Originally Posted by Gloryrider
Havoc, I was only disagreeing with you that haste is simply equally (un)affected by whether or not you choose to halt your healing or not when there is mostly overheal. And following your logic, crit is also unaffected when there is a break due to raid mechanics.....
I daresay crit is less affected simply because it inherently has a shielding mechanic, for reasons I stated above. At least a shield is better than a heal when everyone is already at(/near) full health.
A last thing that pops in my mind is the difference of mana regen between 10 and 25 mans...
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You seem to be confused. Crit is not affected at all by any breaks in casting, whether they are due to mana, raid mechanics, taking a break to ponder the meaning of life, scratching your nose or whatever. You get a % benefit in every cast no matter how many casts you get off. Haste is only unaffected by enforced break in casting because you have to do something else to prevent your raid wiping or because there is no healing to be done. If you run oom, or you decide to not chain cast even through you can the the value of haste plummets. On the other hand crit is strongly affected by high overheal, but haste is not. Shields are not only good when there is constant damage in which case it makes sense to chain cast. Crit has lower value because of overheal even if shields are absorbed 100% but haste is completely unaffected.
So to recap: If you are not chain casting or you are running oom, haste loses value. If you overheal lots crit loses value. Its really simple and there is nothing else that can be said about it really.
Mana regen in 25man can be higher, but mana expenditure is disproportionally higher. We don't always have a shaman and boomkins are not feeding me with innervate. They are feeding everyone else. I have 14k raid buffed spirit so I don't run oom and chain cast constantly without break. I experimented with the spirit I need and I found that by switching food and flask to int I run oom typically in the burn phases where I should be producing my max HPS, so more spirit gives me superior results, especially if something goes wrong and my mana management cannot be maximised.
After hitting 60% mastery raid buffed I started experimenting with adding crit and haste. Haste gives me consistently higher values, so I am going haste.

Originally Posted by Jeges
I think if we could come to a consensus on the value of crit to within 7%... 100 samples allows you to get a pretty good estimate of a mean, even for a funny-shaped distribution.
I'm not using d as a proxy for overheal estimates. Let f be the PDF on health deficits (instead of d, for clarity). Let h be the value of a normal heal. Then the expected actual value of a heal is:
integral_0^h f(x)*x dx + h * integral_h^infinity f(x) dx
The expected actual value of a crit (not counting DA) is:
integral_0^2.06h f(x)*x dx + 2.06h * integral_2.06h^infinity f(x) dx
The best estimators of these values, from the data, are the respective means of heals and crits. You can argue about whether expected value of a heal and expected value of a crit are important metrics, you can propose others and see how they do, etc... To me, for example, I'm most interested in how much I can heal during the most healing-intensive phases of a fight, and so looking at means actually will tend to undervalue crit (since spells are less likely to overheal when there's heavy damage going out). But, to me, looking at the ratio of how much healing I get from an average crit to how much healing I get from an average noncrit is a pretty reasonable way to asses how useful a crit is to me.
In my defense, it was a Poisson plus sometimes a gaussian. But, again, I wasn't trying to accurately model hp deficits, just to show that you could estimate a mean reasonably well with 100 samples. The mean may not be the most informative statistic for a multimodal distribution, of course.
Crits can have 106% value due to meta gem. A
What I see in your example is that using a throughput CD (playing well?) when there's a lot to be healed makes crit a more attractive stat.
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Its 7% with your poisson 10 distribution. Your actual estimates are wildly off and it won't be a 7% estimate for crit value but for the averages themselves. Then when you divide them to get your value you are magnifying the error.
Your calculation is wrong. Because a heal does not have a value h, its value is variable. And no the estimates averages have a large error due to sampling and CD usage.
100% means 100% of the expected value, be it 106% or 1000000006%. Crit can never have more than 100% its expected value. If you are seeing more than 100% then the only explanation is that you are chaining skull banners and you atonement spam 24/7 or you have a sampling error. The latter one is the explanation. 100% value requires either 0% overheal or all heals either overhealing by 100% or 0%. You are not seeing that, so you have an artifact.
I am afraid you see it wrong. What you are seeing is the average being inflated but not the actual value of crit.
You think crit is great for hard spikes but its actually the worse possible stat. Crit only works when there is constant high level damage, and that is rarely the case.
Think of it like this your raid takes 5 big hits over 5 seconds, if you use PoH you can land 3 PoHs in that period of time and then maybe 2 PoH after the spike is over. The first PoH criticals can probably overheal because you pre-cast it and it lands as the damage starts, but all aegis will absorbed. Crits for the 2nd 3rd will probably not overheal but aegis will probably not be absorbed. Any PoHs you will land later crits will overheal and ALL aegis will be lost. That is why crit is terrible, especially with a slow hitting party limited spell.
Even worse you have no guarantee everyone will get a crit. If you are trying to chase serious damage with 3 PoHs, which will be lethal if you don't crit then, even with 35% crit why dont we calculate what the chances are that one person will not get a crit.
The chances of one person getting not getting a crit is (1-0.35)^3 = 0.274625 and you got 5 targets. So what you get is 5*(1-0.35)^3*(1-(1-0.35)^3)^4 = 0.38. If you have to chase damage that is lethal without crit you will lose someone nearly 40% of the time.
Worse of all even if its not lethal damage you just have no guarantee that your next PoH won't crit on those with the smaller deficits.
For atonement and smart heals the fact that you are targeting the lowest health person is slightly better, but the same problem applies you just have no guarantee that you crits will happen at the wrong time.
It is pointless to take crit to increase your burst HPS. Crit has one and only one benefit to increase your overall HPS and mana efficiency over the whole fight. Haste and mastery is what you take if you want to increase your ability to chase burst damage.
Looking at your logs:
Expression Editor - 29-01 20:04 - Exhumed - World of Logs
All your atonement crits.
I add effective healing and overheal, averaged it and divided by two. So if you didnt crit there your average heal would be 22670.5. Your average non crit heal without overheal however is 19808.7. Do you see what I am talking about? you have 67 heals and you have an error in estimating average heal of 15%!!!. This is before you factor in the health deficit distribution.
Now lets go look at another example, of how erroneous your method is: Look at cascade. Your method suggests that you are getting zero benefit from crit:
Details for Chebag - 29-01 20:04 - Exhumed - World of Logs. Crits are roughly equal to heals. Is this true? Lets see
[20:39:33.548] Chebag Cascade Risen Ally +*56684* (O: 41738)
[20:39:36.861] Chebag Cascade Shadowfiend +*23505* (O: 78515)
[20:41:14.277] Chebag Cascade Kapaneus +*52925*
[20:41:15.553] Chebag Cascade Beast +*0* (O: 107528)
[20:41:15.553] Chebag Cascade Axel +*16500* (O: 91028)
[20:41:17.958] Chebag Cascade Fatfu +*97379*
The answer is nope. Crit is still giving you value. because you would lose healing if you converted some of those crits to normal heals.
The sampling error here is really high, but that is because of the small sample size.
Look at this:
Details for Chebag - 31-01 20:13 - Exhumed - World of Logs
You have 1000 heals for atonement here, but just look at how many you have for the rest. Since you are averaging for all spells you are giving all groups the same weight despite the fact that all other groups except atonement have extremely small sample sizes. Look at the overheal of atonement crits vs atonement non crits, which is the only one that actually has a decent sample size (which is still too small for assuming that you have equal distributions of d and accurate estimation of the the average heal).
The rest of your heals have extremely small sample sizes. I don't have time right now to sit down and calculate the value of crit for that aggregate, nor is it worth my time to do so. So I just had a quick look. First I calculate your real crit/non-crit ratio
At: 1.461730463 908
PoH: 2.285245564 170
casc: 2.644428052 162
FHl: 1.952764449 39
PoM: 1.772283875 80
The 2nd colum is crit to non crit and the last is the number of spell casts.
Averaging after weighing for number of casts gives us 1.738102188. Which is for course no where near accurate. My quick look says the ratio is around 1.6.
So even for this large number of casts you are still using a very inaccurate value.
The data you posted at least the stuff I looked at does not support a 2:1 ratio for crits to heals. Not even close. Despite having relatively low overheal values and spamming mostly atonement you are still a long way off from achieving 100% value from crits.
Whether or not you are convinced that you method is wrong and you have handled your data incorrectly is now your problem. I am pretty much done discussing this. Its not worth my time, since your playstyle is very different from mine and any conclusions you make are simply inapplicable to me.
At the end of the day for everyone else, this was as expected a red herring. Crit does not have 100% value ever, not even with the very little overheal (protectors hard) and it is mathematically impossible to get more than 100% value no matter what the fight is like.
Depending on your playstyle you can evaluate crit from 0.7 to 1.7% per point, but that is average over a large range of crit. The first points of crit (coming just from intellect and buffs) have a much higher value than any additional crit you get from rating. Since we are looking at 15-17% base crit, the real value of adding crit is lower.