Black Mage Sanctuary - A Guide to DPS

[Galvuu]

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Read the post above where I have a massive explanation as to why you need to consider Foul and non-Foul rotations.
We don't have a rotation. We have a priority queue. Which is what I said in the "4.0 BLM numbers" thread.
The tl;dr is:
Foul up for UI? Go 3.X
No Foul for UI? Go 4.0 (align Triple with this, it's possible)

EDIT: There's actually a third possibility, since we're discussing this. It's do 4.0 until the Foul clock gets to a point where you'd get 2x Fouls in your UI cycle. Since you going four spells in UI is hella risky, you can only do three- 2xFoul > T3 > 3.X rotation. I didn't consider this because it's very easy to "upset" the Foul clock with mechanics and end up needing to Foul on the AF cycle, or just get a lot of unexpected procs and having to cut a F4 for Foul and other such nonsense. It's best, in my experience, to do what I said in that wall of text.

[Lilyth]

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Hm... let me see how I can explain this. I wanna captalize on this quote here: "The fact 3.X can afford to bypass B4 and go T3>Foul in UI is why it yields higher pps."

The calculations I did regarding the 3.0 rotation assume that you will, everytime, bypass the casting of a filler by having a perfect server tick (the same scenario of casting foul) and have full mana upon returning to AF. Which means the only spells you use during UI is T3. No other filler. It yields 139,3057081 PPS. And for the 4.0 rotation, you will use Blizz 4 (the filler) and Thunder during UI. The yielded PPS is 140,1707923. Both results do not include Foul. I believe so far you reached the same results, no? What we're pondering is whether or not including Foul makes a difference. So to illustrate this, let's make a thought experiment. Let's assume you have a spread of Fouls where you can stack Fouls indefinitely, and everytime you gain Polyglot (30 secs) the Foul stack is increased by 1. You no longer lose Fouls by not casting them before the next Polyglot is obtained. So far we agree that with the new 2.8 cast time and without Foul, 4.0 wins over 3.0. Here are 3 scenarios:

1: You use only the 4.0 rotation in a dummy for 300 seconds and then use all your Fouls. The total potency in this dummy would be something close to (140,1707923) * 300 + 10 Fouls.

2: You use only the 3.0 rotation in a dummy for 300 seconds and then use all your Fouls. The total potency in this dummy would be something close to (139,3057081) * 300 + 10 Fouls.

3: You use a mix of the 3.0 rotation with the 4.0 rotation in a dummy for 300 seconds and then use all your Fouls. The total potency in this dummy would be something close to [(139,3057081 * 150) + (140,1707923 * 150)] + 10 Fouls.

Would you agree that, whether or not I used the Fouls inside the rotations or at the end, the results would be the same? All this considering the 3.0 mana ticks are perfect, which means no filler is needed inside UI? If so, then the only meaningful variables are the rotations themselves. And thus, scenario 1 is the winner.

[Tingaling]

On the live letter it highlights that foul will cost 0mp to address mana issues on black mages. Doesn't this do absolutely nothing to the mana issue because the way theyre suggesting is transpose foul instead of letting us b3 foul

[Galvuu]

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I want to let the readers of the thread know that Thela, Lilyth and I are basically discussing details of experimental method which amount to very small pps gains. I'm doing this because it's fun

Anyway, Lilyth, you just stated the issue with your premise. It's that you don't cast two spells in the UI cycle of your 3.X rotation (when you absolutely must).
Further, there's also the implicit assumption that the rotation is composed of a fraction of 3.X and 4.0 rotations, but it's an sum of (integer) multiples of each.
It might not look like it, but these will slightly skew your results (this part will also address what Thela said).

Consider now a dummy scenario in practice. Let's assume three players. One is only doing the 3.X rotation which, on average, lasts less than 30s.
The second is doing the 4.0 rotation which, on average, lasts longer than 30s.
The last is alternating between both with the scheme I said.

The first player will, at some point, invariably run into a situation where he won't have Foul up in UI. He'll use an arbitrary fill spell (say Blizzard, or Blizzard IV) that's worse than Foul. He'll then continue to use the 3.0 rotation.
The second will, at some point, get to a point where he has a Foul charged and another almost ticking in- he has to use his Foul immediately or lose one Foul. There's some pps cost to the whole rotation if he's forced to this in AF.
The last won't, at any point, run into these issues- he will always use exactly only two spells in UI, and whenever he does, those are the maximum pps available. Further, when he does this and he's forced to use B4, he gets the highest non-Foul pps possible.

The bottom line is: you want to optimise your UI cycles. You want to use exactly 2 spells on your UI cycle at all times, and the highest pps available. So you'll go T3>Foul whenever possible (3.X rotation) and then T3>B4 when you can't (4.0). This way, you spend the least amount of time in UI. Your calculations "mask" that your 4.0 version will spend more time in it's UI cycle.

If you were to repeat the three previous scenarios indefinitely and then stop them at random points in time, both 3.X-only and 4.0-only can be stopped at various poor situations- an AF where you had to Foul for 4.0, a B4 3.X- but the third is always on an "optimal" scenario for his given resources. This is not accounted for when people make pps calcs like that. That's why it's important to see what yields the most gain if you can T3>Foul, and what yields the best gain if you can't and must go T3>B4 (though you wouldn't waste your Umbral Hearts if you just B4'd, but it turns out that even if you considered that, 4.0 would be optimal in the no Foul scenario).

If you were to make a very long table with realistic rotations (trying to put Foul in there and not adding it at the end), the issue would show up.


(This one is a bit harder to digest...)

This is an optimisation problem. It's a maximisation problem (obviously) under a bunch of constraints pertaining to resources and timers and whatever.
For the case of BLM, you can rewrite this as a mutant, hybrid problem- you want to minimise your time in the UI cycle (so, 2 spells, because we're constrained to 2 spells) and maximise your potency in that UI cycle. There's another weird "constraint" that acts as some regularisation parameter that represents the AF cycle pps- think of this as the cost for not using B4, since the AF cycle of 6xF4+F has more pps than 4xF4+F (Firestarter reduces this difference, but let's just assume that we add the expected pps gain from AF as we're talking about lengthier times).
You're implicitly throwing some of these constraints off the window. You're not necessarily forcing two spells each UI on 3.X (which will eventually be a non-Foul spell since the expected duration of the 3.X is under 30s), and you're not accounting for the fact that you'll get messed up Fouls on the 4.0 one. These are punitive factors to each rotation.
That's why you need, at the start of each UI cycle, pick whatever option yields the highest expected pps for the next rotation- 3.X if you know you'll have Foul, 4.0 otherwise.
Obviously procs and mechanics can extend the 3.X, and it's not unreasonable to say "you can probably get away with doing 3.X almost indefinitely". In some cases, yes.
But nothing is going to improve the 4.0 situation in regards to Foul. Unless the stars align, you'll either need to Foul in AF, or double Foul in UI and drop T3.

I'm actually going to make a huuuge table that accounts for Foul positioning just to check, and upload the file somewhere.

EDIT: Wait a minute... 3.X wins out with Foul, but eventually you'll run out of Foul and be forced into the B4 filler... and that happens to be optimal for either case? D... did the devs foresee this? Was this planned? Are they actually really insightful? O.o

[jamvng]

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I see the benefits of mixing 3.x and 4.0, i have two issues/questions:

1) if you came from 4.0 rotation and wanted to switch to 3.0, you'll be using B3 > Foul (won't have mana for anything else), > T3 > F3. If T3 doesnt get refunded before AF, you end up w/120mp on next B3, unable to cast anything. Isn't that just bad?

2) If you do 3.x rotation, get a T3P near the end and have to use it in AF (cant save for UI), then go B3, it's no longer worth hardcasting T3 since you just refreshed the DoT. You're forced to use B4 as a filler spell instead (Foul + B4 as the two filler spells). I guess this isn't really an issue, more like it forces you to do 4.0 rotation again.

I see 4.0 rotation being the primary rotation to use, with 3.x rotation being used in certain situations. Namely, being closed to losing Foul/having to use it in AF, or movement causing loss of F4. And even if I go to 3.x rotation, I'm sorta scared to get mana screwed (120MP)...?

[Galvuu]

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It's bothersome, yes. But this is much like getting a bad manatick when going 4.0 and not getting B4 refunded.
You can learn to somewhat mitigate this by committing the tick timings to memory, but every once in a while I mess it up and just feel bad about myself.

You're right about the TC proc situation. Proc management can (sorta) force you into such a situation.
I'm simplifying the analysis here and will release a new thread when the patch hits.
If you want to be rigorous, there's other things to consider. Say I just got a Balance as I'm mid UI cycle and will have it for 35ish seconds when I hit AF- I'm going to switch to the 4.0 rotation to get 6x Fire IV and Foul buffed by the balance.

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I need to see how much we gain. But between that and Foul costing 0 mp, we may end up with a very strong, 5xFire IV 3.X rotation that would trump the 4.0 one.
(Incidentally, you asked me in some other thread about how I like SMN visually- I actually really like Ruin 3's animations, and the laser-from-the-sky Deathflare. Adding to the fact that we have Bahamut, I'm quite content with it visually. I've always hated the egis, but I can just use a Carby now too, so x) ).

[jamvng]

It's bothersome, yes. But this is much like getting a bad manatick when going 4.0 and not getting B4 refunded.

I'm hoping they actually fix the mana tick situation fully in 4.05 so that we're always able to do 6xF4 if we want to without worrying about mana tick. 0 mana Foul fixes the 120MP situation also for 3.x rotation.

Let me summarize what I'm getting so far from this discussion: 4.0 rotation has more PPS if you do not include Foul (as the # of Fouls never changes in a battle). However, you want to use Foul in UI and not AF, which won't be possible at one point if you just use 4.0 rotation. In addition, if you can't cast 6xF4 after using B4, it is also a loss in PPS as you make it not worth using B4 anymore if you can't cast all 6 F4s. As such, you use 3.0 rotation insteadf of 4.0 in those 2 above case scenarios. And then we have the more niche scenarios like we discussed with procs or buffs. Am I right on that so far?

[Galvuu]

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Yes, that seems more or less to be it.
Ofc without patch notes, we can't be sure. If they alter potencies or have other changes (or even depending on how much MP we get), this can all change.
If the base MP is raised by like, 1000, the the 3.X rotation can now include 5xF4s, and will be better regardless of the scenario (and even have the perfect duration to have Foul up every UI, with Sharpcast and Triple offsetting each other's influence on rotation length and conveniently sharing a cd).

[Lilyth]

Hey, sorry being a little late but work is being a mess lately!

Anyway, Lilyth, you just stated the issue with your premise. It's that you don't cast two spells in the UI cycle of your 3.X rotation (when you absolutely must).

Actually I was simply considering a perfect mana tick scenario for the person using the 3.0 rotation exclusively, in which case a single spell (thunder III) is already enough to get full mana. I know that in your proposed priority system you'll always have foul up for that part which would ignore the mana tic problem, but that's really besides the point. More on that later.

Consider now a dummy scenario in practice. Let's assume three players. One is only doing the 3.X rotation which, on average, lasts less than 30s.
The first player will, at some point, invariably run into a situation where he won't have Foul up in UI. He'll use an arbitrary fill spell (say Blizzard, or Blizzard IV) that's worse than Foul. He'll then continue to use the 3.0 rotation.

In a real scenario, yes. But we're comparing the raw potencies of a perfect executed 3.0 rotation, which is 139,305708 PPS. No Blizzard used.

The second will, at some point, get to a point where he has a Foul charged and another almost ticking in- he has to use his Foul immediately or lose one Foul. There's some pps cost to the whole rotation if he's forced to this in AF.

This is a non issue, honestly. Using only the 4.0 rotation will indeed lead you to this situation. But now with Triple Cast on 60 secs CD, you'll have either Sharpcast or Triple cast up for every single AF cycle while still saving Swiftcast for movement. Not to mention with the new F4 cast time, which pretty much gives us extra 1.2 secs on our AF cycle assuming 6 FIVs, and the 0 Foul mana cost, you'll have more than enough time to fit Foul into AF or even two Fouls into UI if you time it well. But again, that is besides that point and you will see why.

The last won't, at any point, run into these issues- he will always use exactly only two spells in UI, and whenever he does, those are the maximum pps available. Further, when he does this and he's forced to use B4, he gets the highest non-Foul pps possible.

The bottom line is: you want to optimise your UI cycles. You want to use exactly 2 spells on your UI cycle at all times, and the highest pps available. So you'll go T3>Foul whenever possible (3.X rotation) and then T3>B4 when you can't (4.0). This way, you spend the least amount of time in UI. Your calculations "mask" that your 4.0 version will spend more time in it's UI cycle.

If you were to repeat the three previous scenarios indefinitely and then stop them at random points in time, both 3.X-only and 4.0-only can be stopped at various poor situations- an AF where you had to Foul for 4.0, a B4 3.X- but the third is always on an "optimal" scenario for his given resources. This is not accounted for when people make pps calcs like that. That's why it's important to see what yields the most gain if you can T3>Foul, and what yields the best gain if you can't and must go T3>B4 (though you wouldn't waste your Umbral Hearts if you just B4'd, but it turns out that even if you considered that, 4.0 would be optimal in the no Foul scenario).

So here's the important part: everything you just said is already being taken into account. Our calculations have given us 139,305708 PPS which is a number we reached by doing the 3.0 rotation with no filler spell under UI, which is the perfect scenario. What I want you to understand is that, regardless of where you place foul, the final number is the same. And that's what my examples were all about.

A) F4-F4-F1-F4-F4-B3-FOUL-T3-F3

B) F4-F4-FOUL-F1-F4-F4-B3-T3-F3

C) F4-F4-F1-F4-F4-B3-T3-F3-FOUL

These all have the same PPS. We're simply adding potencies since the duration is the same. We could even do something like:

D) F4-F4-F1-F4-F4-B3-T3-F3-F4-F4-F1-F4-F4-B3-T3-F3-FOUL-FOUL

Which is the same as doing A, B or C twice.

I understand how convinient it is to use Foul under UI for 3.0 and 4.0. But this is only for convenience sake. Math doesn't care about that. If you put Foul in the middle of your AF or in the middle of your UI or wherever you want, the end result is the exact same, assuming you can still perform the entire rotation normally.

Ok, but where does this lead us? We don't want this ideal stuff, we want rotations that will work for us on realistic scenarios, right? Yes! So let's get real. If you understand that placing foul whenever doesn't change the end result, we can finally look at realistic scenarios. Your priority suggestion does make a lot of sense. You'll always have foul on UI which is convinient, and I'd definitely go for that too... except it is not optimal PPS.

Look, 3.0(with foul) + 4.0(with foul) does yield a higher PPS than only 4.0 (with foul) over and over again. But you know what you are forgetting? By doing only 4.0 on a realistic level, you will get 4.0 with two fouls and THAT'S where 4.0 wins. 4.0 with two fouls is a huuuuuge PPS gain over 3.0 with a single foul. And how do you gain this double-foul scenario? By repeating the 4.0 rotation. The only argument against it that I can think of is "but this will make your rotation even more tight by fitting in a second foul". And yes that's true. But I'll take it. Bacause it's better. With the new Triplecast CD, that's easily doable. And it is the optimal way to play

This all look great and all but that's not even the point I'm really trying to make. I'm only taking on a more realistic approach to help you see why 4.0 is superior after the update. But the real bottom line is: Foul is a constant. Both rotations have it, equally (because it's on a 30 seconds timer for both), so it doesn't affect the comparison by ignoring it. Foul is as much of a factor as Enochian. If 4.0 is better without Foul, 4.0 will be better with Foul.

If you were to make a very long table with realistic rotations (trying to put Foul in there and not adding it at the end), the issue would show up.

I'd be all for that, actually.

That's why you need, at the start of each UI cycle, pick whatever option yields the highest expected pps for the next rotation- 3.X if you know you'll have Foul, 4.0 otherwise.
Obviously procs and mechanics can extend the 3.X, and it's not unreasonable to say "you can probably get away with doing 3.X almost indefinitely". In some cases, yes.
But nothing is going to improve the 4.0 situation in regards to Foul. Unless the stars align, you'll either need to Foul in AF, or double Foul in UI and drop T3.

What you said is true If Foul wasn't a constant. But it is. I can't reinforce this enough XD. The only downside of 4.0 is that it is tighter. You might, possibly, eventually.... have to drop something on 4.0 because 3.0 which has much more "free" time. But as our SS increases, and accounting for Sharpcast and Triplecast which (now) both have ridiculously low recast times, I strongly believe it's better to stick to the strongest PPS-wise rotation instead of the "easiest" one.

Little PS regarding the MP adjustments: these adjustments might indeed change things. If it will make possible to cast 5 FIVs without needing BIV at all, then that would be a whole different story. We'll have to wait and see.

[jamvng]

Little PS regarding the MP adjustments: these adjustments might indeed change things. If it will make possible to cast 5 FIVs without needing BIV at all, then that would be a whole different story. We'll have to wait and see.

If they increase base MP to allow for 5 F4s without B4, that would also allow 4.0 rotation to have 7 F4s I'm pretty sure. It goes both ways. If they increase base MP by 360, that would eliminate the mana tick issue with 6xF4 rotation. Previously with a bad mana tick, 6xF4 would leave us with 0MP, adding 360 would allow us to B3 and Foul (0MP). On the flipside, you would also be able to 5xF4 w/o B4 WITH full mana, however you would have a mana tick issue afterward still, forcing you to do 4xF4 on the next rotation.

I'm really interested to see how they fix the MP, we'll find out tonight/tomorrow...

RE:rotation analysis
Great insight here. I do love that us getting a Sharpcast or Triplecast every AF will be extremely convenient to fit procs in.