Monday, March 23, 2009

Good things come in pairs, DNC math and other fun things

Funny thing about FFXI stuff that it seems to come in twos... When I got my ZNM pumps, I got Goliard feet two weeks later... when I got my ZNM hands for SCH, Goliard hands dropped the very next time we went for Nyzul... Homam hands & Enkidu mittens were literally three days apart, so when I picked up the SCH relic body on Wednesday, I figured that Goliard body would be coming next...

Which makes my Etoile Cape that much nicer to get :D

With more accuracy than anything else, it replaces my Psilos Mantle as a full-time piece, only swapped out if I end up in a tanking position since my Boxer's Mantle does have more evasion skill. That's my 2nd DNC relic piece, and 6th relic armor piece with BMO so far :D

In other news... other drops haven't been quite as nice as Dynamis... Saturday's Omega we got hands and head... again... which is only slightly better than two head pieces... still, would be nice to get some legs, body or feet pieces sometime! Did KS99 last night with Wu since half of my Nyzul group was missing during gather time, and super-late. I didn't realize I won a lot to go, so I ended up using an orb. No Speed Belt drop, but it had a lot of gil drops and more importantly, a Black Belt item that went to Lemmon! Congrats! I nearly doubled my own gil just from this run alone, which does open up some further possibilities down the road.

Dancer Math
The following section might get a little technical, but it's something that I've been curious about TP gain for a while and wanted to see if I could figure out one of a Dancer's best advantages: the ability to keep going where a mage would have ran out of MP a long time ago.

TP vs. MP conversion
The basic question here is... what is the approximate conversion between TP when used by a Dancer to MP when used by a mage for curing. To answer this, let's look at the basic Waltzes.

Let's compare Curing Waltz III to Cure IV.
- Curing Waltz III: Heals 360 HP, 10 second recast time, 50% TP
- Cure IV: Heals 360 HP, 8 second recast, 2.5 second casting time, 88 MP

Since they heal for about the same amount, we could do an approximation of 1TP = 1.76MP in terms of healing potential. If we take a Dancer's TP cap of 300%, we get that a Dancer at max TP is approximately 528MP of "healing potential" if that same Dancer was a mage. Add in 5 Finishing Moves for another 60% TP, that's a cap of 633 MP, a decent amount, but nowhere near the 800-1000+ max MP that any mage typically has.

TP generation
Simple math so far... we've done a link between TP & MP using one simple metric to link the two: amount healed. Now it's time for some more complicated math, figuring out how much TP a Dancer can generate on a regular basis.

For the purposes of this exercise, let's take an "average" DNC/NIN, dual-wielding delay 201 daggers. This is fairly common since Behemoth +1 knives, Jambiyas are all delay 201, with a few daggers having a lower delay (Kard 190) and some higher (Azoth 210). Let's also say that the Dancer has Suppanomimi for a Dual Wield bonus since many people have that piece of equipment.

According to the Wiki article on TP gain, this Dancer 's delay and TP gain would be:
- Combined Delay: 201 + 201 = 402
- Reduced Delay: 402 * (1 - 0.2) = 321.6
- Reduced Delay per hand: 321.6/2 = 160.8 delay
- TP gain per hand: 5.0 + [(160.8-180) * 1.5/180] = 4.84
- TP gain per round = 4.84*2 = 9.68 TP/round
Which pretty much matches up with what I've seen as DNC/NIN. First round would hit for exactly 10TP for a single step, and subsequent rounds would hit for 10 or 9 TP per double hit.

Every 60 delay = 1 Earth second, so a 321.6 delay would be 5.36s per attack round. So, the above Dancer would be gaining Tp at the rate of 1.806TP/sec. Translated into "ticks" where 1 tick = 3 seconds for purposes of Refresh, we get the Dancer getting TP at the rate of 5.42TP/tick from just swinging daggers.

Now this isn't the only way for a Dancer to get TP. Let's throw in Reverse Flourish math for some fun. IMO, a Dancer would use Reverse Flourish whenever the timer is up, every 30 seconds. This is enough time, if perfectly executed, to use two "steps" for a total of 4 Finishing Moves. Each Step costs 10%TP, so, all in all, we get:
- 46% TP return from Reverse Flourish - 20% TP from two Steps = 26% net TP gain every 30 seconds.
OR, 2.6% net TP gain per "tick"

So, on average, a DNC/NIN stepping constantly and using Reverse Flourish gains TP at a net rate of 5.42% + 2.6% = 8.02% /tick

Using the 1TP = 1.76MP conversion we calculated earlier, this means a Dancer generates "healing potential" at the rate of 14.1MP/tick. Let's say that this Dancer isn't perfect and has only a 80% overall accuracy, this only drops the generation down to 11.3MP/tick.

TP vs. Refresh
Now for the fun part... what's the highest rate of MP generation someone can generate without support... by that, I mean without having a 2nd person helping you. A Dancer can generate TP faster with external help. Haste, March are just two examples of how a Dancer can get a lot more TP than normal. The above calculations were done for a single Dancer without support (and much equipment for that matter!)

Currently, the highest MP generation I can generate solo is either:
- BLU: 6MP/tick during Assault (Auto-Refresh job trait, relic body, Sanction, ToAU ring + /SCH)
- SCH: 6MP/tick during Assault (4MP/Sublimation, Sanction, ToAU ring)

Other jobs that can generate MP:
- Bard: 3MP/tick combined Ballad I + II, doubled to 6MP/tick with Soul Voice
- Corsair: Max of 5MP/tick on a roll of 11 with Summoner in the party
- Red Mage... handled separately.

Red Mage is a special case for two reasons... #1: Refresh requires MP to cast, so it isn't as straightforward as taking the statistic from the Wiki, and #2: Convert
- For #1, every 150MP restored costs 40MP to cast, so really Refresh is 110MP restored over 50 ticks. This is a real rate of 2.2MP/tick
- #2, let's take an average RDM with a MP pool of 900MP. Every 10 minutes (200 ticks), the RDM can refill her MP pool using convert. Assuming the RDM uses Convert every 10 minutes, this is equal to a rate of 4.5MP/tick. A higher max MP pool would of course, increase this.

So, a RDM can put out a respectable 6.7MP/tick MP generation rate, making it the highest of all the mages without special gear. Throw in Sanction, Vermy cloak, ToAU reward ring and even /SMN, we can push that up to 10.7MP/tick without external support.

Conclusion
So... RDM is the only job capable of coming close to a DNC's "healing potential generation" under specific circumstances and gear. Good Dancers will be up there at the accuracy cap, and have additional haste gear to help with TP generation, meaning that the 8.02%/tick or 14.1MP/tick approximation would actually be exceeded, explaining why a good Dancer can not only go on forever and never run out of TP no matter the circumstance. This also explains why, for extended events, I'm always at or near TP cap when mages are out of MP. A Dancer's TP accumulation rate outstrips even that of a RDM when it comes to healing potential.

Maybe sometime in the future we'll have alliance events with one Dancer per party...

Other fun stuff
For other fun stuff... let's see... since Nyzul was all cancelled this week, I managed to pick up two more FL assaults with Lyric. Just one more left until Captain rank! Hopefully I can pick that up this week! Would be nice to have 5 assault tags and not have to pay for using the Runic Portal again.

Burning 99 KS for an attempt at a Speed Belt was worth it IMO... It's not like I have any other use for it... but as I was looking at that, I also realized that I have a ton of other things I could use up. I have over 100K IS, as well as CP, and I think over 600K AN. Maybe it's time to spam some ISNMs to raise some gil!

As for gil... the KS99 did bring me up to more gil than I've ever had, and for once, nothing serious to buy. It's my intention to eventually use Limbus to gil farm whenever I completed my Homam set, but that's far in the future... Still, I'm wondering what to get... a Roundel Earring would be nice for my DNC for 5M, or I could use some gil to fund a new job.

Speaking of new jobs... I'm considering picking up PLD again just to have a tank job. Nothing annoys me more than sitting around and waiting or searching for a specific job to come up in order to take on a mission or quest. Seems that we have a need for tanks these days, and it would be nice to be able to switch into whatever role is necessary to get things moving... I have a DD, two/three healers (DNC & SCH, maybe even BLU), two nukers (BLU & SCH), so all that is missing is a real tank, and a support job :)





4 comments:

Vanh said...
This comment has been removed by the author.
Vanh said...

Reposted due to some typos! =x I'm not perfect! /cry

Wow, such a DNC bias! D:<

But I do like your analysis, it's well thought out and fun to think about :D Let me say before I begin, these are just some of my thoughts in addition to what you have, and it is not my intention to provoke a fight or anything! So please don't hurt me! (too much) /hides. DNCs (good ones) are great to have! (as long as they aren't male characters, then they are made of fail no matter what).

So first part of your discussion you talk about MP cap (in terms of TP) and how the cap essentially breaks down to 300 % max TP, +60% for 5 finishing moves, which I assume is from Reverse Flourish. But then in the refresh portion you mention Reverse Flourish again. That's double dipping! If you're Reverse Flourishing every 30 secs, at 4 finishing moves, then you'll never get to 5 moves for that extra 60% TP!

One simple thing that you left out is that all healing mages (with half a brain) will have a light staff to assist with healing, WHMs will also have Nobles Tunic. Factoring those in will increase their healing potential and thus close the gap between the jobs. I know you were trying to simply your model as much as possible because there's a lot of other factors that could play into the calculations... but I think the staff at the least is a very reasonable tool that can be factored in. ^^;

In terms of 'refresh' potential, sure looks like DNC wins there =o DNC h4x! But RDMs can also convert as often as every 9 Min, 10 Sec (fully merited) which would change their rate/tick.

Then there's a whole category of random factors, which I'll just mention for 'fun' since they have no place in your model. These things can adversely affect mage healing potential, for the better...mostly. Conserve MP would play into refresh potential for mages, but this is wildly random. Light Arts would be a factor with the 10% spell discount. Store TP bonuses from equipment or SAM sub (a sub you didnt mention!) would help DNC out for 'refresh' potential. Then there's mob special abilities: imps, and fomors come to mind in terms of shutting down DNC healing. These I would consider obvious random factors, as they come down to abilities and things you can quantify to a point.

There's also less obvious random factors, which start you down the road of hypothetical, and things that can't be so easily quantified. Mainly this revolves around the fact that DNC are front line jobs. As such, they're constantly giving TP to mobs. This in turn means mobs will most likely use TP more often (and 'most likely' becomes 'definitely' as the mobs HP slips under 20% and they'll use TP ASAP) which can mean more damage that needs to be healed. Now this may appear to be a bit off topic since it doesn't really seem like it fits under 'healing potential'. You may even think, 'wow you're just hating on DNC now'(which I'm not!) But I do think it has it's place in the 'healing potential' topic because it's can be negative factor. It's like undoing some of the healing you did, since you were the direct cause of some of the damage. On HNMs the feeding TP issue is a huge factor, since TP moves can result in deaths, and then your healing potential is 0!

Another less obvious random factor is the issue of enmity. DNC, correct me if I'm wrong, usually don't have -enmity gear. This can mean the DNC taking more damage than a mage since they usually have -enmity on their gear. So this is similar to the problem mentioned earlier being the cause of more damage that needs to be healed. Which means every so often DNC has to toss out an extra heal to undo the extra damage they've caused, whereas a mage wouldn't have to. Fun fact: Cure V creates less enmity than Cure IV, though I don't know how Waltz III compares to Cure IV in terms of enmity. But again, these last two paragraphs rely on the mob's behavior and lots of 'what ifs' so that's why I consider them hypotheticals.

So yeah... sounds like a lot of mage bias, but I think you covered the DNC perspective well enough! Ok, I think I'll go /hide until this topic is forgotten!

Ascule said...

Yay! Vanh is alive! <3
And he's not a Cylon!

Alright, a few things I probably should have made more clear for the analysis... looks like I forgot to put it down xD

1. TP/MP cap - The 300% + 5 finishing moves would essentially be equal to what the maximum is at the beginning, before a fight actually begins. The mage version would be a mage in MP gear which would get swapped out as MP is used. Once the battle begins, the maximum values would never be reached and you'd be dependent on "refresh" to keep going.

2. The analysis was done on unmerited characters, with mostly no special gear. Just has a healers have light staves, Noble Tunics, Dancers with half a brain will have Swift Belt, Rap Harness, Rajas Ring and other things to increase performance. Charisma equipment helps with Waltzes, and there are some, if limited, healing potency items. It might be interesting to do the same analysis on two fully merited, fully geared characters.

3. Just as RDMs can merit Convert, Dancers can merit Reverse Flourish. Saber Dance also increases our TP rate gain by a huge amount. I'm still curious about a DNC vs SAM TP gain comparison.

4. Feeding the mob TP is definitely an issue, even with all the Subtle Blow in the world it won't be enough! A Dancer can switch to not meleeing the mob and just using Steps for TP gain (which brings TP gain down to a low 2.6% TP/tick) but that's not optimal

5. Enmity is... a strange topic actually. Dancers have quite a bit of -enmity gear, mostly the AF and the Cobra Unit Cap set, but the interesting part is that DNC relic armor has +enmity, and Fan Dance actually increases enmity. That's what brought about my whole experimentation with DNC tanking a couple of months ago which lead me to the conclusion of the Dancer's advantage for long fights where a healer will hit the hate cap. A mage will get killed easily by a hard mob like that, but a Dancer has some tools that can help her survive.
- btw: Curing Waltz III should equal Cure IV for enmity generation... Not enough experimentation has been done to compare Curing Waltz IV to Cure V yet

Finally... Vanh! No hiding! /drags out from PS3

Zurar said...

Lol... well, I'd recommend a whole nother topic if you plan to compare Dnc and Sam mains... though if you meant /sam, that won't be as hard.

Really though, Sam has a LOT of tools for gaining TP. First off... the most commonly used (all you have to do is be a sam or sub sam) is, of course, Store TP. Now any smart Sam is able to get this up to areas where they can get a 6-hit, or sometimes even 5-hit build.

Currently, with my Shinsoku, I get about 17-18TP return, resulting in a 6-hit build. This is pretty easy with a Sam Main as I have pretty minimal +store TP armor. Most of it has been sacrificed for accuracy and or haste or dmg gear. With a polearm, I can easily hit 20 TP/hit. I'm not sure why polearms are so much higher, but their delay doesn't warrant that much of an increase, especially considering shinsoku is 450 delay and engesuto is 480. Throw bow in there, and you can get upwards of 22 TP/hit with a bow, and /rng adding rapid shot makes things even faster!

Aside from weapons, Samurai Meditate can regain 100TP at 20TP/tick, or with AF or Relic pieces, can gain 120-140 TP at the same tp/tick rate. Lets not forget, this isn't a 5 minute recast timer either, it's 3 minutes w/o merits and 2.5 with full merits. Speaking of merits... Sam can add 5 to store TP getting 2 added store TP per merit level adding 10 total to their pool before equipment, on top of the 25 from their class traits.

Now, since Store TP is not factored into an enemy's TP gain (enemies gain base TP gain of attacker +3) a samurai is essentially giving the same amount of TP per round (if not less) as a dancer while gaining as much or more. Not very significant to start, but, when comparing to other jobs as well, it can add up; making it easy to see why Samurai are the primary DDs for most extended boss fights. Kinda makes me feel sorry for Blus trying to use physical multi-hit spells... which, btw, give full TP on EACH hit, unlike WSs which have reduced TP after the first hit. Finally explains why the mobs rape us when a certain blu goes wild with Hysteric Barrage and the like... /glare -.-;

Anyway, if all you want is survivability; throw in a soboro and /dnc (maybe swap chest armor for Hachiman or Askar if you want evasion too) and you have TP gain like no-other. The only downside to Sam/Dnc... no Curing Waltz III.

And last but not least... everyone's favorite... the 2-Hour. I mean, come on... who doesn't like an instant 300 TP with limited 100TP drain per WS while still giving out 300 TP dmg that lasts for 30 seconds? I mean... nothing like giving the enemy the old 1, 2, 3... erm, 4... 6... uhh, 8... 10? WS punch? ^^; I guarantee... either the mob's gonna be dead or the Sam will by the end of it.

Lets see, the best I've seen so far: 200+TP at start > Sekkanoki > Yukikaze > Gekko > Meikyo > Kasha for light (or swap kasha and gekko for extended darkness) > Yuki > Meditate > Gekko > Kasha > Dusty Wing > Yuki > Gekko > Kasha... and when all's said and done, you still have about 40-60 TP left after the last Kasha. Now uninterrupted by outside WSs... that's 3 self-created light chains in a row using 3 different WSs 3 times. I've only pulled this one off once uninterrupted, and lets just say... khimaira died in less than 30 sec on floor 100 of Nyzul Isle. If you swap out the 3-WS light chain with the 2-WS, you can do 5 darkness chains if you bring an icarus wing with you for the finale. And if you happen to find a revitalizer (and actually survive the first round) you get to do it all again! Anyway... that's all for now. ^^