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Spirit, Regen, and their effect on time till OOM

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Incidentally, if I'd used the proper (Darkglow-enchanged) cloak, it looks like I would not have run out of mana on that fight.
Posted Dec 8, 12
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Adinne wrote:
Note however that they would not depend on the initial mana pool, and whether we mana pot or not.
Mana pot would be the same as any other regen mechanic (like Tranquility), but doesn't initial mana pool matter? First, Spirit gives regen as a percentage of max mana, I thought, so something like Ember Primal Diamond will improve your spirit regen by 2% as well. And seems like initial mana is an important part of TOOM. Like, looking at the graph of my mana, I would have OOMed earlier if I'd started with 50k less mana. What did you mean that initial mana doesn't matter?
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Would we be off in our comparisons by using the one amount over the other?
I was more concerned with the effect that duration has and didn't stop to consider the magnitude of the other effect. You're right, that's not very different!
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(Regrowth differs a bit because of the increased crit chance).
I think this is the kind of thing Erdluf was aluding to, that individual spell mechanics, fight mechanics, spell cooldowns, and what-not all conspire to make a homogenized formula less accurate.
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EDIT: Nice work on those graphs! Do you have a program that does the combat log processing for it?
It's a perl script that generates a tsv file that I feed into excel to make the graphs. It only knows about stuff that relates to my character, of course, but I'm happy to share it with anyone that's interested.
Posted Dec 8, 12
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Oleander wrote:
Adinne wrote:
Note however that they would not depend on the initial mana pool, and whether we mana pot or not.
Mana pot would be the same as any other regen mechanic (like Tranquility), but doesn't initial mana pool matter? First, Spirit gives regen as a percentage of max mana, I thought, so something like Ember Primal Diamond will improve your spirit regen by 2% as well. And seems like initial mana is an important part of TOOM. Like, looking at the graph of my mana, I would have OOMed earlier if I'd started with 50k less mana. What did you mean that initial mana doesn't matter?

First off I consider one-time mana gains like the mana pot as part of your total mana pool. So if you are planning to use a pot of focus for instance, I would use 345k for your total mana pool. This affects the time to oom of course, but it does not affect what percent of increase to your time to oom a given amount of spirit is. 100 more spirit would increase your time to oom by the same percentage, whether you have 300k mana and oom in 6 minutes or 10k mana and oom in 10 seconds. Of course a 5% increase in your time to oom is more time when your time to oom is more to begin with, but it is not more in relative terms. The percent increase in your overall healing is also the same, regardless of your total mana pool. (effectively the total mana pool amount cancels out when you measure relative increases). It's effectively the same reason why the actual amount of a heal or any extra healing multipliers don't matter when you look at relative increases.

On the same topic, a 5% increase in your total mana pool translates to 5% increase in your time to oom. In particular, using potion of focus is a 15% increase in your time to oom just by itself. Making sure to use a pot of focus is the equivalent of quite a lot of spirit. Using pot of focus instead of mana pot is a 4.5% increase in time to oom (but of course also requires 10 seconds doing nothing).

The amount of regen spirit provides you has nothing to do with your mana pool, it is set and depends solely on your lvl. Of course the size of your mana pool affects your incoming mps by affecting things that are based off your total mana, like Innervate.
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Posted Dec 8, 12 · OP
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Re spirit & max mana: Huh, you're right. I'd just assumed that the 1% was off max mana, and not fixed at 1% of 300,000. But you're right!

Re Percent increase from spirit:
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a 5% increase in your total mana pool translates to 5% increase in your time to oom.
I think this is a perfectly reasonable approximation to use, and what I will use in this poist.
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This affects the time to oom of course, but it does not affect what percent of increase to your time to oom a given amount of spirit is.
I still don't understand this part. I will use your example, and assume a 10k mp5 combat regen.

In a 6 minute fight with 10k mp5, combat regen would contribute 720k mana, which would be roughly 70.6% of total mana. If we add a focus pot, then combat regen drops to 67.7% of total mana. If we consider a focus potion and two innervates, then combat regen drops to 60.7%. Anything that grows combat regen will be scaled by the same percent for its effect on total mana.

Changing the fight length can also mean more innervates just as it means more combat regen, further complicating the model.

Furthermore, a 5% increase in spirit doesn't equate to a 5% increase in combat regen. At 10k mp5, spirit is only 40% of combat regen, so a 5% increase in spirit would be a 2% increase in combat regen.
Posted Dec 8, 12
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Oleander wrote:
I still don't understand this part. I will use your example, and assume a 10k mp5 combat regen.

In a 6 minute fight with 10k mp5, combat regen would contribute 720k mana, which would be roughly 70.6% of total mana. If we add a focus pot, then combat regen drops to 67.7% of total mana. If we consider a focus potion and two innervates, then combat regen drops to 60.7%. Anything that grows combat regen will be scaled by the same percent for its effect on total mana.

Changing the fight length can also mean more innervates just as it means more combat regen, further complicating the model.

But remember we are not talking about fight length, we are talking about time to oom. And Innervates are rolled into Incoming MPS. The formula for time to oom is:

T = TotalMana/(IMPS-OMPS)

Now a change D in IMPS due to spirit would result in time to OOM given by:

NewT = TotalMana/(D+IMPS-OMPS)

What we need to compute now for the percent increase is:

(NewT-T)/T = (NewT/T) -1 = (D+IMPS-OMPS)/(IMPS-OMPS) - 1 = D/(IMPS-OMPS)

TotalMana cancels out. If it's 345k instead of 300k, that means that T becomes 15% bigger, and NewT becomes 15% bigger. But the quantity (NewT-T)/T remains the same.
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Furthermore, a 5% increase in spirit doesn't equate to a 5% increase in combat regen. At 10k mp5, spirit is only 40% of combat regen, so a 5% increase in spirit would be a 2% increase in combat regen.
Correct, but we never talk about a percent of a base stat or rating, we talk about a fixed amount. We wouldn't say for instance "10% more mastery rating", we would say 1000 more mastery rating. It's the same with spirit.
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Posted Dec 9, 12 · OP
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But remember we are not talking about fight length, we are talking about time to oom
Changing toom changes the number of innervates, too. If you can push NewT to the next innervate, you have to adjust Total Mana again to get NewNewT.

Looks like I forgot the first post! Sorry to make you repeat yourself. I played with it a bit, rederived your initial formula, and it all makes sense now.

Looking at just spirit for a moment: 1000 spirit, for me, is about a 4.5% increase in IMPS. That effect on TOOM depends on OMPS of course. At the end of Elegon, it'd be about 2.5% increase in TOOM. For that Will fight I posted graphs of, OMPS and IMPS were much closer, and 1000 spirit is a 20% increase in TOOM (not counting the extra innervate it would have allowed.) I find that result comforting as it matches my intuition that spirit is not strong in really short, high HPS situations. It also clearly illustrates the benefit of keeping IMPS closer to OMPS.

So that leaves the role that throughput stats play in TOOM. Trying to get an actual relationship between throughput and OMPS seems very hard, even for a specific fight. But I think that in most cases, increasing throughput by x% will reduce OMPS by less than x%. And since 1000 int increases my throughput by something like 3.5%, it will be rare that 1000 int will increase TOOM by as much as 1000 spirit. And that's probably what you were trying to get at:
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you have to work out for yourself and your particular fight needs what your "rotation" is likely to be... and how much spirit would be worth.
Posted Dec 9, 12
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I am just averaging out the innervates as a more or less fixed amount of incoming mps, I don't think it's very beneficial nor easy to treat it discretely like that, especially given how much time to oom will vary from case to case, and given that we probably won't agree very easily when the first innervate would be happening, though I suppose we could base that off the remaining IMPS and OMPS. Then we would have to apply the same treatment to things like shaman's mana tide or a priest's hymn of hope, or even more simply the kinds of short cds on trinkets you have. Also this makes your comparison based on a specific amount of spirit only, different amounts of spirit would result in uneven gains this way. I suppose it's like trying to quantify the value of haste, we typically would do it by treating separately the cases before and after a breakpoint. If you are before a haste breakpoint, haste would appear more beneficial if you're using a delta that would make it exceed the breakpoint than if you don't. I think trying to work out "spirit breakpoints" around mana cds is an interesting idea, but I suspect it won't be too easy.

I am not sure how you want throughput stats to affect OMPS and hence TOOM. Haste is the only one I can see directly affecting OMPS, but even then I'd rather not use it for comparisons. We already have established relations between mastery, crit, haste and spellpower, I would use those to decide the value of the throughput stats. What is (sort of) missing, is the relation between spellpower and spirit, which is what I was attempting to establish. I'm guessing you are maybe thinking that with an increase in throughput you would need to cast less? I'd rather think of it as "you'll be able to heal more". That extra healing would in a sense come off your fellow healers. I think of the goal of stat weights and gearing up/reforging as "increasing your healing potential", regardless of who else is healing with you.

Well time to bed for me, and I think I'm starting to blather at this point.
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Posted Dec 10, 12 · OP
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