Final Form Magian Weapons

[mdkuser]

Yeah, you don't need a transition matrix for a simple case like 100% DA and max 2 hits per round. Letting D be the event that a double attack occurs in a single round, it follows that the probability of overflow is

http://latex.codecogs.com/gif.latex?...+ P(D|DD)P(DD)

and the joint probabilities are straightforward to compute from independence of events.

How would you account for situations with non-100% hit rate and like 5 hits possible per round, though? It's easier to set up the appropriate transition matrix, accounting for how much overflow might occur (1, 2, 3, or 4 hits in excess) along with the probabilities of 0, 1, 2, 3, 4, and 5 hits. Then obtain the appropriate n-step transition matrix to get the probability of overflow for any x-hit setup (limited only by the matrix dimensions). You can make the transition matrix as large as necessary to encompass dual-wield scenarios.

Example: 95% hit rate, dual-wielding with 15% double attack rate and 15 hits required to attain 100 TP. Obtain the overflow probabilities (probability of ending with 16, 17, and 18 ) from a 14-step 19x19 transition matrix (you don't really need to go to 14 because probabilities quickly "converge"). They are .4246476, .11025272, and .008391217. The average number of hits is 15.67033, which agrees with an alternative method of obtaining it (brute-force conditional expectation).

You say you have a formula for Love Halberd, but do you know how it really works? If it's like Fortitude Axe, it won't quadruple-attack. If you know that already, are you sure you know how DA interacts with it (where applicable)? If you're wrong, then you would have to go back to the drawing board. Alternatively, you could just crank out the appropriate transition matrix without deriving hard formulas.

NIN DPS: DPS figure follows from the concept of a rate.

OAT and DA: OAT great axe is junk if OAT and DA work like Joyeuse. We'll see.

Oh i see why you mentionned markov chains. But here the model is quite simpler, you can call it a markov chain but its not really one, as what happens on the next round does not depend of the previous round, its just a random walk: For monk and faith's baghnaks for example, you add random numbers varying between 0 and 7 untill the sum exceeds 15, then stop your random walk . This gives you a random number of rounds which is a stoping time, and then there are formulas to find its probability low ( using the power series associated to the RW). For uncapped accuracy, it can go to infinity but it just means the "sum" in the formulas are replaced by infinite series.( it is VERY easy to simulate this on any programming software that can generate random numbers, and I find numbers matching up to the 3rd digits after one million attack rounds ( 10 minutes simulation))

[azagarth]

so is either new sam gkt better then hagun? I just want to know which to upgrade lol.

[pchan]

For the magic accuracy staff I got some not too loong tests in mind to determine if they boost mac more than staves. Level 77 QQ poulterer in the ruins have 65 INT and 290 (+/-1) magic evasion to stone I. Set your total accuracy without weapon at 290+15. With an HQ staff or more, you are expected 95% landing rate exactly, so the chance of 1/2 resists is 4.75% and the chance of 1/4 resists is 0.23% (=1/421). If you do ~100 nukes (should take < 1 hour) and get several 1/4 resist you can be almost certain that acc is not capped and therefore it doen't give 30 magic accuracy. On the other hand if you get less than one 1/4 resist it's high evidence that you get 20 magic accuracy or more.

[CDF]

Oh i see why you mentionned markov chains. But here the model is quite simpler, you can call it a markov chain but its not really one, as what happens on the next round does not depend of the previous round, its just a random walk: For monk and faith's baghnaks for example, you add random numbers varying between 0 and 7 untill the sum exceeds 15, then stop your random walk . This gives you a random number of rounds which is a stoping time, and then there are formulas to find its probability low ( using the power series associated to the RW). For uncapped accuracy, it can go to infinity but it just means the "sum" in the formulas are replaced by infinite series.( it is VERY easy to simulate this on any programming software that can generate random numbers, and I find numbers matching up to the 3rd digits after one million attack rounds ( 10 minutes simulation))

A random walk is a type of Markov process, as where the process goes in the future is only dependent on where it presently is and is independent of where it has been previously. (Edit: you have given a definition of a Markov process.) For getting to 100 TP, all states (total # no hits) are transient except the absorbing states where 100 TP is attained. Instead of simulation, you can just set the appropriate probabilities, use a transition matrix and obtain quickly the probability of overflow given 1-hit, 2-hit, ..., n-hit setups (reading from each matrix row). Simulation as you described is fine, though, especially when you don't want to determine the transition probabilities (of 0, 1, 2... hits in an attack round) in advance.

DPS ratings: (effective) weapon damage per unit time doesn't tell the whole story. Ridill's effective DPS is 19.32, which is much higher than Perdu Voulge's 11.43, but these figures don't account for WS damage, attack, accuracy differences, etc.

Fortitude Axe, continued: just leaving this so we can further doubt Luchtaine.

Using kparser's extra attacks function (it seems to be accurate), I obtained the following counts of single, double, and triple attacks (total) over three stacks of virtue stones (until Campaign ended). 12% DA is the lowest I can go (purpose of minimizing DA is to increase statistical power).

stack 1: 65 99 16 (180)
stack 2: 67 74 16 (157)
stack 3: 51 61 15 (127)

n = 464

1: 183 (.394)
2: 234 (.504)
3: 47 (.101)

Independence model

50% OAT:
1: .44
2: .50
3: .06

Comment: obviously this model is a bad fit to my data. Adjusting the model by changing OAT in either direction just makes it worse.

However, I have a different model where DA and OAT are sort of multiplicative (DA can proc on the normal swing as well as the virtue weapon proc), except quadruple attacks are suppressed. (It's like limiting the number of DAs to 1 per attack round.) It sounds pretty stupid actually (no reason SE wouldn't do such a thing though given track record), but in the absence of quadruple attacks, it's one way to explain the data.

50% OAT:
1: .44
2: .4472
3: .1128

55% OAT:
1: .396
2: .47992
3: .12408

Comment: 50% OAT doesn't really work, but 55% is better. Also, it has been said that the Justice Sword proc rate is ~55% (source, presumably checked w/o DA...), so maybe that's the actual OAT rate for jailer weapons. I haven't been able to find other confirmation of the actual proc rate, though, and I can't do it myself unfortunately.

[Motenten]

Released version 1.5.2 of KParser. Includes the Add'l Effect plugin to show proc rates for status effect additional effects.

Raw proc rate is just procs/hits; applicable for things like Stun where there's no secondary restriction.

Restricted proc rate calculates the rate assuming that there's a 30 second window after any proc that prevents it from occurring again. The number of hits is thus the total number of hits outside those windows. This is the primary rate for the new AE magian weapons testing.

In the case of my Cat's Claws trial, the restricted number of hits was 4934. I had messed up on my original reported hits and forgot to filter out a ghost I fought once, so raw total was 5880, not 5923. Also, the parser only saw 238 procs (AE didn't show up if it happened as I was doing a dance, etc), so there are some windows not accounted for. Reducing by 6.67% to account for probable kicks leaves a rate of 250/4605, or 5.4%.

[Foldypaws]

Raw proc rate is just procs/hits; applicable for things like Stun where there's no secondary restriction.

Stun (and flash) actually does prevent itself from being re-applied, any RDM/DRK who's ever done CSS can tell you this.

That said, duration on mobs is short, so except in high haste/low delay settings, or settings where more than one party member has Stun weapons, it shouldn't come up too often.

That said, what about instead of just a "assumes every hit is plausible" and "assumes 1 hit every 30 seconds is plausible" it was a single box with a option to manually input expected status length. You could throw in 5s for stun, or 30s for defense down, and get better numbers on both.

[Castellano]

its different for additional effect. like if you use the stun katanas on nin you can see it proc on both hits in one attack round

[midguardian]

For uncapped accuracy, it can go to infinity but it just means the "sum" in the formulas are replaced by infinite series.( it is VERY easy to simulate this on any programming software that can generate random numbers, and I find numbers matching up to the 3rd digits after one million attack rounds ( 10 minutes simulation))

If you want to account for uncapped acc/zanshin without resorting to a simulation, you can do as follows.

1. Start with a base multi-hit distribution. For example: (p1 = 0.3, p2 = 0.5, p3 = 0.2).

2. Calculate a new, normalized distribution accounting for accuracy: (p1', p2', p3'). Where p1' + p2' + p3' = 1.

p3' = p3 * (1-p0)^3 / (1-p0' ) (effective chance for 3-hits in an attack round)

p0 = assumed base chance to miss an attack. For example: p0 = 0.05 for capped acc.

p0' = p1 * p0 + p2 * p0^2 + p3 * p0^3 (effective chance for 0-hits in an attack round.)

3. Proceed as you would for perfect accuracy, but using the new multi-hit distribution, using whatever method you like.

4. Divide final result by the effective accuracy: 1 - p0'. This takes into account your potential infinite series of misses before a hit lands.

[Motenten]

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.

Note that this doesn't mean the code is set in stone. I put in what I felt would work best, but if anyone can show that it's incorrect, or that there's a better method, I'll be happy to update for that.

[mdkuser]

If you want to account for uncapped acc/zanshin without resorting to a simulation, you can do as follows.

1. Start with a base multi-hit distribution. For example: (p1 = 0.3, p2 = 0.5, p3 = 0.2).

2. Calculate a new, normalized distribution accounting for accuracy: (p1', p2', p3'). Where p1' + p2' + p3' = 1.

p3' = p3 * (1-p0)^3 / p0' (effective chance for 3-hits in an attack round)

p0 = assumed base chance to miss an attack. For example: p0 = 0.05 for capped acc.

p0' = p1 * p0 + p2 * p0^2 + p3 * p0^3 (effective chance for 0-hits in an attack round.)

3. Proceed as you would for perfect accuracy, but using the new multi-hit distribution, using whatever method you like.

4. Divide final result by the effective accuracy: 1 - p0'. This takes into account your potential infinite series of misses before a hit lands.

like I said it's easy for 2handed weapons and low hit builds, its not possibel to list all possibilities even with 100% accuracy, for a monk with faith's baghnaks for example. I know how to calculate those p0' p1' etc, but im not sure why/what you would divide by 1-p0' at the end. there are some parts you will divide by 1-p0', some by (1-p0')^2 etc... juste dividing by 1-p0' means you neglect cases where two misses ina row happen (still would give an accurate error for the first digit i believe).

[Hanyoko]

I know. For the 6000 hits during the trial, I turned around after each proc until it wore off, then started hitting again. Even allowing for a bit of slop with extra hits landing after the proc, with say 10%-20% being invalid, and removing the ~6.6% of hits that were actually kicks, the proc rate is still in the 5%-5.6% range.

I would frequently go through entire mobs without a single proc. I think my longest stretch was 3 mobs with one proc near the end of the third. Killed a total of 155 hounds, with an average of 38 hits per mob, and 1.6 procs per mob. Estimated average time to proc at about 45 seconds of combat with 24% haste.

Which mobs? If the def down is like acid bolts; it will never proc on colibri.

[Motenten]

Hounds, for the final trial. Hecatomb Hounds and Garms in Bostaunieux Oubliette.

[Byrthnoth]

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.

Lets take the simplest case, a 5-hit scythe with 40% DA rate:
Swing twice (40%): .1% chance of 0 hits, 3.8% chance of 1-hit round, 36.1% chance of 2 hits.
Swing once (60%): 3% chance of 0 hits, 57% chance of 1-hit round

3.1%(p0)/60.8%(p1)/36.1%(p2)

Normalized by doing p1/(1-p0) and p2/(1-p0):
62.75%(p1')/37.25%(p2')


2 Rounds: (p2'^2) = 13.88%
2x2

3 Rounds: (p2'*p1'*2 + p1'^2*p2') = 61.42%
2x1x1
1x2x1
1x2x2
2x1x2
1x1x2

4 Rounds: (p1'^3) = 24.7%
1x1x1

= 3.1082 attack rounds per WS on average over an infinitely long parse

However, this is without misses. Over an infinite sample size, how many misses will you have in 3.1082 attack rounds?

Well, (#Hits/WS)*p0 makes sense, right? p0 is the number of misses you'd expect per attack round after all.
3.1082 + 3.1082*p0 = 3.1082*(1+p0) = 3.2

Dividing by (1-p0) as the above poster suggested gives pretty similar results, though they aren't identical. I can see (#Hits/WS)*n*p0^n being problematic, as the internal "n" should have a max value depending on the

[Foldypaws]

its different for additional effect. like if you use the stun katanas on nin you can see it proc on both hits in one attack round

Isn't this because hits from a single attack round all happen simultaneously?

Does anyone have proof that d/w two def down weapons won't get procs on both hits?

(I've d/w melt daggers before, but the proc rate on that is so terrible that I would never have noticed the missing .004% chance of it happening twice >_> )

[CDF]

So, just curious here about DPS and math because I'm not sure how to calculate this 100% right.


For the Isatu (DMG 34, 232 delay OAT) + Perdu Blade combo, I got around 13.2 DPS, with 15.8 factoring in the OAT which I reduced to a 1.2 mod since it's being Dual-Wielded. Is that right, or do you leave it at 1.4?

At 1.4 that's just monstrous as it gives NIN a combined DPS of over 18... also begs the question if the Katana is even worth it since Mozu with DMG +7 provides around 15 DPS as well with Perdu in offhand (idk how TP gain is affected)

Didn't anyone go over this? Compare each of the following rates (damage per unit delay), ignoring WS damage and attack difference. Suppose 15% DA and let the effective DA rate w/ Isatu be 49% (like Joyeuse), as well as fSTR 4 (...). The reasoning behind the computations should be self-evident.

Mozu/Perdu (A): (47+36)*1.15/(227+190)
Isatu/Perdu (B): (38*1.49 + 36*1.15)/(232+190)
Kuina/Isatu (C): (41*1.15 + 38*1.49)/(201+232)

B is "only" 1.48% larger than A, but C is 3.18% larger than B. Also consider that Kuina/Isatu also has more attack than Isatu/Perdu.

Kuina/Isatu doesn't look fun to get, but that appears to be the best combination for now.

[Cyprias]

so is either new sam gkt better then hagun? I just want to know which to upgrade lol.

The OAT GKT is better, although I wouldn't sell Hagun after finishing it. That way when you fight something that you don't want to give a shitload of TP to, you have an option of going with Hagun instead.

[Demosthenes11]

hagun still best for zergs and fights like DI where you aren't going to be melee'ing on the mob anyways, though it could be argued to go with the new high dmg gkt for that

[pooter01]

A Gkatana without TPbonus would need a DMG of atleast 92 to be comparable to Hagun for WS dmg(at 100%, higher at 200%, but drops off as you approch 300% ofcourse). So the 89dmg still will not beat that of Hagun.

[Demosthenes11]

A Gkatana without TPbonus would need a DMG of atleast 92 to be comparable to Hagun for WS dmg(at 100%, higher at 200%, but drops off as you approch 300% ofcourse). So the 89dmg still will not beat that of Hagun.

hence me talking about meleeing random mobs for tp so your tp wont usually be between 100-200 >.>

[pooter01]

hence me talking about meleeing random mobs for tp so your tp wont usually be between 100-200 >.>

Oh I see, lol. You grouped both Zerg and DI in together, and I just read the zerg. you're right about DI might be better with 89 if you're consistently WSing with more than 200%. In zergs though, Hagun for sure.