What should a SCH be averaging in Final Coil? Should a WHM be using downtimes to cast an Aero(2) or Stone 2?
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What should a SCH be averaging in Final Coil? Should a WHM be using downtimes to cast an Aero(2) or Stone 2?
Gonna reply to the SCH portion of your question.
First things first, while I think that healer off-DPS is a good thing and certainly something to be expected in good or better groups, I would like to point out that the actual numbers vary wildly based on the fluidity of the encounter at hand. You can have X DPS in a run that goes smooth and X - 50 or X - 100 DPS in a run that does not go smooth. The priority is always the raid's safety; you don't wanna be the guy who wiped the raid because of perma-clericing in a situation where it didn't need to be a wipe. Whilst other jobs have more defined figures for certain gear levels (with a BRD's DPS having some song variance per encounter too), the healers have to operate under ever-changing variables.
Now that the hopefully obvious stuff is out of the way... The other things your numbers depend on:
1) How good your WHM is. This part is oft-times ignored, but some of the number pushing comes from the goodness of your WHM rather than the goodness of the SCH. Don't get me wrong, there is a definite difference between 100% Cleric Stance SCHing as well, because of how bad some SCHs are with their micromanagement-game (manual Embrace-spam adds a ton of HPS which eases the WHM's job; some SCHs also suck at using their tools like Eye for an Eye, etc). Still, "maintenance healing" is a shared duty and if you slack on that department, you might overburden the WHM or get the raid killed, which is not good. Calculated risktaking however is okay if the healing synergy is good.
2) Group comp, general fluidity and catering to certain people in the group. No NIN vs. having a NIN, stacked BRD or single BRD and the differences in Foe Requiem playing (lol who stacks BRDs anymore?), whether your tanks rambo everything in SwO and STR-accs or not - and so forth. None of this makes a huge difference usually, but it can add up.
3) Strategies and individual duties. Should be minor this late into a patch, but who handles certain mechanics mid-encounter can change the numbers a bit etc.
4) Whether content is on farm or whether you're progressing through it.
With all this being said... Assuming smooth runs where a SCH does his duties (mitigating on demand for spikes, Embrace-spam, using their kit wisely) whilst more or less 90%+ in Cleric Stance you can hit over 300 for T10, over 250 for T11, 250ish to 300ish for T12 and for T13 it depends wildly on if you merge parses or run continuous ones and whether or not your DPS is good enough that you will have to wait for P3 transitions. (Individual catering being the keyword here). Is it possible to do even more in all of these encounters? Yes, but we're going into faceroll-farming levels then, with your WHM being good and being able to do practical soloheals with a "glorified Regen" at their disposal (the fairy). You can also cheese the numbers up to be higher with comp alterations and stuff.
As for what you should "expect" a SCH to do in the Final Coil? Well, certainly not numbers that are this high, but anything helps and you should always have an idea if you take a look at the full picture of the encounter. If your SCH is idle, it's pretty much visible. Refer to any of the info in my post for specifics.
And for the White Mage portion of your question :P
There are unwritten roles known as Main- and Support healer. The general meta, whether the playerbase is doing it subconciously or not, involves the White Mage being the "main healer" and the scholar the "supportive healer". This means that a good bulk of healing, from both group as well as single target healing, comes from the White Mage. This would allow the scholar to dps more for both obvious and less obvious reasons. I'm not talking about the fairy here, mind you.
This would also mean that White Mages don't have a lot of windows to throw out some damage. This would involve the following factors:
General ability of the Scholar
Some scholars completely neglect the fairy, this will put a dent in the overall healing game and thus making the windows smaller for you to switch to cleric's stace. Whether you believe it or not: Manually spamming embrace and Rouse usage could mean a difference of 110 and 300 hps from the fairy. (Not counting Eos's abilities)
Alternatively, if the scholar is heavily oriented you could switch the roles around.
The White Mage's knowledge of the encounter
You can't just switch to Cleric's Stance whenever you want. If the Scholar is assuming you'll handle most of the healing, he/she will probably be Cleric's Stance. If both of you are in Cleric's Stance at the wrong moment in an encounter, it may or may not lead to wipes.
The kind of tanks you have (see Tranquil's second point)
Much like with proper fairy micro, this will affect your ability to deal damage as a White Mage. Even if the Scholar manages the fairy properly, the amount of incoming damage will increase if the tank's are in Sword Oath or off-defiance while tanking. That said: If the tanks deal significantly more damage like this at the cost of yours as a white mage, it's worth it in most cases (see below)
Confidence of White Mage
This one should be obvious: Those who don't have the confidence to hop to Cleric's Stance for a brief moment because they're worried the tank will die will deal nowhere as much dps as those who do. Do note: Confidence doesn't mean you should be some inconsiderate ass that'll let someone in the party die just so you can deal some damage.
Choice of secondary stats
The choice of stats here affect your DPS game heavily as a white mage. And no, spell speed still does jack here. The one stat that mainly affects this would be Piety and Accuracy. If you're planning to throw out some damage as a White Mage, you'll be casting more Cure IIs and Stoneskins than when focused on healing completely. This would also mean you'll be burning a lot more MP than a completely healing oriented White Mage. The possible windows to cast some Aeros (and maybe a stone or two) are really short. The longest one would be in Turn 11 when Nerve Gas is being cast. Even then this only lasts about 12 seconds or so. As for accuracy, the main source of this specific stat would be a relic weapon and/or crafted gear with accuracy melds. Whether it's worth it is up to you.
So in conclusion:
Due to the meta and distribution of roles of White Mage and Scholar, it's very unlikely you'll reach 3 digits as a White Mage. Possible, but unlikely. It's not uncommon for White Mages to deal 0. But with just Fluid Aura you can reach 5-20 dps throughout the entire encounter - Depending on misses and whether the encounter allows you to approach the boss frequently.
I main WHM and in my static I don't DPS at all (aside from t10 when the boss is charging after the adds die). I don't have the accuracy to hit most things and I don't have the time either. My SCH focuses on DPSing and most of the healing is left solely to myself. If I am in range, I will throw a Fluid Aura on things if I'm in range, because it does not cost MP and it is an OGCD skill, so I don't have to worry about someone dying on me when I push it (in theory).
As a WHM in FCoB there's definitely space to do damage, though in my experience less so when compared to the SCH. It is dependent on the gear level and experience of the party, but a well-geared group of veterans can create the breathing room needed between the times a WHM has to throw out heals. I believe that WHMs are at a slight disadvantage since both Aero and Aero II has a initial damage component which makes them dependent on ACC, a stat that we healers simply don't get as much of in our (non-crafted) gear.
In the end if there is downtime, if you don't feel like mana will be an issue and that helping the DPS will be fun, just go for it and throw some damage spells into the mix. Should you be unsure of your stance-dancing prowess using Aero/Aero II from your normal stance is still a contribution, albeit a weaker one. Who knows, it might be the drop that makes the difference when the boss gets real mad.
White mage's are generally expected to do the majority of the healing and scholars do the majority of the mitigation. When there's nothing to mitigate, which is quite a lot, scholars DPS and just let the faerie handle it.
Don't use Eos in Final Coil progression btw.
I'm not normally a fan of Eos in general, but I have to disagree here.
It's not that Eos' skills are essential but that Selene destroys MNK and NIN TP. Our BRD tends to end up playing Paeon excessively with Fey Light up, decreasing his damage and precluding use of Foes'. I'm of course largely DoT-dependent and our BLM is still learning how to be very effective at BLM in FCOB, so the Fey Glow side of it is mostly wasted.
Maybe if our party dynamic worked a little differently I'd camp Selene as usual and pop out Eos specifically for things like Cov for Nerve Cloud and high-stack Flames of Rebirth, but my physical friends have that TP issue :P
On WHM DPS. While you won't be expected as a WHM to DPS in fights, you can definitely put out a decent bit. As the WHM in my group, there isn't a fight in Final Coil that I have 0 DPS. If you play your cards right and understand a fight well enough, you will always find areas that you can get a couple GCDs of DPS out and retain your MP. Sure, your number won't be huge, for most fights it will only be in the low to mid double digits (20-70 is what I typically do in T11-13), but it's better than nothing. And in general in a raid setting, it's good to push yourself, because you might come across a fight where you're adding quite a bit more than that while effectively healing and not harming anyone else. For example: I'm able to push just over 100 DPS in T10 without detriment to my SCH's DPS or my MP (I've done 170, but that hurt his numbers. We wanted to see what I could do >.> Could've been a bit higher but some people messed up and it got iffy to DPS as much as I was). The fight is designed in a way that gives healers ample time to DPS if you plan your healing out correctly. Your DPS might also be enough to push a phase quicker than before. When my group was progressing through T12, me figuring out where I could DPS during the first phase while letting our SCH go full Cleric Stance was just enough to push us over the hump into 4 Bennus.
The jist of what I'm saying is, I strongly encourage more WHMs to give DPSing a shot, even if it's not expected of you. If you find you have a bit of time where you aren't healing and your MP is alright, then go ahead and throw up some DoTs! If you get your DoTs up and still have time and know nothing's coming that's gonna kill someone (don't forget, HP is a resource. Tanks don't need to be full or even at 50% ALL the time ;)), then start throwing some rocks! If you mess up, then the worst that happens is you know that you can't DPS there anymore. And you've learned something. That's how we get better.
I know healers can really deal it out in FCoB if conditions are right, so take it for what it's worth xD , but the healer #'s for my group are usually:
whm (me): 10-50 dps on 10,11,13 (i haven't really tried to dps in T12, now that i think about it)
Sch: 70-100 dps on 10-13
This is more than enough to get us from phase to phase a little quicker and beat enrage times comfortably.