Posts Tagged ‘theorycraft’

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Zusterke on Inspiration

January 12, 2010

Zusterke strikes again!  This time, he delves into numbers to discuss that basic Priest talent: Inspiration.

Inspiration

Inspiration

Inspiration is a welcome tool, whether you’re making art or healing the tank. Most combat parsers check the uptime of this buff, showing the value of this talent. Sadly logs do not tell us how inspiration evolves with respect to crit and how we can manipulate our healing to work with inspiration. That needs to worked out differently, with pretty colors and graphics.

Inspiration uptime

“Theory”! Ha! Scared you, didn’t I? Due to heavy reader loss last time I wrote a guest post, I promised I’d stop aiming my theory at the readers and put the loaded math down. Still, for sake of completion I present the formula for inspiration uptime. The credit for this formula goes to Dagma at PlusHeal for he taught me both formula and its proof. The faint of hearth are invited to close their eyes for a second, it will not be pretty.

Math for buff duration uptime

Hits denotes the amount of (inspiration able) heals within the buff’s duration that we cast on the target. C denotes critical strike chance.

You may open your eyes again. We have 2 things that effect our chance to proc inspiration: critical strike chance and the amount of spells we cast on the target. This pretty rainbow below shows us by how much. Sadly, there is no pot of gold at the bottom end of this rainbow, only rotten potatoes for that’s where our inspiration ends.

Inspiration Uptime

Each line corresponds to an amount of heals on our target. Crit quickly boosts our inspiration uptime and as little as 20% gives a good uptime for spammy scenarios. For 25% crit we obtain 90% uptime when healing the target 8 times or more within 15 seconds. That’s easy with FHeal and/or penance, our tankhealing tools. Higher crit gives better uptimes, but the benefit from crit diminishes. The difference between 30% and 35% crit is only noticable if we heal the target less frequently. Beyond 35%, the benefit of crit is very low.

A grain of salt for these potatoes

I love theor.. eh.. rainbows but it isn’t 100% reliable. Critical heals are still random. The numbers above give ‘expected values’ but in practice your buff time could differ a little. Still, the more crit we have, the more reliable our inspiration becomes.

Another factor that effects our outcome is how you heal. The formula assumes that our heals are equally spread over time. In-game, this is rarely the case. This could influence your uptime both in a positive and negative sense. While the numbers above remain good indications, they are not 100% on the spot.

Counting on Inspiration

Tankhealers are seldom confronted with this question… but support healers or OT healers might: how often do you need to heal your target to proc inspiration? The answer for pessimists is “infinitely many times”. For all optimists out there, we can work out your chance to proc inspiration depending on how often you heal the target. *crushes door* Here’s theory! While I would enjoy a reign of math terror, you are spared another formula. The chance to proc inspiration, depending crit and your number of attempts, can be calculated with exactly the same formula as above. Consequently, the same rainbow shows you how reliable your chances are to proc inspiration and we can draw the same conclusions.

Inspiration and Surge of Light

Inspiration and Surge of Light

Surge of Light offers a free flash heal, but one that cannot crit. For our global inspiration uptime, it could be noted that SoL has a negative impact. But if we check the graph above, we can see that 1 heal less does not greatly affect our uptime. What’s more: in tankhealing scenarios it is likely to be a proc from a critheal on our tank. It would thus be the same heal that resets the inspiration timer and we should have about 15s time to ‘use’ that FHeal and cast more spells on our tank.

While I doubt the lack of inspiration or the gain of SoL has ever caused a wipe, there is a small risk that SoL procs from PoM or CoH that crits on a player, other than your target. In the (inconceivable) case that this proc would hinder your healing, a holy priest could use Binding Heal on the target as work around. But I have rarely been in a position where this would make a difference.

TLDR, aka the conclusion

For inspiration we note that 20% crit is sufficient to provide a reliable inspiration uptime in a tankheal scenario. More crit is welcome as it gives more freedom of how often we need to heal the tank but there is a diminishing return. At 30% crit, this diminishing return becomes strong and beyond 35% crit it weighs heavily. These numbers are raidbuffed. They should be taken with a grain of salt, so adding or dropping 1% won’t make a tremendous difference. If I remember correctly Jov always promoted 20% crit as minimum for holy priests. I guess I just added a piece of the proof she’s right. (and I’ll probably never hear the end of it) [You just said my two favorite words:  Jov’s right.  Of course you’ll never hear the end of it!  -ed.]

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Guest Post: Yuki Learns You Stat Weighting (p3)

June 25, 2009

sleepyukiAs stated last week, here’s the post outlining how to determine weights to plug into lootrank to figure out your best in slot.  It’s a general list written by (alas) a DPS-type, so it’s not aimed at healers specifically, but I hope you all can still find it useful.  Yuki’s been my guildie, my buddy, and enabler of my anime addiction for several years now.  He’s also the first person who told me that such a thing as mathcraft exists.  Be warned, there’s numbers ahead.

Step 5:  Final Complications

There are basically two things left that haven’t been modeled.  The first is mana regen, which creates some difficulties, and the second is trinkets and the like with activated or proc effects, which presents others.

5a:  Mana Regen

The main thing about mana regen is that it only matters if you run out of mana.  This can make it hard  to model, since it’s not something that easily converts directly into spellpower or attack power.

Probably the most common way of modeling mana regen is in terms of how many extra spells it lets you cast if you WERE to cast until you ran out.  Basically, you figure out how long you can cast without running out of mana, and how much effective healing or damage you’d do on average. Then you see how much 1mp5 would let you cast.  You compare how much a point of spell damage would have added vs. the amount the mp5 added to determine the effective spellpower value of a point of mp5.  This is a popular method because it’s pretty straightforward, and you can modify it a little to include out of 5 second rule regen if you’d like.

Another method is to work backwards:  essentially, you take a length of time longer than the amount of time it would take you to run out of mana chain casting and then calculate how much less time you have to spend on 5-second-rule regen to determine how many more spells you could cast, and use that to derive the relative value.

As you can probably guess, there really isn’t a great way to graft mp5 onto spellpower. Still, these two methods at least produce something, which can be modestly useful for modeling gear.

5b:  Procs

So, we’ve basically covered how to model static stats; what about ones that aren’t so static?  Generally these are in the form of either active abilities (clicky trinkets, for instance) or passive procs (chance-on-hit/crit trinkets).  How to model these?

Actives are actually pretty easy.  You can basically model them as “permanent” power by dividing their effect by the amount of time it spends on cooldown.  So, for instance, a trinket that provides 200 spellpower for 15 seconds on a 1 minute cooldown is effectively the same as one that grants 50 spellpower all the time.  This isn’t wholly accurate (since you can stack some cooldowns to get more out of them, like an unholy DK blowing Gargoyle while her trinket buffs are up), but it’s good enough for government work.

Passives are trickier.  You need to know the proc rate and internal cooldown, which are almost never listed; you’ll need to get them from datamining or testing.  Use these to calculate the average uptime % (which is the proc duration divided by average time to proc + internal cooldown), then multiply the value of the proc by that.  Since this requires you to use the average time to proc, which can vary wildly for low-chance trinkets, and it shares the flaw of not modeling stacked-burst very well with the active version, it’s not wholly accurate, but it gets the job done well enough to compare trinkets.

Step 6:  Putting it all together

At this stage, you have enough information to generate final stat weights:  for each overall stat, add up the weights you calculated for each of their effective ratings you calculated above to determine the final overall weight of that stat.  So, for instance, the value of a point of int is:

Int ESP = Any Value From Talents + (Effective Crit Rating) * (Crit Rating ESP) + (Effective mp5 Rating) * (mp5 ESP)

I used Int on purpose, because an observant reader will note that it provides a benefit we haven’t modeled:  an increase to your base mana pool.  You’ll have to determine what weight (if any) you give to that similarly to how you chose to calculate mp5; I didn’t mention it there mostly so that I could point out that at this stage you should be on the look out for stat effects that you hadn’t considered yet!

Once you’ve done this for everything, you’ll have your final weights for stats as calculated against your baseline!  Now you can use them to help consider gear . . . until you move too far away from your baseline and have to recalculate them.

Closing Thoughts

I’ve always been fairly skeptical of stat weights as anything other than very general comparisons of how “strong” a given stat is.  Having seen this demonstration of what hot dogs are made up, you can probably see why:  there’s a lot of assumptions in the process, and the end result loses value considerably as you move away from your baseline. I tend to agree with Ghostcrawler’s assessment that if you’re just pulling “best” gear from somewhere based on this stuff, you’re not necessarily doing yourself a service as it won’t necessarily actually be “best” for you if your gear is different than the assumptions.

One thing this process will teach you, though, is the underlying mechanics of your class, including what scales with what and how things interact, which is probably the most important thing to learn for any form of theorycraft.  The numbers generated may be of limited value, but the process of generating them has some fairly valuable lessons to be learned along the way.

Aaand done!  You’ve made it!  Special huge thanks to Yuki for putting this together and trying to learn us some math.  Did it work for you?

Also, there’s not gonna be a Tuesday post for me next week.  I’m currently in California visiting my family with the Tarsus; and my mom doesn’t really live in this century as far as internet goes.  But I’ll catch you all the next week!

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Guest Post: Yuki Learns you Stat Weighting (p2)

June 24, 2009

sleepyukiAs stated last week, here’s the post outlining how to determine weights to plug into lootrank to figure out your best in slot.  It’s a general list written by (alas) a DPS-type, so it’s not aimed at healers specifically, but I hope you all can still find it useful.  Yuki’s been my guildie, my buddy, and enabler of my anime addiction for several years now.  He’s also the first person who told me that such a thing as mathcraft exists.  Be warned, there’s numbers ahead.

Step 4:  Methodological Chaos

At this point, there are basically three potential methodologies for settling on the final values to be used:  The Quick and Dirty method, the Numerical Model method, and the Simulation method.

Whichever method you choose, at this point you’ll need to know a few things: the average non-crit heal/damage/threat/whatever for each ability you use, whether and how each ability scales with your baseline stat (so, for instance, if an ability gains extra potency per spellpower due to a talent), and whether the ability scales with any other stats (can it crit?  affected in any way by haste?  etc), and how frequently you use each ability.  For the quick method, you can get the last one from a WWS report, but in general you’ll get better results if you determine it from your ideal usage or rotation.

4a:  Quick and Dirty

The fastest way to generate values is to just do them based on a parse.  First you’ll need to know how much a point of spell power adds to each ability’s net effectiveness.  Look up its scaling coefficient and figure out how much 1 spellpower would actually increase that average use of the ability.  You’ll be using this as a point of comparison to determine how much each ability actually scales per point of other things; I’ll henceforth be referring to it as “the baseline scaling value” of for that ability.

Second, you pull out all your averages for all your abilities, and your % usage for each.  Next, figure out how much each would scale with 1% effectiveness of each rating you’re trying to calculate a weight for.  Divide this value by your baseline scaling value, then multiply it by the % of usage your WWS report shows; sum these values up to get your effective spell/attack power value for 1% of each rating, from which you derive the final ESP/EAP per rating point by dividing by its conversion factor for you level.

Advantages/Disadvantages: The advantages of this method should be clear, as well as its drawbacks:  it’s pretty easy, doesn’t take too long, and requires relatively little mathematical modeling, but it’s also really, really bad at things like haste on abilities with cooldowns. But if you’re just looking for a quick approximation and you don’t plan to redo your weights ever, its numbers aren’t too horribly off unless you’re very dependent on those kinds of things.

4b:  Numerical Modeling

This is the “purest” methodology, and also the one that’ll be your best bet if you’re planning to really do a lot of your own stat weighting, since it’s the easiest to revise.

Essentially, you model what your ideal rotation would look like in practice.  I’m going to use an offensive spell as my example, because it’ll give me a chance to show how to model hit and similar stats.

Start with the average base damage of the spell. Because you’ve already determined how your rotation works, you’ll know how many times you can cast it during that time.  Therefore its total contribution of damage during your rotation is:

Damage = (Times cast) * (Average Base damage)

Now, we add in spell damage scaling:

Damage = (Times cast) * (Average Base Damage + [Baseline Scaling Value * Spellpower] )

To add crit, we’ll start with the value of a crit, which is (1 + Crit Bonus Damage Value).  Now we multiply that by your chance of actually getting a crit, which is Base Crit + Crit Rating/Crit Conversion.  Add all that to one and multiply it by the original  value and you’ll have modeled what your damage from that ability would be with crit!

Damage = (Times cast) * (Average Base Damage + [Baseline Scaling Value * Spellpower]) * (1 + (1 + Crit Bonus Damage Value) * (Base Crit + Crit Rating/Crit Conversion)

Hit works as basically a “penalty” on damage until it’s capped.  Whatever damage you could have been doing would be a miss, so it’s 1 – Miss Rate + Hit Rating/Hit Conversion in a ceiling function that can never be above one.  For notational simplicity I’ll just assume we’re below the hit cap.  Note that  “Miss Rate” above includes everything other than hit rating that increases your chance to hit (like misery or a draenei aura), because we’re only comparing the gear stats, so those should be included in the baseline of the model.

Damage = (Times cast) * (Average Base Damage + [Baseline Scaling Value * Spellpower]) * (1 + (1 + Crit Bonus Damage Value) * (Base Crit + Crit Rating/Crit Conversion) * (1 – Miss Rate + Hit Rating/Hit Conversion)

Haste is where things get interesting.  If the ability in question is not cooldown limited, you can effectively cast it “more times”, so our Times Cast actually scales with haste.

Damage = (Times cast * (1 + Haste Rating/Haste Conversion) * (Average Base Damage + [Baseline Scaling Value * Spellpower]) * (1 + (1 + Crit Bonus Damage Value) * (Base Crit + Crit Rating/Crit Conversion) * (1 – Miss Rate + Hit Rating/Hit Conversion)

What if it IS cooldown limited?  Well, in this case, it basically doesn’t scale with haste even if its casting time would be reduced; you can never cast any more of them than the cooldown allows.  But because you’re casting it faster, you have more room for casting other things in your rotation, so those can actually generally be modeled as scaling normally with haste unless you’re trying for complete precision, because they can fill in the extra time left open even though you’re squeezing them between cooldown casts.

This example should show you basically how to handle all the various ways to scale when modeling.  Your final equation will be the sum of all these terms. Run through it first for only the baseline stats you selected earlier, then once for spell damage; the difference between these two becomes your baseline scaling value for the whole rotation.  Now just add a point to a rating and solve through and divide by the baseline scaling value for the ESP/EAP value of that stat.

Advantages/Disadvantages: If your eyes glazed over reading this section you will probably hate this method. It’s very math intensive, and requires you to think like a numerical modeler, which can be hard if you’re not a numbers person.  Also, an error in the model can lead to grossly inaccurate results; this can occur as a math error, or just in terms of how you model your ideal rotation, so there’s a lot of points of potential fail.

On the other hand, if you get it right, you have a comparatively easy way to change your baseline (just change the values), and you’re ahead of the game if your rotation changes (since you can just fiddle with the numbers a bit).  If done well it also produces the best numbers theoretically possible.

4c:  Simulation

This method is both similar to and very different from the previous.  Basically you build (or download) a simulator for your class that effectively “runs” a combat action-by-action for an arbitrarily large amount of time and reports back its results.  You basically just tweak a base value, run the simulation, and compare it to a baseline simulation to determine the comparative value of each stat.

Advantages/Disadvantages: Building your own sim would, of course, require programming knowledge and a slightly less rigorous form of numerical modeling.  Downloading someone else’s requires neither of these, but also requires that you trust THEIR programming knowledge and numerical modeling.  You could also run in issues of RNG-fail, but a sufficiently arbitrarily large number of actions should statistically smooth those out.

The biggest advantage that this method has is that it’s the best option for procs and other random mechanics.  Trying to do a numerical model for something like Windfury (a 20% proc with a 3 second internal cooldown) will quickly make you want to throw yourself under a bus.  I’ll talk about trying to model procs in the following section, but suffice to say this method produces more accurate results than that one.

Part two is done!  You’ve almost made it.  Stay tuned for the final bit tomorrow!

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Guest Post: Yuki Learns You Stat Weighting (p1)

June 23, 2009

sleepyuki

As stated last week, here’s the post outlining how to determine weights to plug into lootrank to figure out your best in slot.  It’s a general list written by (alas) a DPS-type, so it’s not aimed at healers specifically, but I hope you all can still find it useful.  Yuki’s been my guildie, my buddy, and enabler of my anime addiction for several years now.  He’s also the first person who told me that such a thing as mathcraft exists.  Be warned, there’s numbers ahead.

Step 1:  Choosing A Baseline

In order to compare various stats that scale in wildly different ways, the easiest solution is to create a baseline to compare.  Traditionally, this is either Attack Power  (Effective Attack Power or EAP) for physical classes or Spellpower (Effective Spellpower or ESP) for casters.

Why are they chosen?  Because their effects on damage are very easy to measure.  You could potentially model in terms of direct effect (that is, you could chose the baseline of “1 Effective H/DPS”), but that would make some of the calculations a bit messier and would make the resulting values a bit harder to read, as well as making the model even more sensitive to changes in other stats, so it’s generally better to stick with the simpler version.

You also need to decide at this point whether you’re going to model things that simply provide a percentage increase to your baseline (for instance, the 10% AP buff).  You can in theory leave them out because they can be “canceled out” in that they provide the same benefit to all stats once you’ve converted them to the baseline, but this may not work entirely in practice, which is why you sometimes see stat weights with have things like “1 AP = 1.1 AP” or the like.  I prefer to leave them in even if they’re notationally confusing, simply because it makes the model more robust.

Step 2:  Doing the Easy Math

This is the easy part:  calculating the stat weights for things that simply convert directly into your baseline. For instance, a paladin gets 2 AP from a point of Strength, so before considering other matters, Str would have a value of 2 EAP.

Next, include other scaling factors like talents or percentage-based buffs. Because most paladin builds that care about strength have a talent that increases your total strength by 15%, a point of Strength from gear actually gives you 1.15 strength; furthermore, you should have Blessing of Kings for another 10% (and these are multiplicitive), so the final weight is 1 Str = 2.53 EAP (actually it’s not because I haven’t included Sheath of Light, but I’m simplifying for pedagogical purposes)

You should also take this opportunity to convert stats into their “effective values” of other stats. For example, 166.6… Int = 1% spell crit = 45.91 Critical Strike Rating, so 1 Int is approximately equal to 0.2754 Critical Strike Rating (this math is, of course, for the base value of Int; once you include any talents that increase Int by a percentage and Blessing of Kings, you will of course have a higher amount of effective critical strike per point of Int).

Mana regen is a bit of a special case since it scales with other stats, so we’ll leave it to the side for now.

Step 3:  Setting the Baseline Stats

Because some stats scale as a percentage of your totals (Crit, Hit, Haste, ArP, etc), and other stats scale with each other (Int & Spi => Mp5), in order to compare them, you need a baseline set of stats.  This step is why stat weights will always vary as your gear varies:  where the baseline is set has a fairly direct effect on the values of the various stats, so as you move the stats of the baseline around (by changing the gear, which adds and subtracts stats from your baseline values), your values for each stat will change.  This step is also why people calculating these things rarely agree on the exact value of any given stat.

Most stat weights are done with either a sort of “average” stat mix for a given tier of content (that is, “we expect that most people doing this content will have X spellpower, Y% crit, and Z% haste on their gear when they start”), or by taking the best or average gear from the tier below and using that as the base.  This produces numbers which are not terribly accurate to anyone in particular’s circumstances, but it can be useful to spot trends in gear scaling at your content level; it’s also the only option you have if you’re looking to provide weights for a class/spec rather than for yourself.

If you’re doing this for yourself, the ideal choice is your actual current stats! That way, your final results will tell you what effects adding or subtracting stats will actually have on you.  This is a very good approach for checking out a single piece of gear, but it’ll still be problematic if you’re just trying to figure out what the best overall pieces of gear are for you, since it’s somewhat piecemeal.

At this point, you should also be able to calculate your “effective mp5″ per int or spirit, since you can plug the base values into the regen formula (which I don’t have handy since I don’t ever use it), and then figure out how much MP5 a point in either one would be worth.

Continued in: Yuki Learns You Stat Weighting (p2)

Thanks for reading part 1 (of 3) of this week’s Overwhelming Numbers series.  God I love guest posters!

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Tea with Zusterke part 3: Conclusions

June 4, 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 the final part of his results.

Some Considerations for Holy Spirits

consider

We’ve seen that the optimal ratio turns around 600 spirit for 1300 intellect. But we have also seen that we can easily take 200 spirit or intellect more and keep a fairly balanced score. This gives us some room to tailor our regen stats to our likings, without risking a severe penalty in our regen. So let us examine the factors that impact our balance:

  • Lowered FSR: Some fights have phases and breaks in the healing. This can increase the value of spirit notably (say, 800 spi v 1400 int).
  • Higher FSR: hard fights can be very demanding and rip away that chance on a regen break, decreasing the value of spirit and changing the ratio a few points in favor of intellect. But such fights also diminish your chance on a hymn of hope or it can make relying on Replenishment, shadowfiend etc more risky. In short: our balance favors more intellect but a healthy spirit basis becomes ever more important.
  • Higher Crit: if you like a lot of crit, then you may score higher uptimes for holy concentration. This can easily up your HC time by 20% and really give spirit a push.
  • Single target spam: if you spam a lot more single target heals, you will have more chance to proc holy concentration and up your spirit regen notably.
  • Raid synergy: some raiding guilds really try to min max their raid groups. This means you really rely on some of your manabar based regen effects!
  • Hymn of Hope + Shadowfiend: if you have the chance to use both together, do it! The 20% increase of your max mana effectively increases the performance of your shadowfiend by 20%. This tips the balance a bit in favor of intellect. But a fight that can allows such a break is likely to have a lowered FSR time.
  • Shadowfiend + Bloodlust/Heroism: Bloodlust increases the haste of your fiend, giving more hits and thus more mana. This is a superb way to make your intellect count!
  • Hymn of Hope + Replenishment: the increase of yout max mana increases the effect of your Replenishment. This favors stacking a bit more intellect.
  • Spirit as backbone: when problems come your way, spirit will be your savior. When your group is sub optimal, your cooldowns got burned too early (or messed up!), or the guy providing replenishment bubble hearthstone’s out of Patchwerk, your intellect based regen drops like a stone. Intellect gives great synergy with the group, but that makes the group its lifelink. Having a healthy base of spirit can back you up under those odd circumstances.

There are probably a dozen more considerations that could manipulate the balance between intellect and spirit but I think I summed most of them here. Feel free to comment on more ideas!

Conclusion

It’s been a long post but I think we’ve reached some interesting conclusions for both the holy and discipline priest.

Discipline priests still gain the most out of intellect. In fact, it is unlikely that spirit will ever catch up with intellect as regen stat. Still, spirit beats mp5 for discipline priests with more than 1.1K intellect, which is definitely an eye opener for some!

Holy priests can still stack spirit and intellect with to a 6:13 or 8:13 ratio in favor of intellect and do just fine. Having more spirit will provide a great backbone in your regen model (and SP bonus!), but having more intellect will do great in min maxed raids. In fact, the optimal ratio has a couple of hundred points of leeway. With the current itemization in 3.1, I recommend going for intellect+spirit gear and gemming for intellect whenever you need more regen! I’m still a big fan of a healthy spirit basis, but intellect is definitely our biggest regen stat for now.

Whew! Y’all still there?  Thank you all for your patience in this really awesome discussion.  And again, huge thanks to Zusterke for putting it together for us.  I hope this was helpful to all of you (I know I learned a lot!)  And remember: if you’d like to continue discussion on this, consider heading to PlusHeal and opening it up to the community at large!

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Tea with Zusterke part 2: Versus

June 3, 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 2 of his results.

MP5 vs Intellect

Round 1: Disc priests
It is quite easy to prove that intellect is better than mp5 for disc priests. If we take into account the stat cost of mp5, then we need to compare 1 intellect with 0.4 mp5. We have seen that our manabar regeneration alone provides more mp5 per point of intellect, so intellect clearly wins.

Round 2: Holy priests.
For holy priests, we only got 0.3403 mp5 per point intellect from manabar based regen. So, Intellect is 0.0597 mp5 short to beat the stat mp5. This is where the contribution of intellect in our spirit regen kicks in:intvsmp5So, we need a minimum amount of spirit to support our intellect. This condition is very easy: for 1000 intellect, we only need 308 base spirit or 324 spirit unbuffed. It is fairly safe to assume a holy priest will have that amount of spirit and thus intellect beats mp5.

MP5 vs Spirit

When we inspected the value of spirit in our regen model, we found it evolves with intellect. When comparing spirit to mp5, the evident question we will bump in is not “if” spirit will beat mp5 but “how much intellect” is needed.

brainzRound 1: Disc priest
It has been debated many times whether Disc priests should take spirit or MP5. We know that the value of spirit scales with intellect, and so it is reasonable to assume that spirit may outscale mp5. Let’s check when that happens:spivsmp5disc

Round 2: holy priest
The value of spirit is not limited to its regen for holy priests, thanks to spiritual guidance. Still, it remains primarily a regen stat. We compare 1 spirit with 0.4 mp5:spivsmp5h2Given 1065 intellect unbuffed, spirit can beat mp5 when raidbuffed. Starting raiders without sufficient intellect on their gear may find mp5 slightly more performant at first, but spirit will gradually outscale mp5 by the time they leave naxx 10m and the spellpower bonus from spirit makes the stat preferable quite early in the content.

intellect

Intellect vs. Spirit

With the introduction of manabar based regen in WotLK, intellect climbed to one of the most potent regeneration stats. For disc priests it was considered the most favorable regen stat, while holies tried to balance it with a fair amount of spirit. With the changes in 3.1, spirit regen lost some ground and manabar regen gained some. Let’s see how the balance evolved.balance

Round 1: Disc Priest
For disc priests, we ‘guess’ that intellect still outscores spirit and we try to prove it. We compare their values:spivsintdDoes this make sense? Like… any sense? It does! Basically this comparison tells us that we can stack a boatload of intellect before spirit catches up. For example, with 0 spirit, the optimal value for intellect is 2025! Well, intellect clearly wins this one!

Round 2: Holy Priest
For holy priests, the balance between intellect and spirit was far more delicate in 3.0 than for Disc priests. Typically a 1:1 ratio was considered optimal. For 3.1 we relate the value of intellect by the value of spirit. If it is above 100%, intellect is more valuable than spirit and if it’s below 100% then spirit is more valuable than intellect:spivsinth

At this point, the formula doesn’t seem to make much sense.. at least it doesn’t to me. But we can put it in a spreadsheet and work out the ratio for various stat levels:holy-spiKeep in mind that these are basestats and thus spirit should be a tad higher. Still, it’s quite clear that spirit has lost some considerable ground to intellect! That is, for 20% HC Uptime, 90% FSR and no specific synergy with your manabar regen abilities. Do check that other ratio’s, with some more spirit or some intellect also score quite well as optimal (less than 10% difference).

Stay tuned tomorrow for the final part of this guide. Zusterke will wrap everything up and give those tl;dr math-haters out there the bottom line.

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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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