Spell Coefficients

Nite_Moogle

[top]Definition

The spell coefficient is the number that is used as a multiplier on a player's +damage or +healing when determining the effects of a spell. Lower-ranked spells that are more than 10 levels out of date will receive a lower-than-expected coefficient -- using the top two or three ranks of a spell will still give the player full or acceptable levels of their spell coefficient. Coefficients listed on this page assume the highest rank of the spell is being used.

[top]Calculation

Spell haste never affects the coefficient of a spell. The base cast time of the spell always determines its coefficient, not its post-haste cast time.
Normal non-instant spells with direct damage or healing receive $\frac {cast time}{3.5}$ as their coefficient.
Damage over time (DoT) spells get $\frac {duration}{15}$ as their coefficient.
Instant cast spells are considered to have 1.5 cast time for purposes of determining their coefficient.
Leech spells (drain life, siphon life, death coil, etc) have their coefficient halved.
AoE spells have their coefficient divided by 2.
Spells with an additional non-damaging component such as a snare (mind flay, frostbolt, etc) usually lose some percentage off the coefficient. This varies from spell to spell.
Spells which combine direct damage and a DoT component (immolate, flame shock, moonfire, etc) have their coefficient split between the direct damage and damage over time portions of the spell, proportionate to the base damage of each component. For example, Immolate (which has a 2.0 cast time, some amount of direct damage and a 15 second DoT time) has an average base direct damage component is x, and the dot portion's base damage is y, then the coefficient on the direct damage component is $\frac {2}{3.5}*\frac{x}{x+y}$ , and the coefficient on the DoT component is $\frac{15}{15}*\frac{y}{x+y}$ .

Talents, items or abilities that increase your coefficient will do so at the latest possible point in the calculation (Improved Fireball, etc.). Talents that improve the effect of a spell by a percentage multiplier (such as Purification, Improved Renew) will do so after adding your full spell coefficient.

Talents that decrease the cast time of a spell (Improved Fireball, etc) do not affect the coefficient of a spell except where noted.

[top]Druid

Restoration
Healing Touch: 1.00
Rejuvenation: 0.2 per tick
Regrowth (DH): 0.2898
Regrowth (HoT): 0.706 (0.10 per tick)
Lifebloom (HoT): 0.519 (.074 per tick)
Lifebloom (Bloom): 0.429

Balance
Moonfire (DD): 0.214
Moonfire (DoT): 0.100 per tick
Wrath: 0.571
Starfire: 1.00
Insect Swarm: 0.76 (0.1667per tick)
Hurricane: 0.128 per tick

[top]Mage

Arcane
Arcane Blast: 0.714
Arcane Missiles: 1.429 (0.2857 per bolt)
Arcane Explosion: 0.214

Fire
Fireball: 1.00
Fireblast: 0.428
Scorch: 0.428
Pyroblast: 1.15
Pyroblast DoT duration: 0.2 (0.05 per tick)
Flamestrike DD: 0.236 (= 0.55*1/2*3/3.5)
Flamestrike DoT: 0.12, 0.03 per tick (= 0.45*1/2*8/15)
Blastwave:
Dragon's Breath:

Frost
Frostbolt: 0.814
Waterbolt: 0.714 of pet's +damage which is 0.286 of the mage's +damage
Blizzard: 1.143 (0.142 per tick)
Cone of Cold:
Frost Nova:

[top]Paladin

Holy
Flash of Light: 0.428
Holy Light: 0.714
Consecration: 0.95 (0.11875 per tick)
Hammer of Wrath: 0.428
Holy Wrath: 0.19 per target
Exorcism: 0.428
Seal of Righteousness (1H): .1 per 1.0 weapon speed
Seal of Righteousness (2H): .11 per 1.0 weapon speed
Judgment of Righteousness: 0.714

Protection
Holy Shield: 0.05 per block
Avenger's Shield: 0.19 per target
Holy Shock: 0.428

Retribution
Crusader Strike: 0.0
Seal of Vengeance: 0.17 per tick
Judgement of Vengeance: 0.428
Seal of Blood: 0.0
Judgment of Blood: 0.428
Seal of Command: 0.29
Judgment of Command: 0.428

[top]Priest

Discipline
Power Word: Shield: 0.30
Mana Burn: 0.0
Starshards: 0.857
Feedback: 0.0

Holy
Flash Heal: 0.428
Greater Heal: 0.857
Renew: 0.2 per tick
Binding Heal: 0.428 per target
Circle of Healing: 0.428 per target
Holy Nova: 0.16 per target
Prayer of Healing: 0.428 per target
Prayer of Mending: 0.428 per target
Lightwell: 1.0 per charge
Smite: 0.714
Holy Fire (DD): 0.75
Holy Fire (DoT): 0.25
Chastise: 0.143
Desperate Prayer: 0.428

Shadow
Shadow Word: Pain: 0.183 per tick
Mind Blast: 0.428
Mind Flay: 0.572
Shadow Word: Death: 0.428
Shadowfiend: 0.65
Vampiric Touch: 0.2 per tick
Devouring Plague: 0.2 per tick
Shadowguard: 0.33 per charge
Touch of Weakness: 0.10

[top]Shaman

Elemental
Lightning Bolt: 0.794
Chain Lightning: 0.641
Earth Shock: 0.386
Frost Shock: 0.386
Flame Shock (DD): 0.150
Flame Shock (DoT): 0.52 (0.13025 per tick)
Lightning Shield:
Flametongue Totem: 0.0
Searing Totem:
Magma Totem:
Flametongue Enchant: 0.1 per proc
Frostbrand Enchant: 0.1 per proc

Enhancement
Stormstrike: 0.0

Restoration
Healing Wave: 0.857
Lesser Healing Wave: 0.428
Chain Heal: 0.714 (inital hit, subsequent hits derive from this value)
Healing Stream Totem: 0.044 per tick
Earth Shield: 0.286 per charge

[top]Warlock

Affliction
Curse of Agony: 1.200 (duration)
Curse of Doom: 2.000
Corruption: 0.156 per tick
Siphon Life: 0.10 per tick
Unstable Affliction: 0.200 per tick
Unstable Affliction (dispel bomb):
Death Coil: 0.214
Drain Life: 0.1428 per tick
Drain Mana: 0.000 per tick
Drain Soul: 0.4286 per tick
Seed of Corruption (DoT): 1.50
Seed of Corruption (Explosion): 1.16
Life Tap: 0.800
Dark Pact: 0.960

Demonology
Health Funnel: 2.857

Destruction
Immolate (DD): 0.2
Immolate (DoT): 0.65 (0.13 per tick)
Shadow Bolt: 0.857
Incinerate: 0.714
Searing Pain: 0.429
Shadow Burn: 0.429
Conflagrate: 0.429
Soul Fire: 1.15
Shadowfury: 0.143
Rain of Fire: 0.95 (0.237 per tick)
Hellfire: 2.15 (0.143 per tick)

Roywyn · 04/03/08, 6:25 AM

# AoE spells have their coefficient divided by 3.

This was changed to *divided by 2* in 2.2 or 2.3 or something.

Arcane
Arcane Explosion: 0.214

Fire
Fireball: 1.00, 1.15 with 5/5 empowered

Pyroblast DoT duration: 0.2 (0.05 per tick)

Flamestrike DD: 0.236 (= 0.55*1/2*3/3.5)
Flamestrike DoT: 0.12, 0.03 per tick (= 0.45*1/2*8/15)
(Flamestrike gets 55% on DD, 45% on DoT)

// Blastwave, Dragon's Breath: 0.204, not exactly sure. It's 1.5/3.5*1/2*(0.95 or 0.9 for having a slow component)

Frost
Frostbolt: 0.814, 0.914 with 5/5 empowered
Waterbolt: 0.714 of pet's +damage which is 0.286 of the mage's +damage
// Cone of Cold: 0.193, not exactly sure. It's 1.5/3.5*1/2*(0.95 or 0.9 for having a slow component)
Blizzard: 1.143 (0.142 per tick)
// Frost Nova: 0.043, not exactly sure either. It's 1.5/3.5*1/2*0.2(special for nova*(maybe 0.95 or 0.95)

AoE caps

That's not strictly about spell damage coeffiecients, but still nice to know when your spell damage does nothing at all due to AoE damage caps.

Arcane Explosion (rank 8): 10100

Flamestrike DD (rank 7): 7830
Blastwave (rank 7): 9440
Dragon's Breath (rnk 4): 10100

Cone of Cold (rank 6): 6500
Blizzard (rank 7): 28950 (3620 per tick)

Warlocks
Seed of Corruption (rank 1): 13580

Consecrate, Flamestrike DoT have no caps.
Hellfire, Rain of Fire, Hurricane have caps, but I didn't find any data on it.
Not sure about other spells.

Source:
http://elitistjerks.com/554195-post6.html and following, Arcane Explosion had it's cap raised by 50% in 2.4.
WoW Forums -> Sunday morning PTR AoE Cap testing

[Edit]: I did the tests on the 4 slowing/rooting AoE spells a while ago, I just don't remember the exact numbers on the "slowing penalty" multipliers. I think they were 0.9 for CoC and 0.95 for BW/DB, but I can say for certain.
Decided to post what I remembered at least, it's better than nothing.

Elenmir · 04/04/08, 4:34 PM

I looked at my old data again, adjusted some of it (have to be careful with the base values for spells due to the level-based scaling), and collected some more data to get better bounds and verify some corner cases. As it turns out, the formula from wowwiki seems to be accurate for nearly all spells, with a few notable exceptions.

So:

For spells learned before level 20, there is a penalty that depends only on the level the spell is learned at:

$sub20Penalty = \min(1,1-(20-spellLevel)*0.0375)$

For all spells, there is a penalty that depends on the level of the caster and on the downrankPenaltyLevel of the rank used, i.e. the last level at which there is no downrank penalty for that rank of the spell:

$downrankPenalty = \min(1,\frac{downrankPenaltyLevel}{casterLevel})$

The downrank penalty level is almost always equal to 5 plus the level at which the next rank of the spell is learned.

These penalties apply multiplicatively to the empowered/cast-time coefficient:

$spellCoefficient = sub20Penalty * downrankPenalty * (empoweredTalents + castTimeCoefficient)$

I don't know how the downrank penalties interact with the penalties for things like snares.

I've collected a fair bit of data to get good bounds on the coefficients of all ranks of heal, greater heal, flash heal, and renew. The bulk of the data comes from two sessions, one with a deep holy spec and one with a disc. PvP spec. My data is consistent with the above formulas. All the testing has been done with a level 70 priest, though, so I can't really say anything about the scaling with caster level.

For the spells I've tested, the exceptions to the 'next rank + 5' rule that I've found are:

Greater heal rank 4, 69 (expected 65).
Greater heal rank 5, 70 (expected 68; this is the AQ20 rank).
Heal rank 4, 45 (there's no next rank of this)
Flash heal rank 7, 67 (expected 66)
Renew rank 9, 67 (expected 65; next rank is the AQ20 rank)

Skyhoof · 04/04/08, 5:53 PM

Originally Posted by Elenmir

I looked at my old data again, adjusted some of it (have to be careful with the base values for spells due to the level-based scaling), and collected some more data to get better bounds and verify some corner cases. As it turns out, the formula from wowwiki seems to be accurate for nearly all spells, with a few notable exceptions.

For the spells I've tested, the exceptions to the 'next rank + 5' rule that I've found are:

Greater heal rank 4, 69 (expected 65).
Greater heal rank 5, 70 (expected 68; this is the AQ20 rank).
Heal rank 4, 45 (there's no next rank of this)
Flash heal rank 7, 67 (expected 66)
Renew rank 9, 67 (expected 65; next rank is the AQ20 rank)

Bokomatic in the shaman forum has observed a similar problem with certain shaman spells.

The discussion starts on this page with post #839: How to Heal like a Pro

Here are some other relevant posts:
http://elitistjerks.com/697800-post857.html
http://elitistjerks.com/698285-post863.html

I've suggested that we get a separate thread going in the class mechanics forum to take a closer look at this issue.

Elenmir · 04/05/08, 11:13 PM

Originally Posted by Skyhoof

Bokomatic in the shaman forum has observed a similar problem with certain shaman spells.

The discussion starts on this page with post #839: (snip)

The conclusion there, downrank penalty level equal to level spell is learned at + 11, is consistent with my data.

Squashed · 04/06/08, 12:55 AM

From my own testing (the numbers are lost, but I could certainly do it again), the formula for "Spells which combine direct damage and a DoT component" is not quite a match to the numbers I've seen, however, the method described on WoWWiki matches perfectly.

EDIT: For example, your numbers for Immolate are:

Immolate (DD): 0.198
Immolate (DoT): 0.131 per tick

The numbers I get from WoWWiki's method are:

Immolate (DD): 0.2078 (16/77)
Immolate (DoT): 0.1273 per tick (7/55)

EDIT2: Outdated (see below).

◊ Tanilin · 04/17/08, 6:26 PM

I'm 99% sure that the coefficient on CoH is 0.214 (half of what's listed).

vikinghelmet · 04/23/08, 11:35 AM

Talents, items or abilities that increase your coefficient will do so at the latest possible point in the calculation (Improved Fireball, etc.)

Sorry to nitpick but you actually mean Empowered Fireball here?

Nite_Moogle · 04/23/08, 11:45 AM

Melador · 04/23/08, 8:15 PM

Spells which combine direct damage and a DoT component (immolate, flame shock, moonfire, etc) have their coefficient split between the direct damage and damage over time portions of the spell, proportionate to the base damage of each component. For example, Immolate (which has a 2.0 cast time, some amount of direct damage and a 15 second DoT time) has an average base direct damage component is x, and the dot portion's base damage is y, then the coefficient on the direct damage component is \frac {2}{3.5}*\frac{x}{x+y}, and the coefficient on the DoT component is \frac{15}{15}*\frac{y}{x+y}.

I don't quite understand this part. What are x and y? Isn't x=2/3.5, and y=15/15 for this particular example?

Also, the grammar is making it a bit confusing ("has an average base direct damage component is x").

Melador · 04/25/08, 2:42 AM

Based on my tests on the PTR, moonfire's DoT coefficient is .13 per tick, not .10, and the DD coefficient is .15, not .214.

Edit: Also, Insect swarm's overall coefficient is .76 (which isn't duration/15 for some reason), and it ticks 6 timesfor a per-tick coefficient of .1266, not .1766.

• Adoriele · 04/25/08, 3:55 AM

Originally Posted by Melador

Based on my tests on the PTR, moonfire's DoT coefficient is .13 per tick, not .10, and the DD coefficient is .15, not .214.

Edit: Also, Insect swarm's overall coefficient is .76 (which isn't duration/15 for some reason), and it ticks 6 timesfor a per-tick coefficient of .1266, not .1766.

Yeah, I fell into the trap of .1667 as well. It's poorly-worded, in that .1667 is 1/6, meaning each tick get 1/6 of .76. Incidentally, it's .76 instead of .8 because of the -Hit part of the debuff. Any DoT with a non-damage component receives a reduced coefficient.

As for Moonfire, your tests agree with weighting the coefficient with the DD and the DoT with the same ratio as the base damage, which is consistent with his formula you quoted in your previous post. .10 and .214 correspond to a weighting of 50% to each, which I think is how they used to be weighted, though I'm not sure.

Squashed · 05/18/08, 1:26 AM

I did some more testing of Immolate's coefficients for some spreadsheeting, and this is what I found:

At level 70, the coefficients for the Direct Damage and Damage over Time portions of Rank 9 Immolate are 0.2 and 0.65 (0.13 per tick) respectively, with an error of less than 1%.

Some of the discrepancy of the earlier test came from the way in which Emberstorm and Improved Immolate stack - additively. (i.e. - the total multiplier for 5/5 Emberstorm and 5/5 Improved Immolate is 1.35, not 1.375 as would be expected if they stacked multiplicatively.)

The rest of the discrepancy came from realizing that the base value for the Direct Damage portion of Immolate is not 327, as the spell description on WoWHead and other sites will say, but very close to 331.25. (The additional damage comes from the way the spell scales with level.)

Roywyn · 06/21/08, 9:36 PM

Shaman (tested at 888 damage, level 70, in Stockades)

Searing Totem: 16.8% per hit (450% total)
(from 50-66 to 199-215)

Lightning Shield: 26.7% per charge (80% total)
(from 287 to 524)

Magma Totem: 6.7% per tick (67% total)
(from 97 to 157)
Magma Totem has an AoE cap of 1550 per tick, 15.500 total.

Fire Nova Totem: 21.4% on impact
(Base 654-730. To 853-918. Makes an increase of 188-199, fits the 21.4 which is the coffecient for instant AoE)
Fire Nova Totem has an AoE cap of 9970.

Irise · 03/23/09, 12:28 PM

I was making a long post about the incorrect values listed above which are not only inconsistent with live but inconsistent with the theorycrafting posted at beginning of thread when I realized that the post hasn't been updated since May '08.

For anyone looking for the coefficients note that the theorycrafting is correct but the coefficients are not. The only addendum that needs to be added is that Healing spell get a 1.88 multiplicative coefficient.

So for example the coefficient for Power Word: Shield is 1.88*1.5/3.5

Thedarknes · 05/09/09, 7:41 AM

Not sure if this is being readily update but, per tick, Curse of Agony gets a 10% benefit from spell damage (in line of course with a 120% benefit over the entire duration of the spell, unless you have the curse of agony glyph, in which case you get a 33.33% bonus of 1740 added to a 140% spell damage bonus over the duration).

Spell Coefficients

Contents

[top]Definition

[top]Calculation

[top]Druid

[top]Mage

[top]Paladin

[top]Priest

[top]Shaman

[top]Warlock