Help @ Math probabilities (DA/TA/multihits)

[Masamune]

/nod Ashokan, same question.

Also, do you meant that DA asymptotically reached the theoric value (15%) faster than TA ? and then its a proof enough to say DA checks before TA ?

Edit: just remembered this guy :
http://www.bluegartr.com/forum/44230...ck#post1517995 saying :

It goes: Triple attack JT > Weapon Triple Attack > Double Attack JT > Weapon Double Attack > Kick Attacks > ||Virtue +1 hit||.
Virtue weapons can trigger at the same time as a JT double/triple, since they don't check for it having gone off. Odder still, the check for that is after kick attacks, and reflects that in the sequence of attacks.

Conclusion i made myself from 2 contradicting guys : let's assume NO checks between DA/TA... end of discussion. Right?

[CDF]

Depending on whether sample size or an interval estimate is going to reported (I am skeptical that even sample size was noted when words like "approximately" are used), we could compare TA rate 11% vs. TA rate 9.35% (TA rate conditional on DA occurring). Then again, the sample size requirements to detect that small a difference formally (not b.s. handwaving) are prohibitively high.

[Ultimagi]

How big was the sample?
What was DA parsed rate?

Double Attack rate was ~15%. It was over the coarse of a Dynamis, however large that would be.

[Masamune]

Seconded CDF.

Also, i remember i got a mail convo with one of Kparser dev, who basically told me the current version "attempt" to track the DA/kickattacks... but thats still very very experimental and take results with big grain of salt.

So is there a parser capable to track DA/TAs with a sample size big enough ? i bet no and that the testers did it by hand on like 300 hits at best?

Edit: (posted after Ultima post) er... on a dyna o.O by hand ?!

[Masamune]

ok back to this after being busy irl.

So far, i managed to put together DA, TA job traits with Virtue/Multihits weapons, following the tree of events @ 1st image attached to this post.

Im getting results with thos formulas on Excel that looks realistic, but imnot sure 100%.

On other hand, i'm trying to integrate Zanshin, which is another whole different story.

More precisely, before Zanshin, i was using a simple binomial law to calculate chances to get X landed hits off Y attacks attempted in a round, 0<=X<=Y and 1<=Y<=8. Which gave me in excel what you can see in 2nd image attached.

Then i do a matricial multiplication between the tree of events values, and the "accuracy matrix", to obtain final values.

So, when considering Zanshin, i thought integrating it with the "accuracy matrix", since Zanshin rely on missed hits. But there i failed to get the total sum of probabilities=100% ...

Any help will be greatly appreciated. Feel free to ask any info i might have missed in the above explanations.

EDIT: whole excel file attached.

[CDF]

From the description of Zanshin, it sounds like it would never proc if a multi-hit weapon procs or if DA trait procs.

Since we can compute the probability of observing n "hits" (regardless of accuracy) in one attack round with a multi-hit weapon, that can be a starting point for computing the probability of observing m landed hits in a single attack round.

Let

S - attempted 1-hit (per attack round)
D - attempted 2-hit
T - attempted 3-hit

0H_S - 0 out of 1 hits actually landed for the attempted 1-hit
0H_D - 0 out of 2 actually landed for the attempted 2-hit
0H_T - 0 out of 3 actually landed for the attempted 3-hit

1H_S - 1/1 hits
1H_D - 1/2 hits
1H_T - 1/3 hits

2H_D - 2/2 hits
2H_T - 2/3 hits

3H_T - 3/3 hits

Z - Zanshin procs
MISS - attack misses
HIT - attack lands

Noting that the number of attempted hits is probabilistically independent of whether they actually land, the probabilities of observing m actually landed hits is then

P(0) = P(S)P(0H_S) + P(D)P(0H_D) + P(T)P(0H_T)
P(1) = P(S)P(1H_S) + P(D)P(1H_D) + P(T)P(1H_T)
P(2) =               P(D)P(2H_D) + P(T)P(2H_T)
P(3) =                             P(T)P(3H_T)

Whatever P(S), P(D), and P(T) are depends on how you think TA and DA interact (mutually exclusive or DA takes precedence over TA).

Now, if you want to incorporate Zanshin, I would assume that Zanshin never procs if a 3-hit or 2-hit round occurs, so Zanshin doesn't change P(2) or P(3). Moreover, Zanshin procs only if a miss occurs, so Zanshin would modify only P(0) and P(1), specifically the terms that involve only a 1-hit round (before Zanshin). Then the modified probabilities are

P(0) = P(S)P(0H_S)*[1-P(Z)] + P(S)P(0H_S)*P(Z)*P(MISS) +               P(D)P(0H_D) + P(T)P(0H_T)
P(1) =                        P(S)P(0H_S)*P(Z)*P(HIT)  + P(S)P(1H_S) + P(D)P(1H_D) + P(T)P(1H_T)
P(2) =                                                                 P(D)P(2H_D) + P(T)P(2H_T)
P(3) =                                                                               P(T)P(3H_T)

Now, for actual numbers.... notice that the P(xH_S), P(xH_D), P(xH_T), x = 0, 1, 2, 3, are probabilities from the binomial distribution.

For example, P(0H_T) is the probability of missing all hits of a 3-hit attack round. Given 95% hit rate, this is (.05)^3 = .000125. P(1H_T) = choose(3,1)*(.95)^1*(.05)^2 = 0.007125, and so on.

[dawdr]

Seconded CDF.

Also, i remember i got a mail convo with one of Kparser dev, who basically told me the current version "attempt" to track the DA/kickattacks... but thats still very very experimental and take results with big grain of salt.

So is there a parser capable to track DA/TAs with a sample size big enough ? i bet no and that the testers did it by hand on like 300 hits at best?

Edit: (posted after Ultima post) er... on a dyna o.O by hand ?!

I realize I'm responding to a post that's fairly old, but testing for which takes precedence really shouldn't be that hard. A Thief with Assassin's Charge can force a Triple Attack, and subbing Warrior with a Brutal Earring should give you a Double Attack in short order. Stacking Assassin's Charge and Sneak Attack for any of the one hit weapon skills will guarantee that everything hits.

I came up with this because I noticed while doing several Kirins on Thief/Warrior I noticed that I would occasionally get a six TP return on Mandalic Stab after putting up Assassin's Charge and not screwing up the lineup. These were with a 201 delay dagger, so there's no way to account for that number without Double Attack blocking the Triple Attack from happening.

[CDF]

And what if triple attack trait overrides a "guaranteed" DA from Warrior's Charge?

At least that is more persuasive than "parsing" in Dynamis, though.

[dawdr]

Easy enough to test for that too, though it could take a bit longer. Triple Knife and Algol have Triple Attack on them and can both be used by Warrior.

[Masamune]

ok, thank you CDF for your inputs that showed me where i made 2 mistakes.

Indeed, i admit i missed the fact Zanshin couldnot occur if DA or TA occur. But still anyone could confirm this is still true for if Jailer or Multihits weapons occur ?

As for what you wrote cdf, yes im totally agreed, i even followed that model as you can see in the tree of events.

Firstly, i rephrased your syntax to avoid confusion between a single/double/triple/Nth attach(s) round and actual job traits D/T with:

N1 - attempted 1-hit (per attack round)
N2 - attempted 2-hit
N3 - attempted 3-hit
etc...
N8 - attempted 8-hit

Then, what i actually did is converting that :

P(0) = P(N1)P(0H_N1) + P(N2)P(0H_N2) + P(N3)P(0H_N3)
P(1) = P(N1)P(1H_N1) + P(N2)P(1H_N2) + P(N3)P(1H_N3)
P(2) =                 P(N2)P(2H_N2) + P(N3)P(2H_N3)
P(3) =                                 P(N3)P(3H_N3)

to...

	P(0)		P(1)		P(2)		P(3)
	 =		 =		 =		 =
N1	P(N1)P(0H_N1)	P(N1)P(1H_N1)
	+		+
N2	P(N2)P(0H_N2)	P(N2)P(1H_N2)	P(N2)P(2H_N2)
	+		+		+
N3	P(N3)P(0H_N3)	P(N3)P(1H_N3)	P(N3)P(2H_N3)	P(N3)P(3H_N3)

which is esssentially :

      -----------------------------------------------------------     -------
      |	P(0H_N1)	P(1H_N1)				|     |P(N1)|
      |								|     |     |
      |	P(0H_N2)	P(1H_N2)	P(2H_N2)		|  X  |P(N2)|
      |								|     |     |
      |	P(0H_N3)	P(1H_N3)	P(2H_N3)	P(3H_N3)|     |P(N3)|
      -----------------------------------------------------------     -------

where P(0), P(1), P(2) and P(3) are the sum for each column of the resulting matrix.

Now, the 1st matrix on the left is what i called on my previous post the "accuracy matrix" with all the binomial terms regrouped (check 2nd image attached); while the 2nd matrix on the right is the model you proposed accounting DA/TA/Jailer/Multihits weapons (1st image attached).

As for your solution regarding Zanshin incorporation into that, the resulting matrix would become :

		P(0) = 						P(1) =					P(2) =			P(3) =
	P(N1)P(0H_N1)*[1-P(Z)]				P(N1)P(1H_N1)
	P(N2)P(0H_N2) + P(N1)P(0H_N1)*P(Z)*P(MISS)	P(N2)P(1H_N2) + P(N1)P(0H_N1)*P(Z)*P(HIT)	P(N2)P(2H_N2)
	P(N3)P(0H_N3)					P(N3)P(1H_N3)					P(N3)P(2H_N3)		P(N3)P(3H_N3)

There can see in bold the added terms representing Zanshin.
Then, can see that the added term @ position (Line2;Column2) isnot factorizable... so in excel i add "manually" those added terms.

The 2nd mistake i made was to trying to incorporate Zanshin to the "accuracy matrix"... while i should have work on the resulting matrix.

For actual numbers, i get better % for P(1) while P(0) "loses" %, which means Zanshin indirectly enhances accuracy by reducing the % of misses.

[Masamune]

For Dawdr, there s a problem in what you assumed: "Sneak Attack guarantee only 1st hit of multi weaponskills".
While yur MandalicStab stacked with AssassinCharge can be seen as a triplehit weaponsksill. So when yu stack SA on that pseudo multihit WS, only the 1st will be guaranteed.

Result yu got on those Kirin means yur assassin charge were totally useless (missed the 2 other MandalicStabs)

[Masamune]

Regarding the job abilities Warrior/Assassin's Charge, i never seen anywhere someone even implying that DA/TA job traits could overrides those 2 JAs when they active.

Example: a THF with Brutal Ear equipped hit AC button, but, surprisingly, only see 2 hits going off o.O. I honestly never heard such story.

So can "safely" assume those 2 JAs overrides the jobtraits DA/TA ?

[CDF]

Regarding the combination of Sneak Attack, Warrior's or Assassin's Charge, and one-hit weapon skills, I did several SA+WC Hard Slash (114 great sword skill) with a blinding potion in Campaign yesterday (yay for Daedalus Wings) and I didn't miss the DA once, so SA does seem to ensure the hits from a DA/TA proc following a single-hit WS actually land.

[Ultimagi]

I'm sure that has nothing to do with single hit weapon skills being 95% accurate anyway.

[Masamune]

Mmmm... indeed cdf, does blinding potion ensures a potent enough blind to ensure a 100% miss on additional hits from WC/AC ? A priori yes should be, i dunno :s

But then dawdr's test would hold water and implies models we assumed for how DA interacts with TA might have to be adjusted ?

[CDF]

Indeed, if DA/TA hits receive the accuracy bonus (I recall someone arguing this a while ago anecdotally with WC+Steel Cyclone) then the SA/AC example is by no means conclusive.

[dawdr]

For Dawdr, there s a problem in what you assumed: "Sneak Attack guarantee only 1st hit of multi weaponskills".
While yur MandalicStab stacked with AssassinCharge can be seen as a triplehit weaponsksill. So when yu stack SA on that pseudo multihit WS, only the 1st will be guaranteed.

Result yu got on those Kirin means yur assassin charge were totally useless (missed the 2 other MandalicStabs)

Actually, Sneak Attack and Trick Attack (with Assassin) both give 100% accuracy to your normal round plus any mutli-hit procs that come with it, but not additional hits in weapon skills. To put it another way, were you to go Thief/Ninja and get a Triple Attack proc on both hands during one of the abilities, all six hits would land. Were you to add something like Dancing Edge to the mix, you'd get three hits off the main hand, and one hit from the offhand, but the other four hits are determined by your accuracy.