.430
Arcane Blast (3 charges)2.264
Frost Bomb 2.092
Nether Tempest2.088
Living Bomb2.085
Arcane Missiles (1 charge)2.025
Arcane Barrage (4 charges)1.942
Arcane Blast (2 charges)1.941
Frostbolt1.892
Fireball1.884
Frostfire Bolt1.884
Arcane Barrage (3 charges)1.699
Ice Lance (Fingers of Frost)1.655
Arcane Missiles1.620
Arcane Blast (1 charge)1.617
Arcane Barrage (2 charges)1.457
Ice Lance (frozen target)1.324
Arcane Blast1.294
Arcane Barrage (1 charge)1.214
Arcane Barrage0.971
Fire Blast/Inferno Blast0.789
Waterbolt0.568
Combustion0.532
Ice Lance0.331

This does not tell the whole story, however. Normalizing the coefficients for cast time tells us a great deal more about the relative scaling power of the spells.

SpellCoefficient
Pyroblast (Hot Streak)2.811
Arcane Missiles (4 charges)1.620
Arcane Missiles (3 charges)1.418
Frost Bomb1.395
Nether Tempest1.392
Living Bomb1.390
Arcane Barrage (4 charges)1.295
Arcane Blast (4 charges)1.294
Frostfire Bolt (Brain Freeze)1.261
Arcane Missiles (2 charges)1.215
Pyroblast1.205
Arcane Barrage (3 charges)1.133
Arcane Blast (3 charges)1.132
Ice Lance (Fingers of Frost)1.103
Arcane Missiles (1 charge)1.013
Arcane Blast (2 charges)0.971
Arcane Barrage (2 charges)0.971
Frostbolt0.946
Frostfire Bolt (glyphed)0.942
Ice Lance (frozen target)0.883
Arcane Missiles0.810
Arcane Blast (1 charge)0.809
Arcane Barrage (1 charge)0.809
Fireball0.754
Frostfire Bolt0.754
Arcane Blast0.647
Arcane Barrage0.647
Fire Blast/Inferno Blast0.526
Combustion0.355
Waterbolt0.227
Ice Lance0.221

A few observations:

  • Frost Bomb has the highest coefficient of the three bombs, but remember also that the others scale with haste, gaining extra ticks. Frost Bomb also scales with haste, but only in terms of being able to cast it more often (which, conversely, you can't do with the others).
  • Arcane’s spells have great coefficients when they have charges stacked, but keeping them stacked is expensive. A four-stack Arcane Blast is going to cost about 8% of your total mana after regeneration while casting is taken into account.
  • Ice Lance cast with Fingers of Frost is clearly meant to be a significant factor for Frost, scaling nearly as well as a three-charge Arcane Blast.
  • Pyroblast is a brute.

Area Effect Spells

Flamestrike includes its DOT damage. The Cone of Cold glyph triples the spell’s damage.

SpellCoefficient
Blizzard2.096
Cone of Cold (glyphed)1.431
Frozen Orb0.580
Flamestrike0.576
Cone of Cold0.477
Arcane Explosion0.393
Dragon’s Breath0.215
Frost Nova0.188

And once again, normalizing for cast time:

#bbbbbb; border-style: dashed;" border="0">
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Spell#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Coefficient
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Cone of Cold (glyphed)#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">0.954
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Frozen Orb#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">0.387
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Cone of Cold#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">0.318
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Flamestrike#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">0.288
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Blizzard#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">0.262
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Arcane Explosion#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">0.262
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Dragon’s Breath#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">0.143
#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">Frost Nova#000000; font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 10px; cursor: text; border-width: 1px; border-color: #bbbbbb; border-style: dashed; margin: 8px;">0.128

Observations:

  • Glyphed Cone of Cold has the scaling power of a primary nuke; it will hit very hard. The spell has traditionally not been used for its damage, but if burst AOE is important, perhaps that will be reconsidered.
  • Frozen Orb already has a forum reputation of being a weak hitter, but the frequency of its attacks means those hits add up; outside of the bomb spells and glyphed CoC, it’s the most effective AOE GCD we have (well, Frost has), especially considering how its 35% chance to proc Fingers of Frost interacts with glyphed Ice Lance.
  • Blizzard, Arcane Explosion, and Flamestrike, our three traditional AOE spells, are the low-end fillers, but they do shine, even relative to Living Bomb and Nether Vortex, given a large number of targets. And of course Blizzard and Arcane Explosion have utility elements to them.

Discuss, comment and speculate!

Comments

Submitted by Lhivera on

...I just didn't say it very clearly. 200% bonus damage plus 100% normal damage = 300% total damage.

Submitted by alia on

I'm guessing they're playing with the standard/frozen damage ratio to avoid creating a spell that does significant damage to non-frozen targets to discourage strafe kiting while keeping the design theme they are aiming for of making it the go-to spell against frozen targets, increasing the "fun factor" of frost.  That was a poorly worded sentence. 

Submitted by Malon on

Very interesting Lhiv, thanks for posting these. I was initially disappointed to see the ABG coefficient was so much lower than AM/AB, but with normalised cast times it looks much better.

Submitted by Kuni Zyrekai on

Attempting to follow your math shows ice lance(fingers) at 2.205 and 1.470 for each list this patch, respectively. Of course, that's assuming they didn't change anything other than the frozen modifier.

Correct me if I'm wrong, as it is 3:30 AM.

Submitted by Lhivera on

I've changed the numbers for Ice Lance. The base coefficient was reduced from 0.441 to 0.331, and the higher multiplier resulted in miniscule 0.001 increases to the Frozen and Fingers of Frost values. Seems like the frozen damage was where they wanted it, but they're trying to eliminate its use against non-Frozen targets (which is totally fine).

Submitted by Aowyn on

Before anything, good analysis on the coefficients, thank you for including frozen targets as well =)

I didn't see Scorch listed, I'm curious to see its power to compare it with the other mobile options available. I'd also like to suggest normalizing the spells when they are used with Presence of Mind; seeing the normalized Hot Streak and Brain Freeze was interesting on its own and normalized Arcane Blast surpass Missiles when used with PoM being second only to Hot Streak (1.725 scaling power with four stacks).

Listing Pyroblast with its direct damage and dot separated is interesting as well, since they interact differently with Combustion, Ignite, Inferno Blast and reapplication of Pyroblast before the dot ends (Hot Streak and Presence of Mind). It may help to foresee how much Fire's AoE will be affected by bad RNG and how helpful PoM might be as a fallback for Hot Streak.

Submitted by Tiga on

My first reaction was that you are ignoring mastery here, but that's fine as long as the coefficients are meant to be used as a basis for further theorycrafting. However, you also compare arcane blast with 3 stacks to a fingers of frost ice lance and in that case I think you either shouldn't compare the spells or you should mention mastery. Someone reading this list may draw the conclusion arcane blast with three stacks hits scales more than ice lance with fingers of frost. In reality, the spell power scaling of ice lance in frost PvE will be a lot higher.

Submitted by Lhivera on

Sure, Ice Lance's damage will be higher than shown when Frostburn is taken into account. And all of Arcane's will be higher when Mana Adept is taken into account, and several of Fire's will be higher when Ignite is taken into account. But we can't really figure Mastery in without making an assumption about the Arcane Mage's average mana level.

The Spell Data feature will ultimately allow you to select a level and some stats to see average damage numbers at those stats. But in the meantime, discussing the fixed values sans stats is reasonable, and as the benefit from spell power is affected by the fixed multipliers built into some mechanics, it seems reasonable to include the effective coefficients when those mechanics are in effect.

Submitted by Fennor on

I'll never understand why every spell has its own coefficient. Why can't 1 spell power just increase our damage by x percent, no matter what spell we cast?

Submitted by Lhivera on

Apparently they like the fact that spells shift in power as we gear up. The argument, as I recall, was that it's supposed to be interesting when a spell becomes useful in rotation due to scaling. The problem is that as often as not, it goes the other way around, and a spell drops out of rotation, which is far less interesting. Straight percentage scaling seems much more sensible.