+Healing and +Damage Formulæ

[Aethelwulf]

(The following has been converted from an old wiki page.)

You may have seen items or effects with bonuses like the following:

"Increases healing done by spells and effects by up to 42."
"Increases damage and healing done by spells and effects by up to 42."
"Increases Fire damage done by spells and effects by up to 42."

The common misconception surrounding these bonuses is that the item grants a random bonus between 1 and 42 for each spell cast. In actuality, each spell gets a fixed bonus that is determined by the spell type, casting time, target and/or way the spell is applied.

To determine how much +Healing, +Damage/Healing and +Damage you have, simply add together the totals from each item: these bonuses stack additively. If you had two items that each give +20 Nature damage, one that gives +10 damage/healing, and one that gives +10 healing, your healing spells would have an advertised benefit of 20 and your nature-damage spells would have an advertised benefit of 30, and all your other damage spells would have an advertised benefit of 10.

Formulas for Different Spell Types
The calculations below end in a decimal result that should be less than 1. To get the % multiply that decimal by 100.

Different types of spells have their damage and healing bonuses calculated differently. There are three base types of spells: standard, over time or a combination. Area of Effect and Channeling spells also take different bonuses. After the proper bonus is calculated, penalties are calculated to achieve the final damage.

Standard Spells
Standard spells are spells that apply all the damage or healing at one time. To determine the plus Healing or Damage benefit for these spells the following formula is used:

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(Cast Time of Spell) / 3.5

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3.5+ sec = 100%
3.0  sec = 85.71%
2.5  sec = 71.43%
2.0  sec = 57.14%
1.5- sec = 42.86%
Instant  = 42.86%

Spells with a cast time longer than 3.5 seconds are capped at 100%. The casting time used in the calculation should be the base cast time before effects from talents or gear are applied. Note that the tooltip in game includes those effects; refer to a database to find the base cast times of all spells.

Examples of such spells include: Healing Touch (Druid), Frostbolt (Mage), Greater Heal (Priest), Lightning Bolt (Shaman), Shadow Bolt (Warlock)

Over Time Spell
Over Time spells apply healing or damage over a period of time in ticks. Ticks can vary from one second apart to three seconds apart. Some spells specify the length of each tick and others require testing to determine.

If a spell has less than five ticks, each tick receives one-fifth of the bonus per tick. If an over time spell has 5 or more ticks, the spell receives full benefit, divided equally between the number of ticks.

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(Number of ticks in Spell / 5) =  Benefit

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1  tick  = 20%
2  ticks = 40%
3  ticks = 60%
4  ticks = 80%
5+ ticks = 100% (divided equally between the number of ticks.)

Note that the cap for this calculation is 1x (100%), more ticks than five will not give you over 100% benefit. +Healing and +Damage benefit for the spell is divided equally to each tick. If talents or gear add more ticks, count the extra tick in your calculations as it may change the benefit.

Examples of these spells include: Rejuvenation (Druid), Renew (Priest), Corruption (Warlock)

Combination - Standard and Over Time Spell
Why are these treated differently? Usually in all other spells discussed the damage or healing is all applied in one way. It may be delivered all at one time or split up into equal parts and distributed over time. With these spells the damage or healing is not divided equally and is applied in two or more different methods.

That Standard portion of the spell does not receive the full benefit because some of the benefit is moved to Over Time portion. So first you need to know what benefit goes to each section of the spell.

Calculation for determining the Portion to the Over Time part of the spell:

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(Number of ticks / 5) / ((Number of ticks / 5) + (Cast Time of Spell / 3.5)) = Portion to Over Time

So to get the Amount to the Regular part of the spell:

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1 - Portion to Over Time = Portion to Standard

Now remember the rules for Standard and Over Time spells still apply. So we have to now consider the cast time of the spell for the Regular part and the number of ticks for the Over Time part.

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(Cast Time of Spell / 3.5) * Portion to Standard = Benefit Regular part of the spell

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(Number of ticks / 5) * Portion to Over Time = Benefit Over Time part of the spell

See the notes in the Standard and Over Time spell formula sections to note any definition of terms or explanations on how to determine the Cast Time of Spell or Number of Ticks.

Examples of these spells include: Moonfire (Druid), Immolate (Warlock)

Channeled Spell
Channeled spells have their benefit distributed evenly over the time the effect lasts, getting 100% benefit for the whole spell (not per tick). The duration of the spell cast time is used as with a standard spell to calculate the total benefit, then divided equally between the number of ticks.

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Cast Time of Spell / 3.5 =  Benefit

Examples of these spells include: Hurricane (Druid), Arcane Missiles (Mage), Mind Flay (Priest), Hellfire (Warlock)

Area of Effect Spell
Area of Effect spells receive only 1/3 or 33.3% of the benefit. The cast time is used as with a standard spell to calculate the total benefit, then divided by 3.

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(Cast Time of Spell / 3.5) / 3 =  Benefit

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3.5+ sec = 33.33%
3.0  sec = 28.57%
2.5  sec = 23.81%
2.0  sec = 19.05%
1.5  sec = 14.29%
Instant  = 14.29%

Examples of these spells include: Tranquility (Druid), Arcane Explosion (Mage), Prayer of Healing (Priest), Hellfire (Warlock)

Note that some spells fall under the rules for multiple spell types. Hurricane, Tranquility and Hellfire for example are all Area of Effect and Channeled. Prayer of Healing is both a Standard Spell as well as an Area of Effect spell.

Rules for Applying +Healing and +Damage

1. You calculate spell time using the base spell cast time BEFORE talents and gear reductions to the cast time. (Notice that your casting time in the in-game tool tip will subtract time based on your talents.)
2. The factor for the casting time is capped at both ends. For the purpose of these formulas, spells that take longer than 3.5 seconds are considered to have 3.5 sec, and spells faster than 1.5 sec are treated like they had 1.5 sec (this is the global cast cooldown).
3. The number of ticks for a spell is capped at 5 for the purposes of working the equation (but bonus is divided equally between the number of ticks).
4. Damage benefits are applied before any talents or buffs that may increase your damage by a flat percentile. Healing spells are opposite; all talents are added to the base first then healing benefits added. For example: A spell that normally deals 100 damage that receives a +10 plus damage bonus, and a 10% damage bonus from talents, would deal 121 damage. A spell that normally heals 100 damage, that receives a +10 plus heal bonus, and a 10% heal bonus from talents, would heal for 120.
5. Spell criticals are an extra 50% of the original calculated value of the spell after benefits. So if the spell would do 100 damage or healing normally then the critical would be 150.
6. Gear benefits are added to spells before critical hit modifications are made.

Penalty Rule

Spells learned before level 20
Many spells have multiple ranks. To avoid having players using these lower ranks to deal constant damage at a negligable mana cost, any spell with a level requirement lower than 20 has a large penalty applied. If the spell has a shorter cast time, this is also taken in to account. This level penalty can be worked out by taking off 3.75% for each level lower than level 20.

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(20 - Level Spell is Learned) * .0375 = Penalty

Additional effects
Spells with additional effects (like slow) get a 5% penalty to benefit. This penalty is applied before other penalties and to the base calculation for the spell. Example a standard spell that is also AOE with an additional slow effect would be calculated:

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((Cast Time of Spell / 3.5 ) - .05 Penalty for extra effect) / 3 = Benefit

Examples of these spells include: Entangling Roots (Druid), Mind Flay (Priest), Blast Wave (Mage), Frostbolt (Mage)

Spells that do Damage and Healing
Some spells, both damage the target and heal the caster. These spells have a 50% penalty to the bonus they receive, but damage gear increases both the damage and the healing of the spell equally. These spells receive no bonus from gear that only increases healing.

Examples of these spells include: Devouring Plague (Priest), Drain Life (Warlock)

Exceptions to the Rules

1. Pyroblast was changed in patch 1.9 to deal 100% of +spell damage on impact and 71.4% of +spell damage to it's DoT component.
2. Fireball has a small damage over time component, but is not considered a hybrid spell, so it receives only the Direct Damage bonus to its direct damage component. Spell damage gear never increases the DoT on fireball.
3. Curse of Doom receives a 100% coefficient.
4. Mind Flay receives around 45.7% of spell damage.

Additional notes

1. +Damage amount has no effect on chance to crit with spells.
2. +Healing does not apply to bandages or potions. Trinkets should no longer be affected.
3. Shaman totems receive benefit from +Damage.
4. Hunter Traps don't get any benefit from +spell damage.

[Guybrush]

Great post.

Isn't there a penalty for snare effects as well?
For example Frostbolt should be multiplied by 0.95.

[Aethelwulf]

That's listed under Penalties > Additional Effects, but I'll add Frostbolt as an example. The examples aren't meant to be an exhaustive list though.

[Tinkertown]

The only thing that I can find missing is Mind Flays additional ~44% penalty.

[Aethelwulf]

Mind Flay's penalty is a bit odd. Investigating. A regular 3 second cast (with slow) should get around 81.4% of spell damage. I can't find any logic behind it but I am finding a 45.7% spell dmg coefficient for Mind Flay, so it seems to have a custom coefficient.

Channeled spells are ostensibly treated as continuous casting, although the 100% cap across an entire channel will really punish extended durations. A Warlock's Hellfire for instance really gets shafted by this since it's a 15 second channel on a 1 second interval, making 15 ticks on top of being an AoE, So you take 33% of spell damage (aoe penalty), and divide it across 15 ticks making for 2.2% of your spell damage in added AoE DPS. By contrast spell damage is supposed to give around 9.5% in DPS to AoE. For channels and DoTs, extending the duration actually hurts the spelldmg DPS (if it has at least 5 ticks) because the spelldmg is getting divided across more ticks (so a Priest with 2/2 Improved Shadow Word: Pain goes from 16.66...% spell power per tick to 12.5% spell power per tick).

Another thing worth noting about this is that spells with lowered casting times from talents and gear get a proportional benefit to the DPS they can squeeze out of spelldmg. Spelldmg is supposed to give roughly a 28.6% boost to DPS for chain-casting. But take an Ele Shaman's Lightning Bolt. Its base cast time is 3 seconds, but its lowered cast time is 2 seconds. That means he gets 50% more dps from spamming lightning bolt, so spellpower actually gives him roughly 42.9% in DPS. If he were casting Chain Lightning (which cannot exactly be spammed well given 6 sec CD and mana cost), it would go from 2.5 sec to 1.5 sec, making roughly 47.6% DPS from spellpower.

We can also note that the first rank obtained at level 20+ is typically the most mana efficient for spamming since it gets full benefit of +dmg and +heal. That's not strictly true because maybe you have a rank at 18 (7% heal/dmg penalty) and another at 26 which is much more expensive, but now you can figure out the math.

To combine the above two points, we can look at the mage's Fireball. It gets a .5 second cast time reduction. The Rank 5 (lvl 24) gets full spelldmg, plus factoring in the cast improvement (from 3.5 to 3), it gets 33.3...% spell damage in DPS at a mana cost of 140. The Rank 4 Fireball is at level 18, and it gets 93% of spellpower, but factor in the faster casting (from 3 to 2.5), and it gets roughly 32.6% of spell damage in DPS at a mana cost of 95. That would mean Rank 4 Fireball is far more mana efficient since the rank 5 only does 2.3% more DPS (+14.3 DPS from base damage and +1 DPS from the DoT = +15.3 DPS) at roughly 47.4% more mana cost. Factoring in the cast time difference (2.5 vs 3), Rank 5 is only 22.8% more mana expended per second, which is still enough to make Rank 4 more mana efficient.

[Tinkertown]

Mind Flay's penalty flows from the above calculations. It comes from the 5% penalty for providing a slow and a 40% penalty for being a DoT with just 3 out of 5 ticks. This is why Mind Flay only gets 57% of spell damage (for a 43% penalty) across its 3 seconds of channel.

Mind Flay scales at 45.7%, or at least it did in vanilla. Try again.

[Aethelwulf]

Alright, I've checked the math and done more research on it. Testing back in vanilla indicated that it was around 45.7%, yes. I can't figure out any factors for this one, so it seems to be a custom coefficient. Also, calculating channels as a DoT wasn't exactly right. The math turns out the same if it's more than 3.5 seconds with at least 5 ticks, which happens to be most channeled abilities, but not all.

As a side note, charts I've found indicate that Curse of Doom uses the damage for an instant cast (42.7%). (EDIT: Sources contradict, and at any rate Nostalrius uses 100% here, so it's back to 100%.)

I've edited the posts.

[Keftenk]

*Lights the Stalk beacon*

The beacon's are lit, the beacon's are lit!

[Praxxia]

I found this interesting- it seems some spells gain talents like Darkness before spellpower, while others gain it after.

http://forums.elitistjerks.com/topic/8334-mind-flay-how-much-does-it-benefit-from-spell-damage/

It's 45%. Due to the large number of people that didn't know what it was or falsely claimed it was some other value I went and FRAPS'd me testing it.

For Mind Flay and SW:P our talents (Darkness) apply after +dmg is added.

For Mind Blast however Darkness only applies before +dmg is added. The other talents still apply after +dmg.

Shadow Mastery affects these -before- gear:
drain life
sihpon life
curse of agony

and these -after- gear:
shadow bolt
deathcoil
corruption

[Stalk]

Some spells, both damage the target and heal the caster. These spells have a 50% penalty to the bonus they receive, but damage gear increases both the damage and the healing of the spell equally. These spells receive no bonus from gear that only increases healing.

This is actually incorrect. +damage will increase the damage component of the spell; +healing will increase the healing done by the healing portion of the spell. The discrepancy here arises from items will have +damage and +healing wrapped into a single item which is a good portion of the gear that all of the casters wear. Holy Nova for instance should receive a coefficient of 1.5/3.5/3/2 = 7.1% for either its damage or healing. Currently, it is getting more than 40% on its healing bonus.

It is not the +damage that is increasing the healing done by these hybrid spells. It is the +healing which usually accompanies it on most dps items.