Saturday 29 December 2012

5.2 Mindbender vs PW:Solace


      5.2 Mindbender vs PW:Solace

Ding Ding Ding!
The fight is back on between these two bad boy talents with Blizzard's new ideas as per priest regen patch 5.2, so let's have a look at the nitty-gritty maths (you can skip to the bottom if you just want to know who wins. That's cool.)

(This time we'll also consider the Hymn of Hope buff and how it affects both the new spells, which is a treatment we have not considered before. We will only consider your own HoH as you may not have control over the other priests in your raid.)

Mindbender Maths

Mindbender hasn't really changed, so I'll just give you the basic version:

The mindbender
  • replaces Shadowfiend,
  • restores less mana per hit back
  • only a 1 minute cooldown.
  • active for 15 seconds
  • attacks 11 attacks, with each attack restoring 1.46% mana.
Hymn of Hope has a 6 minute cooldown and a buff lasting 8 seconds – the buff increases your maximum mana by 15%, giving you 345000 max mana.

This means withing a 6 minute time period you will cast MB:
5 times without HoH buff, giving (5 * 11 * 1.46% of 300k) 240,900 mana back
Once with HoH buff for 8 seconds, giving (5 * 1.46% of 345k + 6* 1.46% of 300k) 51,465 mana back

So in a 6 minute period of the fight, you gain 292, 465 mana

Giving the MB talent a mp5 of 4,060.625

PW:Solace

The new solace:
  • will replace Holy Fire,
  • is instant cast,
  • has a 10 sec cd,
  • and restores 1% mana.

Solace will thus give an mp10 of 1% of 300k = 3k
and an mp5 of 1,500

This can be cast in conjunction with Shadowfiend, which:
  • has a 3 minute cd
  • restores 3% mana per attack
  • attacks 10 times

Mana back from shadowfiend:
Without HoH – 30% of 300k = 90 k mana
With HoH – 5 * 3% of 300k + 5 * 3% of 345k = 96,750 mana.
Over 6 minutes, Shadowfiend will restore: 186750 mana
Which gives it a mp5 of 2593.75

In total, with the PW:Solace talent, you gain an mp5 of 4,093.75

Comparison

You can come out now,all ye who hate theorycrafting ! Conclusion time.

MB talent - mp5 of 4,060.625
Solace talent - mp5 of 4,093.75


Thus you are going to get a very slight mp5 increase by taking Solace over MB. Whilst it uses 6 times the number of global cooldowns per minute compared to mindbender, Solace also provides an atonement heal.  Can't wait to find out which will be better !

Tuesday 18 December 2012

Disc Spell Book for Beginners


Disc Spell Book

Basics

Greater Heal
Pretty much our go-to heal for single target healing when Penance is on cooldown - usually tanks. Two heals of this will pretty much cap out Spirit Shell (see below).
Prayer of Healing
The bread and butter of disc raid healing. This heals everyone in a party, though The party members to have to be in range of your target. Can be used to cast through line of sight if a player is standing in such a way as being LoS of neither you nor the target. Casting this will always cause a divine aegis (shield, see below) which means it can be used to absorb predictable aoe. Particularly strong with Spirit Shell (see below).
Power Word: Shield (Weakened Soul)
Power Word: Shield is akin to another Flash Heal for us, is instant cast, and absorbs damage instead of healing it back up. This is amazingly useful for people soaking big hits (Gara'jal voodoo dolls, Wind Step targets on Blade Lord, debuffed targets on Protectors. However, casting PW:Shield on a target also causes a debuff called Weakened Soul, which prevents another PW:Shield being cast on the same target for the length of Weakened Souls duration.
Penance
This is a channelled heal with three ticks to it, and is the disc “token” spell. It can be used offensively on a hostile target to proc a stack of evangelism and an atonement heal, or defensively on a friendly target to give 3 stacks of grace and heal them. Incredibly strong heal-to-mana makes this particularly useful in single-target damage phases.
Prayer of Mending
Useful to cast-while-moving in heavy raid damage situations. This goes to the person you've specified and when they next take damage heals some of that up and then bounces to a nearby target.
Flash Heal
Useful in emergency situations if other healers are incapacitated/out of range, or in situations such as tank damage on Will of the Emperor. Burns mana like heck, so only use when necessary.
Smite
Our version of Heal – cast on hostile mobs, it procs “atonement” which heals a nearby injured raid member, acting as a smart heal, and grants a stack of Evangelism.
Holy Fire
Same as Smite, also puts a DoT (damage over time) on the boss.
Binding Heal
Pretty weak (despite being strong for holy)
Heal
Pretty wet noodle – never really use it when you can cast smite or holy fire (or penance).
Cooldowns


Inner Focus
Reduces the mana cost of Flash Heal/Greater Heal/Prayer of Healing by 25% and increases crit chance by 100%. Doesn't use a global so can be put into a macro with Prayer of Healing (see Macro section). Use pretty much on cooldown.
Spirit Shell
For 15 seconds, Heal/Flash Heal/Greater Heal/Prayer of Healing no longer heal, but instead create absorption shields for the amount they would have healed, that last 15 seconds. This means you can fully blanket two parties from predictable aoe (provided that they are reasonably close to each other), or save a tank from a one shot if he has high stacks of some debuff or other (most notably the former usage). This is the cooldown that makes disc so op at the moment, and you'll be pretty much using it as often as you can – especially since it has only a 1 minute cooldown. Some examples are given below.
Shadowfiend
Summons a pet that hits a mob and gives you 3% mana back each time it hits. Shadowfiend is pretty much immune to boss aoe, lasts 12 seconds and has a 3 minute cooldown.
Hymn of Hope
Channeled spell that returns 2% mana to 3 nearby low mana targets (friendly of course) every couple of seconds for ~ 8 seconds, depending on haste. It also increases their total maximum mana by 15% for 8 seconds (ie, if you have this buff, its a good time to use Shadowfiend/Mindbender. However, we must channel to keep casting, so attempt to use it when nothing you need to move out of is coming and you are unlikely to be stunned, feared or mindcontrolled.
Pain Suppression
3 minute cooldown. Reduces the targets damage taken by 40% for 8 seconds and their threat by 5% (pretty much nothing). Tanks will usually call for this, although if they don't ever use it, you should use it on them at your discretion, or even dps/healers who are about to take a lot of damage.
Power Word: Barrier
Summons a big dome that reduces damage done to friendly targets by 25% whilst within its range, and means that spellcasting is not interrupted by damage. The barrier lasts for 10 seconds and has a 3 minute cooldown. Useful for any situtation where the raid is stacked up or a certain group of the raid is stacked up and about to take mass damage (think Zor'lok, melee on Stone Guard, everyone on Gara'jal).
Archangel
Consumes Evangelism to increase healing by 5% for each Evangelism stack (maximum of 25% extra), lasts for 18 seconds with a 30 second cooldown. Lines up nicely with Spirit Shell – use once inbetween Spirit Shells and then every time with. Doesn't even need to by a 5 stack evangelism to be useful – every little helps.
Fear Ward
As the label says – wards a friendly target against fear. After consuming one fear, the buff will disappear. Has a 3 minute cooldown and duration. Useful on any boss that fears, including Empress 2nd phase, Zor'lok mindcontrols, Sha platforms (I use mine on the tank for Sha of Fear since they are the ones who have to run around and get hit all the time, picking up orbs). Casting Fear Ward on someone who already has the buff will simply refresh the duration, leaving both Wards on cooldown, and only consuming one fear.
Fade
Temporarily removes all threat for 10 seconds – after which it all comes back again. Pretty much never used – use when adds first spawn as necessary, examples; Empress, Lei Shi, Tsulong.
Purify
Dispels harmful magic and disease from friendly targets, 8 second cooldown, costs 7800 mana – use wisely. Most used on: Elegon, Protectors of the Endless, Tsulong, occasionally Sha. The hostile version of this spell is Dispel Magic, which costs 7,800 mana, and has no cooldown (used on Spirit Kings, Wind Lord and Protectors) – see macros.
Mass Dispel
Costs a ridiculous amount of mana – use with great care (ie, force boomkins (with symbiosis) and shadow priests to do it for you wherever possible). Uses up 39,000 mana – removes all harmful spells from 10 friendly targets and all beneficial spells on 10 enemy targets within its boundaries.
Leap of Faith
Moves the target from wherever they were to directly infront of you. Used to save lives on any boss with serious fire for the dps to stand in / dc'd persons to unwittingly stand in. Can be used during Spirit Kings to move pinned targets into melee to be cleaved down if all BoPs are on CD, for example.
Psychic Scream
Causes 5 enemies within 8 yards to flee for 8 seconds (damage will interrupt). Useful on Imperial Vizier Zor'lok (put it on cd and keep it on cd 3rd platform onwards), Lei Shi (keeps those nasty Protect adds away from you) and Will of the Emperor (forces fixated adds to rechoose their fixate.
Void Shift
You and your target swap health percentages, and increases the lower percentage of the two to 25% if it was previously below that. Useful in all emergency situations – just be careful not to kill yourself by using it before an aoe! Healthstones are definitely useful straight after using this – so is shielding yourself.
Symbiosis – Cyclone
Pretty much won't ever get symbiosis, which is sad. Its not amazingly useful and it certainly doesn't improve our quality of life. Safe to say you can quite happily never use it. On the other hand, balance druids receive mass dispel, Feral druids Dispersion, Guardian druids take Fear Ward and Restoration receive Leap of Faith, so they might give it to you for a particular boss if they require the spell you grant. I have had a total of one symbiosis whilst we were learning the Sha of Fear dance so the guardian druid could have fear ward. One pull. :(


Rapture

This passive gets a section all to itself, as it is crucial in understanding why disc is in such a strong place with mana right now. Rapture occurs when your PW:Shield is completely absorbed by damage (or dispelled in pvp). When this occurs, the caster recieves 200% of their spirit value as mana back. You do have to consider the mana cost of casting PW:Shield, so mana back per rapture is (2*spirit – 18300).
To make PW:Shield mana neutral you need only 9150 spirit.
Rapture has a 12 second cooldown, so having an addon to track the cooldown of rapture will greatly help with mana management – something like this.


Buffs

Inner Fire
Increase armor from items by 60% and spell power by 10%. You'll pretty much run with this all the time, unless your mana drops below 5-10%.
Inner Will
Reduces the mana cost of instant cast spells by 15% and increases movement speed by 10%. The movement speed increase does not stack with the boot enchant. Only useful in situations where you have no mana and want a Shield to grant rapture.
Power Word: Fortitude
Lasts 60mins, increases the stamina of all party or raid members by 10% – put up before combat, rebuff when someone is combat ressed.
Borrowed Time
15% spell haste for your next spell after casting Shield, lasts for 6 seconds. Glyphed Holy Fire (instant cast) consumes it. Casting penance does not consume Borrowed Time (neither does Renew) so you can always cast Penance(/Renew) straight after Power Word: Shield, and then use Borrowed Time for a Greater Heal, Smite or Prayer of Healing.
Grace
This buff stacks up to three times, and increases the healing done by you on the buffed target by 10% a stack (30% at 3 stacks). Penance applies three stacks of grace per cast – everything else only applies one stack per single target heal (not shield, renew, prayer of mending, atonement heals, etc
Evangelism
When you deal damage with Penance, Smite or Holy Fire, you gain a stack of Evangelism (max 5 stacks). This increases the damage done by those spells by 4% per stack, and reduces their mana cost by 6%. You consume these stacks when you use Archangel.
Divine Aegis
Critical heals (all heals from Prayer of Healing) create a shield which absorbs 30% of the amount healed, and lasts 15seconds. Divine Aegis caps at about 16% of your health (with no mastery) – will edit this once I work out the exact maths.

Passives

Focused Will
Whenever you are a victim of any damage greater than 10% of your total health, or critically hit by a non-periodic attack, you gain this buff. It reduces all damage taken by 10% and lasts for 8 seconds. Focussed Will can stack up to two, reducing damage by 20%. This is a very good passive for constant damage fights such as Garalon and focussed attacks such as Gara'jal.
Divine Focus
Reduces the pushback suffered from being attacked while casting by 70%.
Divine Fury
Gives us 100% hit for: Penance, Smite, Power Word: Solace, Cascade, Divine Star, Halo, Holy fire.
Meditation
Allows 50% of your mana regeneration from Spirit to continue while in combat.
Mysticism
Increases Intellect by 5%
Train of Thought
When you Greater Heal, you reduce the cd on Inner Focus by 5 secs; when you Smite you reduce the cd of Penance by 0.5 secs.


Talents

Tier 1 – Level 15

This is the crowd-control tier for priests.

Void Tendrils
Psyfiend
Dominate Mind
Works as a snare, rooting up to 5 mobs within 8 yards for 20seconds. Snares can be insanely dangerous in pve situations with lots of adds, as a snare causes the mob to ignore threat and instead hit whoever is close to it – oftentimes someone in cloth who will then die.
Useful on some encounters such as Will of the Emperor and Lei Shi. Instant cast, 10 second duration, 45 second cooldown. The Psyfiend will stand in place, fearing nearby enemies every 2 seconds. The mob remains feared for 30secs unless damaged. Pretty much works as a second Psychic Scream.
Pretty much useless for PvE encounters, although it is fun. Bosses are immune.

Tier 2 – Level 30

This tier is all about movement speed.

Body and Soul
Angelic Feather
Phantasm
Whenever you cast PW:Shield or Leap of Faith, you increase the targets movement speed by 60% for 4 seconds.
Advantages:
  • easily granted to specific target.
  • Strong for disc as its one of our token spells
Disadvantages:
  • Cannot be given to the same target twice (with PW:Shield) until Weakened Soul has run its duration.
  • Costs mana.
Places a feather at the target location, which will increase the movement of the next ally to walk through it by 60% for 4 seconds. Has a maximum of 3 charges, and once less than through a new charge is gained every 10 seconds.
Advantages:
  • Costs no mana
  • Can be placed in advance
  • Same target can be boosted 3 times in a row.
    Disadvantages:
  • Cannot be given to a specific target.
When you fade, you remove all movement impairing effects from yourself, you become untargettable by ranged attacks, and your movement speed is unhindered for 3 seconds.

Not really found a use for this one in PvE.

Tier 3 – Level 45

This is our mana tier. I have ignored the damaging version of thee talents, as this is not a consideration when choosing talents as discipline for PvE encounters.

From Darkness, Comes Light
Mindbender
Power Word: Solace
You have a 15% chance when you Smite/Heal/Flash Heal/Binding Heal/Greater Heal to cause your next Flash Heal to be instant cast and cost no mana. You can store up to two of these instant cast Flash Heals.
Whilst it obviously has great single target throughput, comparing this talent with the others in the tier means it is a weak mana management talent.
This replaces your Shadowfiend with the much superior mindbender that gives less mana back per hit but has only a 1 minute cooldown, meaning over the course of a boss fight, using mindbender on cooldown grants a lot more mana back than using shadowfiend on cooldown.
This is a spell with a 1.46 sec cast, which grants 0.7% mana back per cast. Whilst it is nice because it can be spam cast, it is nowhere near as strong as mindbender is.

Tier 4 – Level 60

And here comes the survivability!

Desperate Prayer
Spectral Guise
Angelic Bulwark
Costs no mana, heals for 30% of your hp instantly, 2 min cooldown. Although you need a global to cast this, the spell itself is off the global cooldown – similar to health stone.
Puts you in a form of stealth for 6 seconds, leaving a dummy you behind whilst you are free to move about (though still in combat). If the dummy gets hit twice you are removed from the stealth early.
Passive When a damaging attack brings you below 30% of your hp, you gain a shield equal to 20% of your health, which lasts 20 seconds. This shield has a 90 second cooldown.

Over 6 minutes Desperate Prayer is 90% of your hp, Angelic Bulwark is 80%.
Whilst bulwark is slightly less healing potential than Desperate Prayer, it has higher utility as it can proc while stunned, and while casting. Bulwark is also an sbsorb – the best kind of heal. However, this is fight dependent, and Desperate Prayer can be used in conjunction with Void Shift if you have no healthstones to make sure you don't commit suicide.

Tier 5 – Level 75

This is more of a throughput tier than anything else.

Twist of Fate
Power Infusion
Divine Insight
After damaging or healing a target below 20% health, you deal 15% increased damage and healing for 10 seconds. There are better options.
2minute cooldown, gives you 20% increased casting speed and reduces the mana cost of all spells by 20% for 20 seconds. Absolutely beautiful when lined up with Spirit Shell.
When you cast Penance, there is a 40% chance that your next PW:Shield will both ignore and not cause the Weakened Soul debuff – pretty useless since casting it on a target with PW:Shield already active simply removes the PW:Shiled they already had – nor does it give a new speed boost if you have Body and Soul spec'd.

Tier 6 – Level 90

Cascade
Divine Star
Halo
Cascade is very useful for spread out groups, as it heals more the further it travels. It costs the most to cast of the spells in this tier.
Divine star is good on stacked up fights as it heals everybody in a line. Its a long line. You will break cc if you are not careful, as it also deals damage.
The least useful talent of this tier is halo because in a stack-up situation you must be far away from the group you wish to heal. Halo however has the most theoretical output.



Tuesday 11 December 2012

Discussion of 2 and 4-set bonuses for Disc


Tier 14 Priest Two- and Four- set for Disc:

First a reminder of what the set bonuses are
2-set – Reduces the mana cost of your Flash Heal spell by 20%
4-set – Reduces the cooldown of your Penance spell by 4 sec.


2-set

Lets look at how this improves the HPM of flash heal:

2set
Heal
Cast Time
Mana Cost
HPS
HPM
Without
57890
1.44
17700
40201
3.27
With
57890
1.44
14160
40201
4.09

But let's compare this with other single-target heals(and ignoring binding heal's self heal):

Spell
Heal
Cast Time
Mana Cost
HPS
HPM
PW:Shield
93949
1
18300
93949
5.13
Binding Heal
40411
1.44
16200
28063 (56126)
2.49 (5.00)
Greater Heal
77202
2.4
17700
32168
4.36
Penance (glyphed)
67203
1.92
11160
35001
6.02

From a purely tank healing perspective, 2set flash heal is still really low hpm, although it is about 5-7k higher hps. However, disc's job at the moment (5.0.4) is to raid heal!

Now have a look at some logs, see whether disc priests are actually using fheal (chosen at random), and show how much mana having 2set would/did save them:

Imperial Vizier Zor'lok:

Name
Guild
Number of Flash Heals
Mana saved
% of Healing
Arnymacsek
Grim Funeral
1
3540
0.1
Medii
Midwinter
0
/
0
Shibo
Insomnio
8
28320
2.3
Sevillia
Scrubbusters
12
42480
2.5
Healdegard
For the Horde
0
/
0
Pews
Vodka
2
7080
0.5

Garalon:

Name
Guild
Number of Flash Heals
Mana saved
% of Healing
Stronzium
Set sail for Fail
0
/
0
Medii
Midwinter
0
/
0
Hailow
Legends Never Die
0
/
0
Sevillia
ScrubBusters
0
/
0
Xabok
Method
0
/
0

And from Security's logs for Grand Empress Shek'zeer over all fights:

Player
No. of Flash Heals
Mana saved
% of Healing
Mana saved on Average per pull!
Care
168
594720
1.7
31301
Leeloo
14
49560
0.2
1709
Anjanas
31
109740
0.4
3784

So let's take Sevillia's mana saved from Imperial Vizier Zor'lok, 42480.
Which is 393.3 mp5 saved, equivalent to 696 spirit for a gnome, or 675 spirit for a human (not counting rapture, which would devalue it further).


This means taking the two set over other gear, on a fight where the occasional fheal is necessary, is only viable when the other gear is of less than 696 spirit upgrade, and only if you're going to use the fheals :P


4-set Bonus:

This improves the healing of Penance overall across the fight (if we were casting it on cd orgiinally, and wanted to cast it more)

Recycling the charts from above:

Spell
Heal
Cast Time
Mana Cost
HPS
HPM
Penance(glyphed)
67203
1.92
11160
35001
6.02
PW:Shield
93949
1
18300
93949
5.13
Binding Heal
40411
1.44
16200
28063 (56126)
2.49 (5.00)
Greater Heal
77202
2.4
17700
32168
4.36
FHeal(2set)
57890
1.44
14160
40201
4.09

Penance is disc's highest HPM spell, with below average HPS. However, glyphed it can be cast whilst moving (particularly useful in heavy single target damage situations where moving is important).

Returning to logs to see how many times per kill penance is used:

Imperial Vizier Zor'lok:
Name
Guild
Number of Penance Ticks
% of Healing
Arnymacsek
Grim Funeral
18
0.8
Medii
Midwinter
0
0
*Shibo
Insomnio
63
4.4
Sevillia
Scrubbusters
3
0.3
Healdegard
For the Horde
19
1.6
Pews
Vodka
8
0.5

*has four set.

Garalon:

Name
Guild
Number of Penance Ticks
Mana saved
% of Healing
Stronzium
Set sail for Fail
0
/
0
Medii
Midwinter
0
/
0
Hailow
Legends Never Die
0
/
0
Sevillia
ScrubBusters
0
/
0
Xabok
Method
0
/
0


And from Security's logs for Grand Empress Shek'zeer over all fights:


Player
No. of Penance Ticks
% of Healing
Care
213
0.7
Leeloo
573
1.9
Anjanas
685
3

But the only situation I can see casting penance on cd is sustained tank damage with no aoe, or if a disc is assigned to the tank. For raid damage it appears to have little hps benefit to us, and is of no benefit hpm wise.

Now looking at gear, assuming a stat prio of :
Spirit to comfort > Intellect > Spirit > Mastery > Crit > Haste

BIS list (pure stat) Discipline
Head: Tier Head
Shoulder: Tier Shoulders
Chest: HoF Wind Lord
Gloves: HoF Zor'lok
Legs: MGV Stone Guard

For certain fights having the set bonus may be recommended. For all but Tsulong (which everyone in existence (and myself) is holy for) I haven't even had 2-set (let alone 4). Thus, I can only suggest that 4set is probably useful on Sha HC phase 2, but it isn't game-breaking, and I'll add further to this once I've been able to see Sha in a bit more detail (ie, tonight – hopefully).

Thursday 6 December 2012

Disc Mana Regen - 5.0.1

Discussions with a fellow guildie and friend Derpfu lead to this post (he also double checked my maths).



Exploring spirit as disc

With no rapture

First let us consider the relationship between mp5 and spirit from gear.


Mp5
Spirit
Intellect
13162 12690 14540
12534 11578 14540
12534 11578 13325
12242 11061 12401


Simply from looking at the table, we see that intellect has no impact on mp5.

Assuming that mp5 is proportional to spirit, we can say (where c=some constant of proportionality)

change in mp5 = c * change in spirit

Plugging the values in c = 0.565

And base:

MP5 Spirit
6125 222

We can conclude that
Total mp5 = base mp5 + (0.565*spirit)
And using these values :
6125 = base mp5 + (0.565 * 222)
base mp5 = 6000

Total mp5 = 6000 + (0.565*spirit)


Rapture

Rapture returns 200% spirit, with a 12s cooldown.
PW:Shield costs 18300 mana.
On proc, rapture returns 2*spirit mana - 18300

Mana per minute = n * (2*spirit – 18300)
Mp5 = (n/12)(2*spirit - 18300)

Utilizing rapture n times a minute (where n ϵ [0,5] ) gives an equivalent mp5 of:
mp5 = (n/12)(2*spirit -18300)
Mp5 from rapture = (n/6)(spirit – 9150)



Combining Rapture and Passive Regen

Total mp5 = 6000 + (0.565*spirit) + (n/6)(spirit-9150)

Total mp5 = (0.565 + n/6)spirit + 6000-1525n

Spirit from gear as a human.

Total mp5 = 6000 + (0.565*1.03*spirit from gear) + (n/6)(1.03*spirit from gear – 9150)

Extra mp5 for human racial = (0.565 * 0.03*spirit from gear) + (n/6)(0.03* spirit from gear)

Extra mp5 for human racial = (0.005)*(3.39+n)*spirit from gear


Extra mp5 from being gnome.

Mp5 Spirit
13363 12500

Mp5 = base + 0.565*spirit
base = 6300
As this correlates with the gnome racial *1.05, we conclude that the base mp5 is related to the mana pool size.

Base mp5 = 0.02 * base mana pool

and for a gnome the base mana pool is 1.05 times bigger, and gnomes get an additional:

Extra mp5 for gnome racial = 0.05*300000*0.02 =300


Combining the two, we have:

Thus we have:

mp5 = 6000*mana pool modification +(0.565*spirit modification*spirit from gear) + (n/6)(spirit from gear*spirit modifier – 9150)

Human Mana pool mod = 1 Spirit mod = 1.03
Gnome Mana pool mod = 1.05 Spirit mod = 1.00
Meta gem Mana pool mod = 1.02 Spirit mod = 1.00



Now let us consider mindbender:

Mindbender returns 1.46% mana per attack, and attacks 10 times before despawning.
This gives us a total of 14.6% max mana.  
(nb: this does assume you can cast mindbender on cd, ie that the boss doesn't go immune).
mps = 0.146 * 300000*mana mod * (1/6)

mp5 = 3650* mana mod

Finally, a complete equation for the mp5 as disc:

mp5 = 9650*mana pool modification +(0.565*spirit modification*spirit from gear) + (n/6)(spirit from gear*spirit modifier – 9150)
Human Mana pool mod = 1 Spirit mod = 1.03
Gnome Mana pool mod = 1.05 Spirit mod = 1.00
Meta gem Mana pool mod = 1.02 Spirit mod = 1.00


Using this, we can discuss the two main meta gems healing has to offer:
Revitalizing Primal Diamond +432 Spirit
Ember Primal Diamond 216 Intellect and 2% max mana

I'm a human, which meta should I use?

Mp5 Revitalizing = 9650 +(0.565*1.03*(spirit from gear+432)) + (n/6)((spirit from gear+432)*1.03 – 9150)
Mp5 Ember = 9650*1.02 +(0.565*1.03*spirit from gear) + (n/6)(spirit from gear*1.03 – 9150)

And the difference between the two can be given by taking ember away from revitalizing:
Mp5 (revitalizing – ember) = -9650*0.02 + (0.565*1.03*432) + (n/6)(432*1.03)
= 251.4024 – 193 + (74.16n)
= 58.4 + 74.16n

And thus we see that the revitalizing pulls ahead even with no rapture a minute - the more rapture you do, 

I'm a gnome, which meta should I use?:

Mp5 revitalising = 9650*1.05 +(0.565*(spirit from gear+432)) + (n/6)((spirit from gear+432)– 9150)
Mp5 Ember = 9650*1.05*1.02 +(0.565*spirit from gear) + (n/6)(spirit from gear– 9150)

The difference between the two:
Mp5 (revitalizing – ember) = -9650*0.02 +0.565*432 +(n/6)(432)
= 51.08 + 72n

Showing that for a gnome the revitalizing still leads, although in this case with less margin and less contribution from rapture.

Comparing gnome and human racials (or, I just made a priest, should I be human or gnome?)

Mp5 as a human = 9650 +(0.565*1.03*spirit from gear) + (n/6)(spirit from gear*1.03 – 9150)
Mp5 as a gnome = 9650*1.05 +(0.565*spirit from gear) + (n/6)(spirit from gear– 9150)

mp5 (human – gnome) = -0.05*9250 + (0.565*spirit from gear * 0.03) + 0.005n*spirit from gear
Mp5 = 0.005n*spirit from gear + 0.01695 * spirit from gear – 0.05*9650
= (0.005n + 0.01695) * spirit from gear – 0.05 * 9650

To make the two equivalent, we see:
0.03195*spirit from gear = 0.05*9650
spirit from gear = 15101.7
(3 rapture a minute)
(0.005n + 0.01695)spirit from gear = 482.5
spirit from gear = 482.5/(0.005n + 0.01695)
(n rapture a minute)

So you would need 15.2k spirit from gear & flasks to make being human give more mp5 than being gnome as a disc priest, assuming they use rapture 3 times a minute.

The more we rapture, the less spirit we need from gear : 11501.79 spirit from gear is needed to make human better than gnome at 5 rapture a minute (literally rapture on cd).

Of course, this does not take into account the human racial “trinket”, which is incredibly useful in pve boss encounters. I list a few:

  • get out of “amber prisons” on Windlord
  • remove fear in Grand Empress
  • Remove pinning arrow on Spirit Kings