BLM AOE Rotation

[daespinoza]

I know that casting Flare after Freeze makes it go off faster, but wouldn't it be more efficient to first cast Fire III after Freeze to get the Astral Fire damage bonus for the two Flares?

[Rongway]

I know that casting Flare after Freeze makes it go off faster, but wouldn't it be more efficient to first cast Fire III after Freeze to get the Astral Fire damage bonus for the two Flares?

Here are some quick numbers (Not accounting for Thunder IV, Foul, and oGCDs, which would just increase numbers all around)

[Gruntler]

I know that casting Flare after Freeze makes it go off faster, but wouldn't it be more efficient to first cast Fire III after Freeze to get the Astral Fire damage bonus for the two Flares?

Rongway has the hard bruteforce math, but think of a different question:

'Wouldn't it be more efficient to do only an AoE rotation, instead of interrupting your AoE to do minor single target damage?'

Not to mention, single target damage doesn't always affect the time-to-die of an AoE pack, which means that it doesn't always count in terms of efficiency.

[daespinoza]

I didn't even think of it that way. Thank you so much for the input!

[Fenli]

Always cast Fire III.
That math is bad; it's missing Crits. You should have around a one in six chance to crit, which is nothing to scoff at, and those crits deal +50% damage. Also missing Direct Hits, which have around a one in four chance to happen, dealing a flat +25% damage, which stacks with crits (should they happen simultaneously).
Those chances are so high, that even with the worst luck in the world, you're dealing one or the other multiple times a fight.
It's simple maths: when you multiply a big number instead of a small one, you get an even bigger one. A crit "cold" Flare is a sad, sad thing, where a crit "hot" Flare is glorious.

Plus, Triplecast (and Manafont) exist. Why wouldn't you be using all the tools at your disposal?

[Rongway]

That math is bad

You didn't provide a quote, so I'm going to assume you're talking about mine.

Plus, Triplecast (and Manafont) exist. Why wouldn't you be using all the tools at your disposal?

I addressed this. They're excluded from the math because they won't change the conclusion. If you use all the same oGCDs in both rotations, all the extra Flares will be performed under the same conditions in both rotations and will increase the numbers in both scenarios in similar ways. Any difference between the two rotations will come down to starting with (Fire III + Flare) vs just casting Flare. I never said not to use them. They just don't matter when the specific question is "should I cast Fire III or not?"

it's missing Crits. You should have around a one in six chance to crit, which is nothing to scoff at, and those crits deal +50% damage. Also missing Direct Hits, which have around a one in four chance to happen, dealing a flat +25% damage, which stacks with crits (should they happen simultaneously).
Those chances are so high, that even with the worst luck in the world, you're dealing one or the other multiple times a fight.
It's simple maths: when you multiply a big number instead of a small one, you get an even bigger one. A crit "cold" Flare is a sad, sad thing, where a crit "hot" Flare is glorious.

These also don't matter when the specific question is "should I cast Fire III or not?"

The expected damage of a Fire III hit is
(critrate * (1+critbonus)) * fire3dmg + (1-critrate)*fire3dmg
=(critrate + critrate*critbonus + 1 - critrate) * fire3dmg
=(1 + critrate * critbonus) * fire3dmg

Each Flare hit is an independent event, and the expected outcome of each independent Flare hit is
(critrate * (1+critbonus)) * flarehit_i + (1-critrate)*flarehit_i
=(critrate + critrate*critbonus + 1 - critrate) * flarehit_i
=(1 + critrate * critbonus) * flarehit_i

The sum of the expected damage from each Flare hit is
(1 + critrate * critbonus) * flaredmg_1 + (1 + critrate * critbonus) * flaredmg_2 + ... + (1 + critrate * critbonus) * flaredmg_n

Or
= (1 + critrate * critbonus) * sum[i=1..n](flaredmg_i)

So if you want to compare the damage between a "cold" Fire III and a "cold" Flare, you can compare them directly without worrying about crit, because inequality relations are preserved under (positive) multiplication and division.
(1 + critrate * critbonus) * fire3dmg < (1 + critrate * critbonus) * sum[i=1..n](flaredmg_i)
===> fire3dmg < sum[i=1..n](flaredmg_i)

Critting a single target attack doesn't make it better than an AoE attack just because of the crit; the AoE attack will crit just as often, on average, and what matters is the total damage across all hits in the cast.

[PyurBlue]

It's simple maths: when you multiply a big number instead of a small one, you get an even bigger one.

That's why skipping Fire III can be good. F3 can only ever hit one target so its damage is proportional to potency * 1. Flare can hit many targets so the damage it produces is roughly potency * (potentially big number). Flare is also higher potency than F3 in the fire place, and when used under Umbral Ice they both cast faster than their recast time, so F3 isn't any faster.

[Jonnycbad]

OP why do you have a second Enochian in your rotation?

[Hasrat]

I know it already looks to be sorta covered, but B3 is probably unnecessary in OP's rotation as well. Just start with Freeze. Also everything after that second double Flare looks a bit of a mess. Transpose (which already covered unnecessary), leading into a F3 into F2 into Flare. Seems pretty sketchy to rely on MP ticks from one UI stack being enough to get you through that, even with Triplecast. And F2 when you could be double Flaring again.

[Fenli]

what matters is the total damage across all hits in the cast.

Correct, which is why you want AF3 crit Flares