Discipline HPM Stat Weights and Optimisation Spreadsheet

[jstefanop]

Ok either I completely don't understand how to use this spreadsheet or is haste our main stat now? Under normalized weights haste is above mastery at .68 vs .65....is this correct?

[Kirsan]

Ok either I completely don't understand how to use this spreadsheet or is haste our main stat now? Under normalized weights haste is above mastery at .68 vs .65....is this correct?

No, I think Myllior need to put this:

use somewhere between 60% and 75% of the value given in the spreadsheet for Haste, depending again on how you're going for mana (higher if you're not struggling for mana; lower if you are). If you're playing a Holy Priest, use the sum of the HPET and HPM numbers for Haste from the Holy Priest spreadsheet as the value to be reduced.

directly in Spreadsheet with bold red text

[Myllior]

No, I think Myllior need to put this:
directly in Spreadsheet with bold red text

That would give the spreadsheets quite the dramatic flair, wouldn't it? Unfortunately, the 60-75% range is pretty much just a gut feeling - almost completely arbitrary - rather than anything arrived at systematically, so I'd rather leave it out of the spreadsheets. The spreadsheets do warn that "Haste (HPET) is treated extremely superficially.", but maybe I should lengthen the warning somewhat to include "Do not take the below values for Haste (HPET) at face value.", or something like that.

Regarding the actual question, Haste has the potential to provide a greater increase in output than Mastery does, even more so when you have a high uptime on Borrowed Time, but this potential can only be realised if you have the mana to sustain the faster casting pattern (and probably a million other things); judging whether or not you have the mana available is up to you. Regardless, I'd still give Mastery a decent lead over Haste, in general, since it is a phenomenal stat for increasing your output and it also has no additional mana costs associated with it.

[VigilantRose]

That would give the spreadsheets quite the dramatic flair, wouldn't it? Unfortunately, the 60-75% range is pretty much just a gut feeling - almost completely arbitrary - rather than anything arrived at systematically, so I'd rather leave it out of the spreadsheets.

Using any constant number like this to model the lack of efficiency gains from Haste is inherently flawed. Basically, you've got a three phase function:
1. Low duration event. In this case, you suffer no losses from the lack of efficiency because you can't (realistically) run out of mana anyway.
2. Standard duration event. In this case, you suffer some slowly increasing loss. Effectively you're arguing that the 'cost' of equipping Haste is that you need to equip an additional amount of Spirit (whose return is time-based). If you manage to compute that Haste should have a 30% cost penalty in a 12-minute raid (with your gear), you'd probably have a 0% cost penalty in a 6-minute raid.
3. Long duration event. Here, the value of Haste drops to zero because you're no longer time-limited but rather mana-limited. Additional Haste can never yield more healing because you're already transforming all of your mana into healing in less time than you have available.

Given the enormous range of event times (the longest raid is twice or more the size of the shortest), any average you come up just isn't very useful.

I should note there are a few other Haste nuances that often get overlooked:
1. Cooldowns. Let's say you have two instant casts. One heals for 10k. The other heals for 50k with a 15 sec cooldown. In a rotation, this yields 10k * 9 + 50k = 140k/15 = 9.33k hps. If we add 10% haste, this would change to 10k * 10 + 50k = 150k/15 = 10k hps. So while we added 10% Haste, we only got about 7% more actual healing.

At intermediary values, you also run into a balancing act between delaying your cooldown to fit in another spell or doing nothing for a brief moment to hit your cooldown exactly.

2. 'Lost' haste. Haste doesn't increase your healing so much as it increases your time. But getting 0.2 sec more time is meaningless. You only gain value from haste when you accumulate enough to cast another spell. This means that at any given time, you effectively have 'stacks' of 'saved time'. But if you stop casting for any reason, these 'stacks' decay. So if movement/raid events/whatever stops your casting, you lose value on your haste.

3. Rearloaded HoT. HoT benefit abnormally well from Haste, but this benefit is rear-loaded. If you have a 12 sec HoT that heals for 10k, you deliver 50% of that healing in 6 sec. If you have 10% haste, you deliver 50% of your healing at 6.54 sec (if the healing was continuous). While obviously 50% healing is better on the 10% Haste HoT, there is some (unknown, non-zero) discount rate that means you're realistically getting less than 10% additional healing.

These three concepts could be modeled as a constant penalty to haste. Computing an exact value would be extremely complex. However, we can take a look at casting patterns and get a general impression of how important they are to Discipline:
1. Cooldowns. Discipline doesn't actually have 'rotation' cooldowns for most purposes. Barring dedicated single target healing, Discipline spammable heal (PW:S) is higher throughput than it's cooldowns (Penance, Holy Fire/Solace) or its cooldowns are situational (Archangel/PoH, etc.). So there's actually no haste penalty here.

2. 'Lost' Haste. Because PW:S is instant cast (can be cast while moving, without fear of interruption) and because it's proactive (can be cast usefully even when no damage exists to heal), there are very few situations beyond rare raid events that the Discipline Priest needs to stop casting and might lose accumulated haste.

3. Rearloaded HoT. Discipline's only HoT is Holy Fire/Solace and I submit we can safely disregard it.

Given all this, I'd suggest that Discipline is natively 'friendlier' to Haste than any healing spec except possibly Resto Druids (where the penalties from #1 and #2 are offset by the massive use of HoT). Whatever penalty we assign would be relatively small, so if there's a massive statistical lead for Haste (which is the case for non-Mastery stats) then it's probably a good indication Haste is a decent idea.

[Myllior]

I agree fully; a most excellent write up VigilantRose. I can't really say I've examined the mana/Spirit availability this tier, but the feeling I'm getting from looking around is that we're already hitting the stage where we have plenty of mana, in which case Haste would sit in a comfortable position after Mastery but before the remaining stats. I'll post a link to your post in the opening post of this thread.

One quick question, regarding,

If you have a 12 sec HoT that heals for 10k, you deliver 50% of that healing in 6 sec. If you have 10% haste, you deliver 50% of your healing at 6.54 sec (if the healing was continuous).

Since heal over time effects no longer have their duration altered by Haste, but rather have shorter times between ticks and full/partial ticks added as Haste increases, if we're treating the healing as continuous, would we not still have 50% of the total heal delivered by 6 seconds? Obviously, if you don't treat the healing as a continuous stream, then more of the healing will be relegated to later in the HoT duration (unless you've just hit the next even numbered full tick). I get the feeling I may have missed something here.

[VigilantRose]

Since heal over time effects no longer have their duration altered by Haste, but rather have shorter times between ticks and full/partial ticks added as Haste increases, if we're treating the healing as continuous, would we not still have 50% of the total heal delivered by 6 seconds? Obviously, if you don't treat the healing as a continuous stream, then more of the healing will be relegated to later in the HoT duration (unless you've just hit the next even numbered full tick). I get the feeling I may have missed something here.

I threw up the graph and it should actually be the same at 50% - I must have missed something in the numbers. I'm not entirely sure the principle is wrong - I was just adapting it from elsewhere - but the argument I gave is incorrect.

[Deleted]

I dont know if you guys raid end content or not but haste is really really bad stat. Short explanation would be to aks you and go raid hc/myth content and find out why. Let me put it like this, more haste =more spirit. If you need extra haste us PI. You wont be able to spam spam spam with high haste all the time. Belive me on that one. I have spirit in every single item possible and with ilvl 688 i am out of mana fast with haste gear. Either listen to my advice or dont. I am only beeing honest and letting you know fact. Stop with this "paper looking good" stats speculation. Make a char and go try it out and you will see what haste will do to your mana.

[PosPosPos]

I dont know if you guys raid end content or not but haste is really really bad stat. Short explanation would be to aks you and go raid hc/myth content and find out why. Let me put it like this, more haste =more spirit. If you need extra haste us PI. You wont be able to spam spam spam with high haste all the time. Belive me on that one. I have spirit in every single item possible and with ilvl 688 i am out of mana fast with haste gear. Either listen to my advice or dont. I am only beeing honest and letting you know fact. Stop with this "paper looking good" stats speculation. Make a char and go try it out and you will see what haste will do to your mana.

Hi, most of us are Mythic raiders. I don't have problems ooming early with 20% haste raid buffed + Borrowed Time up myself.

All you need to do is to make sure you game Mindbender with PI/hero + Borrowed Time, the extra ticks on a hasted Mindbender makes up for the increased mana consumption.

[Myllior]

I threw up the graph and it should actually be the same at 50% - I must have missed something in the numbers. I'm not entirely sure the principle is wrong - I was just adapting it from elsewhere - but the argument I gave is incorrect.

All good! I was just worried that I'd missed something. I do have an extra question or two, but I may PM them to you.

I dont know if you guys raid end content or not but haste is really really bad stat. Short explanation would be to aks you and go raid hc/myth content and find out why. Let me put it like this, more haste =more spirit. If you need extra haste us PI. You wont be able to spam spam spam with high haste all the time. Belive me on that one. I have spirit in every single item possible and with ilvl 688 i am out of mana fast with haste gear. Either listen to my advice or dont. I am only beeing honest and letting you know fact. Stop with this "paper looking good" stats speculation. Make a char and go try it out and you will see what haste will do to your mana.

Except for logging onto the PTR every month or so to test something, I don't even play the game anymore. But that's besides the point. In addition to VigilantRose's post above, it may be good to read this post I wrote a while ago. You can see that, if you're mana-limited and Borrowed Time is in play, you essentially need 1 additional point of Spirit per additional point of Haste to balance the additional mana requirements; this is particular to the rotation examined though, and assumes no breaks in casting. (Note that the second Haste weight, for a 986.6 rating increase, is obtained for an increase in Haste and a corresponding increase in Spirit to compensate for the additional mana requirements. However, I've treated both Haste and Spirit as having the same value there; if we separate them linearly, and give Spirit at least an 0.77 weight, then Haste would be worthless).
The point is, we both recognise that mana is the main limitation on the value of Haste, but when/if this limitation doesn't exist, or is not particularly noticeable, then Haste is good; if you're mana-limited, Haste is bad. That all being said, things can change. At the moment, I'd probably put Haste in second place, but essentially in the same pack as the non-Mastery stats (with Versatility bringing up the rear), but what if there was a noticeable increase in the usage of DA-producing spells? Then Critical Strike would probably be the better candidate for second place.
Another question I've wanted to look at for Haste is, given excess available mana, is increasing your Haste the best option, or are you better off increasing another statistic and incorporating more high output, low efficiency spells into your casting? Admittedly, the only spell that seems to beat PW:S in output and can be spammed (mana allowing) is PoH, which has an inordinate mana cost, so the question is barely worth asking at this point.

The long and short of it is that additional Haste can be a good thing, and you should be able to get away with a decent chunk of it without too many issues (there seems to be a fair few Mastery/Haste pieces in BRF anyway), but whether you want more or not is up to you to decide. Personally, I love my efficiency stats, but until we get more stats (maybe next tier?) or there's a shift in healing, Critical Strike won't take its rightful place (EAA is a heretic ) as our second best stat (possibly first if the shift is sufficiently dramatic), and Haste will have a number of situations where it should be quite useful. (Excepting ludicrous scenarios, not as useful as Mastery, but still useful).

[Deleted]

I dont know if you guys raid end content or not but haste is really really bad stat. Short explanation would be to aks you and go raid hc/myth content and find out why. Let me put it like this, more haste =more spirit. If you need extra haste us PI. You wont be able to spam spam spam with high haste all the time. Belive me on that one. I have spirit in every single item possible and with ilvl 688 i am out of mana fast with haste gear. Either listen to my advice or dont. I am only beeing honest and letting you know fact. Stop with this "paper looking good" stats speculation. Make a char and go try it out and you will see what haste will do to your mana.

I'm raiding mythic and I disagree.

You need to be able to manage your mana, adding haste requires you change how you play in the same way that adding spirit does in order to optimize your casting choices.
I'd certainly say there are situations where haste is extremely valuable and situations where haste is maybe your least valuable stat and there's a lot of balancing to be done, on fights with high burst healing requirements haste is going to perform extremely well vs other stats during those burst periods. If the challenge of the fight is mana then it may not be so useful, in any case it's never 'bad'.

Just for some clarification of what I mean by mana being the challenge it isn't simply that you go oom, you can go oom on most fights if you wanted to, rather that over the course of the fight you're always able to fall back on your most efficient spells, you aren't spending EVERY GCD on renew, you aren't throwing in extra flash heals etc etc, if you're struggling to maintain that level of efficient healing and you're using GCDs to regen then haste isn't going to be offering you very much. However, as soon as you add in an HPS requirement, the value of haste skyrockets.


I kind of think of fight types like the phases of margok mythic.
P1+P2 would be your 'standard' healing mode, you're mostly efficient, it's not mana neutral but you could sustain this for a LONG time, at least the length of any reasonable fight, p2 kicks it up a notch but you shouldn't be struggling with mana even if these phases were lasting to the 10min mark

P3. You're going HAM. There's damage to be healed and you're going to heal it. Pull all the stops, mana is not the concern, keeping people alive is. You'll be lucky to last past 2-3 minutes like this but that's fine, periods of this kind of healing don't usually last long.

p4. Fumes. You essentially enter this phase with 0 mana, you're relying purely on your regen for your healing, completely mana neutral.

In P3 haste has extremely high value, your only goal is to keep people alive, to push HPS as high as possible over a short duration, this kind of healing isn't supposed to be sustainable so spirit doesn't really enter the equation. This is where some of the spreadsheets and maths do become kind of useful, it would suggest that for raw HPS (note: not 'total healing') haste may be rivaling multistrike for the top spot (ignoring int!)

p4 haste has little to no value. You're spending time doing nothing whilst you regen mana to cast your most efficient spells (which mostly all have CDs anyway), there's some value haste will give to renew but you probably can't afford to cast many of those anyway. In this example spirit is going to be far and away your most valuable stat.

P1+P2 are what I'd suggest make up the majority of your time healing and sit somewhere between the examples of p3 and p4, getting that balance is what is important

[Iliara]

I'm having trouble following the disc opt bounds page.

Earlier in this topic you said I need to put in the values for the effectivness and spell types, which I've done. And then columns B-E would give me ratios, but the ratios don't seem to make sense to me.

Up to 1700 total secondaries I should have 100% mastery, which is unrealisitic since gear comes with two stats. So I'll assume that's something that just doesn't work at low values (ie things tend to break at extremes).

But up 5k secondaries, I should put everything that isn't mastery into crit, which is where I'm confused b/c the stat weights that were calculated put crit and ms almost equal. So why would all those extra secondaries be dumped into crit if crit and ms are about equal? Shouldn't I want a roughly 1:1 distribution?

I'm thinking I'm misunderstanding the values, since if I look at the multistrike w_i, it's 6600 instead of 66. Does that mean in the table if I have 3000 secondaries I should look at 30000?

[Myllior]

The values given in columns B-E are the theoretical rating amounts you'd want; they do not consider whether or not you are actually able to reach said numbers. Because of this, they serve best as a guide of what stats to aim for, although, in general, this always just seems to be "more Mastery".

The stat weights and optimisation pages are telling you different things. The stat weights look at your current stats (M, C, etc.), so, a specific allocation of ratings, and gives an indication of the desirability of the various stats from there. The optimisation is slightly different in that it doesn't look at your current stat allocation; it looks at the total amount of rating available and then determines the best way to distribute that rating amongst the stats (at least, I hope it does ). Because of this, while your current gear may suggest that Critical Strike and Multistrike are of (roughly) equal value, this doesn't mean that it's optimal to have equal amounts of them.

The values used for the w_i's on the optimisation sheet are the amount of rating required to increase the stat by 1, or 100%. I do it this way so that I don't have to divide by 100 to get M/C/MS/V from m/c/ms/v (those conversions have to be done a lot in the equations in columns B-E, so it saves some space and makes it easier for me to write).
PS: The values of w_i are also adjusted to account for any stat attunements (ie. Critical Strike for Discipline and Multistrike for Holy). As such, the numbers given for 'c' for Discipline, and for 'ms' for Holy, are prior to the 5% increase due to the stat attunement.

[Talhooo]

I dont know if you guys raid end content or not but haste is really really bad stat. Short explanation would be to aks you and go raid hc/myth content and find out why. Let me put it like this, more haste =more spirit. If you need extra haste us PI. You wont be able to spam spam spam with high haste all the time. Belive me on that one. I have spirit in every single item possible and with ilvl 688 i am out of mana fast with haste gear. Either listen to my advice or dont. I am only beeing honest and letting you know fact. Stop with this "paper looking good" stats speculation. Make a char and go try it out and you will see what haste will do to your mana.

with ilvl 688 I think you are the one not raiding end content. I suspect you are just 10/10hc, or maybe 2/10M.

I've asked this in another thread (got no answer), but should we stop stacking haste at 918 ? If you'd use PI on cd, 1/6th of the time you would be gcd capped with 918 haste. Which means haste value drops 1/6th and this makes haste go below multistrike. Should we be aiming for 918 haste and nothing more ?

[Myllior]

Oops, I did see that. The main reason I didn't offer an answer is that I don't know. Obviously, if you're casting Prayer of Healing, Heal, or Clarity of Will while both PI and BT are active (with the raid buff), then you will still get the benefit of reduced cast time, for those spells, from Haste, up to ~5816 Haste rating (obviously, you can't only cast those spells, otherwise BT would drop off). Really, this is another of those things that makes a basic simulation code desirable for Haste; even if we decided to reduce Haste's value by 1/6th due to this (and I'm not saying that's a good way to go about it), we still don't know what the initial value that we want to discount is.

EDIT: I'll pop this over in that other thread as well, since you has a couple of other questions there too. Also, Penance (if you're not clipping it at the GCD) benefits from the additional cast time reduction.

- - - Updated - - -

Well damn, I was browsing through my copies of the Discipline spreadsheet and found a bug. When calculating HPET (in column AB of the Disc Stat Calc sheet), the formula that should be applied is simply the healing divided by the cast time (GCD if instant), which is the base cast time divided by the Haste factor. In other words,

HPET = Healing/[Base Cast Time/(1 + H)]

For whatever reason, when I first wrote the Discipline spreadsheet, I directly multiplied the Healing amount by (1 + H) in the HPET column, rather than dividing the base cast time by (1 + H); when I changed it to divide the base cast time, I forgot to remove the multiplying factor of (1 + H) from the Haste column. I've just updated the spreadsheets in the opening post to fix this.

This bug was present in the Discipline spreadsheets, not the Holy spreadsheets, and for those who want to fix their HPET values but preserve their pre-existing Discipline spreadsheets, rather than copy all their info over to new sheets, what needs to be changed is that the formulae in column AB on the Disc Stat Calc sheet should read "=AAXX/AEXX" instead of "=AAXX*(1+$D$4)/AEXX" (i.e. remove any (1+$D$4) factors from column AB). Sorry for this!

[Myllior]

Okay, time for the next round of spreadsheets! In order to use these, you must have iterative calculations enabled in EXCEL (File > Options > Formulas > Check 'Enable iterative calculation'). These spreadsheets have been dubbed 'experimental', and so be wary when using them, especially the Holy spreadsheet (as described below). First, the spreadsheets and accompanying equations documents,

Discipline experimental spreadsheet: https://drive.google.com/file/d/0B1C...ew?usp=sharing
Discipline experimental equations: https://drive.google.com/file/d/0B1C...ew?usp=sharing

Holy experimental spreadsheet: https://drive.google.com/file/d/0B1C...ew?usp=sharing
Holy experimental equations: https://drive.google.com/file/d/0B1C...ew?usp=sharing

The equations documents have been dubbed 'full' in the documents themselves, since they utilise as much information as I know how to draw from the 'Healing' tab with 'Tables' selected for presenting the data. Each spreadsheet has the Stat and Log Input sheet first, where you enter the desired values into the tan coloured cells. The next two sheets have the stat weights and healing amounts (including the overhealing factors, which are aggregate, not individual to each spell) and the HPM optimisation. The final two sheets are copies of the second and third sheets, but with no overhealing (i.e. examining raw healing).

The Discipline spreadsheet isn't much different from the current one (you still need to be careful in dissecting the empowered and non-empowered healing amounts), and so is probably good to go (despite what I said in the first paragraph), but the Holy spreadsheet is very different from the previous one, and also has a kind of fatal flaw built into how it calculates overhealing factors for criticals (including critical multistrikes).
Essentially, the healing registered in logs for criticals includes the base healing and the extra healing due to the critical; these components need to be separated for the overhealing behaviour of criticals to be evaluated. This is easy for Raw Healing (since a critical is simply twice the size of a non-critical), but not so for Effective Healing since, unless we trawl through the entire combat log, we can't know how much of the overhealing came from the critical portion of the heal, and how much came from the baseline portion. That being said, we know that we should expect more overhealing to come from the critical portion than the baseline portion, so the spreadsheet currently assigns ALL overhealing of criticals to the critical portion. This is obviously no more realistic than using the base numbers available from logs, and so pushes down the value of Critical Strike to some degree (this effect also cannot be quantified by only examining the Table on the Healing tab).
As you can see, this is indeed quite the fatal flaw for examining Critical Strike for Holy; it's also why I've put in sheets without overhealing factors, so that the numbers can be compared to hopefully keep things somewhat level. I'm hoping that there's some way of improving the overhealing factors for criticals without trawling through combat logs, but I'm not overly hopeful (if I did have to do so, it would probably lead to an entirely different set of spreadsheets).

So enjoy, but be careful with Critical Strike for Holy If you happen to have any particular way you want to calculate Holy's overhealing factors for criticals, go for it, and it'd be great to hear from anyone who has any thoughts of how to fix/circumvent this issue.

[VigilantRose]

That being said, we know that we should expect more overhealing to come from the critical portion than the baseline portion, so the spreadsheet currently assigns ALL overhealing of criticals to the critical portion. This is obviously no more realistic than using the base numbers available from logs, and so pushes down the value of Critical Strike to some degree (this effect also cannot be quantified by only examining the Table on the Healing tab).

I haven't looked at this particular issue in a few expansions. The conclusion I came up with them (for direct heals) was "eh... about 5% - 10% worse" - and I based this on looking at the differences in overheal percentage for the normal and critical versions of a given heal. So you'd see that your normal Flash Heal overhealed 15% and your critical Flash Heals overhealed 22% - and that difference would be the 'critical penalty'. I'm not sure how to break down overhealing between criticals/non-criticals in warcraftlogs, though.

However, what I did notice is that this was really a 'critical penalty' so much as a 'heal size' penalty. All else being equal, larger heals overhealed a greater percentage than smaller heals did (criticals just happened to be much larger versions of heals with the exact same casting mechanics as the original heals). More importantly, once you were below a certain percentage of player health, heal size was effectively meaningless in terms of predicting overheal percentages - all of the overhealing came from the mechanics of the heal, not its size.

Which, if you think about it, makes a good deal of sense. If I have a 1 point heal, a 2 point critical is just as likely to overheal as the base heal - there is effectively no statistical difference between "1 damage" "2 damage" and "no damage" when you've got hundreds of thousands of health.

If you look at your logs, you'll probably see 30% overhealing or so from Renew, 20% from Circle of Healing and 5% from Prayer of Mending. However, the prime driver of this overhealing is almost certainly (respectively) the delay in healing, the unavailability of targets and general log glitchiness (Prayer of Mending really shouldn't be able to overheal in a raid setting). In the absence of evidence, my general feeling is that there's no actual 'critical penalty' for the bulk of Holy's healing.

To really drive this home, consider Lightwell Renew. The only way Lightwell Renew can possibly overheal is to be sniped. To trigger, the target needs a health deficit well over double the total healing of Lightwell Renew. Even if every tick crits, Lightwell Renew can't come close to overhealing the target. So even without delving into logs, I can safely assert that the 'critical penalty' for Lightwell Renew must necessarily be '0%' (note: I recognize that this doesn't quite jibe with the statistical method I used to determine 'critical penalty' since overhealing includes both 'legitimate' overhealing and 'sniped' overhealing, but in the grander philosophical sense of what it means to be penalized for overhealing it's a more accurate reasoning - we just can't easily divide overhealing into legitimate and sniped from a log).

[Myllior]

I haven't looked at this particular issue in a few expansions. The conclusion I came up with them (for direct heals) was "eh... about 5% - 10% worse" - and I based this on looking at the differences in overheal percentage for the normal and critical versions of a given heal. So you'd see that your normal Flash Heal overhealed 15% and your critical Flash Heals overhealed 22% - and that difference would be the 'critical penalty'. I'm not sure how to break down overhealing between criticals/non-criticals in warcraftlogs, though.

If you're looking at the overall numbers reported for non-critical and critical versions of a given heal, then I agree with numbers like that; for the example log analysed in the above Holy spreadsheet, the ratio between critical heal effectiveness and non-critical heal effectiveness is ~0.9617 for spells that produce Echo of Light, and ~0.8977 for heal over time effects. The reason I feel we can't use this though, is that the first half of the raw healing of any critical would have occurred regardless, so if we do the above, then we're ascribing overhealing behaviour to critical strikes that really belongs to a combination of base healing and criticals.

This then comes back to, as you said, the fact that any overhealing factor examining criticals is really looking at how the random events of double the usual magnitude are overhealing compared to the normal events; I agree with this, but then that's literally all a critical strike is (for Holy; Discipline is incredibly lucky in this regard). I think where this comes back to then is locality; these numbers we're processing are by looking at an entire fight, which includes all the low damage periods where random burst events (multistrikes, critical multistrikes and criticals) are going to do more overhealing than the regular versions of spells. So the question is, how should one break down their logs? I guess that examining the overall log, as well as the periods where healing actually mattered, both with and without overhealing factors, is the best way to approach it because only looking at the entire fight is going to skew the value of those stats downwards. (E.g. For Blackhand, something like examining Phases 1 and 3, while ignoring Phase 2, would probably be a good approach for this).

Different spells certainly have different overhealing behaviours, which is why I've got different hit, critical, multistrike and critical multistrike overhealing factors for spells that produce Echo of Light and for heal over time effects. Because of this, we can isolate the overhealing behaviour due to the different spell type from the overhealing behaviour of criticals and the like, because we don't take the critical overhealing factor in isolation, but compare it to the non-critical overhealing factor; so if we have separate sets of factors, we can deal with that.

Carrying on from the above, since it's all about comparing overhealing of critical and non-critical healing, sniping affects all stats. Again looking at the log assessed in the above spreadsheet, the ratio between critical heal effectiveness and non-critical heal effectiveness for Lightwell Renew is ~0.9908 (if we use the numbers directly from the log), so while there may be sniping occurring (the overall effectiveness factor for the spell is ~0.8699), it's not making a significant difference in how much more criticals overheal compared to non-criticals. Of course, then we again have the issue that the criticals recorded are really base healing and a critical component. Regardless, since it's all about how much criticals overheal compared to non-criticals, the issue of sniping becomes essentially the same as the earlier issue of choosing the right portions of the log to analyse.

All-in-all, I think it comes back to the fact that criticals and multistrikes, much like Echo of Light, are healing that occurs after an initial 'hit' of healing, and so are more susceptible to overhealing. The question of how to accurately assess this is, as you've pointed out, more complicated than simply looking at an overall log, but I think that, perhaps, examining localised portions of logs should help give a more realistic assessment. This is also why I decided to put in copies of the sheets that ignore overhealing; while breaking down an overall log may make Critical Strike look atrocious for Holy, it's worth noting that its ability to increase raw healing output is significant, and, in an ideal fight in progression, you should be straining to reach your maximum output.

PS: Before I settled on the current way of treating overhealing factors for criticals, which is essentially to go from (1+C) to (a_D + a_C*C), I was thinking of decomposing the factor into its non-critical and critical components, then applying overhealing factors calculated from the numbers given explicitly in logs; i.e. (1+C) --> (1-C) + 2C --> a_D*(1-C) + a_C*2C --> a_D + (2*a_C-a_D)*C. The reason I didn't implement this is because, in calculating a_C, it essentially assumes that half of the overhealing of criticals is due to the critical portion and the other half is due to the baseline portion; however, since the critical portion essentially comes after the baseline portion, the only way this can be true is if the criticals were 0% or 100% overhealing. Of course, if 2*a_C-a_D < a_D (which is the same as a_C < a_D), then there would be a small penalty introduced, but by looking at individual spells in a log, there are a number of instances where, if a_D and a_C are calculated from the explicit log numbers, then a_C > a_D, which would imply that the critical portions of healing, which come simultaneously with, but also after, the baseline healing amount, are more effective than the baseline healing amount, which seems absurd; hence why I ditched it.

EDIT: Thinking more about the a_D + (2*a_C-a_D)*C model, it's not actually impossible for a_C > a_D to occur, just (quite/really/very, take your pick) unlikely. Consider a theoretical scenario where all non-criticals occur when their targets are on full health, but all criticals occur just as the targets lose enough health for the full critical heal to not overheal. In this case then, a_C = 1, since the critical portion never produces overhealing, while 0 < a_D < 1 due to the overhealing of the non-critical heals and the effective healing of the baseline portions of the critical heals. Maybe I should just dig through the log and find out what the actual a_D, a_C values are, then go from there.

[VigilantRose]

If you're looking at the overall numbers reported for non-critical and critical versions of a given heal, then I agree with numbers like that; for the example log analysed in the above Holy spreadsheet, the ratio between critical heal effectiveness and non-critical heal effectiveness is ~0.9617 for spells that produce Echo of Light, and ~0.8977 for heal over time effects. The reason I feel we can't use this though, is that the first half of the raw healing of any critical would have occurred regardless, so if we do the above, then we're ascribing overhealing behaviour to critical strikes that really belongs to a combination of base healing and criticals.

Try thinking of it in terms of two spells that are identical in all respects except their size. You've got Flash Heal and Double Flash Heal. You cast them under all the same conditions, for all the same reasons and you don't know beforehand which you're casting (so you can't consciously choose one over the other). It's just that one happens to heal twice as much as the other.

If you're looking in your logs, in the "Flash Heal" row you might have 10% overheal. In the "Double Flash Heal" row you might have 15% overheal. Since everything else about these heals is identical, this disparity must arise from the size of the heal. So we make the argument that, on a 1k heal, going from 0% to 100% critical should increase our healing by 100%. But it actually increases our healing from 900 (1k * .9) to 1700 (2k * .85) - 89%. We don't need to muck around assigning blame, we can just observe that this is actually what happens: that +100% critical only yields +88% more actual healing.

What you seem to want to do is break it down on a cast-by-cast basis. We can break down normal heals that overheal (so any potential critical would overheal 100%), normal heals that just barely don't overheal (so any potential critical would overheal 0% - 100%) and normal heals with plenty of room (so any potential critical doesn't overheal at all). But now we need a distribution function to determine how many casts fit in each category.

But we already know this distribution function (or, at the very least, it's effects) - because it's included in our original overhealing disparity above. The "88% as effective" number I came up with is actually the answer to the long, complex process of breaking down each individual cast and combining all the probabilities - as long as our data set is large enough, we can save ourselves a lot of work by just looking at the results of the data rather than trying to invent a distribution function to predict it.

The key takeaway is that any valid distribution function must necessarily reproduce (within a margin of error) the results we saw with the simple disparity calculation - because that's the actual, objective reality our logs showed.

The reason I didn't implement this is because, in calculating a_C, it essentially assumes that half of the overhealing of criticals is due to the critical portion and the other half is due to the baseline portion; however, since the critical portion essentially comes after the baseline portion, the only way this can be true is if the criticals were 0% or 100% overhealing.

Note that the 0%/100% cases are actually very common. If you use Prayer of Healing on a group with only 3 targets injured, that's 40% overhealing - with all of the overhealing coming from the 0% case. On the other hand, the overwhelming majority of your Flash Heals hit for 100% whether they crit or not - the norm isn't that you slightly overheal with Flash Heal. Either you don't overheal at all or you massively overheal, with the average ending up somewhere in the 5% range.

However, there are two main advantages of the decomposition method:
1. You don't have to calculate a_C. You just copy it directly from the log.
2. Philosophically, your current model is claiming that the overhealing chance on the spell you're casting right now is dependent on whether you had a critical two minutes ago. Effectively, you're varying the amount of critical overhealing based on the critical percentage rather than treating them as independent functions. With the decomposition model, the claim is that the overhealing percentage for critical heals will not change based on the number of critical heals you get.

That being said, it's a bit of an angels-dancing-on-the-head-of-a-pin discrepancy. The method you're using will over/under state what I'd predict to be the healing (depending on what point you use to compute a_C) by a relatively small amount (5% or so) over the range of expected values for critical/overhealing/etc.

[Shinhan]

How do I need to fill the Prayer of Healing and Empowered Healing if I'm only casting PoH while under the Empowered Archangel?

When I put all 0 in PoH row and fill only empowered poh row I get 0 a_PoH and entire HPM Optimisation tab is full of #DIV/0!

[Myllior]

If you're looking in your logs, in the "Flash Heal" row you might have 10% overheal. In the "Double Flash Heal" row you might have 15% overheal. Since everything else about these heals is identical, this disparity must arise from the size of the heal. So we make the argument that, on a 1k heal, going from 0% to 100% critical should increase our healing by 100%. But it actually increases our healing from 900 (1k * .9) to 1700 (2k * .85) - 89%. We don't need to muck around assigning blame, we can just observe that this is actually what happens: that +100% critical only yields +88% more actual healing.

It hadn't occurred to me to look at the average healing numbers, as opposed to just overall healing numbers; it does look like it should work if applied correctly. I haven't looked at this properly yet, but there would be a few things to work around to get it working as a single factor; it should be doable (at least approximately), so I'll see how I go.

Regarding the factor in general, I went through the log and pulled out all of the critical and critical multistrike events, so that I could run through it all. The results, as well as the sorting and such of the events, can be found here: https://drive.google.com/file/d/0B1C...ew?usp=sharing. (The fourth sheet can be ignored). I'm surprised how close the factors are to those obtained by simply using the values directly extracted from the log (although, in light of the paragraph below, it's not so surprising), so I've changed the experimental Holy spreadsheet to use those because, even though it's still not 100%, it's infinitely better than the way I was doing it.

Note that the 0%/100% cases are actually very common.

I'd never looked at (or really thought about) this prior to doing the above analysis, so it was surprising to find just how true this is. Of the 414 critical non-multistrike events, only 47 were neither 100% effective nor 100% overhealing, while of the 266 critical multistrike events, only 4 were neither 100% effective nor 100% overhealing. This then explains why the factors calculated directly from the logs, without separating base and critical healing amounts, seem to provide a decent approximation to the 'exact' values (at least in this case).

Philosophically, your current model is claiming that the overhealing chance on the spell you're casting right now is dependent on whether you had a critical two minutes ago.

I think I see what you mean, but that's what happens when you try to use a single factor to gauge the overall healing behaviour of something that varies locally; if we added a single extra Renew tick to the end of the log, our factors would indeed change, but we don't know how. (The same would also be true of the above method comparing averages, since the averages would change depending on how the new cast behaves). I guess my way of looking at the spreadsheets is that they do some analysis of, effectively, a simulation, the simulation being the fight/log itself; if you change the log, the results change. I'm not trying to analyse how overhealing varies with gear, spell choice, raid composition, the fight being healed, etc.; I'm just trying to get a sense of what happened, and how the stats vary should things be the same (they never will, but that's life).

How do I need to fill the Prayer of Healing and Empowered Healing if I'm only casting PoH while under the Empowered Archangel?

When I put all 0 in PoH row and fill only empowered poh row I get 0 a_PoH and entire HPM Optimisation tab is full of #DIV/0!

If all of your Prayer of Healing casts consumed the Empowered Archangel buff, then when you hover over the horizontal bar for it, it should only show numbers for 'Critical Hit' and 'Multistrike Critical Hit'. These numbers then get put in cells C21 and E21 of the 'Stat and Log Input' sheet, and the remaining cells for Empowered PoH (and all of the cells for normal PoH) should then be set to zero (assuming the question is regarding the experimental spreadsheet).

I'm afraid I don't know what's causing the #DIV/0! issue sorry; I've tried setting all the PoH numbers to zero in my own copy of the spreadsheet and everything works fine. If you haven't already, maybe try re-downloading the spreadsheet. Also, ensure you're using Microsoft EXCEL (I can't guarantee that everything will work in other programs), and that iterative calculation are enabled.

Awesome spreadsheet

Thank You

Thank you, and you're most welcome.