Analysis, Lunar Guidance, Obsolete
With the release of Patch 2.4, the way that Spirit-based mana regeneration is calculated will be changing so that Intellect is also a factor. On the up side, it’s a marked improvement for Spirit-based spellcasters, and the improvement actually scales exponentially with gear. Notably, all mana users will now use the same base formula for their mana regeneration with no more delineations by class. Classes like the Druid and Priest will still derive additional benefit when talenting Intensity and Meditation, however, and the Druid spell Innervate means that we get an even larger benefit than most. Notably, this also means that a Druid who shifts into Bear Form or Cat Form will continue to regenerate her mana just as before rather than at the decreased rate prior to Patch 2.4.
On the down side, it obsoletes many of the previously written articles here at Resto4Life that deal specifically with the issue of mana regeneration. Slowly, I’ll be replacing those out of date articles with new ones to help you continue to make the best decisions with regard to your gear and playstyle. This article will be focused on helping you determine the optimal ratio between Intellect and Spirit. Because of the complicated interaction between the two, this is no longer a set number and changes based on how much Intellect/Spirit you have, the length of the fight, the use of Innervate, the presence of Intensity, and the use of the Bangle of Endless Blessings. For those that don’t want to get into the gritty details presented below, a good rule of thumb for boss fights will be to aim for 40% more Spirit than Intellect.
Table of Contents
- The New Mana Regeneration Formula
- Optimizing Intellect and Spirit
- The Mana Regeneration Coefficient
- Optimizing Intellect and Spirit with MRC
- ** Significant Observations
** For the TLDR folks. You know who you are!
Base Mana RegenInt, Spi, Level = S * Base_Regen(Level) * √I * 5 + 0.001
As you can see, there is a new variable being introduced by Blizzard, a base mana regeneration factor determined by your current level. For levels 58-70, these factors are:
This factor scales inversely with level. Due to its relation within the new formula, as you level up, you will require more Intellect and more Spirit to derive the same level of return. This is of course consistent with previous Blizzard design philosophy which encourages continued gear progression.
While level is more or less a factor outside of our control, we can make gear selections based on the other two variables: Intellect and Spirit. Many people have concluded that the ideal method of optimizing these two will be to have your Spirit be double the value of your current Intellect (proof).
2I = S
In other words, if you are currently sitting at 200 Intellect and 450 Spirit and have the choice between an item with 40 Intellect and 40 Spirit, when optimizing for mana regeneration, select the item that will bring your Intellect/Spirit ratio closer to 2 or, in this case, the 40 Intellect. Similarly, if you had the choice between the same two items but had 400 Spirit and 250 Intellect, you would want to choose the item with 40 Spirit.
While the 2:1 rule is both easy to apply and understand, it doesn’t tell the whole story, and following it by rote will actually lead to subobtimal gear choices. Just as before, there is additional value associated with Intellect. Not spell crit, from which Restoration Druids derive little benefit, but rather the value of mana provided by Intellect. You can consider the mana provided by Intellect as "bonus" regeneration spread out over the course of an encounter. Thus, to determine the value of Intellect, a necessary component is time, and we must modify our original formula to account for this factor. To do so requires the use of partial derivatives (the proof of which can be found at the bottom of this article), but the final result comes out to the following with "t" representing "# of ticks in the fight":
S = 2I – 30√I / (t * 0.046635)
We can then plot the value of Intellect relative to Spirit over various fight lengths, deriving the following graph:
As you can see above, the 2 * Intellect = Spirit guideline is oversimplified to the point of being incorrect. Also note that the above graph does not factor in the effects of Innervate, Intensity, the percent time spent within the Five Second Rule, or the most popular mana regeneration trinket, the [Bangle of Endless Blessings]. To account for these factors, here is a summary of how they will affect our formula:
- % Time in Five Second Rule
This is the percent of the time you find yourself within the Five Second Rule, the time in which your mana regeneration is reduced to a fraction of what you would experience if not casting. For most Druids, this percentage is at least 30% due to 3/3 Intensity. This base reduction (70%) can be mitigated by other factors, however. As a rule, more time spent in the 5SR will increase the value of Intellect relative to Spirit since, while both Intellect and Spirit are now factored into "Spirit-based" regeneration, Intellect also affords additional mana "up front," mana whose value increases since it does not need to be regenerated.
The Druid talent Intensity increases mana regeneration while within the Five Second Rule by 30%. It and the Priest-equivalent talent, Meditation, is the reason that Spirit continues to be a preferred stat for these two classes while Shamans and Paladins instead prefer MP5. Since as a rule more mana regeneration while inside the Five Second Rule tends to devalue the up front mana contribution by Intellect, the effect is to increase the relative value of Spirit.
The class skill Innervate increases Spirit-based mana regeneration by a factor of five for at least 20 seconds out of every 360 seconds or 5.56% of the time. The effect of this is to discount the value of the "up front" mana afforded by Intellect, making Spirit more valuable
- [Bangle of Endless Blessings]: Proc
When the Bangle of Endless Blessings procs, it effectively removes you from the Five Second Rule for 15 seconds. The effect of this is to increase the value of Spirit since, like Innervate, it serves to discount the value of up front mana. For a lengthy discussion of the effects of the Bangle’s proc on mana regeneration, please see the previous article, Arrrghhh!!! Trinkets!!!
- [Bangle of Endless Blessings]: On-Use Effect
The on-use effect of the Bangle of Endless Blessings is to afford an additional 140 Spirit. As it is generally used in conjunction with Innervate, further augmenting the 500% rate of regeneration, it also de-emphasizes the value of Intellect. However, as it innately provides an additional 140 Spirit, it will tend to move the "optimum" ratio back toward a higher value for Intellect since your Spirit will be increased 5.56% of the time.
To simplify determining the mathematical contribution of these factors, it’s easiest to think of most of them in terms of how they augment the percentage of your base mana regeneration you will receive over time. Going forward, I will refer to this value as the "Mana Regen Coefficient" or "MRC." The contribution of % time in the FSR is pretty straightforward. By its definition, any time spent outside the FSR (1 – %Time in FSR) will grant 100% of your base mana regeneration. Effects such as the proc from the [Bangle of Endless Blessings] will also increase your mana regeneration, but only during time that would otherwise be considered inside the FSR (you can’t get more than 100% of your base mana regen except through Innervate). For example, if you were to spend 90% of the time in the FSR, and the Bangle’s Proc is active 23% of the time (cast frequency: 2.0 sec; proof), you would combine the two as follows:
MRCFSR, Bangle = ((1 – 0.9) * 100%) + (0.9 * 0.23 * 15%) = 0.131
While inside the 5SR, Intensity will afford you 30% of your base regeneration, a bonus that stacks with the proc from the Bangle. To also include the effects of Intensity, we modify our calculation like so:
MRCFSR, Bangle, Intensity = ((1 – 0.9) * 100%) + (0.9 * 0.23 * 15%) + (0.3 * 0.9) = 0.401
Because Innervate multiplies your base mana regeneration by five, it should considered isolated from the other factors listed above. To include the contributions from Innervate, we separate our function into two parts: the portion effective while under the effects of Innervate and the portion effective otherwise:
MRCInnervate, FSR, Bangle, Intensity = (500% * 20/360) + (MRCFSR, Bangle, Intensity * 340/360) = 0.657
Unfortunately, the on-use effect of the Bangle of the Endless Blessings combined with the use of Innervate greatly complicates things, marginally moving things in favor of Spirit but more significantly increasing the relative value of Intellect. This modification will be handled in a future article. For now, using the values supplied above, we can assume that our Mana Regeneration Coefficient will be close to 65.7%.
The MRC can be added to the derived mana regeneration formula by multiplying it into the denominator (which includes your total mana regeneration):
S = 2I – 30√I / (t * 0.046635 * MRC)
This revised formula can be plotted in the same way we plotted the earlier formula. Using the values described above to derive an MRC of 0.657, we can generate the following the graph:
The following observations can be made with regard to this change to mana regeneration:
- The longer the fight, the greater the value of Spirit relative to Intellect. This makes sense since longer fights place a higher premium upon the ability to regenerate mana over having mana available up front.
- As fight length increases, the value of Spirit relative to Intellect gets closer to 2. However, generally the amount of Spirit required will be less than twice the Intellect value, and you should base your optimization upon average fight length.
- At Spirit values between 300 to 450 and fight lengths between 8 and 10 minutes, you will want 30-50% more Spirit than Intellect based on the graph above. Therefore, as a general rule, aim for 40% more Spirit than Intellect.
- As your gear improves, you will want to move away from MP5 and toward Intellect and Spirit because the mana return from Intellect and Spirit increases exponentially while MP5 mana regeneration remains linear. The "break even" point where MP5 is roughly equal to Blizzard’s value of Intellect/Spirit is around 350 Spirit.
- While Spirit now benefits Shamans and Paladins, they are not likely to begin rolling on Cloth and Leather Spirit-gear since they lack talents such as Intensity and Meditation. This means that MP5 will continue to be a more attractive mana regeneration choice for them.
- Other classes that do not regularly receive Innervate will want significantly more Intellect than these graphs indicate.
- Trinkets that augment or that are based upon Spirit-based mana regeneration will become exponentially better. This has tremendous significance for Innervate.
This analysis is, of course, completely irrespective of +Healing and is intended to help you optimize your mana regeneration. How you value +Healing relative to mana regeneration has little to do with the figures and formulas presented here as the only relationship that exists between the two is from the 25% Spirit to +Healing Tree of Life aura. Determining the relative values placed upon +Healing (HPS) and mana regeneration will be revisited in a later article once Patch 2.4 has been released.
For those curious, here is the proof behind the formula to determine the relative values of Intellect and Spirit.
m = MP5
S = Spirit
I = Intellect
t = ticks in fight
Deriving the original 2 * Int = Spi formula:
- m = S * 0.009327 * 5 * √I + 0.001
- ∂m/∂S = 0.046635 * √I
- ∂m/∂I = S * 0.046635 / 2√I
- ∂m/∂S = ∂m/∂I = S * 0.046635 / 2√I = √I * 0.046635
- S/2√I = √I
- S = 2I
Deriving the adjusted Intellect vs. Spirit formula by taking into account fight length in ticks:
- m = S * 0.009327 * 5 * √I + 0.001 + 15I/t
- ∂m/∂S = 0.046635 * √I
- ∂m/∂I = S * 0.046635 / 2√I + 15/t
- ∂m/∂S = ∂m/∂I = S * 0.046635 / 2√I + 15/t = √I * 0.046635
- S/2√I + 15/t = √I
- 2I = S + 30√I / (t * 0.046635)
- S = 2I – 30√I / (t * 0.046635)
To apply the MRC value to the above formula, simply multiply it into the denominator.
Credit to Mr. Phae’s Calculus background for the above proofs and other mathematical analysis. Credit to reader Nebelmond of Die Silberne Hand (EU) for sending me the original information from Whitetooth which served as the launching point of this series. Finally, credit to Whitetooth both for his amazing dedication in determining the starting formula and his work on the highly valued RatingBuster addon which is tremendously helpful to theorycrafters.
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