Method: Coefficient Testing
Published on March 8, 2008 by PhaeliaAnalysis, Lunar Guidance, Spells and Talents
12 Comments
Excited about the upcoming changes to Regrowth‘s mana cost, I have been working on a comparative analysis of Regrowth‘s HPM value to that of Lifebloom. Part of any analysis of this nature is factoring in the +Healing coefficient for each spell — no small task when you consider the number of talents that can affect your final numbers! Usually, I’ll check WoWWiki to look for the relevant numbers. When I pulled up the numbers for Regrowth, however, I noticed something odd: WoWWiki lists the +Healing coefficient for the direct heal of Regrowth as 16.6%. That’s really low, even for a spell that takes 2.0 seconds to cast and even considering that the spell includes a HoT component with a coefficient of its own. It also didn’t seem consistent with the numbers I experience when using Regrowth. So I loaded up the game and tried it out for myself. I discovered a coefficient of 0.4582. I’m going to describe how I performed these tests in the hopes that some readers can do the same and let me know what results they get.
Because the direct heal component of Regrowth exists as a range of numbers, it’s more difficult to determine its coefficient than for something simple like a HoT tick or the bloom of Lifebloom. Therefore, I cast Regrowth on myself about 100 times to find a maximum, non-crit value of 2140 and minimum of 1989. These numbers were generated at 1617 +Healing. I don’t have 5/5 Improved Regrowth which made testing easier since I didn’t have to worry as much about critical heals (I excluded the few that did crit). If you decide to perform this test on your own (and I hope that you will), you should disregard any critical heals that you get; we can factor the crit rating and bonus in later. For the sake of clarity, I performed my calculations with Gift of Nature (+10% to all heals) and Empowered Rejuvenation (+20% to +Healing effects on Heals over Time), two talents that most non-Dreamstate, healing Druids are likely to have.
The formula to determine the healing coefficient of a spell is:
(Coefficient * +Healing) + Base Heal = Avg. Amt. Healed with +Healing
So plugging my numbers into this equation and solving for the coefficient, I get the following:
(Coefficient * 1617) + 1325.5 = 2064.5
1617 * Coefficient = 2064.5 – 1325.5
Coefficient = (2064.5 – 1325.5) / 1617 = 0.4582
That’s a pretty substantial difference and means that Regrowth will scale far better than the number on WoWWiki indicates. This calculation doesn’t account for spell crit, either the ~10% most of us will have due to Intellect or the 50% + ~10% a Druid with Improved Regrowth will have. To find those values, we adjust our formula like this:
(Coefficient * +Healing) + (Base Heal * (1 + (0.5 * Crit%))) = Avg. Amt Healed with +Healing * 1 + (0.5 * Crit%)
Therefore, the coefficient when factoring in these two crit ratings would be:
Coefficient_{10% crit} = (2167.725 – 1391.775) / 1617 = 0.4799
Coefficient_{60% crit} = (2683.85 – 1723.15) / 1617 = 0.5941
So my question to you is this: am I crazy? Where is this 16.6% coefficient coming from? Oddly enough, the coefficient listed for the HoT portion of Regrowth (1.194) only matched the number I found (0.9227) if I assumed 2-piece T5 set bonus, a bonus that extends the life of your Regrowth HoT by 2 ticks (a stipulation not specified by the author) and would cause me to multiply the coefficient by 9/7.
And for those curious, my numbers for Lifebloom differed from those on WoWWiki, though less than my numbers for Regrowth:
I Found | WoWWiki Lists | |
Lifebloom, HoT |
0.6858 |
0.6216 |
Lifebloom, Direct* |
0.4533 |
N/A |
* I tested the "Lifebloom, Direct" figure on the PTR since it will change in 2.4. Therefore, I am not listing the comparison from WoWWiki. If you decide to do any testing for Lifebloom, be sure you don’t have any Lifebloom-affecting idols equipped.
I would really love to hear some feedback from the rest of you if you have the opportunity to do any testing on your own!
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Another smart post that reveals a little more regarding 2.4 changes and the Regrowth and Lifebloom coefficients!
4:57 pm on 3/8/08Do you think rejuvenation will go “out of style” in a ToL’s healing rotation now that regrowth’s mana cost is so low (and the hot lasts longer.. albeit healing for fewer per tick, than rejuvenation)?
Part of the discrepancy seems to be a matter of the talents you don’t account for. Wowwiki spell coefficients are generally listed based on untalented casts.
To account for the talented effects on your data, we should use the following equation:
G*(B+(E*H*C))=A
where:
G=1.1 (Gift of Nature)
B=1325.5 (Average Base direct heal value for max rank)
E=1.2 (Empowered Regrowth)
H=1617 (your +heal value)
A=2064(Average value healed from your observations)
C=the unknown (that is, the +heal coefficient)
Solving for C, we get:
C=((A/G)-B)/(E*H)=((2064/1.1)-1325.5)/(1.2*1617)
C=.28
This is still significantly higher than the reported Wowwiki value, but less so that your ~.46
5:04 pm on 3/8/08@Hecuba: Very interesting! I didn’t realize that Empowered Rejuvenation affects the direct component of Regrowth. I was able to confirm this on the PTR, and that does explain why Blizzard has said that Lifebloom’s direct portion has not properly been benefitting from Empowered Rejuvenation. By detalenting back to only Gift of Nature (without the benefit of Empowered Rejuvenation) and finding a new average heal of 1964.5, I came up with a coefficient of 0.3952 (1964.5-1325.5/1617). Dividing out Gift of Nature, the base coefficient is around 0.3592 which is still very different from the value being presented on WoWWiki. I believe that Empowered Rejuvenation affects different spells at different rates and may not afford the entire 20% benefit, particularly for spells with a direct and HoT component. In this case, it appears to be adding 15.94%.
It does seem that WoWWiki should be corrected. The relevant number in my mind will be one with all the numbers included since you can’t break them apart in a predictable manner (particularly Empowered Rejuvenation).
It would seem that with all the relevant talents (GoN, Empowered Rejuv, Imp. Regrowth) figured in, the coefficient comes out to 0.5941. Without these included, it’s around 0.3592. Things are looking good for Regrowth. Still, why couldn’t Blizzard just make all this easy with a handy tab in your character sheet that breaks all this down? ^_^
6:56 pm on 3/8/08Oh, I didn’t know Empowered Rejuvenation affected regrowth, that’s good news. Funny, however, that in my experiment explained in http://www.resto4life.com/2007/10/24/tier-5-set-bonus-and-saving-for-season-3/ I got around 37%, where I didn’t consider this talent (yet nobody corrected me!)
Anyway, I’ve always found regrowth extremely useful and this makes it even better. I hope those few regrowth-phobics still walking around with HT spam will now see the light and embrace the spirit of the tree
9:01 pm on 3/8/08Thanks Phae for another great analysis!
I wrote a quick-and-dirty addon for the PTR, which counts your non-critical regrowths and calculates the healing coefficient. Feel free to download it here: http://81.169.188.141/RegrowthCoefficient.zip. Just type “/rc show” after a few Regrowths to see its values in your default chat. This should simplify the data gathering.
At 1847 +Healing on PTR Build 8031 my coefficient is as follows:
9:43 am on 3/9/08With no talents at all: ~0.29
With 5/5 Gift of Nature: ~0.39
With 5/5 Gift of Nature and 5/5 Empowered Rejuvenation: ~0.45
Args, accidentally submitted the wrong email adress in the post above so Gravatar did not recognize me any more.
9:50 am on 3/9/08Just an FYI, I think you meant to say 2-piece T5. Two piece T6 reduces the swiftmend cooldown.
3:38 pm on 3/9/08@Ermengol: I’d love to hear your thoughts on my most recent article. As a historical proponent of the use of Regrowth, I bet you’re hopping up and down with excitedment over the reduced mana cost!
@Nebelmond: You rock. Thank you for this addon. I can’t wait to try it out for myself!
@Kalaghan: Thanks for the correction! I’ve edited the post.
10:44 pm on 3/9/08Wow, this was an interesting experiment.
Over 100 casts, my low was 1984 and the high was 2135. This is with my +1602 healing, and every healing talent you can get (1/0/60 here).
Two things that I found really interesting while casting was how often I was getting a critical heal, and the proc of my t4 bonus. It took me 407 casts to get 100 non-critical heals. That’s with 5/5 Improved Regrowth, but still that’s much better than the 50% I was expecting (I have only a 10.93% base crit bonus).
I wasn’t so excited to see that in those 407 heals, I gained the 120 mana from “infusion” from my t4 2-pc bonus set only 7 times. At one point I had 76 casts in between infusions. At only 120 mana per infusion, I’m not going to lose much sleep when the decision to replace t4 pieces and lose that bonus comes up.
3:52 am on 3/10/08@Leighbra on T4 set bonus, yeah… The set bonuses for T4 are allmost worthless. I never even took T4 healing gloves over the non tier kara gloves because of that. Two of my close friends had reported that their mana procs never did…well…porc and that the set bonus was not worth it. I must allso add that after getting my T4 shoulders, gloves, and pants for my offspec balance set that it allmost never procs for balance as well. At least the Balance 4 piece bonus actually might be used at some point, at least it used to be usfull back when we actually worried about mana. =P
3:56 pm on 3/16/08Your testing (and others) pretty clearly shows untalented regrowth coefficients are very nearly 30% for the direct heal and 70% for HoT.
Theorycraft for “pure” direct spells says a direct spell’s coefficient is (cast_time)/3.5, using untalented cast-times. Instant-casts use a “cast-time” of 1.5s. HT and SF both get 100%. Wrath gets 2/3.5 = 57.1%.
Theorycraft for “pure” HoT/DoT spells says the coefficient is duration/15. Rejuv gets 80%. IS would also get 80%, but it is “penalized” 5% because in addition to doing damage, it applies an extra debuff to the target. As a result IS gets only 80%*95% = 76%.
For hybrid spells (MF, Regrowth) the computation involves two steps. First compute the coefficients for both parts as-if they were pure spells:
Direct
MFA = 1.5/3.5 = 42.9%
MFB = 12/15 = 80%
RgA = 2/3.5 = 57.1%
RgB = 21/15 = 140%
The coefficients then get reduced by a proportioning rule. wowwiki (http://www.wowwiki.com/Formulas:Plus_damage_and_Plus_healing) currently says the proportioning rule is based on the numbers above meaning
MF direct = MFA * MFA/(MFA+MFB) = 52.1%
MF dot = MFB * MFB/(MFA+MFB) = 15.0%
Rg direct = RgA * RgA/(RgA+RgB)= 16.6%
Rg hot = RgB * RgB/(RgA+RgB) = 99.4%
The MF numbers look pretty good, but as you pointed out, the Rg numbers are way off. Elitist Jerks says the correct proportioning rule is based on base damage, not time. That means
MF direct = MFA * 331/(331+600) = 15.2%
MF dot = MFB * 600/(331+600) = 51.6%
Rg direct = RgA * 1285/(1285+1274) = 28.7%
Rg hot = RgB * 1274/(1285+1274) = 69.7%
Those numbers look pretty good for both spells. Maybe if your +heal is high enough, you can tell if the Regrowth ticks are using a 10% or a 69.7%/7=9.957% coefficient.
Note that some spells just seem to break the rules. Lifebloom doesn’t seem to fit at all, although pre-nerf the bloom coefficent was pretty close to what you’d expect from an instant cast direct heal (1.5/3.5 = 42.9%).
I love your writing. It is the only resto blog this featherkin reads on a regular basis.
8:48 am on 4/15/08Wow, thanks Erdluf! I may actually have to bookmark your comment for future reference. Glad you enjoy the blog!!
11:42 am on 4/15/08