Formulas:Plus damage and Plus healing
From WoWWiki
 
(Also referred to as +heal, +dmg, or spellpower.)
 
You may have seen items or effects with statements that say:
 
    "Increases healing done by spells and effects by up to 42."
    "Increases damage and healing by spells and effects by up to 42."
    "Increases fire damage done by spells and effects by up to 42"
 
And maybe you wondered "What do these mean?" Well many people assume (wrongly) that the item grants a random bonus between 1 and 42 for each spell cast. But that is not the case, in fact each spell gets a fixed bonus that is mostly determined by the casting time of the spell. In general, you can divide the casting time of a spell by 3.5 and get a rough estimate of how much benefit it will get per cast of the spell. Of course, as with everything there are a few special cases just waiting to mess things up.
 
    ActualBenefit = AdvertisedBenefit * (CastingTime / 3.5) * Penalty Factor  
    (CastingTime above 3.5 is ignored for this equation)  
 
The factor for the casting time is capped at both ends. For the purpose of this formula, 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). So, for example, Scorch (1.5 second cast) and Fire Blast (Instant Cast) both get a bonus of about 0.429 (which is 1.5/3.5) times the advertised benefit. This might at first seem unfair to shorter cast spells, since Scorch gets only 42.9% of the benefit that Fireball (3.5 second cast) gets. However, in the time it takes to cast 3 Fireballs (10.5 seconds) you could cast 7 Scorches. A bit of quick math shows that 7 x 42.9 = 300.3. Or in other words, +damage gear normally increases your damage per second (dps) by a constant amount.
 
Here are some other examples of damage or heal bonus coefficients for direct damage and healspells. (Source: Thundgot, English Community Manager)
 
    Shadow Bolt (3 second casting time): 0.857
    Smite (2.5 second casting time): 0.714
    Wrath (2.0 second casting time: 0.571
    Flash Heal (1.5 second casting time): 0.429
    Scorch (1.5 second casting time): 0.429
    Fire Blast (instant casting time): 0.429
 
On the other hand studying certain game mechanics further we can see that 3 untalented Fireballs take more like 12 seconds to cast rather than 10.5 and 7 Scorches take more like 14 seconds to cast rather than 10.5. This relates both to human reaction factor and latency. So no, there is no constant impact on DPS of spells that don't hit special cases. I'm currently trying to research exact loss of time per cast. --Drundia 14:19, 8 May 2006 (EDT)
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Special Cases
 
First, a short overview of the common penalty factors:
 
    * Channeled spells, DoT and HoT have their benefit distributed evenly over the time the effect lasts
    * Spells with additionals effects (like slow) get a 5% penalty
    * Area of Effect spells receive only 1/3 of the benefit
    * If casting low rank of a spell (learned before level 20), the bonus is reduced  
 
And here is the complete list with examples:
 
   1. Damage over Time (DoT) and Heal over Time (HoT) spells use a different formula. The bonuses for DoTs and HoTs are determined by the number of ticks the spell receives. If they have 5 or more ticks, the full bonus is divided among all of the ticks. This means that although Shadow Word: Pain is an instant cast spell, it still gets the full advertised benefit, and 1/6 of that benefit is added on to each of its ticks. If the spell has fewer than 5 ticks, the spell gets 1/5 of the bonus added to each tick. So, in theory Mind Flay, which is a channeled DoT spell with 3 ticks would get 1/5 of the bonus on each tick. In practice, Mind Flay actually gets a small bonus because it hits another special case. Rain of Fire receives 1/4 of the benefit per tick which is further reduced by it's AoE nature.
   2. Spells that either snare (slow down) or root (stop) a target have a penalty applied to their bonus, usually 5%. So, instead of receiving 3/5 (60%) of the advertised benefit, Mind Flay only receives (95% of 60%) 57% of the advertised bonus or 19% on each tick. Some spells, ie Cone of Cold receive a larger penalty (20%).
   3. Additionally, Area of Effect spells, such as Flamestrike receive only 1/3 of the cast time benefit, so Flamestrike would receive 28.5% of your +damage bonus. The developers have balanced these spells so that you only maintain the same constant dps if you are hitting 3 targets. Of course, channeled spells such as Hurricane have the DoT damage bonus divided by 3 as well. So Hurricane receives 3.16% bonus per tick because it has 10 ticks, has an attack speed slowdown, and is an AoE spell.
   4. Many spells have multiple ranks. To avoid having players using these lower ranks to deal constant damage at a negligable mana cost, any spell which can be learned at a level 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. So EffectiveBonus = (1-((20-LevelLearnt)*0.0375))*AdvertisedBonus. With this said most mana effecient rank is usually lowest rank learned at level 20+.
   5. Hybrid Direct Damage and DoT or Direct Heal and HoT spells also behave differently. Essentially these are spells like Immolate Rank 7 which deals 258 damage and then 485 over 15 seconds. That initial component does not receive the full benefit as some of the damage is moved to DoT component. The Direct Damage component receives the damage bonus determined by the 2 second casting time (2/3.5 or 57.1%) multiplied by the percentage of the direct damage compared to the DoT 258 / (258 + 485) = 34.7% for a final bonus of 19.8%. The DoT component then receives a benefit of 65.3% over 15 seconds, or about 13.1% per Tick. Regrowth Rank 9 works exactly the same way, healing for 1003 to 1019 and 1064 over time. Thus it recieves a benefit of about 27.84% on the direct heal and 51.3% divided among each of the 7 healing ticks of the HoT part of the spell.
   6. So far we've talked about damage spells and healing spells, but some spells, like Devouring Plague (Rank 6) 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. However, these spells receive no bonus from gear that only increases healing. So the damage dealt by Devouring Plague is only 50% of the advertised benefit, or 6.25% per Tick. However, it will also heal the caster for 6.25% more per tick.  
 
This is also the case regarding the Warlock spell-line Drain Life. it is a 5 tick channeled DoT (and thus recieves full +damage ammount) and have 50% of added to damage, 50% to healing.
 
   1. Lastly, some spells are exceptions to the general 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. This is currently the only known spell which recieves more than the advertised benefit.
         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. Hunter Traps don't get any benefit from +spell damage. Shaman totems used to not recieve any either but this was changed in patch 1.11  
 
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Additional Notes
 
   1. If you ever see an item which advertises "increases [...] spells and effects by up to 1 to 42," then it still follows the above formula for the top limit. However, each cast of the spell will give you a random benefit between 1 and what would normally be the actual benefit based on casting time. However, these items should have all been removed from the game before patch 1.8.
   2. The CastingTime value used to calculate ActualBenefit for a particular spell does not change if a player has a Talent, buff, or debuff affecting cast time.
   3. Benefits are added to spells before critical hit modifications are made. So, yes, these will raise your criticals.
   4. Benefits are also applied before any talents or buffs which may increase your damage by a flat percentile. For example, having 5 talent points in Fire Power will gain you 10% of your normal fire spell damage and 10% of your bonus spell damage. Exceptions are Healing spells, Curse of Agony, Drain Life and Siphon Life, which have talents applied before gear (buffs such as Curse of Shadow will still increase the +damage however)
   5. Rejuvenation: This spell only has four ticks of healing, so it only receives 80% of your +healing bonus.
   6. Renew: This spell has five ticks of healing and you get 100% of your +healing bonus.
   7. +Healing does not apply to bandages or potions. Trinkets should no longer be affected.
   8. +Healing, +Damage/Healing and +Damage stack together. If you had two items that each give +20 shadow 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 shadow-based spells would have an Advertised Benefit of 30, and all your other damage spells would have an Advertised Benefit of 10.
   9. As of Patch 1.11, Rejuvenation and Renew will use the +healing bonus you had when you initially cast the spell. Previously, there had been a bug that caused each tick to use the caster's current +healing value.
  10. In this General forum post by Tseric on May 31, 2006, it was clearly stated that your +dmg amount has no effect on your chance to crit with spells.