spell coefficient (WoW)  

Spell Coefficient

The Spell Coefficient is the amount of bonus healing or bonus spell damage that a spell benefits from. Typically, this follows the formula:
     [Cast Time of Spell] / 3.5 = [Coefficient].
Up to a maximum of 200%. Instant cast spells are considered 1.5 second cast times.

Special Cases

"Over-Time" spells

This category includes both Damage over Time spells (DoTs) as well as Healing over Time spells (HoTs). The standard formula for "Over-Time" spells is:
     [Duration of Spell] / 15 = [Coefficient]

The added damage or healing is divided equally among each tick of the spell.

Hybrid spells

This category includes damage and healing spells with both a direct portion as well as an "Over-Time" portion. The standard formula for these spells is as follows:
     Over-Time portion: ([Duration] / 15) / (([Duration] / 15) + ([Cast Time] / 3.5)) = [Over-Time portion]
     Direct portion: 1 - [Over-Time portion] = [Direct portion]

The duration and cast time limitations are then applied:
      Over-Time portion: ([Duration] / 15) * [Over-Time portion] = [Over-Time coefficient]
      Direct portion: ([Cast Time / 3.5) * [Direct portion] = [Direct coefficient]

For the Over-Time portion, the added damage or healing is applied equally across each tick of the spell.

Channeled spells

This category includes spells that require channeling to continue the spell cast. The general formula for these spells is:
     [Cast Time] / 3.5 = [Coefficient]

Channeled spells gain the added damage or healing over the duration of the spell, divided equally among each tick.

Area of Effect spells

This category includes spells that deal damage or heal more than a single target. The general formula for these spells is:
     ([Cast Time] / 3.5) / 2 = [Coefficient]

AoE spells also have been given diminishing returns based on the number of targets hit with the spell. This formula is still unknown.

Paladin Specials

Some Paladin spells do not fall under any of the categories above, these spells have their own formulas for calculating the added damage.

Holy Shield/Retribution Aura

Reflects damage back to the attacker:
     5% of [bonus spell damage] = [amount of damage per charge]

Note: this is a special case for these two paladin spells only, reflected damage from other spells (i.e. Thorns) do not gain any benefit from bonus damage.

Seal of Righteousness

Deals additional holy damage to the target.
One Handed weapons
     9.2% * [Weapon Speed (in seconds)] = [Amount of Damage]

Two Handed weapons
     10.8% * [Weapon Speed (in seconds)] = [Amount of Damage]

Pentalties

Certain spells will also have various coefficient penalties associated with them.

Spells below level 20

Casting a spell that is below level 20 incurs a significant penalty to the coefficient of the spell. The formula for this is:
     (20 - [Spell Level]) * .0375 = [Penalty]

Downranking

Downranking also has significant effects on the spell's coefficient. The forumla for this is:
     ([Level of next rank - 1] + 5) / [Character Level] = [Downranking Coefficient]

What the "Level of next rank - 1" means is the level right before the caster would get the next rank of the spell. For example, Greater Heal (Rank 3) would be considered a level 57 spell for this calculation, since Greater Heal (Rank 4) is a level 58 spell.

Additional Effects

Some spells have additional effects, such as Frostbolt or Blizzard. The formulas for single target and AoE spells are slightly different. Since patch 2.1, not all spells with additional effects will follow this calculation as several have been given their own specific modifier (Blast Wave, Dragon's Breath, and Frost Nova for examples).

Single Target

Single target spells incur a 5% penalty to the coefficient:
     ([Cast Time] / 3.5) * 0.95 = [Coefficient]

AoE

AoE spells incur the same 5% penalty, as well as an additional penalty:
     (([Cast Time] / 3.5) * 0.95) / 3 = [Coefficient]
Note the change from dividing by 2 to dividing by 3 for the AoE spells.

Damage and Healing spells

Some spells do both damage to the target as well as healing to the caster. These types of spells receive a flat 50% penalty to the coefficient they would normally receive. They also only benefit from bonus damage effects and gain not benefit from bonus healing effects, however, the amount of bonus damage they receive applies equally to both the damage portion as well as the healing portion of the spell.

Putting it all together

Will all those numbers above, it can seem difficult to grasp how a particular spell's coefficient is determined. The basics of this process is as follows:
     [Basic Coefficient] * [Downranking Penalty] * [Sub Level 20 Penalty] = [Effective Coefficient]

A few notes on this process:

1. All cast times are considered before any spell haste or casting time talents are applied.
2. All talents or buffs that increase the damage or healing from spells are applied after the coefficient calculations.
3. All DoT/HoT durations are considered before any duration buffs or talents are applied. Keep in mind that these talents simply add extra ticks of damage or healing for the same amount that the spell would do otherwise.

Exceptions

There are several exceptions to the above rules, see the detailed spell coefficients page for actual numbers.

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