v3.1
Next we look at mana pool and abilities which effect mana pool. There a number of parts to discuss in this post. Base mana pool and calculating the effective MP5 of a static mana pool for a specific fight duration is first followed by Replenishment, Shadowfiend and Rapture for Disc priests.
Assumptions:
- MP5 for mana pools is based on a 6 minute (360s) fight over which the entire mana pool is depleted.
- Discipline has 1092 Intellect
- Holy has 950 Intellect
- Replenishment is assumed to have an 80% uptime and returns 0.25% of the mana pool every second.
- Shadowfiend returns 5% of the mana pool per hit and strikes for an average of 8 times per use. It is only used once per 6 minute fight.
- Rapture returns 2.5% of the mana pool each time it procs and does so once every 15s. In theory it can proc every 12s but this seems unlikely in reality.
Mana pool
This is also called maximum mana. To calculate the MP5 value of this firstly we need to calculate what the mana pool actually is. This calculation is fairly straight forward.
Maximum mana = Base mana + 20 + (15 x (Total Intellect – 20))
Base mana@80 is 3836 so the maximum mana is 19943.5 for Disc and 17806 for Holy. Over a 6 minute fight this is (Maximum mana/360)x5 = MP5 or 277 MP5 for Disc and 247 MP5 for Holy.
The Intellect MP5 weighting for maximum mana = Max mana Mp5/Intellect so we get these weightings:
- Intellect MP5 weighting for Discipline maximum mana = 0.253541
- Intellect MP5 weighting for Holy maximum mana = 0.260322
Edit: As obichad pointed out each additional point of Intellect gives 15 mana so Intellect MP5 weighting for maximum mana = 15 / fight length x 5 = 0.20833 for both Disc and Holy.
Edit2: As serrif pointed out a point of Intellect actually gives differing mana to each spec because of talents such as Mental Agiltiy (+15% Int to Disc). Intellect MP5 weighting for maximum mana = 15 * stat mod * / fight length x 5. Intellect stat mod is 1.15 for Discipline (+15% Int from Mental Agility). It remains 1 for Holy as they have no Intellect stat modifier. These sta modifiers apply to each type of mana regen in this post.
- Intellect MP5 weighting for maximum mana (Disc) = 0.2395
- Intellect MP5 weighting for maximum mana (Holy) = 0.2083
Replenishment
Replenishment MP5 = Maximum mana x uptime x mana return per second x 5
This results in 19943 x 80% x 0.25% x 5 = 199 MP5 for Discipline and 17806 x 80% x 0.25% x 5 = 178 MP5 for Holy.
The Intellect MP5 weighting for Replenishment = Replenishment Mp5/Intellect so we get these weightings:
- Intellect MP5 weighting for Discipline Replenishment = 0.182549
- Intellect MP5 weighting for Holy Replenishment = 0.187432
- Intellect MP5 weighting for Replenishment (Disc) = 0.1725
- Intellect MP5 weighting for Replenishment (Holy) = 0.15
Shadowfiend
Shadowfiend MP5 = (Maximum mana x mana return per hit x number of hits) / Fight duration in seconds x 5
This results in (19943 x 5% x 8 ) / 360 x 5 = 111 MP5 for Discipline and (17806 x 5% x 8 ) / 360 x 5 = 99 MP5 for Holy.
The Intellect MP5 weighting for Shadowfiend = Shadowfiend Mp5/Intellect so we get these weightings:
- Intellect MP5 weighting for Discipline Shadowfiend = 0.101416
- Intellect MP5 weighting for Holy Shadowfiend = 0.104129
- Intellect MP5 weighting for Shadowfiend (Disc) = 0.0958
- Intellect MP5 weighting for Shadowfiend (Holy) = 0.0.833
Rapture
Rapture MP5 = ((Maximum mana x mana return per proc) x (1/proc frequency)) x 5
Rapture MP5 = (19943 x 2.5%) x (1/15) x 5
Rapture MP5 = 166
The Intellect MP5 weighting for Rapture = Rapture Mp5/Intellect so we get this weighting:
- Intellect MP5 weighting for Discipline Rapture = 0.152124
Edit: As obichad pointed out each additional point of Intellect gives 15 mana. Intellect Rapture MP5 value for Disc is Mana return % x mana per Int / Proc frequency x 5 (to get mana per 5s). Mana per Int needs to include the +15% Intellect modifier from Mental Agility (i.e. 17.25 mana per Int, no t15).
- Intellect MP5 weighting for Discipline Rapture = 0.1437
Notice that Discipline’s mana return talent Rapture appears to be producing about the same MP5 as Holy’s Holy Concentration (166 MP5 vs 142 MP5).
I was glad to see that The Doctor’s numbers on Elitest Jerks agree. The thread is worth a read:
http://elitistjerks.com/f77/t54629-discipline_healing_compendium_v3_1_a/
I keep getting around .2 for the mana pool instead of the number you used. The EJ post you linked is using a fight length of 300 seconds while you are using 360, and since your numbers match, seems like something might be off here.
From what I can tell, one Int is going to make your mana pool bigger my 15. So isn’t it simply 15/(fight length)*5? 15/360*5=.2083 I’m coming at this from the holy side of things.
Also, for replenishment and shadowfiend, I’ve found it helpful to go through some WWS logs and try to calculate an efficiency number. For my raids thus far it’s about 80% on replen and 95% on the fiend. Not a huge difference, but I’m a fan of using all the data I have.
Your calculation ignored both Base Mana (3836@80) and the fact that the first 20 Int only give 1 mana, not 15.
WWS logs are a good idea and something I should look at a few more of. 95% shadowfiend sounds unlikely to me in a raid environment. They get killed by boss AoE a fair bit and sometimes appear to die for no reason. If you had 95% uptime you’d get about 10.5 hits per use (I think) and the numbers would be 0.1331 for Disc and 0.1367 for Holy.
Gobble gobble.
My current int is 962. Using your base mana formula that gives me a 17986. If I increase my int my 1, so using 963, and using the forumula, that gives me 18001. That’s a difference of 15. The mp5 value of the mana gain fron 1 int over a 360 second fight would then be 15/360*5, giving us .2083. I’m not saying I’m right here, just explaining my logic. Feel free to poke holes.
For the fiend, I was using a Naxx farm run as my base, and it truly was 95%. Likely not the best sample to use since where this kind of stuff really matters is on cutting edge content and the fiend is much more likely to die when you don’t exactly know when best to use it.
Oh I should have read your original post more carefully. Your logic looks pretty sound to me. Might have to update the post. Thanks.
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Updated.
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Incidentally 0.2083 is the value my calculation approached as Intellect went up.
Gobble gobble.
What about Mental Strength? Shouldn’t that make the disc numbers 15% larger, as each point of int in gear actually gives 1.15 points of intellect on the character sheet?
Yup. Check out:
https://bobturkey.wordpress.com/2009/04/22/priest-theorycrafting-introduction-part-1/
However you have got me thinking that the stat modification talents aren’t quite being taken into account correctly.
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OK i’ve updated the numbers to take that into account now. That idea actually affected any area where spirit or intellect was used.
Thanks.