Final Form Magian Weapons

[Tsuko_Asura]

Why TP off anything but DI?

[Demosthenes11]

cuz its really annoying to constantly run around dodging rampant stance, spear, and wrath.

[Marcicus]

Why TP off anything but DI?

^, DI's attacks are easily avoidable unless you lag like a motherfucker(like I do).

[Villian]

Isn't DI a bit evasive unless you're eating sushi anyway?

[Tsuko_Asura]

Isn't DI a bit evasive unless you're eating sushi anyway?

A bit, but its not absolutely horrible to land hits on him. I've always gone as SAM using sushi, but I'd imagine the DD that benefit more from attack could manage with a good build and pizza.

[Demosthenes11]

fuck that shit, meat the fuck up and kill low mobs. Not having to dance with DI for 20min ftw

[Tsuko_Asura]

cuz its really annoying to constantly run around dodging rampant stance, spear, and wrath.

Call me an overachiever(or lazy), but I always go /NIN and ask for carol/barthunder. Only TP move that doesn't miss/do ~20 damage to me is Kick, but those are going to happen randomly regardless :/

[Malacite]

Could someone please answer my question about DW the OAT Katana?

[Byrthnoth]

Could someone please answer my question about DW the OAT Katana?

CDF did further up the page.

[Xanthe]

Indeed. Stun was perhaps not the best example, but for Stun/Dispel/Poison/Flash/Blind/etc additional effects, the AE can always reapply immediately. The defense down of Acid Bolts can also proc while the effect is already in place, so I didn't add that aspect of the calculation to ranged attacks at all.

This is not always the case. Blind Bolts will not overwrite themselves. I use them quite regularly when soloing on THF and if a bolt has already proc'd once you will simply get damage from subsequent shots until the effect wears off. Sleep Bolts only "overwrite" because the mob is woken by the bolt damage before the additional effect is applied.

[CDF]

Could someone please answer my question about DW the OAT Katana?

A weakness of my paper-napkin approach is the implicit assumption is that TP-phase damage is the same proportion of total damage for any combo, which one should expect isn't true.

One could expect, though, WS damage for Isatu/Perdu to be close to Mozu/Perdu damage. A 9 base damage difference would not be as influential if the second DA occurs on the off-hand (is this true?), thereby affecting only four hits (3 main hits on Blade: Jin and one DA) out of six. I am assuming OAT wouldn't work on WS... otherwise Isatu/Perdu is obviously better...

Suppose the small difference in WS damage manifests such that the TP-phase damage proportion is .66 for Mozu/Perdu and .65 for Isatu/Perdu. That's "only" a .01 difference, but then the % difference in overall (rate of) damage between the two would increase to 2.25%, which is a little better than the 1.48% computed previously. I also worked out the calculations very explicitly and got 2.79%, a figure that is based on many assumptions about Blade: Jin damage that I am not sure are valid (crit all hits, one DA main hand, one DA off hand, etc., etc.)

Perhaps when doing quick calculations you can cite observed TP:WS ratios from parser results as a reflection of reality, acknowledging that those are subject to sampling error.

Modified calculations:

Mozu/Perdu: (47+36)/.66*1.15/(227+190)
Isatu/Perdu: (38*1.49 + 36*1.15)/.65/(232+190)


More Fortitude Axe data: finished this yesterday (no more stones...) but can't think of a good way to explain the result. Again, 12% DA (WAR, 2 DA merits).

trial 1:  65  99  16 (180)
trial 2:  67  74  16 (157)
trial 3:  51  61  15 (127)
trial 4:  49  71  11 (131)
trial 5:  40  26   7  (73)
trial 6: 144 161  37 (342)
trial 7:  80 100  15 (195)
trial 8:  99 105  16 (220)

n = 1425

single: 595 (.418)
double: 697 (.489)
triple: 133 (.093)

[Allelujah]

Anyone else finish the OAT bow or the 46 base damage gun?

[Byrthnoth]

What were you subbing when you did these tests CDF? DNC, SAM, NIN? Wondering if we have any Zanshin to account for.

42/49/9

I guess the weirdest part of the distribution is the triple attack frequency. I like your idea from before for it.

You take 100 swings, 12 of them double attack:
88/12/0

Now you have a ~50% DA rate on the first or second swing (or both swings of a double attack)
44/47/6/3
However, the quadruple attack cases are suppressed because only one virtue stone can be expended per round:
44/47/9
do you leik hao i rationarize?

With something closer to 53% Jailer Weapon Proc it comes closer to mimicing your distribution, but I don't know that the difference between this distribution and yours are far enough to justify any changes.
53%: 41.36/49.2908/9.3492

Edit: If it is possible that you took a few swings without virtue stones on, swings that killed monsters, etc, it would shift your distribution a little low and perhaps 55% Jailer Proc rate is reasonable.
With a 55% Jailer Weapon Proc rate and 22% DA rate (more standard for WAR) the Fort (D64) distribution would be:
35.1/47.355/17.545
DPS of 13.9, higher WS frequency (but weaker WSs).

New OAT GA (D76) with 40%/22% would be:
46.8/53.2
DPS of 13.6, potential to 6-hit /NIN

Perdu (D96) with 22% DA would be:
78/22
DPS of 13.94, lowest WS frequency but strongest WSs.





Fort Axe: 35.1/47.355/17.545
2 Rounds: 19.7%
3x2 (2) - 16.616% [32 23]
3x3 (1) - 3.0782% [33]

3 Rounds: 58.48%
2x2x2 (1) - 10.619% [222]
2x2x3 (1) - 3.9344% [223]
1x2x2 (3) - 23.613% [212 122 221]
1x2x3 (4) - 11.665% [123 213 312 132] (23X or 32X are already accounted for in the previous round)
3x1x1 (3) - 6.4846% [311 131 113]
3x1x3 (2) - 2.1609% [313 133]

4 Rounds: 20.31%
1x1x1x2 (4) - 8.1911% [1112 1121 1211 2111]
1x1x1x3 (1) - .7587% [1113]
1x1x2x2 (3) - 8.288% [1122 1212 2112]
1x1x2x3 (3) - 3.0708% [1123 1213 2113]

5 Rounds: 1.518%
1x1x1x1 (1) - 1.518% [1111X]

3.0367 rounds to 100TP on average with 22% DA and no accuracy correction assuming our model of Fortitude Axe behavior is correct.

[CDF]

Points of clarification and random thoughts: ninja subjob, so no Zanshin. No other gear. I was whacking a fortification for hours, so no kills (but any hits on the killing round are ignored by kparser anyway). Sadly, I was also monitoring the virtue stone count in the equipment menu so I could equip a new stack when I ran out. I rechecked my merits menu and I still only have 2 DA merits.

[pchan]

trial 1:  65  99  16 (180)
trial 2:  67  74  16 (157)
trial 3:  51  61  15 (127)
trial 4:  49  71  11 (131)
trial 5:  40  26   7  (73)
trial 6: 144 161  37 (342)
trial 7:  80 100  15 (195)
trial 8:  99 105  16 (220)

n = 1425

single: 595 (.418)
double: 697 (.489)
triple: 133 (.093)

Could it be possible that DA proc on the normal swing as well as the added swing but that if both DA happen, only one is taken ? Like if N is the number of hit/round

N=X1+X2+min( 1 , Y1+Y2 )

where X1 ~ bernouilli of parameter 0.95 is the normal hit
X2~0.5*0.95 (or something else..) is the OAT hit
Y1~0.12*0.95 is the DA from trait on normal hit
Y2~0.12*0.95 is the DA from trait on OAT hit

Using this model I find

Proba(N=3)=0.95*(0.5*0.95)*( 0.12*0.95*2 - (0.12*0.95)^2 )
=9.7%

edit : nvm, did a little mistake, so yeah it seems that's how it works ?

[midguardian]

So, the whole p0 thing. Misses are cases that don't actually contribute to the number of ways you can productively get 100TP, which is why it makes sense to normalize them when constructing your distribution. Because they don't contribute to your criterion (100TP) you can ignore them for later.

Yes, misses lead to infinite series, so the idea is to manage them by renormalizing the multi-hit distribution.

With perfect accuracy, you have a multi-hit distribution like: (p1, p2, p3, ...) where p1 = probability for 1-hit in an attack round, p2 = probability for two hits, etc... and p1 + p2 + p3 + ... = 1. For Soboro you might use (0.3, 0.5, 0.2) and for a non-multi-hit weapon you might use (0.95, 0.05, 0) if 5% DA is uncluded.

With imperfect accuracy, you get a new distribution: (p0', p1', p2', p3', ...).

p0' = p1 * p0 + p2 * p0^2 + p3 * p0^3.
p1' = p1 * (1-p0) + 2 * p2 * (1-p0) * p0 + 3 * p3 * (1-p0) * p0^2.

Now this distribution still includes misses. In each attack round, you can miss, hit once, hit twice, etc... Because of the chance to miss, you can in principle have an infinite number of attack rounds before an attack ever connects.

Renormalization

Misses can be effectively removed from the multi-hit distribution, but there is a consequence, which I'll get to later. Consider the simple case where you just want the probability for one hit to land (no multi-hit chance).

p1'' = p1' + p0' * p1' + p0'^2 * p1' + p0'^3 * p1' + p0'^4 * p1' + ....
p1'' = (1 + p0' + p0'^2 + p0'^3 + p0'^4 + ...) * p1'
p1'' = 1/(1-p0') * p1'

This result is just p1' divided by 1-p0', which is the effective accuracy. Rename this p1'' -> r1 and call it the renormalized probability for one hit, given that a hit lands! This result holds in the same form for more than one hit. (Note that the final identity is NOT an approximation.)

Now the renomalized multi-hit distribution is: (r1, r2, r3, ...) such that r1 + r2 + r3 + ... = 1. Misses have been effectively removed from explicit consideration.

The consequence of this renormalization is that the concept of the attack round has changed. Before, an attack round was of a fixed length, independent of accuracy, and each round you could miss or hit one or more times. In the renormalized model, you hit one or more times every attack round. So the effective length of the attack round has to be renormalized as well. Luckily this is easy to do. Just divide again by the effective accuracy: 1-p0'.

For example, if you use the renormalized multi-hit distribution to calculate that a multi-hit weapon averages 3.14159 "renormalized" attack rounds to 100+ TP, then you need only divide this result by 1-p0' to get the result in terms of actual attack rounds.

Simple Example

Take a weapon with no multi-hit capability. Assuming perfect accuracy, the multi-hit distribution is: (p0, p1, p2) = (0, 1, 0). If you need 5 hits to reach 100+ TP, then it will take 5 attack rounds exactly.

Now include imperfect accuracy. Assume capped hit rate, so 95% accuracy. Now the new multi-hit distribution is: (p0', p1', p2') = (0.05, 0.95, 0).

Renormalize this to r1 = p1' / (1-p0') = 0.95/(1-0.05) = 0.95/0.95 = 1. Now the renormalized distribution is: (r0, r1, r2) = (0, 1, 0). It takes 5 renormalized attack rounds to get 100+ TP. (Note: r0 = 0 because misses are taken into account by the renormalization.)

The number of actual attack rounds is: 5/(1-p0') = 5/(1-0.05) = 5/0.95 = 5.26.

Conclusion

As has been said, the "hard" part is determining all the various paths to 100+ TP. However you choose to do that, you can effectively "ignore" accuracy considerations during the "hard part" if you renormalize your multi-hit distribution, which is easy to do.

[Malacite]

...

In plain English how do you account for multi-hit procs on a weapon when it's being dual-wielded into the DPS calculation?

Cut it in half since you're not swinging as often? (which would change the final multiplier to 1.2 in this case)

[Byrthnoth]

...

In plain English how do you account for multi-hit procs on a weapon when it's being dual-wielded into the DPS calculation?

Cut it in half since you're not swinging as often? (which would change the final multiplier to 1.2 in this case)

(OAT Base Weapon Damage * Proc Rate distribution (1.4 for these weapons) + Other Base Weapon Damage)/(Delay*Dual Wield/60) = DPS

[Magicide]

Turning attention for the moment away from general melee theory and over to the staves, has there been any add'l info gathered regarding the "Elemental Affinity: Magic Accuracy +x" stat on the Stage 4 and completed Teiwaz? I know testing m.acc is problematic, but I wouldn't think it would be that hard to eyeball and see if resist rates approximated an elemental staff or if they approximated a staff with plain old m.acc +3.

Also, just to make sure I'm not mangling this, is the current hypothesis that elemental staves have the same hidden effects on them that the Teiwaz lists out, right? So, say, a Thunder staff would have:

Thunder Affinity: Magic Damage +1 (equivalent to 1.10 dmg coefficient)
Thunder Affinity: Magic Accuracy +1

While a Jupiter's staff would have:

Thunder Affinity: Magic Damage +2 (equivalent to 1.15 dmg coefficient)
Thunder Affinity: Magic Accuracy +2

While the Magian weapons can be upgraded to have +1 to one stat and +3 to the other, where Magic Damage +3 has been confirmed to be a 1.20 dmg coefficient?

I apologize for repeating what's already been said but wanted to make sure I was reading it right before crapping in my pants unnecessarily. Because, um, holy shit.

[CDF]

Could it be possible that DA proc on the normal swing as well as the added swing but that if both DA happen, only one is taken ? Like if N is the number of hit/round

N=X1+X2+min( 1 , Y1+Y2 )

where X1 ~ bernouilli of parameter 0.95 is the normal hit
X2~0.5*0.95 (or something else..) is the OAT hit
Y1~0.12*0.95 is the DA from trait on normal hit
Y2~0.12*0.95 is the DA from trait on OAT hit

Using this model I find

Proba(N=3)=0.95*(0.5*0.95)*( 0.12*0.95*2 - (0.12*0.95)^2 )
=9.7%

I let kparser do the tabulation, and it recognizes misses as those of a given attack round, so hit rate (accuracy) need not be considered. I did consider this probability model:

50% virtue proc rate
1: .4400
2: .4472
3: .1128 (quadruples suppressed)

55% virtue proc rate
1: .39600
2: .47992
3: .12408 (quadruples suppressed)

So, the observed triple attack proportion (133/1425 = .0933) alone is much lower than would be predicted by either.

What were you subbing when you did these tests CDF? DNC, SAM, NIN? Wondering if we have any Zanshin to account for.

42/49/9

I guess the weirdest part of the distribution is the triple attack frequency. I like your idea from before for it.

You take 100 swings, 12 of them double attack:
88/12/0

Now you have a ~50% DA rate on the first or second swing (or both swings of a double attack)
44/47/6/3
However, the quadruple attack cases are suppressed because only one virtue stone can be expended per round:
44/47/9
do you leik hao i rationarize?

With something closer to 53% Jailer Weapon Proc it comes closer to mimicing your distribution, but I don't know that the difference between this distribution and yours are far enough to justify any changes.
53%: 41.36/49.2908/9.3492

I never actually thought (and never would) about conditioning the number of OAT procs on whether a normal double attack occurs (another way of describing your idea), so thanks for the idea. I do have another small data set with manually counted landed hits:

(n = 236)

0: 5 (.0212)
1: 96 (.4068 )
2: 100 (.4237)
3: 35 (.1483)

Conditions: 95% hit rate, 21% double attack rate. Compare to the following distributions under Byrthnoth's idea:

50% virtue proc rate:
0: .0209
1: .4185
2: .4188
3: .1418

55% virtue proc rate:
0: .0190
1: .3838
2: .4454
3: .1518


236 is a rather small sample to rule anything out, but when accounting for misses, this model plausibly still holds for both 50% and 55% virtue proc rate.

Just for fun: note that both probability models give the same expected number of hits per attack round even though the underlying probability distributions are generally different (except when DA rate = OAT rate). For example, given 12% DA and 50% virtue weapon proc rate (100% accuracy), the expected number of hits per round is 1.12*1.50 = 1.68. However (ignore quadruple attack suppression for now)...

Probability model 1 (the number of normal DA trait procs is conditional on whether OAT procs):

1: .4400
2: .4472
3: .1056
4: .0072

Probability model 2 (the number of OAT procs is conditional on whether normal DA trait procs)

1: .44
2: .47
3: .06
4: .03

Some of you might be wondering WTF any of this matters, and I understand the sentiment. Having insight on how "occasionally attacks twice" works for virtue weapons may help people figure out how Magian OAT and normal DA interact if it turns out not to be that obvious (the observed absence of triple attacks alone for OAT dagger has helped to narrow things down somewhat though).