Damage Formula Thread

[EasymodeX]

Umm ...

Edit: That sounds mostly good except I'm not sure how you get a "potency" change from changing Int/Dtr/WD. Although I guess you can just call it an adjusted potency ... but if you have all stats accounted for just call it DPS, not potency, heh.

The only thing that the ability rotation PPS is affected by in terms of stats is Spell Speed. Crit, Determination, Int, and WD all scale normally with the BLM ability damage output regardless of what your "rotation" is. In terms of BLM rotation-ing, a 40% firestarter and 5% TC is pretty easy to model without horrendous error.

So just plug in a general PPS (IIRC someone simmed something that resulted in 209-ish PPS last patch). Then you need to re-model or re-sim the scenario with SS+ .... 10. That is your new "SS+10 PPS". The rest of the math as you stated. You will just need to do a sanity check of the Spell Speed weight against how your TC/Firestarter modeling is skewed, since that is the only stat affected by the modeling assumptions.

Edit: In terms of BLMs in particular, there was a thread awhile back with a guy who wrote a BLM sim. It seemed ok, although it was last patch. IIRC Puro's spreadsheet also had some flavor of BLM damage model, although I'm not sure how it was presented.

For physical classes it's slightly different since all of them have crit modifiers for abilities in some form or fashion, so the ability PPS for the rotation is different for the crit case if you set it up that way. I have a spreadsheet that models DRG, MNK, and BRD potency pretty robustly.

[Kenji1134]

You mean this guy?

http://forum.square-enix.com/ffxiv/t...ab#post1523825

Namely post #48, its a slightly more realistic model for viable Firestarter usage.
So back then I had an higher average of 109ish PPS. If I have time, I may rewrite that code with the new UI3 changes, or just use Excel.

The way I see it, there are a finite number of Fire Cycle Rotations, depending on Firestarter procs and if we assume that we are always casting something... OR we wait 0.5s for a possible proc on the last Fire, or manage to break B3 to use the proc when it appears.

So something like... (1 = F1, 3 = F3, 1! = F1 that got a proc)
1. 1! 1 3 1! 1 3 1! 3 - Wait
2. 1! 1 3 1! 1 3 1 - Keep Casting
3. 1! 1 3 1 1! 1 3 - Keep Casting
4. 1 1! 1 3 1! 1 3 - Casting
5. 1 1 1! 1 3 1! 3 - Wait
6. 1 1 1! 1 3 1 - Casting
7. 1 1 1 1! 1 3 - Casting
8. 1 1 1 1 1! 3 - Wait
9. 1 1 1 1 1! - Casting
10. 1 1 1 1 1 - Casting and awful luck

I think thats about all of the possible general scenarios. Then we have the issue of percents.
Keep in mind its been years since I did statistical probability, and I was never terribly fond of it.

K, did some of my excel probability modeling, basically making a 5x10k array of random data 1-100, then another array to convert it into procs if the value is >=60 to make a 40% chance.

So Case 1 has a ~6.4% chance, based on .4^3, and the model.
Case 2, which shares a probability with case 1, has a 9.6% chance.
Cases 3 to 5 all have a 16% chance.
Cases 6 to 8 all have a 40% chance.
And Cases 9-10 effectively have have a 7.8% chance (0.6^5 failures).

Now the fun part, combining like case probabilities to make everything add up to 100... This was the part of statistics I kinda sucked at... Q.Q

So that should cover the fire cycle. The ice/regen cycle has maybe 4 variants.
1. B3-T3-F3 with waits inbetween
2. B3-T2-F3 with waits
3. B3-Sc-T2-F3 with less waits
4. B3-B1-T2-F3 with less waits

It is up to the player to select which version of the regen cycle they want to use. Each one has a slightly different potency and total time.
Once we have selected a regen cycle we like, then we just add the total potency of EACH case of the fire cycle plus the regen cycle, add the times, see how much of our chosen Thunder dot went off, and we have total pot over total time = PPS.
PPS * Damage/Potency = DPS. Done.

[EasymodeX]

You mean this guy?

http://forum.square-enix.com/ffxiv/t...ab#post1523825

Oh yeah that guy .

Now the fun part, combining like case probabilities to make everything add up to 100... This was the part of statistics I kinda sucked at... Q.Q

Um, I think you need to separate out whether you're waiting or casting, and then doing the %chance of each sequence of events. Your cases aren't clear form a permutation or combination standpoint.

1 1 1 1 1 - 13.0%
1 1 1 1! 1 3 - 8.6%
1 1 1! 1 3 1 - 14.4%
1 1! 1 3 1 1 - 14.4%
1 1! 1 3 1! 1 3 - 9.6%
1! 1 3 1 1 1 - 14.4%
1! 1 3 1 1! 1 3 - 9.6%
1! 1 3 1! 1 3 1 - 16%

Those are all the basic fire cycle cases assuming 5x fire1s and you never stop casting to watch. Also, assuming you do not care about getting a FS proc on the last fire (if you do then a few of those listed would be split).

It is up to the player to select which version of the regen cycle they want to use. Each one has a slightly different potency and total time.

IMO this is the only complex part, because the UI phase sequence is sensitive to Spell Speed, hence affecting the final coefficients. Past certain thresholds of SS you may "really want to" switch to a different UI phase approach (e.g. using B1 + T2 instead of T3).

[Kenji1134]

There is also the issue of exactly when in the 3s global tick you entered into UI3.

Lets say you need 2 full ticks to get to full mana, and then want F3 to go off a bit after the 2nd tick, so you end up with max mana - 133.
Now for the effects of Spell Speed. based on Puro's testing, the equation at 50 is roughly:
Reduction in Sec = 0.0009524x - 0.3224043. (gonna call this 'r')
That is to say, when you have 341 speed at 50 with no gear, this formula gives a reduction of 0.00237, which is not even displayed on the tooltips. Also, my spell speed of 491 would give me a reduction of 0.1452, which matches my tooltip's gcd of 2.35s. So with this data we can get an idea of "when" to switch to a different rotation... But the larger issue tends to be where you are in the global tick. You can do the same rotation, but if you get your tick just BEFORE UI3 turned on, then you will likely clip. If you got your tick just AFTER UI3 turned on, then you are probably wasting time. =P

So back to rotations in general. We need 6 seconds to get full mana. So lets start with 2 base rotations, B3-T2 and B3-T3.
6 - B3(0) + T2(3-r) + stuff = 0 -> Exact time to get 2 ticks, so we need to solve for stuff.
6 - B3(0) +T3(3.5-r) + stuff = 0 -> Same thing, but now "ideally" stuff should take less time. Keep in mind that "stuff" can be waiting for a tick to happen.

So I guess...
B3->T3->Wait = 6-3.5+r+stuff=0 , stuff = 2.5+2r if we cast another spell, we need another 'r'. Or we can just wait out the 2.5+2r.
B3->T2->Wait = 6-3+r+stuff=0 , stuff = 3+2r.
B3->B1(or scathe)->T2 = 6-(2.5-r)-(3-r)= 0.5+2r of maximum waiting time for the last tick... Now we can throw the F3 out before the tick lands, F3 would be ... how here's a fun little interaction that I just noticed which makes some of my data a bit wrong =)

At 491 Speed, my GCD is 2.35, F1 is 2.35, F2 is 3.30... 2.5-.1452 = 2.35, but 3.5-1.452 =/= 3.30... BUT (2.5-.1452)/2.5 = 0.9419, and 3.5*0.9419 = 3.2996!
So for longer cast time spells, we dont actually see a static time reduction, we see a percentage scaling equal to the effective scaling of the baseline GCD... Fuck this makes the math longer... Yeah, im gonna take a lil break, get a sammich... EasymodeX, back to you.

[EasymodeX]

*Jedi force deflection*.

[Nyaanyaa]

Hi guys,

I did some more testing. Long story short, the min cure for my data point with 35MND was 1HP too high, i.e. the actual min cure is 64HP, not 65. I did some mistakes calculating RHP range, too. The actual ranges are even closer to integers. To truly keep this short,

I am absolutely certain that the rounding in the cure formula follows this model:

HP Cured = floor(3% ± floor(RHP))

As before, RHP is "Raw Healing Power", or where all the "MND*WD" and all that stuff would go.

Cheers,
Nyaanyaa

[Size]

Wow you guys make my head spin. EasyX, from your formula I see you use (DTR-202). Are you observing that DTR does basically nothing or even reduces damage below 202 and only adds damage above 202?

[EasymodeX]

At level 50 you have 202 DTR with no items, e.g. 202 base DTR.

A DTR debuff below 202 should reduce your damage -- this can be seen on Titan HM.

[Kenji1134]

Grad School has resumed, so my game time is being cut a little bit for a while.
I'll try to get some solid data for WHM when I have some time and compare it with the BLM data... hopefully they will match and fit the same equation.

But all in all... in another thread, someone, I think it may have been EasymodeX mentioned that Det "may" have been undervalued in a lot of BiS lists.
All of my data, even fugly incomplete data for melee dps and paladin, all shows the same trend... WD >>> Str/Dex/Int/Mnd > Det > Spd/Crit... WD tends to be worth 5-6-7 times as much as your main stat. Then Det is worth ~0.3-0.25 of 1 main stat, speed is worth ~0.2, and crit is worth ~0.19.

Again this is on a class-by-class basis, but the first 3 should hold for everyone.
Speed and Crit offer similar returns, so the order is very class specific.
Monk gets a buff to speed, Bards get free attacks from Crit, BLM can cast forever so speed is good, SMN's dps is mostly on a 3 sec global tick so speed does jack... etc.

[T0rin]

I did some testing with SMN DoTs using this formula:

(WD*.2714745 + STR*.1006032 + (DTR-202)*.0241327 + WD*STR*.0036167 + WD*(DTR-202)*.0010800 - 1) * (Potency/100)

With 71 WD, 490 INT and 280 DET, I came back with an real average of 104.35 (99-110) for Bio, and a calculated value of 104.6545.

I calculated my current stat weights with my current i89 SMN gear to be:

WD 5.954011
INT 1
DET 0.282081
CRT 0.176962

I also played around with various gear sets (i70 vs i90, etc.) and found some interesting results...

WD weight scales upward as INT goes up
CRT weight scales upward as INT goes up

WD weight scales upward as DET goes up
CRT weight scales upward as DET goes up

CRT weight scales downward as CRT goes up

DET weight never scales regardless of any stat changes.

So on a point for point basis, DET is always worth more than CRT. It also comes in smaller quantities. There also seems to be diminishing returns with CRT, and that stacking CRT in a bubble will result in lower worth per point the higher you go. I didn't bother calculating the value of SS, since it relies on establishing a rotation, and for SMN, that is a fairly arbitrary concept due to the mechanics of their skills. (mainly the abundance of DoTs)

Then there is the value of crit for purposes of triggering pet spell speed procs, which in turn increase pet DPS. Not even sure I want to go there in attempting to calculate the true weight of stats with pet damage included.