Jundicator[Kin]
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Spirit to Mana/5 to Int - 2006/02/17 04:03
I first posted this baby in the WoW priest forums, but I figured it would be useful here as well. Enjoy!
One key concept:
I don't care where my mana comes from after I've used it. Just tell me how to regen the most mana in the shortest period of time!
The key here is the 5 second rule.
Here is how much spirit you would need, in order to generate the same mana as 1 mana/5 based on your time spent in the five second rule (FSR)
warning, Math Model:
2(mana every 5s)/5 = (spirit/4)(1 - % time spent in FSR) + (spirit/4 * % regen during casting)*(% time spent in FSR)
table 1: 0% regen while casting(normal)
mana/5....... spirit........ Time spent in FSR
1.00..........160.00.......99.00%
1.00......... 16.00........ 90.00%
1.00......... 8.00......... 80.00%
1.00......... 5.33......... 70.00%
1.00......... 4.00......... 60.00%
1.00......... 3.20......... 50.00%
1.00......... 2.67......... 40.00%
1.00......... 2.39......... 33.00%
1.00......... 2.29......... 30.00%
1.00......... 2.00......... 20.00%
1.00......... 1.78......... 10.00%
1.00......... 1.60......... 0.00%
Basicly this means that if you spend 99% of your combat time in the five second rule (FSR) then you need 160 spirit to regenerate the same mana as 1 mana every 5 seconds. The middle percentages are the interesting ones, as they are closer to actual boss fights. I've added that 2.391 and the percentage because that is the blizzard gear comparasion ratio. Meaning for gear of a simliar level they put about 1 mana/5 for every 2.391 spirit. So you'd need to spend about 67% of your time non-casting to regenerate the most possible mana with any given comparable gear.
table 2: 15% regen while casting(meditation or 3-piece transcendence)
mana/5........spirit.........Time spent in FSR
1.00......... 10.67........100.00%
1.00......... 6.81......... 90.00%
1.00......... 5.00......... 80.00%
1.00......... 3.95......... 70.00%
1.00......... 3.27......... 60.00%
1.00......... 2.78......... 50.00%
1.00......... 2.42......... 40.00%
1.00......... 2.39......... 39.00%
1.00......... 2.15......... 30.00%
1.00......... 1.93......... 20.00%
1.00......... 1.75......... 10.00%
1.00......... 1.60......... 0.01%
Now here is the same type of table but this time we have 15% regen from spirit while casting. See the explaintion at the end of table 3
table 3: 30% regen while casting (transcendence and meditation)
mana/5.......spirit......... Time spent in FSR
1.00......... 5.33........ 100.00%
1.00......... 4.32......... 90.00%
1.00......... 3.64......... 80.00%
1.00......... 3.14......... 70.00%
1.00......... 2.76......... 60.00%
1.00......... 2.46......... 50.00%
1.00......... 2.39......... 47.30%
1.00......... 2.22......... 40.00%
1.00......... 2.03......... 30.00%
1.00......... 1.86......... 20.00%
1.00......... 1.72......... 10.00%
1.00......... 1.60......... 0.01%
Now compare table 1 (0% regen from spirit) with tables 2 and 3 (15% and 30% regen from spirit). Notice what this does to the higher percentages compared to table 1. FSR percentages above 50% are very unforgiving to spirit with 0% regen durning casting. However, 30% regen during casting shows a significant decrease in the spirit required to match 1 mana/5. So with 30% regen while casting you get the same equvilance at 40% in FSR as 60% in FSR with 0% regen. Lower FSR % give some benefit but not nearly as much. Finally notice what happens to the blizzard comparable gear ratio at 30% regen. The percentage increases from 33% with 0% regen to 47.30% with 30% regen.
Actual equations for Math people:
m = x mana every 5 seconds
p = % of time in FSR
s = spirit
k = regen while casting = .00, .15, .30
To get spirit:
S(m,p) = 1.6*m/(1-p+k*p)
To get mana every 5
M(s,p) = ((s/4*(1-p)+(k*(s/4)*(p)))/0.4)
To get %FSR
P(s,m) = ((m/5*2)-(s/4)*k)/((s/4)*(1-k))
Converting to Intellect
Now that we have a solid footing of how we regenerate mana we can use this to easily convert to other aspects of the game.
Here is intellect.
Using table one from above lets see what it looks like:
table 1.1: 0% regen while casting(normal)
mana/5....... spirit........ Time spent in FSR.....mana per tick.........int per tic
1.00..........160.00.......99.00%.............................0.80...................0.05
1.00......... 16.00........ 90.00% ............................0.80...................0.05
1.00......... 8.00......... 80.00% .............................0.80...................0.05
1.00......... 5.33......... 70.00% .............................0.80...................0.05
1.00......... 4.00......... 60.00% .............................0.80...................0.05
1.00......... 3.20......... 50.00% .............................0.80...................0.05
1.00......... 2.67......... 40.00% .............................0.80...................0.05
1.00......... 2.39......... 33.00% .............................0.80...................0.05
1.00......... 2.29......... 30.00% .............................0.80...................0.05
1.00......... 2.00......... 20.00% .............................0.80...................0.05
1.00......... 1.78......... 10.00% .............................0.80...................0.05
1.00......... 1.60......... 0.00% ...............................0.80...................0.05
Because of our assumptions above we don't need more then one observation from this table, but I'd figure that its easier to understand it this way. You see that if you stack mana/5 and spirit at the correct FSR% ratios then your mana regen per tic is constant over all FSR%. This makes intellect per tic constant over all FSR%, and all we need to figure out how useful intel is the length of the fight. Here is the equation:
I(r,t) = r(t/2)/15
r = mana per tick from regen modal above = (2*m/5)+(s/4*(1-p)) +( k*(s/4)*p)
t = combat time in seconds
In conclusion, these tables (and more importantly the mathematical model) are merely tools for us priests to understand our class better and make more informed desicions when selecting gear. My aim is to clear up this fake debate over spirit vs mana/5. The answer to the question "which is better" is NOT some flat unchanging value, but a percentage. In order to decide if x mana every 5 seconds is better then y spirit then you need to know the percentage of time in the five second rule. This percentage is what makes playing the game fun and will keep it challenging.
For intellect we include a second variable, length of time in combat. So as priest healers we need to consider only two variables for a fight when deciding between spirit, mana every 5, or intellect. Those variables are length of time in combat and percentage of that time in the five second rule. Once those two variables are known then the equations above will tell you exactly which combination of spirit, mana every 5, and intellect will suit you the best. Now we are free to go out and develop better healing strategies based on the information I've presented here.
Jundicator
Post edited by: jundicator[kin], at: 2006/02/17 04:05
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Des
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Re:Spirit to Mana/5 to Int - 2006/02/17 05:51
Awesome post hun! Will be linking to guildies.
Thanks
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prästen
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Re:Spirit to Mana/5 to Int - 2006/02/20 19:06
Intresting reading 
But just wondering about table 1.1...
Is not the tick for mana regen from spirit 2 sec? Should not the table say 0,4 mana / tick and 0,02-0,03 int / tick?
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Xelakis
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Re:Spirit to Mana/5 to Int - 2006/02/21 19:03
This gives valuable info.
However, most of time, my fights are not that linear.
Usually, it's something like :
- I cast shield, renew or whatever, have few seconds to regen
- I continuously heal
- use trinket, mana pot
- then I'm oom
- then I do what I can with the regen that comes.
If you think that to be oom, you will have time for 25 FH casts (let's say you have 10k mana pool), which is approximatively 40 seconds and you will regen nothing with spirit and 8 with 1 mana/5 sec, then you'll have a hard time gather enough mana for just one extra FH (would require 47 mana/5 sec). With Meditation, you will regen 0,75 mp/spirit point during the same time (ie, with 400 spirit, this will regen 300 mp).
Also, innervate works with the rough mana regen (I don't even know if it takes mana/5 sec into account), and it has to be done when not casting to be efficient. So spirit is the key there.
So basically, what I count is only 1 mana/5 sec = 1.6 spirit.
With Int, the length of the fight is obviously the main factor.
1 Int point = 20 Mana points (so, 1 FH = 19 int). With 19 spirit, it will take 160 sec without casting to regen this (2 min 40 sec).
Typically, in high level fight, I will have more mana regen. In common raid/instances (UBRS and similar) I'll have more intellect.
Devout gives 115 spirit and 0 mana/5 sec.
Prophecy gives 117 spirit and 18 mana/5 sec.
Transcendence gives 127 spirit and 7 mana/5 sec + 15% meditation like.
But, I guess this is not that complicate. It's even more. It includes also +heal bonuses and critical (+int may increase the crit%). Even talents like Inspiration may impact the choice (how much hp will it absorb when proc?).
Ok, let's choose between 2 items.
Devout skirt = 15 int, 23 spirit
Padre Trousers = 20 int, 6 mana/5 sec, +42 heal
OMG !
The +42 heal means +2% on FH.
The 6 mana/5 sec = 10 spirit
The extra 5 int points = 100 mana points.
Let's say, MT takes 40k damage. I have 300 on the rest of my equipment. And 10k mana.
I have meditation and I heal continuously with 1000 FH on him.
With Devout pants, it will takes 40 FH.
On 60 seconds of continuous heal, my available mana pool is : 10000 + (spirit 300/4 *0,15* 60/2 = 363 mp) + 2000 (mana pot) = 12363 mp. I need 15200 to cast my 40 heals. I'm 2837 mp short.
With Padre Trousers, it will takes 39 FH.
On 58.5 seconds of continuous heal, my available mana pool is : 10100 + (300/4 *0,15* 39*1.5/2 = 329 mp) +(mana/5 sec 39*1,5/5*6=70) + 2000 (mana pot) = 12499 mp. I need 14820 to cast my 39 heals. I'm 2321 mp short.
If Padre pants would not have the +heal bonus, this would give :
40 FH on 60 seconds. Mana pool = 10100 + (300/4 *0,15* 60/2 = 337 mp) +(40*1,5/5*6=72) + 2000 (mana pot) = 12507 mp. I need 15200 to cast my 40 heals. I'm 2693 mp short.
Considering the poor bonuses of the devout set, I will always choose padre pants over devout pants, probably until I have 7-8 pieces of the set.
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