Posts Tagged ‘Strat’

Healing Comparison

@wowwiki
  
hpmtabletalented
   
Spell  The name of the healing spell.

Healing  The average amount of healing done by the healing spell.

Mana  The mana cost of the spell

Cast time  The amount of time it takes to cast a spell.

Duration  The duration of Heal over Time type spells or a conservative guess for spells with multiple charges.

Scaling  The percentage of bonus healing effects from gear the healing spell recieves. See Spell power coefficient for a full list.

HPS  Healing per second; the amount of healing the spell does over a period of one second.

HPM  Healing per mana; the amount of healing this spell does per point of mana spent.

+x HPS  The healing per second when you have a total of x bonus healing from gear and/or buffs.

+x HPM  The healing per mana when you have a total of x bonus healing from gear and/or buffs.

SPS  Scaling per second; a value that says something about how well the HPS of the spell improves with bonus healing effects. a value of 100% means that 3.5 bonus healing increases the HPS by 1.

+H/HPM  Bonus healing per HPM; the amount of bonus healing needed in order to increase the HPM of the spell by 1. 
  • Healing spells that heal the entire group, heal an average of 3 wounded units.
  • The healers have 300 intellect, 300 spirit and 5% base crit chance with spells. (edit: This assumption may result in bias because Paladin and Shaman healers have little use for Spirit and the spell crit chance of Paladin Healers is normally much higher.)
  • A bonus of 5% critical strike chance to healing spells results in an average of 2.5% more healing done.

 This is a comparison of most (if not all) healing spells of the four different healing classes. There are both values available for spells with and without talents. Each section is ended by a list of top healing spells in different categories.

Conclusions

  • Top HPS spells
    1. Tranquility
    2. Binding Heal
    3. Holy Light + BoL
    4. Prayer of Healing
    5. Holy Light
  • Top HPM spells
    1. Healing Stream Totem
    2. Lightwell
    3. Tranquility
    4. Lifebloom (stacked) – Tree of Life
    5. Lifebloom (single cast) – Tree of Life
  • Top HPS scaling spells
    1. Binding Heal
    2. Swiftmend (rejuvenation)
    3. Chain Heal
    4. Swiftmend (regrowth)
    5. Greater Heal
  • Top HPM scaling spells
    1. Healing Stream Totem
    2. Lifebloom
    3. Earth Shield
    4. Rejuvenation
    5. Flash of Light
  • Note: The author only counts one jump of Prayer Of Mending, ProM can jump up to five times. Seems inconsistent compared to Shaman’s chain heal where it is given credit for three.

 Caster Form

List of considered talents

  • Naturalist: -0.5 seconds Cast time for Healing Touch
  • Tranquil Spirit: -10% Mana for Healing Touch, Tranquility
  • Improved Rejuvenation: +15% Healing for Rejuvenation
  • Gift of Nature: +10% Healing for all spells
  • Empowered Touch: +20% Scaling for Healing Touch
  • Improved Regrowth: +50% Crit for Regrowth
  • Natural Perfection: +3% Crit for Healing Touch, Regrowth, Swiftmend
  • Empowered Rejuvenation: +16% Scaling for Rejuvenation, Swiftmend (Rejuvenation); +14% Scaling for Regrowth, Swiftmend (Regrowth); +10% Scaling for Lifebloom (single cast); +31.2% Scaling for Lifebloom (stacked)

Todo: Add a similar table that removes Empowered Rejuvenation, but adds Moonglow (-9% mana to HT, Rejuv, Regrowth) and Lunar Guidance (25% of Int is added to +Heal)

Tree of Life Form

List of considered talents

  • All talents of Caster Form
  • Tree of Life: -20% Mana for all spells; +86 Healing for all spells

Comparison

Our first table gives the figures for the spells assuming no +heal whatsoever. Time is cast time plus spell duration.

 

 

 

0 +heal
Spell Healing Mana Time HPM HPS Contribution from +heal
Healing Touch 2952 935 3.5 (3.0) 3.16 843.43 (984) 100%
Rejuvenation  1060 (1219)   415 12 2.55    (2.93) 88.33 (101.6 ) 80%
Regrowth 2559 675 23 3.97 111.3 100%
Lifebloom (sequential) 1680 220 7 7.63 124.7 86.1%
Lifebloom (3x refreshed) 702 220 6 3.19 117 52% ‘per stack'(effectivly 133%)

 

 

 

 

1000 +heal
Spell Healing Mana Time HPM HPS Contribution from +heal
Healing Touch 3952 935 3.5 (3.0) 4.22 1129 (1317) 100%
Rejuvenation 1860 (2139) 415 12 4.48 (5.15) 155 (178) 80%
Regrowth 3559 675 23 5.27 155 100%
Lifebloom (sequential) 1680 220 7 7.63 240 86%
Lifebloom (3x refreshed) 2039 220 6 9.26 340 52% ‘per stack'(effectivly 133%)

 

 

 

As can easily be seen, stacking lifebloom and keeping it stacked not only becomes highly mana-efficient: it’s healing per second also rises considerably. In practise, druids will stack 3 lifeblooms and a rejuvenation on the target, providing around 500 HPS, and use regrowth for additional bursts of healing. This is made even more mana-efficient by tree of life form, which reduces the mana cost of all these spells by 20%.

 

 So for zero +heal, casting lifebloom every 7 seconds provides the highest heal per mana. The picture changes dramatically when we have +heal, though.

 

 

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Coefficients

@wowwiki

coefficients

Direct (instant-effect) spells

Direct spells are spells that apply all the damage or healing at one time. That is, they have an instant duration. The amount of bonus damage or bonus healing depends on the cast time of the spell before any talents or abilities are applied to them. Spells with a cast time of less than 1.5 sec or greater than 7.0 sec are treated as having a cast time of 1.5 sec and 7.0 sec, respectively.

Direct Damage spells:

C = Cast Time / 3.5

Direct Heal spells:

C = (Cast Time / 3.5) * 1.88

Table of coefficients

Cast time Damage Coefficient Healing Coefficient
1.5- sec 42.86% 80.57%
2.0 sec 57.14% 107.43%
6.5 sec 185.71% 349.14%
7.0+ sec 200.00% 376.00%

As of Patch 3.0.2, it is necessary to multiply the results of the standard equations by a factor of approximately 1.88 for all healing spells. This is a proportionality constant introduced to account for the fact that bonus healing behaved differently from bonus spell damage prior to the patch, and took on a different range of values.

Direct (instant-effect) spells

Direct spells are spells that apply all the damage or healing at one time. That is, they have an instant duration. The amount of bonus damage or bonus healing depends on the cast time of the spell before any talents or abilities are applied to them. Spells with a cast time of less than 1.5 sec or greater than 7.0 sec are treated as having a cast time of 1.5 sec and 7.0 sec, respectively.

Direct Damage spells:

C = Cast Time / 3.5

Direct Heal spells:

C = (Cast Time / 3.5) * 1.88

Table of coefficients

Cast time Damage Coefficient Healing Coefficient
1.5- sec 42.86% 80.57%
2.0 sec 57.14% 107.43%
6.5 sec 185.71% 349.14%
7.0+ sec 200.00% 376.00%

Example calculation using Rank 11 (L80) of Fire Blast (Mage):

Cast Time = 0.0 (treated as 1.5)

C = 1.5 / 3.5
  = 42.86%

Examples of such spells include: Healing Touch (Druid), Greater Heal (Priest), Shadow Bolt (Warlock)

Some exceptions of this rule are:

Over time spells

Over time spells apply healing or damage over a period of time in ticks. The spell power coefficient depends on the duration of the over time effect.

Damage spells:

C = Duration / 15

Healing spells:

C = (Duration / 15) * 1.88

This coefficient applies to the entire duration of the spell. With a few exceptions, each tick receives an equal bonus. Therefore, the per-tick coefficient can be found by dividing the overall coefficient value by the number of ticks.

Prior to patch 2.0.1, there was a 100% cap on over time spells longer than 15 seconds. This cap has since been removed. There is no minimum duration cap for over time spells.

Table of coefficients

Duration Damage Coefficient Healing Coefficient
3 sec 20.00% 37.60%
6 sec 40.00% 75.20%
15 sec 100.00% 188.00%
18 sec 120% 225.60%
21 sec 140% 263.20%

Example calculation using Rank 15 (L80) of Rejuvenation (Druid):

Duration = 15
Number of Ticks = 5

CTotal = 15 / 15 * 1.88
   = 188.00%

CTick = CTotal / 5
   = 37.60% per tick

Examples of these spells include: Rejuvenation (Druid), Renew (Priest)

Some exceptions to this rule are:

Hybrid spells (Combined standard and over-time spells)

The bonus for spells that have both a direct and an over time component is divided between these components. Currently, the equations are unknown for hybrid healing spells. Several equations have been proposed, but none of them provide correct results for all (or most) hybrid spells. Because there are so few hybrid healing spells, it may be the case that their coefficients are not set by equations at all, but are chosen directly by the developers.

For hybrid damage spells, the equations are:

x = Duration / 15
y = Cast Time / 3.5

CDoT = x2 / (x + y)
CDD = y2 / (x + y)

CTotal = CDoT + CDD

Example calculation using the Rank 14 (L80) Moonfire (Druid) spell:

Duration = 12.0 sec
Cast Time = instant (treated as 1.5 sec)

x = 12.0 / 15.0 = 0.8000
y = 1.5 / 3.5 = ~0.4286

CDot = 0.80002 / (0.8000 + 0.4286)
   = 0.6400 / 1.2286
   = 52.09%

CDD = 0.42862 / (0.8000 + 0.4286)
   = 0.1837 / 1.2286
   = 14.95%

So the DoT portion of Moonfire (4 ticks) has a coefficient of 52.09% (~13.02% per tick). The DD portion has a coefficient of 14.95%. The total coefficient is 52.09% + 14.95% = 67.04%. This agrees very closely with the empirical values of 52% and 15%, respectively.

Examples of these spells include: Moonfire (Druid), Immolate (Warlock)

Exceptions to this rule include

Channeled spells

Channeled spells, like over time spells, have their benefit distributed over the entire duration of the spell. It is split evenly over each tick assuming that each tick causes the same amount of damage/healing. The duration of the spell cast time is used to calculate the total coefficient:

For damage spells:

CTotal = Duration / 3.5

For healing spells:

CTotal = (Duration / 3.5) * 1.88

For both:

CTick = CTotal / Number of Ticks

Example calculation using Rank 13 (L79) of Arcane Missiles (Mage):

Duration = 5.0
Number of Ticks = 5

CTotal = 5 / 3.5
   = 142.86%

CTick = CTotal / 5
   = 28.57%

Examples of these spells include: Hurricane (Druid), Arcane Missiles (Mage), Hellfire (Warlock). An exception to this rule is:

Area of effect spells

Area of Effect spells receive only 1/2 of the total bonus that they would if they were single-target spells. As with a direct spell, the cast time is used to calculate the coefficient. The 1.5 second minimum and 7.0 second maximum apply to area of effect spells.

Damage spells:

C = Cast Time / 7

Healing spells:

C = (Cast Time / 7) * 1.88

Table of coefficients

Cast time Damage Coefficient Healing Coefficient
1.5- sec 21.43% 40.29%
2.0 sec 28.57% 53.71%
6.5 sec 92.861% 174.57%
7.0+ sec 100.00% 188.00%

Example calculation using Rank 7 (L80) of Circle of Healing (Priest)

Cast Time = instant (treated as 1.5)

C = (1.5 / 7) * 1.88
  = 40.29%

Examples of these spells include: Arcane Explosion (Mage), Prayer of Healing (Priest), Circle of Healing (Priest)

In the Burning Crusade and patch 2.0 there is a diminishing return against multiple targets. That is, as the number of targets your spells affect increases, the less damage you will deal to them. The numbers for this mechanic aren’t yet known.

Rules for applying spell damage and healing

  1. Calculate spell time using the base spell cast time before talents and gear. (The in-game tool tip will include those bonuses; refer to WoWWiki’s spells section for base cast times for all spells.)
  2. Spells that take longer than 7.0 seconds to cast are treated as if their casting time was 7.0 seconds, and spells faster than 1.5 sec are treated as if their casting time was 1.5 seconds.
  3. Damage benefits are applied before any talents or buffs that may otherwise increase your spell damage.

Penalty rules

Spells learned before level 20

Many spells have multiple ranks. To avoid abuse of lower ranks to have a similar effect at a negligible mana cost, any spell learned below level 20 receives a large penalty. If such a spell has a shorter cast time than a higher rank, this is also taken in to account. This penalty can be calculated by subtracting 3.75% for each level lower than 20.

(20 - Level Spell is Learned) * .0375 = Penalty

Downranked spells

Main article: Downranking

Downranking, the act of purposefuly using a lower-rank cheaper spell, no longer has any mana benefit as of Patch 3.0.

Spells with additional effects

Spells with additional effects, like a slowing effect, receive a penalty for each effect. Typically the penalty is 5% per additional effect, but can vary according to the developers’ whims. For instance, here is the calculation for Rank 7 (L80) of Insect Swarm (Druid), which is an over time spell with a chance-to-hit debuff:

C = (12.0 / 15.0) * 0.95
  = 76.00%

Examples of these spells include: Blast Wave (Mage), Blizzard (Mage), Insect Swarm (Druid)

Spells that both damage and heal

Some spells, namely Life Drains, both damage the target and heal the caster. The bonus is split between the healing and damaging portion, roughly in proportion to the amount of healing and damage involved. That is, if a spell heals 4 points for every 1 point of damage, 1/5 of the spell’s bonus will go to damage and roughly 4/5 will go to healing. Because bonus healing does not apply to these spells, the 1.88 multiplier is not used for the healing portion.

Thus Drain Life’s bonus is applied 50%/50% to damage/healing, while Devouring Plague’s bonus is split roughly 75%/25%. The exact equations are unknown at this time, but a reasonably close answer can be obtained by:

CDamage = CTotal / (Damage Amount / [Damage Amount + Healing Amount])
CHealing = CTotal / (Healing Amount / [Damage Amount + Healing Amount])

Examples of these spells include: Devouring Plague (Priest), Holy Nova (Priest), Drain Life (Warlock)

How do talents like “Empowered Rejuvenation” Affect Coefficients?
The Empowered Rejuvenation talent reads:
Increases the bonus healing of your heal over time effects by 20%

What this means is that for all HoT effects, you take your current +healing and add 20%. So if you had 1000 +healing, your HoTs would act as though you had 1200 +healing.

Gift of Nature increases the effect of all healing spells by 10%. Does this stack with +healing?
Yes.

For example, if your healing touch would normally heal for 2800, and you had a 1000 +healing, then here’s what this talent would do for you:

 (2800 + 1000) x 110% = 4180

With Empowered Touch (+20% Bonus Healing on Healing Touch) and Gift of Nature, here’s how the math works out:

 [2800 + (1000 x 120%)] x 110% = (2800 + 1200) x 110% = 4400

Lifebloom : Numbers

@Wowforum

For an average boss fight of 5 minutes:

Pre-nerf:

1 LB stack = 366*3 = 1098 + 366 every 9 seconds (using LB glyph, but taking into account that we can’t time it exactly ms into ms to get full 10 sec out of it)

1098 + 366*300/9 = 13298 Mana spent per fight.

At 2100 +Healing in ToL hot heals for 1045, Blooms for 2900 (not letting it bloom)

1045*9 = 9405 healing per 9 seconds

9405*300/9 = 313500 Healing per fight.

313500/13298 = 23.57 HPM

GCDs spent: 3+1*300/9 = 37

Post-nerf:

1 LB stack = 732*3 = 2196

Keeping it up: 2196 + 732*300/9 = 26596 Mana per fight

313500/26596 = 11.78 HPM

GCDs spent: 3+1*300/9 = 37

Letting it bloom: 2196*300/10 = 65880 Raw mana spent; 65880/2 = 32940 Mana spent per fight

Healing for 1045*10 + Bloom for 2900*3 = 19150 per 10 seconds

19150*300/10 = 574500 per fight

574500/32940 = 17.4 HPM

GCDs spent: 3*300/10 = 90

 

@druid.wikispaces

+2195 Healing
Lb  1x Mana cost: 220 / 179
   Total Healing    3600
    HPM        16.4/20.5
    HPS        514
    HPSC      2400
    HPT        258
    Bloom        1695
Lb 2x Mana cost: 220 / 179
    Total Healing    3612
    HPM       16.4/20.5
    HPS        516
    HPSC       2408
    HPT        516
Lb 3x Mana cost: 220 / 179
    Total Healing    5418
    HPM        24.6/30.8
    HPS        774
    HPSC        3612
    HPT        774

Regrowth Mana cost: 845/676
    Total Healing    6418
    HPM        7.6/9.5
    HPS        305.6
    HPSC        3208.8
    HPT        490.5
    Direct Heal    2984
    Direct Heal %    46.5% 

Rejuvenation Mana cost: 415/332
    Total Healing    3959
    HPM      9.5/11.9
    HPS        330
    HPSC        2639.3
    HPT        990

Healing Touch (Mana cost: 841)
Total Healing    6834
Total Healing    ~6462
    HPM        8.1
    HPS        2278

Swiftmend (Rej)

Mana cost 379/303 + Lost ticks from consumed
    Total Healing    3959
    HPM        10.4/13
    HPS        2639.3

Swiftmend (Reg)

(Mana cost 379/303 + Lost ticks from consumed)
Total Healing    3434
    HPM     9/11.3
    HPS        2289.3

@hotrstree

A Few More Lifebloom Calculations from the PTR

Raaff (Druid Heal!) threw some Lifebloom numbers out there first, looking at its new efficiency and throughput. His post left me asking two questions:  
1. Does equipping 2pT7, which lowers the cost of Lifebloom have any affect on the amount of mana you get back when it blooms?
2. What is the throughput and efficiency of just Lifebloom? (Since Raaff’s calculations were for a full reasonable cast cycle.)
Averna (Nerf this Druid) ran some numbers on throughput of Lifebloom alone. Her calculations included the bloom portion. This left me asking:

3. In a worst case scenario, or most like the current situation scenario, the bloom will all be overheal. What does this mean for Lifeblooms efficiency and throughput?

Scroll to the bottom to skips mathz and see conclusions.

This post has been highly inspired by Raaff and Averna and may subconsciously draw from their work, although I did all my own number crunching using my gear. If you haven’t checked out their 3.1 PTR work yet, please do so.

Currently a Lifebloom cycle is 10 seconds long (with Glyph), costs 366 mana (with 2pT7), and a single Lifebloom ticks for 400 (for me), 800 for two, and 1200 for 3. I am going to ignore the mana cost and time to get the stack up, since most druids will not let that stack fall off the main tank.
Throughput:
1,200 HP ticks @ 1 tick/sec for 10 sec =
12,000 HP healed in a cycle
1,200 HP/10 sec = 1,200 HPS

Efficiency:
1 cast every 10 sec @ 366 mana/cast = 366 Mana spent in a cycle
12,000 HP/366 MP = 33 HPM
PTR Rolling (w 2pT7) The only change from the current numbers is that the cost will be 733 mana up from 366.
Throughput will remain the same: 1,200 HPS

Efficiency:
1 cast every 10 sec @ 733 mana/cast = 733 Mana spent in a cycle
12,000 HP/733 MP = 16 HPM
PTR Rolling (w/o 2pT7) The only change from the current numbers is that the cost will be 782 mana up from 366 (current) or 733 (w/ 2pT7).
Throughput will remain the same: 1,200 HPS

Efficiency:
1 cast every 10 sec @ 782 mana/cast = 782 Mana spent in a cycle
12,000 HP/782 MP = 15 HPM
PTR Blooming Overheal (w/ 2pT7) For this calculation I will assume that all of the Bloom over the healing done by a normal tick will go to overheal, since it is very difficult on most fights to predict damage 10 seconds into the future. A Lifebloom cycle is now 12 seconds long, since we need to rebuild our stack of 3. Half of mana refunded at the Bloom is equal to 1469 mana refunded.
Throughput:
1,200 @ 1 tick/sec for 10 sec = 12,000 HP
12,000 + 400
(1st tick) +800 (2nd tick) = 13,200 HP healed in a cycle
13,200 HP/ 13 sec = 1,015 HPS

Efficiency:
3 casts every 13 sec @ 733 mana/cast = 2,199 Mana spent in a cycle
2,199 mana spent – 1469 mana refunded = 730 Net Mana spent in a cycle
13,200 HP/730 MP = 18 HPM
PTR Blooming Overheal (w/o 2pT7) The same as the above calculation, except Lifebloom now costs 782 mana per cast.
Throughput will remain the same as above: 1,015 HPS

Efficiency:
3 casts every 13 sec @ 782 mana/cast = 2,346 Mana spent in a cylce
2,346 mana spent – 1469 mana refunded = 877 Net Mana spend in a cylce
13,200 HP/877 MP = 15 HPM
PTR Blooming Not Overhealed (w/ 2pT7) This is a calculation that is probably too good to be true. But once and a while we may get lucky and our entire bloom may go to effective healing. My bloom heals for 9703 HP.
Throughput:
400 (1st tick) + 800 (2nd tick) + 1,200*9 (ticks 3 though 11) + 9,703 (bloom) = 21,703 HP Healed in a cycle
21,703 HP/13 sec = 1,669 HPS

Efficiency:
3 casts every 13 sec @ 733 mana/cast = 2,199 Mana spent in a cycle
2,199 mana spent – 1469 mana refunded = 730 Net Mana spent in a cycle
21,702 HP/730 MP = 30 HPM
PTR Blooming Not Overhealed (w/o 2pT7) Same as above, but costs 782 mana per Lifebloom application.

 

Throughput will be the same as above: 1,669 HPS

Efficiency:
3 casts every 13 sec @ 782 mana/cast = 2,346 Mana spent in a cylce
2,346 mana spent – 1469 mana refunded = 877 Net Mana spend in a cylce
21,702 HP/877 MP = 25 HPM
Conclusions
1a. Equipping 2pT7 does not effect the amount of mana you get back when Lifebloom blooms. It was 1,469 mana returned with or without it. It makes casting Lifebloom 6% more efficient if you are rolling blooms and 20% more efficient if you are letting the blooms bloom. 4pT8 is going to have to be really really good to get Resto Druids to give up 2pT7.
2a. If your bloom is not overhealing, this will actually be a 39% buff to the throughput of Lifebloom. At least they threw us some consolation prize.
2b. Sadly, we are experiencing a 10% increase to the cost of Lifebloom. This is the best case scenario, if your bloom is going to effective healing.

3a. Throughput of Lifebloom ticks alone will drop 15%. This assumes all the bloom is overheal. I predict we will not notice any change in throughput for Lifebloom, since most of the time the bloom will be overheal, but once and a while it will actually contribute something. Your ability to predict the future… I mean damage… will make a big difference on how much of a nerf/buff this is to your Lifeblooms.
3b. The nerf could be as high as a 83% increase to cost. Again, your ability to predict the future will determine where you fall on the 10% to 83% cost increase spectrum. If you plan on rolling those blooms still, you are looking at a 106% increase, that you can do nothing about. Ouch!

Suggestions
1. Wear your 2pT7 until you absolutely have to break it. Make sure you are going into T8 with all 5 pieces of T7, even if you are not wearing them now. This will give you the most flexibility to keep the 2pT7 bonus as you pick up new pieces of gear after the patch.
2. Be prepared to not roll Lifeblooms. Start practicing now in heroics, 10 mans, and/or on 25 man trash. You have a bad habit to break, even though it was once good. This is like unlearning to brush your teeth in the morning and unlearning to put on your seat belt in the car. It will feel very very wrong, but it is the way to be mana efficient.
3. Whether this will be a nerf or a buff to your Lifebloom throughput and how badly of a nerf it will be to your efficiency will depend on your ability to predict damage. If you are not running BigWigs or Deadly Boss Mod timers, for heaven’s sake get them. Practice now watching cool downs on abilities and finishing the three stack (ie adding the final LB to a stack of 2) 10 seconds before you know the tank will take increased damage. Some fights this will be impossible. Other fights it will just be freaking hard.

Any questions/comment/complaints welcome as always. I did most of this math on a note card waiting for Watchmen to start (good movie!) so I am very open to “Aert, you can’t add here.”