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Tea with Zusterke part 1: The Groundwork

June 2, 2009

A few weeks ago, we ran the idea of having Zusterke (of PlusHeal fame) do a post outlining the actual math part of regen to answer all of your priesty questions.  Thankfully, since the Snark Mavens do very little in the way of hardcore mathcraft, he said yes.  This is part 1 of his results.

Stat Wars

There are two challenges about theorycrafting. The first part is the theorycrafting: how to examine and calculate what you need. The second part, is translating it into human language. I found that part 2 is often more challenging and requires more patience than part 1. When Joveta kindly asked me if I would give a shot at explaining our regen model in human language, I accepted the challenge. I leave it to the faithful readers of Snarkcraft.com to judge whether I succeeded.

theorycraftThe regeneration model of WoW has seen a lot of changes with patch 3.1: spirit/intellect regeneration was nerfed outside the five second rule, the shadowfiend is buffed, Rapture and Holy Concentration have changed. The regeneration model is so complex it almost obscures the effectiveness of our regeneration stats and leaves us guessing how to gear. Unfortunately there is no straight answer as circumstances and gear level have a great impact on our regeneration model. So, I’ll try to tackle some of these problems and provide a more detailed answer.

Manabar Regen

WotLK introduced several abilities that grant us a fixed % of our maximum mana over a period of time. Some of these have changed in patch 3.1 so we’ll go over them one by one.

Replenishment
Replenishment is now available for frost mages and destro locks. This makes the availability of Replenishment more reliable and ever more important to take into account.

The regeneration offered by Replenishment remains the same. It offers 0.25% of your manabar every second, which is 1.25% of your manabar every 5 seconds. But it is optimistic to consider it fully effective the whole time. At plusheal, we observed that the effect of Replenishment does not work 100% because refreshing buffs or missed refreshes can diminish the amount of ticks you get. You can easily verify this in any WWS parse (see image).

replenishmentHaving checked dozens of WWS parses, it seems Replenishment ticks 75-95% of the time (see screenie). I consider 85% an average which yields me: 85%*1.25% = 1.0625% of my manabar as mana every five seconds.

Shadowfiend
The shadowfiend was buffed in patch 3.1. It now delivers 5% of your maximum mana per attack, rather than 4% per hit. It can total to 60% of your manabar over 5 minutes which is equivalent to 1% of your maximum mana per 5 secs.

Hymn of Hope
Hymn of Hope changed a lot in. While it is still a channeled spell, it choses 3 targets randomly every 2 seconds. The spell is quite situational and unreliable when used. Therefore, I will not use its regen in this theorycraft.

Mana Tide Totem
The mana tide totem yields 6% mana every 3 seconds for 12 seconds. With a 5 minute cooldown, this gives about 0.4% of your maximum mana every 5 seconds. In my guild we tend to give this totem to dps, rather than healers, and I’ve read from several players that I’m no exception. I will not include it in this theorycraft, but for those who are interested in it: it yields 0.06 mp5 per point of intellect.

Rapture
Rapture is a fundamental regen talent for any Disc priest. It can yield 2.5% of your mana, every 12 seconds, when a shield is absorbed. However, timing this shield consumption is hard to control. Let’s add a few seconds as safety line and assume it procs every 15 seconds on average. This corresponds to shield spamming the main tank who will absorb his shields anyway. In this case, we get 2.5% every 15 seconds or 0.8333% of your maximum mana every 5 seconds.

Our maximum mana can be calculated as follows:maxmanaWe can calculate the percentage of maximum mana per 5 seconds we get for both Disc and Holy priest. We can use that percent to calculate how much mp5 per point of intellect we get from manabar based regen but here we must take into account the bonus on intellect accordingly: Mental Strength for Disc and Blessing of Kings for both Disc and Holy. We get:manabarregen

Spirit Regen

Our spirit/intellect regen changed a lot in patch 3.1. The base regen of spirit and intellect was nerfed by 40% but our regen while casting from meditation was increased to 50%. As a net result, we get the exact same amount of regen while casting but notice a considerable nerf in our mana regen while not casting.

To make matters more complex, Holy priests now get Holy Concentration: a regen buff that depends on crit. The uptime of Holy Concentration can vary wildly depending on playstyle and healing assignment so I won’t go into details about it for now. Perhaps this may interest some in another guest post, if fate, Seri and Jovi will be so kind. For now, I recommend to check your WWS parses to see what uptimes you obtain from Holy Concentration.regen2

SenseThese values probably like an odd mix of Thalassian and Chinese so let’s simplify them. We assume 90% time spent inside the five second rule and for holy priests we add 20% Holy Concentration uptime (see image). This is a bit pessimistic but it’s better to play safe. Holy priests tend to have a notably higher mana consumption when raidhealing and most raidhealing spells do not trigger holy concentration.holyconcentrationTaking into account buffs from talents and Blessing of Kings, we get:valueholy

valuedisc

These formula’s do not reveal immediately the value of intellect or spirit. But it does reveal an important property of both:

  • Spirit evolves with the amount of (/square root of) intellect you have.
  • Intellect evolves with the ratio it has with spirit.
  • Stay tuned tomorrow for a special Wednesday Snarkcraft. Zusterke will cover the Int vs Spirit debate. Thanks for reading and a special thanks to Zusterke for putting this thing together!

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    18 comments

    1. Zusterke – this is really awesome and interesting. One small request – I personally need a bit more rationale about where some of the numbers in your formulas come from. For example: in the maximum mana formula, I understand base mana, but where does 20 come from? And why does it come off int too? is it that the first 20 int just give 20 mana (instead of 300 + modifiers/buffs)? Similarly, the regen formula is awesome to see spelled out, but needs, imho a bit more explanation of each single factor.


    2. Hi Tsark,

      Manabar: The first 20 points of intellect give only 1 point of mana and I assume every priest (of raid level) has at least 20 int. Therefor I add the 20 points of mana, and deduct 20 points of intellect from your total intellect ‘int*bonus’. This makes the formula accurate, while clearly revealing that each point of intellect is worth 15 points of mana (times the bonus on intellect) IF we have more than 20 intellect.

      Regen: it is indeed a long a tough formula to crack. The base of the formula comes from wowwiki – http://www.wowwiki.com/Mana_regeneration
      The elements are,
      – Base: your base regen. This factor is fully determined by Blizzard. It is the factor that makes our regen scale with each level and was reduced by 40% in patch 3.1.
      – spi*bon-spi: your spirit and its bonus. I write “spi*bon-spi” while in fact this is an abstraction for “spirit * (1+ bonus1) * (1+bonus2) …”. For example, with Spirit of Redemption you get: “Spirit * (1+ 5%)” or “Spirit * 1.05″. If you add Blessing of Kings, this becomes “Spirit * (1+5%) * (1+10%)” or “Spirit * (1+15.5%)” or “Spirit * 1.155″. I abstracted this to one term because it allows me to fill in the details of the bonus later, depending on spec and buffs.
      – The same story for “int*bon-int”
      – “hc” stands for the bonus of holy concentration. Much like the spirit or intellect bonus, it is an abstraction for “(1+ 50% * HC-uptime)”. If you have 0% HC uptime, or you are a Disc priest then this becomes “(1+ 50% * 0%) = 1″ which is basically the same as deleting the factor in the formula.
      – “fsr” denotes the impact of the five second rule. This one is a bit more complex. It stands for: “(IFSR-time * regen-while-casting + OFSR-time * 100%) = (100% – (regen-while-casting * IFSR-time))”. If you have 90% IFSR time and 3/3 meditation, this becomes (100% – 50% * 90%) = 55%.

      I can understand it is a lot to digest. That formula has become extremely complex in 3.0 and 3.1. I tried to make the formula a bit lighter to read and work with. I actually use it this way myself when doing some maths out of my head.

      If you have more questions, I’ll gladly answer them!
      Zus


      • Yay score one for me for still being able to get (some) meaning from the formula. Really didn’t know about the first 20 int being totally different from the rest. The mana formula I had figured out after posting – but thanks for spelling it out more clearly anyway. Ah, also – I think in the other comment you wrote “20 mana” instead of “20 int” ;-P


    3. According to http://www.wowwiki.com, base mana for a level 80 priest is 3863. Not sure how accurate it is since it is as of 3.0.8.

      My biggest question is where do the +20 and the -20 go in your second line of the max mana equation?? The way the fomula is written they would not cancel each other out. Perhaps I am missing a step


      • You know, I’m so used to math abstractions that I forget they can be tricky for readers! My appologies.
        Let’s work it out, step by step.
        If you have less than 21 intellect (up to 20) you have:
        manabar = basemana + int = 3863 + int
        if you have 20 mana, this becomes:
        manabar = basemana + 20 = 3863 + 20 = 3883
        if you have more than 20 mana you get:
        manabar = ‘previous manabar’ + 15 * (rest of your int)
        The rest of your int is your intellect minus the first 20 intellect so it becomes:
        manabar = basemana + 20 + 15 * (int – 20)
        manabar = 3863 + 20 + 15* int – 15 * 20
        manabar = 3863 + 20 – 300 + 15 * int
        manabar = 3583 + 15 * int

        Throw in a bonus factor of intellect and you get the formula from above.

        I hope this is clear :) If not.. I’ll brave another attempt to explain it.


        • Argh! that should be:
          if you have 20 INT, this becomes:
          manabar = basemana + 20 = 3863 + 20 = 3883
          if you have more than 20 INT you get:

          Thanks Tsark ! :)


    4. *head explodes*

      Why are you making me read math? ARG! I’m a lemming. I come here to get the info I need!!! Not think!!!

      Please rephrase your post in the form of: Nerdly, at your current gear level, you should have a INT/SPI ration of X/Y.

      Thanks!! :)


      • Nerdly, please stay tuned, the TL;DR conclusions will be posted in part 3. ;)


      • I think that is the point of Zusterke’s post. Its not so simple as a ratio of X/Y. The formula is very complicated now give talents, buffs, and changes made by blizzard.

        I give huge props to Zusterke. While I don’t necessarily understand everything posted I think he hs done a noble job of providing the information for others to digest.

        Bruennor aka Narya on Eredar Holy Priest!


    5. I’m with Nerdly! My poor brain just can’t take all that math! I tried really hard to make sense of all those numbers….but it hurt my brain! :’(


    6. I just think it’s great that you got Zusterke here to explain these things. I don’t follow the math, but knowing the math is underlying the conclusions makes it MUCH easier to accept.

      And if you two ladies want to make Zus a semi-regular here, I won’t object! :D


    7. Nice post Zusterke.

      re:Rapture – your “0.8333% of your maximum mana every 5 seconds” is right but the next part where you are talking about 0.5495 MP5 per Int looks to big. Are you forgetting that the 2.5% regen only happens every 15s not every 5s?

      I’m looking forward to the other parts.

      Gobble gobble.


      • Hey Bob! I think it’s very cool you dropped in a line, thanks :)

        Rapture is worth about 0.833% of your max mana or, in case of a Disc priest buffed with BoK, (0.008333 * 15 * 1,265 =) 0.1581 mp5 per point of intellect. The total value 0.5495 mp5 per point of intellect includes shadowfiend and replenishment.


    8. Ahh Rapture makes sense now (0.833%*15*1.15*1.1=0.1581).

      The other is about he same as mine. The exact numebr depends on assumptions about replenishemnt uptime, number of times shadowfiend hits and fight length.

      In some deep nerdy math part of my brain i find it interesting (but not unexpected) that we come up with the same numbers via different routes.

      Gobble gobble.


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