Restoration Glyphs - Page 13

Paininabox · 05/14/09, 9:44 PM

Originally Posted by Rijndael

Ok, let's do a little math.

Let's assume your crit values, 45% for Nourish, and 18% for GHT. We get an average healing value for Nourish of 0.45 * 1.5x + 0.55 * x = 1.225x. We get an average healing value for GHT of 0.18 * 1.5y + 0.82 * y = 1.09y. I claimed non-crit GHT heals for as much as non-crit nourish with 2 hots on target. Glyphed nourish will be boosted by 2 hots by 1.2 * 1.12, so say y =~ 1.344x. Solving, we get that GHT hits for 1.09 * 1.344 x = 1.465 x > 1.225 x.

If we also assume living seed will always be used, we get an additional 0.45 multiplier on crits. Redoing our calculations, we get:
0.45 * 1.95x + 0.55 * x = 1.4275x for Nourish and 0.18 * 1.95y + 0.82 * y = 1.171y for GHT. Solving, we get that GHT hits for 1.171 * 1.344 x = 1.574x > 1.4275x. (This is given a wildly unrealistic assumption of not wasting either the crit value or the living seed).

Nourish gets a 20% casting boost if spammed almost all of the time, which still puts it behind GHT casting time.

This is all assuming expected values, which we both agree is not a good way of estimating burst healing value, since if you do you end up gambling with your raid members' lives too much. A much better way, in my opinion, of estimating burst healing value is to look at the worst case, which is the minimum healing value and worst possible casting time. Since Nourish heavily relies on crit-luck for its HPS, it doesn't do very well in the worst case.

On the other hand, all of these disadvantages of Nourish go away when used on the tank.

edit: fixed calculations to account for the multiplicative nature of the glyph, per correction in subsequent post.

The problem with these calculations is that it pivots on your being right that one glyphed HT cast = a 2 hot'd nourish. So, I crunched the numbers on your gear setup in a raid environment:

HT crit: 18.02%
Nourish crit: 43.02%
SP: 2664

Average non-crit nourish (no hots)= (2035+0.69*SP)*GoN*ToL*MS= 4696
Average non-crit glyphed HT= (4100.5+(1.62*ET)*SP)*GoN*Glyph*ToLheal*MS= 6149
Average nourish crit: (4696)*LS*1.5= 9157
Average glyphed HT crit: (6149)*LS*1.5= 11990

Average glyphed HT hit: 11990*.1802+6149*(1-.1802)= 7201
Average nourish hit (no hots): 9157*.4302+4696*(1-.4302)= 6615

What this shows is that even without hots, nourish is approximately even, though below, HT. At less extreme gear levels, nourish will be at least equal if not more than HT. The reason this occurs is that HT has a stronger coefficient, which allows it to scale past nourish. I calculate that with a plethora of raid buffs, 2k SP is the point at which HT scales higher. Unbuffed, it jumps to 2072. It does strongly show that there's no way in hell that nourish won't be leagues better at 2 hots. However, this is all irrelevant since we have already decided that one shouldn't count on crits in burst scenarios. When I said "does not void my argument", I meant the part about you don't need glyphed HT if your raid doesn't ride the short bus. Nourish does just fine in 80% of near death cases, SM and NS+HT cover another 10%, and other raiders can be expected to cover at least 9% if not the rest. Of course these numbers are completely arbitrary, but they feel right to me. Thus, you're left with only a small portion of all situations of near death as possible candidates for justifying having a glyphed HT. In my opinion, I'd rather take that small chance to take other talents/glyphs to improve my healing overall instead of a small amount of the time.

EDIT: I'll fix my conclusions later.

Erdluf · 05/14/09, 10:25 PM

A possible point of confusion:

Paininabox (and Norfair in the first post of the Itemization thread) show ET as being additive with the untalented and unglyphed HT coefficient.

Wowwiki, and Rawr source code both show it being Multiplicative. I couldn't find any raw test data, so I don't know which is right. It changes the calculated value for non-crit GHT by about 11% of your SP (very rougly 300 healing using Pain's SP of 2664) which might be adding to the confusion here.

Test results anyone?

Paininabox · 05/14/09, 10:46 PM

Originally Posted by Erdluf

A possible point of confusion:

Paininabox (and Norfair in the first post of the Itemization thread) show ET as being additive with the untalented and unglyphed HT coefficient.

Wowwiki, and Rawr source code both show it being Multiplicative. I couldn't find any raw test data, so I don't know which is right. It changes the calculated value for non-crit GHT by about 11% of your SP (very rougly 300 healing using Pain's SP of 2664) which might be adding to the confusion here.

Test results anyone?

Well, from the way ET is worded, I think it supports additive. "Your Healing Touch spell gains an additional X% of your bonus healing ". Mathematically, I think it would look like:

(Base heal + Coef*SP + ET*SP)
simplified:
(Base heal + (Coef + ET)*SP)

EDIT: I found out that the priest talent, empowered healing, which is worded identically to ET, is additive.

"The final formula for computing benefit to a Greater Heal from Empowered Healing with Cast Time coefficients:

[ Base_Healing_Range + HSE * 3.0/3.5 + 0.40 * spellpower]" Source: http://elitistjerks.com/f77/t54618-w...craft_dargons/

"Your Greater Heal spell gains an additional 40% and your Flash Heal and Binding Heal gain an additional 20% of your bonus healing effects."

Erdluf · 05/14/09, 11:00 PM

I agree that the ET wording is also very similar to the Balance WoC wording, and it is additive. However, tooltips can sometimes be misleading, so testing is good. I also couldn't tell what formula Rij is using.

Rijndael · 05/15/09, 1:02 AM

Originally Posted by Paininabox

It does strongly show that there's no way in hell that nourish won't be leagues better at 2 hots.

Look guy, it's very easy to log in and check how much Nourish + 2 hots hits vs GHT without raid buffs. I did it before I posted. With raid buffs GHT only gets stronger because of better scaling.

Paininabox · 05/15/09, 1:25 AM

Originally Posted by Rijndael

Look guy, it's very easy to log in and check how much Nourish + 2 hots hits vs GHT. I did it before I posted.

I apologize for the tone, but my calculations say that it is so. I'm not saying that they're infallible, but I don't currently have any reason to believe that they're wrong. I checked in-game on my doll and they seem right. The only thing I can think of that got this screwed up was that your low-bound non-crit 2 hot'd nourish is 5740 and your non-crit glyphed HT max is 5715, so I can see how you might have gotten some statistical anomalies that made it seem like they were approximately equal.

EDIT: I'm going to test empowered touch and see if it's multiplicative or additive.

Data set: 32 entries
Min: 5159
Max: 5581
Mean: 5379
Median: 5399

Min Co-ef: ((5159)/(MS*ToL*Glyph*GoN)-3761)/1993=2.382
Max Co-ef: ((5581)/(MS*ToL*Glyph*GoN)-4440)/1993=2.391
Mean Co-ef: ((5379/(MS*ToL*Glyph*GoN)-4100.5)/1993=2.394
Median Co-ef: ((5399/(MS*ToL*Glyph*GoN)-4100.5)/1993=2.410

Average Co-ef: 2.394
(2.394)/1.4= 1.710
vs.
2.394-.4= 1.994

Base co-ef= 1.62

Conclusion: It's pretty obvious that ET is multiplicative from these data. My apologies to Rijndael and thanks to Erdluf for bringing that to my attention. I'll go back and fix those calculations from the previous post.

Erdluf · 05/15/09, 11:16 AM

Originally Posted by Paininabox

Average Co-ef: 2.394
(2.394)/1.4= 1.710
vs.
2.394-.4= 1.994

Base co-ef= 1.62

Conclusion: It's pretty obvious that ET is multiplicative from these data. My apologies to Rijndael and thanks to Erdluf for bringing that to my attention. I'll go back and fix those calculations from the previous post.

Actually, that gap between 1.71 and 1.62 is a lot bigger than we should be seeing. Theorycrafting can usually get those gaps down to something less than 1%.

ET is boosting the coef from about 1.62 to about 2.386. That is a multiplier of 1.47, a lot more than the tooltip.

I played around with different formulas, trying to get a better match. The best I could come up with was

40% boost is in +Heal terms (not +Spell terms).
Conversion from +Heal to +Spell is about 1.89 (for instance, a 3s heal in BC would have a +heal coefficient of 3/3.5. HT has a coefficient of 1.62. 3/3.5*1.89 = 1.62).
40%*1.89 = 75.6%

162%+75.6% = 237.6%

That is pretty close to Pain's test value (which I'd put at 238.65% +/- 0.35%).

It doesn't really matter whether you add 76% or multiply by 1.47. Do it either way and you'll match Pain's numbers. However, just multiplying by 1.4 doesn't seem to be enough.

HT ranks 1-3 have shorter cast times and presumably different coefficients. Assuming the old downranking penalties have been removed (they don't seem necessary with level mana costs), they could be used to explore the behavior in more detail.

Rijndael · 05/15/09, 2:34 PM

Very interesting. I made no serious attempts to confirm that existing understanding of coefficients from talents and glyphs actually matched what was happening in game. I am glad we are having this conversation! Unfortunately, there doesn't seem to be an explanation which doesn't involve someone at Blizzard overlooking the Empowered Touch talent, so the current behavior is unlikely to stay. If Empowered Touch is brought in line with other similar talents, it is likely the Healing Touch glyph will lose most of its usefulness.

edit: Thanks for the hard work testing this, Pain!

Paininabox · 05/15/09, 4:18 PM

Originally Posted by Erdluf

Actually, that gap between 1.71 and 1.62 is a lot bigger than we should be seeing. Theorycrafting can usually get those gaps down to something less than 1%.

ET is boosting the coef from about 1.62 to about 2.386. That is a multiplier of 1.47, a lot more than the tooltip.

I played around with different formulas, trying to get a better match. The best I could come up with was

40% boost is in +Heal terms (not +Spell terms).
Conversion from +Heal to +Spell is about 1.89 (for instance, a 3s heal in BC would have a +heal coefficient of 3/3.5. HT has a coefficient of 1.62. 3/3.5*1.89 = 1.62).
40%*1.89 = 75.6%

162%+75.6% = 237.6%

That is pretty close to Pain's test value (which I'd put at 238.65% +/- 0.35%).

It doesn't really matter whether you add 76% or multiply by 1.47. Do it either way and you'll match Pain's numbers. However, just multiplying by 1.4 doesn't seem to be enough.

HT ranks 1-3 have shorter cast times and presumably different coefficients. Assuming the old downranking penalties have been removed (they don't seem necessary with level mana costs), they could be used to explore the behavior in more detail.

Yeah, I noticed that there was a bit too large a difference, as well. I think the sample size might have been too small, so I re-ran the test to 100 casts, and here are my calculations:

Data set: 100 entries
Min: 5126
Max: 5570
Mean: 5337
Median: 5322

Min Co-ef: ((5126)/(MS*ToL*Glyph*GoN)-3761)/1984=2.366
Max Co-ef: ((5570)/(MS*ToL*Glyph*GoN)-4440)/1984=2.392
Mean Co-ef: ((5337/(MS*ToL*Glyph*GoN)-4100.5)/1984=2.370
Median Co-ef: ((5322/(MS*ToL*Glyph*GoN)-4100.5)/1984=2.357

Average Co-ef: 2.371
(2.371)/1.4= 1.693
vs.
2.371-.4= 1.971

Base co-ef= 1.62

Erdluf · 05/15/09, 4:58 PM

Another possibility that gets within 1% of both of your sets of numbers (I'm just looking at min/max results):

ET is additive. HTGlyph is additive with GoN, giving a formula of

Non-crit heal = (base+(1.62+ET)*SP)*MS*ToL*(1-0.5+0.1)

This is not as far-fetched as it seems:
GoN is additive with Genesis and IR
Insect Swarm Glyph is additive with Genesis
Moonfire Glyph is additive (and subtractive for direct-damage) with Moonfury, Improved Moonfire, and Genesis

This should be relatively easy to prove or disprove since it changes both the base and the scaling.
You can test at zero SP, in caster form. One formula gives Base*.5, the other gives Base*.6, a difference of roughly 400 healed.

It seems likely that blizz would not consider this to be a bug (HTG behaving similar to ISG and MFG)

Paininabox · 05/15/09, 5:49 PM

Originally Posted by Erdluf

Another possibility that gets within 1% of both of your sets of numbers (I'm just looking at min/max results):

ET is additive. HTGlyph is additive with GoN, giving a formula of

Non-crit heal = (base+(1.62+ET)*SP)*MS*ToL*(1-0.5+0.1)

This is not as far-fetched as it seems:
GoN is additive with Genesis and IR
Insect Swarm Glyph is additive with Genesis
Moonfire Glyph is additive (and subtractive for direct-damage) with Moonfury, Improved Moonfire, and Genesis

This should be relatively easy to prove or disprove since it changes both the base and the scaling.
You can test at zero SP, in caster form. One formula gives Base*.5, the other gives Base*.6, a difference of roughly 400 healed.

It seems likely that blizz would not consider this to be a bug (HTG behaving similar to ISG and MFG)

That seems plausible. Gift of Nature has always been weird with other multipliers. I'll go test it and get back with my results in a bit. Using this theory, it would predict that without GoN the average hit will be 83% of a GoN'd glyphed HT.

Data set: 100 entries
Min: 4275
Max: 4645
Mean: 4455
Median: 4448

Min Co-ef: ((4275)/(MS*ToL*Glyph)-3761)/1984=2.014
Max Co-ef: ((4645)/(MS*ToL*Glyph)-4440)/1984=2.010
Mean Co-ef: ((4455/(MS*ToL*Glyph)-4100.5)/1984=2.007
Median Co-ef: ((4448/(MS*ToL*Glyph)-4100.5)/1984=2.001

Average Co-ef: 2.008
(2.008)/1.4= 1.434
vs.
2.008-.4= 1.608

Base co-ef= 1.62

Problem solved. ET is additive then, but glyph is also additive with GoN. Thus the formula is:

Avg non-crit HT= (4100.5+(1.62+ET)*SP)*MS*ToL*(1+GoN-Glyph)

Well spotted, Erdluf. This has some interesting ramifications on the worth of the spell. I'll do some follow-up after I fix this.

Harmankaya · 05/17/09, 11:55 AM

Math aside, I just swapped out my Nourish-glyph back to Regrowth. My reasoning behind this is: I use Nourish actively (so that it feels nice to have it maxed) when I run content I massively outgear anyways (solohealing naxx10, maly10 comes to mind).
However, in the content where I need to push my char to the limit (the fight that eventually made me swap was Mimiron10 hardmode, allthough Freya25 2, council10/25 hard and Hodir25 contributed) Nourish is a spell that remains unused. We got other healers for that stuff, I need to spread hot-love around.
Don't get me wrong, I love Nourish, but yeah, you know what I mean.

I healed with another tree (a guildie), and without any sort of arrangement beforehand - he healed with Rejuv/WG/Nourish - in that order (%-wise), and I healed with Rejuv/Regrowth/WG - in that order.
In a fight where everyone needs healing, all the time - it was creepy how close to eachother we ended each fight/attempt on a fight on effective healing (+/- 1%), with pretty different strategies.

When I noticed 81% of my Regrowth-healing was from the hot, I decided to switch. The Nourish-glyph is really nice, but as I keep convincing myself - When I actually need it, I'm in a place I outgear. If it's cutting-edge progression, I will always have a paladin or two running around. To have the option of a 20% stronger regrowth-hot is something I realized I wanted healing Mimiron10hard.

Anyone else done this?
I have no idea if I will be happy with this result, but I feel I owe it to the once amazing glyph to try - the Nourish-glyph just seems so ... obscenely situational.

Rijndael · 05/17/09, 2:03 PM

Originally Posted by Harmankaya

The Nourish-glyph is really nice, but as I keep convincing myself - When I actually need it, I'm in a place I outgear.

A lot of raid damage in Ulduar is not well suited to be healed by a druid. As such, druids often find themselves assigned to tanks. When that happens, you want the Nourish glyph. My experience is the precise opposite of yours, actually. When I am healing tanks in a place I outgear my hots tick for so much relative to the damage that I don't need to use Nourish on the tank. But for something like General or Mimiron Plasma, it's hard to get by without Nourish.

I used to think I would carry two sets of glyphs -- one set for tank healing and another for raid healing. Eventually I ended up not doing that, partly because there are so few genuinely good glyphs, and partly because druids are well suited to the 'swing healer' role where you spend part of your attention on the tank and part on the raid in a single encounter.

Nut · 05/17/09, 2:55 PM

Originally Posted by Rijndael

A lot of raid damage in Ulduar is not well suited to be healed by a druid. As such, druids often find themselves assigned to tanks.

Your opinion is not shared by many. In the future, please back up such generalizations in order to help avoid spreading misinformation to decision makers that don't play resto druids but read EJ forums to keep themselves informed (guild masters, raid leaders, etc.).

Harmankaya · 05/17/09, 7:21 PM

My thought exactly. I generally heal my fair share on the tanks, but I never ever get assigned to one. Raid healing's where it's at, and I rock at doing it. We rarely use more than 5 healers (2 palas, 3 raidhealers), and so far we're coping really, really well.

The only real tankhealing I do in Ulduar (with actually weaving in some sort of direct heal) is Vesax & Plasma blast, and it feels just right this way.