Formulas:Mana Regen
From WoWWiki
The condition of a game character gaining mana points over time is referred to as mana regeneration. There are several sources of mana regeneration, each with their own characteristics.
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Spirit-based regeneration
All characters with mana points passively regenerate some mana in ticks of 2 seconds. The amount of mana gained per tick is based on the character's intellect and spirit attributes as well as level. The regeneration rate is typically expressed as Mana Per 5 Seconds (MP5) which can be calculated by multiplying mana-per-tick by 5/2.
Research by Whitetooth[1] shows that with release of 2.4, mana regeneration formula is now uniform across all classes and can be calculated with the following formula:
MP5 = 5 * (0.001 + sqrt(Int) * Spirit * Base_Regen) rounded up
Base_Regen is a variable dependent on character level and is summarized in the following table:
| LEVEL | BASE_REGEN | LEVEL | BASE_REGEN | LEVEL | BASE_REGEN | LEVEL | BASE_REGEN | LEVEL | BASE_REGEN |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.034965 | 15 | 0.023345 | 29 | 0.016581 | 43 | 0.013363 | 57 | 0.011342 |
| 2 | 0.034191 | 16 | 0.022748 | 30 | 0.016233 | 44 | 0.013175 | 58 | 0.011245 |
| 3 | 0.033465 | 17 | 0.021958 | 31 | 0.015994 | 45 | 0.012996 | 59 | 0.011110 |
| 4 | 0.032526 | 18 | 0.021386 | 32 | 0.015707 | 46 | 0.012853 | 60 | 0.010999 |
| 5 | 0.031661 | 19 | 0.020790 | 33 | 0.015464 | 47 | 0.012687 | 61 | 0.010700 |
| 6 | 0.031076 | 20 | 0.020121 | 34 | 0.015204 | 48 | 0.012539 | 62 | 0.010522 |
| 7 | 0.030523 | 21 | 0.019733 | 35 | 0.014956 | 49 | 0.012384 | 63 | 0.010290 |
| 8 | 0.029994 | 22 | 0.019155 | 36 | 0.014744 | 50 | 0.012233 | 64 | 0.010119 |
| 9 | 0.029307 | 23 | 0.018819 | 37 | 0.014495 | 51 | 0.012113 | 65 | 0.009968 |
| 10 | 0.028661 | 24 | 0.018316 | 38 | 0.014302 | 52 | 0.011973 | 66 | 0.009808 |
| 11 | 0.027584 | 25 | 0.017936 | 39 | 0.014094 | 53 | 0.011859 | 67 | 0.009651 |
| 12 | 0.026215 | 26 | 0.017576 | 40 | 0.013895 | 54 | 0.011714 | 68 | 0.009553 |
| 13 | 0.025381 | 27 | 0.017201 | 41 | 0.013724 | 55 | 0.011575 | 69 | 0.009445 |
| 14 | 0.024300 | 28 | 0.016919 | 42 | 0.013522 | 56 | 0.011473 | 70 | 0.009327 |
The chart here was generated using this data. We can see by looking at the formula that increases in spirit relates linearly to regeneration and that intellect relates inverse exponentially, IE diminishing returns. Also note that the base regeneration goes down as level increases, this one assumes is to compensate for the scale of stat increases as a player levels and acquires gear. If one plots the base_regen rates it looks like levels 1-10 has one curve, 11-60 has another, 61-70 have a jagged but almost linear decrease which seems to have been tweaked by hand. Realistically, this equation seems to merely enforce balanced stats, so stacking spirit do the detriment of intellect is to be avoided. The sweet spot of 1 spirit = 1 MP5 seems to be the target of the game designers, provided that the caster has an appropriate level of intellect.
What to Stack?
Look at these two enchants: [Enchant Chest - Major Spirit] [Enchant Chest - Restore Mana Prime]. Lets have an example level 70 caster with 500 Intellect and 500 Spirit. By the formula, the spirit enchant will give about 16 MP5, and the MP5 enchant is only +6 MP5, granted that the Restore Mana Prime includes regeneration while casting. Lets conclude that spirit is better attribute to stack than MP5 but MP5 is still very beneficial when it comes to chain casting.
The 'sweet spot' of intellect for a level 70 is around 459, where 1 spirit = 1 MP5. Going above is where the bonus comes in, below is a penalty. If the intellect on our priest reached 550 then 15 Spirit would yield 17 MP5. If the intellect were 450 then its 14 MP5. Its clear that the intellect should not be sacrificed in favor of spirit or MP5.
Five Second Rule
After a character expends mana in casting a spell, the effective amount of mana gained per tick from spirit-based regeneration becomes a ratio of the normal listed above, for a period of 5 seconds. During this period mana regeneration is said to be interrupted. This is commonly referred to as the five second rule.
Channeled spells are handled a little differently. The five second rule starts when the spell's channeling starts; i.e. when you pay the mana for it. The rule continues for at least five seconds, and longer if the spell is channeled for more than five seconds. For example, Mind Flay channels for 3 seconds and interrupts your regeneration for 5 seconds, while Tranquility channels for 10 seconds and interrupts your regeneration for the full 10 seconds.
By default, your interrupted mana regeneration ratio is 0%, meaning that spirit-based mana regeneration is suspended for 5 seconds after casting. Several effects can increase this ratio, including:
| Effect | Interrupted mana regeneration ratio increase |
|---|---|
| Arcane Meditation (Mage talent) | 10%-30%* |
| Intensity (Druid talent) | 10%-30%* |
| Meditation (Priest talent) | 10%-30%* |
| Mage Armor (Mage spell) | 30% |
| Spirit Tap (Priest talent proc) | 50% (and increases mana regeneration to app. 200%) |
| Darkmoon Card: Blue Dragon proc (Aura of the Blue Dragon) | 100% |
| Bangle of Endless Blessings proc (Meditation) | 15% |
| Innervate (Druid buff) | 100% (and increases mana regeneration to 500%) |
* Depending on rank
Multiple ratios do stack, but can never exceed 100%.
Note that spells which don't cost mana will not start the 5 second timer and will let you continue regenerating mana. Nature's Swiftness costs no mana, and thus will not invoke the five second rule. Spells cast with the Clearcasting state will also not start the 5 second timer. (Note that this does not apply to the Shaman Clearcasting state, as it only gives 60% mana cost reduction.) Totems, on the other hand, will start the 5 second timer. Also, item procs that reduce the cost of a spell to below its total mana cost will also not interrupt mana regeneration (i.e. Eye of Gruul).
Prior to the 1.4.0 patch, you also did not regenerate mana during the casting of the spell. In-game textual references to the five second rule still read "while casting" where they actually should read "after casting".
Mana per 5-sec (MP5) item bonuses do not fall under this rule and are applied at all times regardless of recent spellcasts.
Direct regeneration
Many effects increase mana regeneration directly i.e. without increasing spirit. These effects are governed by different rules than spirit-based regeneration.
Mod Power Regen effects
Most items which restore mana, including various types of water as well as equipable items such as Anathema, works similarly to spirit-based regeneration in that they regenerate mana in ticks of 2 seconds. Unlike the spirit-based regeneration, however, the five second rule does not apply to these effects. That is, after casting a spell, mana regeneration from these items will continue. This can make a difference in fights, where long chains of uninterupted spell casting both drains mana and halts spirit-based regeneration.
Periodic Energize effects
A few items, such as Second Wind, as well as some spells, like Blessing of Wisdom, does not regenerate mana in 2 second ticks but rather in the intervals actually advertised in their tooltips. The five second rule does not apply to these effects either. Note that it appears that Blessing of Wisdom regenerates mana in 2 second ticks as of patch 2.1.2.
Comparing spirit based and direct regeneration
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In theory, direct regeneration is preferable over spirit-based regen, as it is not subject to the 5 second rule. If for example a priest could give away 8 spirit, and gain 5 mana/5, the latter would give the same regen as the spirit at all times, and thus be better (disregarding HP regen). The factor where Spi and mana/5 give the same base amount of regen (outside the 5 second rule) is 1.6 spirit for 1 mana/5 for priests and mages, and 2 spirit for all others.
The correct way to find out which is better would be to find your personal percentage spent inside the 5 second rule, e.g using an addon like Muse or RegenFu. Knowing the percentage, you now have a base to compare the relative merits of different item sets with high accuracy. CAUTION: The times where mana regeneration are most critical are when you are in high damage boss battles and may well be chain-casting, so the most conservative approach is to assume that you are never outside the 5 second rule.
A simpler approach can be found using the Item Values article, where an attempt is made to reverse-engineer the factors Blizzard uses when creating Items. These factors can be understood as a kind of price tag for item properties. According to that analysis, 1 mana/5 has the same "cost" as 2.4 spirit. Comparing items of otherwise similar properties, the only difference being that one has Spi and the other mana/5, mana/5 gives mages and priests (1.6/2.4 =) 66% of the regen which they would get from spirit. All other classes get (2/2.4 =) 83% of the spirit regen. Be aware that these percentages are only valid if you compare items which are otherwise very alike.
Example: Comparing Tooth of Gnarr and Seal of Rivendare. According to the Item Value analysis, items on neck and finger are directly comparable. The stats on both items have nearly the same value. The 3 mana/5 from the Tooth needs to be compared to a spirit regeneration of 4.4 mana/5 for Mages and Priest, and 3.5 mana/5 for all other classes. The other classes face a rather easy decision, since it's highly probable that they will spend more than 15% of the combat time inside the 5 sec rule, whereas Mages and Priests would have their break-even point at 32%, offering no clear solution.
Priest Mana Regeneration Equation
Here is how much spirit you would need, in order to regenerate the same mana as 1 mana every 5 seconds(mp5) based on your time spent in the five second rule (FSR)
2(mp5)/5 = (spirit/4)(1 - % time spent in FSR) + (spirit/4 * % regen during casting)*(% time spent in FSR)
Notice what higher regen while casting does to the higher FSR percentages. FSR percentages above 50% are very unforgiving to spirit with 0% regen durning casting. However, 30% regen during casting shows a significant decrease in the spirit required to match 1 mana/5.
Actual equations for creating the Graph above:
m = x mana every 5 seconds
p = % of time in FSR
s = spirit
k = regen while casting = .00, .15, .20, .30
To get spirit:
S(m,p) = 1.6*m/(1-p+k*p)
To get mana every 5: M(s,p) = ((s/4*(1-p)+(k*(s/4)*(p)))/0.4)
To get %FSR: P(s,m) = ((m/5*2)-(s/4)*k)/((s/4)*(1-k))
For more information and discussion see Jundicator's post in the priest forums: http://forums.worldofwarcraft.com/thread.html?topicId=11893046&sid=1
Additional notes
- You do not regenerate mana faster if you are sitting down or standing up.
- Spell casting never stops direct mana regeneration effects from items, nor does it reset your mana regen timing (much like casting a spell resets your auto-attack)
Calculator
- A small utility to aid in the calculation of mana regeneration for priests and mages can be found here.
- See also: Spirit
