Weapon Skill probability

[Frodorn]

I am trying to do some Calculation to see just how much adding 1 more Store Tp will help me with a Multi Hit Weapon Skill, but probability isn't my strong suit.

How do you Calculate the Hit Rate in a WS considering the first hit Must hit, then the Percentage of hit on the rest of the swings?

I have already figure out that adding 1 more Store Tp will allow me to maintain my 6-Hit with a 4/5 Penta Trust. I want to know how often I will Hit the first swing + 3 of the other 4 compared to 5/5.

[RKenshin]

Depends on your accuracy and how much DA/TA you have.

Assuming capped accuracy and factoring out DA/TA, you have a 95% chance of landing the first hit. Then it's about an 98% chance of landing any 3 hits. 98%*95% = about an 93% chance of landing the first hit + any three hits.

In the same situation, it's about an 80% chance to land all 5 hits of Penta.

Did a bunch of rounding and stuff, but that's all about accurate.

[Frodorn]

Thanks... just how did you Calculate that?

[RKenshin]

With 95% accuracy, it's a 95% chance to land any given hit.

Calculating the probability of landing an additional 3 hits is a pain in the ass equation to do by hand/calculator, easiest thing to do is open up excel and use a function.

=BINOMDIST(N, T, P, C)

Where N = number of hits, T = number of trials, P = probability, and C = 0 for most purposes you'll use it for. Or, rewritten it's now:

=BINOMDIST(3,5,.95,0)

Enter that and you get about a 98% chance of landing 3 hits. 98% * 95% = 93% chance of landing the first swing and 3 other hits.


*Reviewing what I said in the last post I picked up on a few mistakes, corrected them. I might've made some other mistakes too in assumptions, but in a rush! D:

Another way that is a little more simple (but not as accurate?) is .95*.95*.95... etc, for the number of swings.

[Frodorn]

Another way that is a little more simple (but not as accurate?) is .95*.95*.95... etc, for the number of swings.

That is pretty much what I did...

[hitrate]^[#swings]

[Chupunpupun]

One thing I'd like to add is that the ACC% you get from a parser is your TP ACC, unless you're using WS in your TP gear, the ACC% when you WS could be lower or higher.

[Frodorn]

One thing I'd like to add is that the ACC% you get from a parser is your TP ACC, unless you're using WS in your TP gear, the ACC% when you WS could be lower or higher.

Well ya...
Unless you got a Parser that can use Tp return to Cal' WS acc =P

and if you do....
You had better share!

[Ophannus]

In the same situation, it's about an 80% chance to land all 5 hits of Penta.

Yikes...how about Asuran Fists?

[LD]

~66%, iirc.

[Ophannus]

So then MNKs have 2/3 chance of landing all 8 hits in asuran fists even if their acc is omg? damn, that makes me rethink multi hit ws ._.

[FailureMidgard]

If you don't want to use excel or something, you can do it relatively (haha!) quickly with a few calculations:

First off, I think you are looking at an irrelevant stat by including the first hit in your probability. The first hit should be essentially the same as any normal melee hit. If it misses, you swing one more time, same as any other swing. A 6hit build isn't suddenly considered a 7hit build (afaik anyway) if your accuracy is 84%. Furthermore, the probability of landing X/Y hits and the first hit has to be 1 of those hits, is upper capped (and will be pretty close) to your assumed hit rate.

What is important is that your extra hits give enough TP so you don't get stuck at 96% TP or such. If you hit can hit 50 storeTP, you only need 2 of the last 4 hits to connect, which isn't very hard at all.

As for the method, it's as follows.

1. Decide how many hits you want to see land. In each line below, make sure your hit percentage is there a number of times equal to (exactly) the # of hits you want to see land.
2. Write out a few lines where "hit" stands for your hit percentage (should be a decimal between 0 and .95) and "miss" is your miss percentage (1 minus your hit percentage). The goal is for each line to reach the desired # of hits, then stop and move to the next line. You are trying to get different (order matters) permutations.
3. Add those decimals together. This represents your chances to hit at least X hits (that you chose).

Example: I have a 95% hit rate and I want to hit 2 out of 4 hits (I'm ignoring the first hit for now, and have 50 store TP so I want to land 2 out of my last 4 hits).

.95*.95 = .9025
.95*.05*.95 = .0451
.95*.05*.05*.95 = .0022
.05*.95*.95 = .0451
.05*.95*.05*.95 = .0022
.05*.05*.95*.95 = .0022

The total # of lines will always be (#swings!)/[(#swings-#hits)!(#hits)!]. That's the standard combination equation. For non math people, n! = n*n-1*n-2...*1. With 4 swings wanting 2 hits, thats (4*3*2*1)/[(2*1)*(2*1)] or 24/4=6. The max number of numbers per line should be the number of swings you have total, or 4 in this case.

The sum of those is actually .9993. The chance to land any 2 of them AND the initial hit would be that times .95. Basically, the chance of landing the initial hit is going to be the mitigating factor to the situation you actually outlined at high accuracy values. Even at 80% accuracy, you're going to be in the ~97% range to land 2 out of 4 hits.

Sorry if that was less simple than you wanted, it really is the most straightforward way to do it by hand though. Use excel if you want the easy way out. ;p

[FailureMidgard]

So then MNKs have 2/3 chance of landing all 8 hits in asuran fists even if their acc is omg? damn, that makes me rethink multi hit ws ._.

Sure, but Asuran Fists with 95% accuracy per hit has a 94.2% chance to land 7 or more hits. Statistics are funny if you don't fully understand them, and can be bent to seem like they mean something that isn't quite true.

[Zilong]

So then MNKs have 2/3 chance of landing all 8 hits in asuran fists even if their acc is omg? damn, that makes me rethink multi hit ws ._.

Sure, if you asuran fist with a bunch of arrows