Posts Tagged ‘Zusterke’

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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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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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