Stringing Pummel ResearchFollow

The Idea:
Stringing Pummel is a sixfold attack with a chance of critical hits, varying with TP. With the new hand-to-hand skill raise, we're not reliant on accuracy as much as before. A question came up in my end-game linkshell: "How would reaching the dDEX cap and using Critical Hit bonus equipment effect this weapon skill, compared to a straight build consisting of accuracy, attack, and Stringing Pummel's modifiers?" Let's find out. For testing purposes, we'll use Greater Colibri, and a standard merit point party with a Puppetmaster (BRD, RDM, SAM, SAM, SAM, PUP).
Also, for testing purposes, we'll say that you are an Elvaan and your subjob is Warrior.

To hit the dDEX cap on Greater Colibr, you need 117 DEX total.

[b]Stringing Pummel[b]
Delivers a sixfold attack. Chance of critical hit varies with TP.
STR: 32% / VIT: 32%
Aligned with the Shadow Gorget, Soil Gorget, and Flame Gorget.

*Question 1: What is the chance of Critical Hits at 100%, 200%, and 300% TP?

At 75 PUP/WAR Elvaan, you have:
69STR 67DEX 66VIT

As far as gear/merits/etc. go, I'm only going to write the stats that will be involved in the calculations next to the gear. Now, let's say these are the merits you have set already:
8/8 Hand to Hand Skill (+16 Skill) for a total of 272 Hand to Hand skill.
5/5 STR (+5 STR)
4/4 Critical Hit Rate (+4% Critical Hits)

For this idea, we'll compare 2 sets of WS gear. A control set (what most people probably use for Stringing Pummel at best right now), and the theoretical set (dDEX, Critical Bonus, etc). If you want to help test and replicate results, please post what gear you used and parsed data, in case you can't use what's tested in this theory.

Weaponskill Set 1 (Control) - Accuracy, Attack, STR, DEX, Other
Weapon: Wagh Baghnaks (Latent- +5 Accuracy, +14 Attack, DMG:18)
Ranged: Animator +1 (+4 DEX)
Head: Anwig Salade (+4STR, +15 Weaponskill Accuracy, +10 Accuracy, +5 Attack)
Neck: Faith torque (+7 H2H)
Ear1: Brutal Earring (+5% Double Attack)
Ear2: Hollow Earring (+3 Accuracy, +2 DEX)
Body: Usukane Haramaki (+8 STR, +8 DEX, +12 Accuracy)
Hands: Enkidu's Mittens (+5 Accuracy, +4STR, +4DEX)
Ring1: Rajas Ring (+5STR, +5DEX)
Ring2: Toreador's Ring (+7 Accuracy)
Back: Pantin Cape (+4 DEX, +15 Attack)
Waist: Virtuoso Belt (+12 Accuracy, +4 Attack)
Legs: Surge Subligar (+12 Accuracy, +6 Attack)
Feet: Puppetry Babouches +1 (+5STR, +5 Accuracy)
FOOD: Squid Sushi +1 (16% Accuracy, 6 DEX)
*Good alternate rings to this set's are Ulthalam's, Lava&Kusha, etc.

---

Weaponskill Set 2 (Experimental) - DEX, Critial Cit Mods, Acc, etc.
Weapon: Wagh Baghnaks (Latent- +5 Accuracy, +14 Attack, DMG:18)
Ranged: Animator +1 (+4 DEX)
Head: Maat's Cap (+7 STR, +7 DEX, +7 VIT)
Neck: Love Torque (+5 DEX)
Ear1: Adroit Earring (+2 DEX)
Ear2: Hollow Earring (+3 Accuracy, +2 DEX)
Body: Shikkoku Togi (+8 STR, +8 Accuracy, +8 Attack, Increases Critical hit DMG)
EVOLITHS: vs. Birds: Attack+10, Accuracy+9
Hands: Shikkoku Kote (+3 STR, +5 Accuracy, Increases Ciritcal hit DMG)
EVOLITHS: vs. Birds: Attack+10, Accuracy+9
Ring1: Rajas Ring (+5STR, +5DEX)
Ring2: Zilant Ring (+6 DEX, +3 Accuracy)
Back: Pantin Cape (+4 DEX, +15 Attack)
Waist: Forest Sash (+4 DEX)
Legs: Enkidu's Subligar (+4 STR, +4 DEX)
Feet: Usukane Sune-Ate (+7 Accuracy, +7 Attack)
FOOD: Squid Sushi +1 (Dex+6, Acc+16%)
*This reaches the dDEX cap of 117, exactly. Yes, I know, this set would be extremely hard to obtain. Realize, this is just an idea, not something I'm going to try and get in a 1 week's time.

---

Totals:

CONTROL: WS Set 1- 71 Accuracy, 44 Attack, 26 STR, 33 DEX, 16% Accuracy, 5% Double Attack, 15 WS Accuracy, 7 H2H Skill

VS

EXPERIMENT: WS Set 2- 50DEX, 27STR, 7VIT, Critical Hit DMG Bonus x2, +49 Accuracy, +16% Accuracy, +68 Attack

I'll update this as things move along. Still a theory in progress. :) any contributions are appreciated! Thanks!
Here's the WS Damage formula for the experimental set. I'm still working on it, since using wiki to figure out how to calculate it is still a bit confusing even though they post everything there. :(

Damage = WD * PDIF = ( D + fSTR + WSC) * fTP * PDIF

WD= ??
D: 50
fSTR: 9
WSC = ??
fTP : ??
PDIF: 1.24770642

75 Elvaan PUP/WAR:
101STR, 117DEX, 73VIT, 408 Attack

Greater Colibri
Level 82: Defense 327, Evasion 339, VIT 67, AGI 67

Edited, May 10th 2010 4:55am by xKirin

Edited, May 10th 2010 5:00am by xKirin

Edited, May 10th 2010 5:04am by xKirin

the DoT value of +crit is really easy to find. you just look at your cRatio (or projected average pDIF given our most recent approximations of how to get it, if you're a stickler), your base crit rate, and then compare with the new crit rate for a % increase. easy stuff.

however, if you guys don't know the % crit chance at 100%/200%/300% (i don't know it, and have never known it for sure with solid testing for any WS), and you test that, it will certainly be a valuable contribution.

Have you merited as PUP/WAR lately? I've been having trouble keeping my hate under control as PUP/DRG.[/quote

Got myself about 5 merits last night on PUP/WAR, it's damned fun, but I should level /drg, if only so I can hit the 25% haste cap! I bought the earring already, so right now it's useless with my DRG26 lol.

But yeah, between ventriloquy, and StringingPummel I had hate so much. At one point I got down to 26 HP before the lolibri decided to change targets!

Pre tags, folks. If you want text formatted, you gotta put them in tags.

I don't think you have any of those values in the equation correct. WD is wrong, D is wrong, fSTR is way wrong, WSC is wrong nope WSC is ok dunno how I messed it up at the first glance, fTP is wrong for 5/6 hits (fTP is always 1.00 after the first hit), pDIF is insanely wrong.

I honestly am curious as to how you came up with some of these values. I think if you can show me the steps of how you came up with the numbers that you got, I can show you where you went wrong. Some of them I can see: D = 18 because it's on the weapon as 18 dmg, but that's not right because it's DMG plus 18, and fTP is listed as .75 on wiki for the WS and you just weren't aware that it only applied to the first hit - I can understand not knowing that point.

fSTR 34 is nearly 2x as high as the highest possible fSTR cap in the game, even just taking 101 STR and dividing by 4 you only get 25 (floored), how you're getting a fSTR of 34 is totally beyond me. pDIF of 81 trumps them all in magnitude though, the absolute cap on pDIF is 3.15 with a critical hit, so you're more than 25x over the cap.



Edited, May 10th 2010 4:11am by bsphil

D isn't right. It should be near 50. It depends on your h2h skill - how much do you have? Because that's going to matter to what D is.

D for h2h users isn't going to be what's listed on the weapon. You have a base damage with no weapon equipped, and that's equal to floor((h2h skill * 0.11) + 3). So, for 272 h2h skill, that's 32.92, which is floored to 32 DMG. Once you add the DMG+ on the h2h weapon you wind up with the actual value of D used for melee/WS equations, which is 32+18 = 50.

So, D = 50.



fSTR as you stated is roughly floor(((your STR - target VIT)+4) / 4), so for 101 STR (IIRC greater colibri have 67 VIT) that would be ((101-67)+4)/4 = floor(9.5) = 9. While we're at it, I'll touch on weapon rank. Weapon rank is used to determine the lower and upper caps for fSTR. It's just floor((weapon dmg)/9), or for h2h users, floor((weapon dmg + 3)/9). So for waghs, using the DMG+13 base (the non-latent value on waghs/blau/perdu/etc. applies even under 100 TP and on WS), the formula is floor((13+3)/9) = 1.777... = 1. Now where that matters is that the lower cap of fSTR is -(weapon rank) and the upper cap is (weapon rank + 8), so waghs have a lower cap of -1 and an upper cap of 10, meaning that fSTR is capped. _{EDIT: Always forget about the +4 in fSTR, and wow fSTR =/= WSC.}

So, fSTR = 9.




WSC for Stringing Pummel is 32% STR 32% VIT, which fits into the formula floor((floor(your STR * 32%) + floor(your VIT * 32%)) * alpha). To take your values of 101 STR and 73 VIT, that would give you at level 75: floor((floor(101 * 0.32) + floor(73 * 0.32)) * 0.83) = ((32 + 23) * 0.83) = 45.65 = 45.

You're correct on WSC = 45.



fTP as I mentioned before only applies to the first hit of a WS, so if you have an fTP of something other than 1.0, you need to break down the equation into the first hit and then into every other hit (whether they be just remaining hits on a multi-hit WS or DA/TA procs).







pDIF is truncated at 3 decimal places, so just drop everything after that. It's also randomized (this is where the fluctuations in your damage will come from), so typically you can only present a range of pDIF values rather than an explicit number, or rather just a cRatio value. I'd highly recommend referring to the wiki page for pDIF because it is slightly more involved than the rest of the damage formula.

To get a pDIF range you need to come up with cRatio, which is where the level correction on attack will factor in. To get cRatio, you have to come up with an attack:defense ratio (simply named Ratio) which is where you actually take your attack and divide it by the target's defense. 408/327 = 1.247. For one handed weapons and h2h, the cap for Ratio is 2.0, for two handed weapons, it's 2.2, but we're well under the cap so no need to worry about that. On anything lower than Even Match your cRatio is exactly the same as your Ratio, otherwise (for melee, not ranged damage) you subtract 0.05 for ever level of difference. Standard practice is to compare yourself to the highest level mob in the level range, so a level 82 greater colibri. cRatio = Ratio - (level difference * 0.05) = 1.247 - ((82-75) * 0.05) = 1.247 - 0.35 = 0.897.

So, cRatio = 0.897.

Now as for pDIF, plug 0.897 into the appropriate formulas, again here on the wiki page for pDIF, and you get a max of 1.076 and a min of 0.576. Since the max is greater than 1.000 and the min is less than 1.000, a large number of values (a third or so?) will actually center around 1.000 rather than in the mathematical mean of 0.826. If you could think of a standard bell curve, imagine it with the peak at 1.000 on the x-axis cutting down sharply on the right and trailing out gradually on the left. We don't really have a description of the probability model for pDIF so it's hard to say where the average will be. For sake of simplicity I usually just refer to cRatio when doing abstract comparisons rather than extending the formulas in full to account for pDIF, because it's too much math for what is supposed to be a quick, simple comparison.

This is where critical hits are accounted for, they simply add 1.000 to the pDIF value that is output. For a relatively low pDIF value of 0.500 a critical will triple the damage (1.5 / 0.5 = 3), for a relatively high pDIF value of 2.000 a critical will only mean a 50% increase (3.0 / 2.0 = 0.5). So, the lower your attack, the more valuable crits are. Though to be fair, if you're averaging a 0.500 pDIF, you'd benefit far more from an attack bonus (typically) than a crit bonus. Critical pDIF is capped at 3.000; non-critical pDIF is not capped.

After all of that, there's also a random 1.00-1.05x multiplier applied to the final pDIF value (whether a crit or not) making the absolute maximum you can get pDIF up to is (3.000 * 1.05) = 3.150. I'm not sure exactly how the multiplier works, from what I've heard it's a random number between 1.00 and 1.05.



Edited, May 10th 2010 5:00am by bsphil

It's still not right. Neither was I, fixed a detail I forgot.



Edited, May 10th 2010 4:04am by bsphil

Simple errors on the gear listing, Pantin Cape is 5 dex, not 4. Shredder body is 4 str, not 8.

Honestly, I don't see a dex build worth it for PUP because while we use a ton of dex gear, the dex gear that we're not using...we're not using for obvious reasons.

Usu body, enkidu mittens, pantin cape, 6dex ring, rajas, hollow, usu legs and ani+1 are basically the best pieces we would consider using, giving us 39 dex. That leaves 11 from other gear, or 5 with food - this looks promising until you realize that you have very little gear flexibility as is (also that the 6dex ring and hollow aren't super common).

You could argue maat's cap, but you'll like be dropping 25acc anwig for it, that maat's isn't common, and that it's basically the only head piece besides gnadbhod's helm or enkidu's helm with dex on it.

Seranto's or Enkidu's leggings would be another 3-4 dex, but you're giving up str and potentially accuracy.
Adroit earring would not be on my list to drop brutal for.

On top of that you would want to use the crit gloves, which means another 4 dex that could maybe be coming from ancient torque or kubiara beads.
If you dropped usu body for the crit body you need another 8, RSE belt

Getting to the mid forties sounds completely doable in gear we would want to use. Trying to replace usu body and enk's mittens for the shredder crit pieces makes it significantly harder.

Remember that a single crit will increase your damage by 1/6 or 1/7 (likely to DA). Increasing that increase by 10% or 25% or whatever the shredder pieces give will only be giving you a fraction of a fraction. Now against birds, you could easily justify both shredder pieces with evoliths, but at the moment they will probably give a standard build a decrease in damage.

This would also be replacing pieces like flame ring, virtuoso belt, aesir earring, sea gorget/faith torque etc that have consistent returns on damage.


If I were a mithra with dex merits and had a base of 82 dex, meaning I would only need 30 dex after food, this could totally be worth considering since hollow/rajas/6dexring/usu legs/af2 cape/anti+1 gives me 27 dex, so I could swap out for shredder body and gloves and then only sacrifice 1 slot of gear to hit dDex. Now take the opposite case where you are an elvaan needing 15 more dex on top of that forcing you to wear silly belts and necklaces.

Edited, May 10th 2010 10:55am by Requim