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



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