Posts Tagged ‘nerf’

Mana Regeneration

@wowwiki

Spirit-based regeneration

The main base stat which regenerates mana is spirit. To a lesser extent, intellect also contributes, and the character level adversely affects regeneration. It’s a good rule of thumb to assume that 1 spi = 1 mp5 while not casting.

 MP5 = 5 * (0.001 + sqrt(Int) * Spirit * Base_Regen) rounded up

Base Regen lvl 80: 0.005575

705px-mp5-chartChart

The above chart was generated using this data. The formula shows that regeneration increases linearly with spirit and with the square root of intellect. The base regeneration goes down as level increases. When analyzing the plot it appears that levels 1-10 have one curve, 11-60 another and 61-70 have a jagged but almost linear decrease which seems to have been tweaked by hand.

Together these design elements seem to enforce balanced stats, so that stacking spirit to the detriment of intellect is to be avoided. It seems that 1 spirit = 1 MP5 was the target of the game designers. A level 70 caster needs about 460 intellect to reach this point.

Five Second Rule

After a character expends mana in casting a spell, the effective amount of mana gained per tick from spirit-based regeneration is reduced (interrupted) for a period of 5 seconds. This is commonly referred to as the five second rule (FSR).
Channeled spells are handled a little differently. The FSR starts when the spell’s channeling starts; i.e. when mana is expended. The interruption continues for at least five seconds, and longer if the channeled takes more than five seconds. For example, Mind Flay channels for 3 seconds and interrupts regeneration for 5 seconds (from the moment the spell cast starts), while Tranquility channels for 10 seconds and interrupts regeneration for the full 10 seconds, but not longer.
By default, the interrupted mana regeneration ratio is 0%. Several effects can increase this ratio, including:

Spells which don’t cost mana do not start the FSR. This includes spells with a normal mana cost of zero (e.g. Nature’s Swiftness), but also spells whose effective cost is reduced to zero by some effect (e.g. by Clearcasting or an item ability or proc like Eye of Gruul).

Effect Interrupted mana regeneration ratio increase
Intensity  10%-30%*
Innervate 100% (and increases mana regeneration to 500%)

 

Direct regeneration

Many effects increase mana regeneration directly i.e. without increasing spirit. These effects are governed by different rules than spirit-based regeneration, in particular they’re never subject to the five second rule.

The most frequent source of non-spirit-based regeneration is the “regenerates X mana in 5 seconds” stat on items. This stat is usually written abbreviated as “mp5”.

Comparing spirit based and direct regeneration

In theory, direct regeneration is preferable as it is not subject to the FSR. Unfortunately though, mp5 is much harder to get and more “expensive” than spirit. All attributes have an Item Value, a kind of “cost” associated. This value for mp5 is 2.5 times higher than for spirit. For example the two top mana regeneration enchants for chest items yield either 15 spirit or 6 mp5 ([Enchant Chest – Major Spirit] and [Enchant Chest – Restore Mana Prime]) – this shows the factor of 2.5 very clearly.

In order to find out what’s better, characters should first find out their personal time spent inside the FSR, e.g using an addon like Muse or RegenFu. It’s important to perform the measurement under realistic conditions – the time spent inside the FSR while grinding is typically much lower than during a boss fight. Some players actually argue that in a tight situation, it’s safe to assume that the FSR is in effect 100% of the time. It is possible to calculate the percentage of time which has to be spent outside the 5 second rule so that 2.5 points of spirit are more effective than 1 point of mp5. Examples:

Average lvl 70 priest with maxed Meditation: 2.5 spirit return 2.5 mp5 outside the FSR, and 0.75 mp5 inside. The mathematical form of the question is thus

2.5 * x + 0.75 * (1 - x) = 1
1.75 * x = 0.25
x = 0.14

So if that priest spends 14% percent of the time outside the FSR, the enchant with 15 spirit yields a higher regeneration than 6 mp5. If the time inside the rule is 86% or more, 6 mp5 is more efficient.

For lvl 70 characters without spirit regeneration inside the FSR:

2.5 * x = 1
x = 0.4

That is they have to spend 40% of their time outside the rule for spirit to be better than mp5.

MP5 vs Intellect and Spirit – Formulas

The following formulas relate intellect, spirit, and mp5 to mana regen both in and out of FSR in an attempt to help establish a relative value between them depending on your current stats.

Based on the formulas for spirit-based regeneration above…

ManaRegen(Int,Spirit,MP5) = [0.001 + sqrt(Int) * Spirit * 0.005575] * 5 + MP5 ManaRegenCasting(Int,Spirit,MP5) = [0.001 + sqrt(Int) * Spirit * 0.005575] * 5 * Coeff + MP5 where Coeff is the decimal percentage of spirit-based mana regeneration that is allowed to continue while casting

The mana regen benefit per 1 point increase of Spirit, Intellect, or Mana/5 can be calculated as…

While not casting:
 NC_RegenPerInt = 0.027875 * Spirit * [sqrt(Int+1) - sqrt(Int)]
 NC_RegenPerSpirit = 0.027875 * sqrt(Int)
 NC_RegenPerMP5 = 1

While casting:
 C_RegenPerInt = Coeff * NC_RegenPerInt
 C_RegenPerSpirit = Coeff * NC_RegenPerSpirit
 C_RegenPerMP5 = 1

As you can see, MP5 is the only stat whose effect remains constant both in and out of casting. If you have no talents allowing mana to regenerate from spirit while casting, MP5 is the only way to do so. Even with them, MP5 is still quite valuable, given the most common of these effects (listed above) cap at 30% spirit-based regeneration.

Multiple ratios do stack, but can never exceed 100%.
 

Formula

Research by Whitetooth[1] shows that since Patch 2.4, mana regeneration is uniform across all classes and based on the following formula:

Mana Regen = 5 * sqrt(Int) * Spirit * Base_Regen In effect, the regeneration rate depends on Int, Spirit and character level. A 1% increase in Spirit increases mana regeneration by 1%, and 1% Intellect yields 0.5% more regen. This is a rough rule of thumb, but is accurate enough for most situations.   Intellect doesn’t influence mana regen linearly, rather the square root of Intellect is used. This means that higher Int values yield diminishing returns, as can be seen in the following table:

Intellect vs Spirit Coefficient

intsprcof

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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.”