Test: Double Attack during WS

[Armando]

Disclaimer: This is still a work in progress. Doing even just 100 WS is time-consuming! Updates will be slow since both Lmnop and I have time constraints, but bear with us.

Anyways, about a week ago I sent a PM to Lmnop and we agreed to do some testing on Double Attack during WS, since I've never bought into the "You can only DA once per hand" theory. The idea is to do 200 WS with Fast Blade (2 hits,) Raging Rush (3 hits,) and Vorpal Blade (4 hits) to record the number of apparent Double Attacks as well as find an instance of 2 Double Attacks happening in the same WS. All of this is without Dual Wield, of course. Why did I say "apparent?" Well, we can't have perfect accuracy, so some WS may get a Double Attack yet also miss a hit, making it look like the DA never happened at all. Anyways...

Hypothesis: Each hit has a chance to get a Double Attack. For now we'll only be dealing with Double Attack and 4-hit WS at most, so the 8 hit cap won't be an issue. Assuming each hit has a chance to Double Attack, the rate of apparent Double Attacks should exceed 10%, and we should eventually see two Double Attacks happen in the same WS.

I just finished doing 100 Fast Blades. I'll be doing the other 100 next weekend (I can't play during the week. Internet issues, don't ask.) Here are the test conditions:

Lv.63 Paladin/31 Warrior
Attack: 292
Defense: 306
STR: 70+7
DEX: 50+8
Bronze Sword (DMG: 6 | Delay: 231)
Main targets: Bull Dhalmel, Zu

References:
TP per hit = 6.2
1 TP = 1st hit missed
2 TP = 1st hit miss + 1 DA's
3 TP = 1st hit miss + 2 DA's
6 TP = 2nd hit missed
7 TP = 2 hits
8 TP = 3 hits
9 TP = 4 hits

Damage ranges at 100 TP:
1 hit max: 91
2 hit max: 182
3 hit min: 182
3 hit max: 273
4 hit min: 243

Double Attack rate: 10%
Odds of two DAs in a row: 1%
Odds of landing two consecutive hits at 95% hit rate: 90.25%
Odds of landing three consecutive hits at 95% hit rate: 85.74%
Odds of landing four consecutive hits at 95% hit rate: 81.45%

No.) Initial TP, TP return, Damage
001) 105, 6, 62
002) 109, 7, 159
XXX) 102, 7, 147
003) 131, 7, 181
004) 104, 8, 238
XXX) 111, 7, 150
005) 112, 7, 146
006) 108, 7, 141
007) 100, 7, 146
008) 100, 7, 145
009) 120, 1, 64
010) 118, 7, 167
011) 108, 7, 177
012) 104, 7, 148
013) 102, 1, 60
014) 102, 7, 147
015) 118, 1, 70
016) 102, 7, 154
017) 102, 7, 157
018) 100, 7, 149
019) 100, 7, 144
020) 100, 7, 156
021) 102, 7, 150
022) 101, 7, 167
023) 120, 7, 164
024) 108, 7, 164
025) 101, 7, 167
026) 100, 7, 151
027) 104, 1, 62
028) 100, 7, 140
029) 123, 7, 135
030) 110, 7, 155
031) 113, 1, 89
032) 104, 8, 226
033) 111, 6, 74
034) 107, 7, 132
035) 104, 1, 89
036) 110, 7, 155
037) 126, 8, 238
038) 102, 7, 137
039) 133, 7, 169
040) 104, 7, 122
041) 110, 7, 153
042) 104, 8, 208
043) 105, 7, 171
044) 100, 7, 146
045) 133, 7, 175
046) 100, 8, 235
047) 128, 8, 253
048) 111, 8, 208
049) 136, 8, 246
050) 113, 8, 234
051) 101, 7, 166
052) 104, 7, 172
053) 135, 7, 185
054) 109, 7, 146
055) 101, 7, 156
056) 123, 7, 182
057) 104, 7, 169
058) 106, 7, 140
059) 100, 7, 169
060) 106, 7, 152
061) 110, 7, 142
062) 140, 7, 153
063) 139, 7, 167
064) 106, 7, 147
065) 101, 7, 130
066) 106, 7, 155
067) 101, 7, 144
068) 100, 7, 138
069) 102, 7, 153
070) 108, 7, 175
071) 108, 8, 216
072) 108, 7, 149
073) 102, 7, 141
074) 104, 7, 163
075) 114, 7, 127
076) 102, 7, 161
077) 104, 7, 156
078) 100, 7, 155
079) 104, 7, 140
080) 102, 7, 146
081) 102, 7, 159
082) 118, 7, 156
083) 100, 8, 186
084) 128, 7, 150
085) 106, 7, 130
086) 100, 7, 129
087) 102, 8, 209
088) 106, 7, 123
089) 104, 7, 163
090) 108, 7, 163
091) 102, 7, 128
092) 102, 8, 190
093) 102, 8, 223
094) 101, 7, 164
095) 100, 7, 132
096) 110, 7, 139
097) 108, 7, 150
098) 104, 7, 174
099) 102, 7, 160
100) 100, 8, 227

*WS with XXX in their number were overkills and were recorded just in case, but excluded from the tests unless we happen to get an overkill with 2 DAs.

Data:
Exactly 6/100 Fast Blades missed the first hit (~95% accuracy cap)
At least 2/100 Fast Blades missed the second hit.
At least 15/100 Fast Blades had one Double Attack.

So far, no 4 hit Fast Blade. That's reasonable, since the odds of two Double Attacks in a row are 1%, but only 81.45% of those 4-hit Fast Blades will land all hits, so it's more of a 0.8145% chance. However, I did confirm 15 Double Attacks, and like I said earlier, that's only the minimum, since some of the 3 hit Fast Blades will miss a hit and look like a normal 2 hit Fast Blade. That's significantly higher than what I should've seen if only one hit has a chance at Double Attacking (in that case, we would've seen under 10% with the misses factored in) so so far it looks like the hypothesis may be right.

Hopefully after 100 more Fast Blades I'll find a 4 hit one. Well, that's all for now.

EDIT: Oh, yeah, I almost forgot. Anyone here really good at statistics? I'd like to know the correct way of calculating the odds of an X hit WS getting a single Double Attack, the odds of missing a certain number of hits out of 3, 4, 5, or 6 consecutive hits at 95% acc (to have an idea of how many Double Attacked Fast Blades/Raging Rushes/Vorpal Blades would look like a lower-hit WS.)

[Malacite]

Re: Test: Double Attack during WS

I've gotten as much as 18% TP on rampages on my WAR/NIN, and it actually happens quite often thanks to my Double Attack merits + gear.

I average 6 TP a swing I believe with DW2, so that's 12 base, so 4 more swings since it's a 5-hit WS boosts that to 16. There's your proof right there; Double Attack can and does proc on both hands.

Also, I occasionally swing 4 times in an attack round. I've never ever seen rampage return more than 18%, so I'm going to bet that you can only DA once per hand.

[Saren]

Re: Test: Double Attack during WS

EDIT: Oh, yeah, I almost forgot. Anyone here really good at statistics? I'd like to know the correct way of calculating the odds of an X hit WS getting a single Double Attack, the odds of missing a certain number of hits out of 3, 4, 5, or 6 consecutive hits at 95% acc (to have an idea of how many Double Attacked Fast Blades/Raging Rushes/Vorpal Blades would look like a lower-hit WS.)

It has been a while since I did any so it was actually fun to sit and work this out. If anything here is unclear or just wrong please shout me. I used factorials and I am not sure how widely known they are.


Chance of a Single Double attack on an X hit weapon Skill:

Convert the percentages to decimal form for the calculation.

Chance = X * [ (chance of double attack) * {(1 - chance of double attack) ^ (X - 1)} ]


Chance of Y double attacks occurring on an X hit weapon Skill:

I know you didn't ask for this specifically but I have included it because the chance of more than one double attack gets a bit more complicated. This equation is assuming your theory is correct and that every single hit has the same chance of a double attack. Again, you have to convert the percentages to decimals for the calculation.

Chance = [X! / {Y! * (X-Y)!}] * [ {(Chance of Double Attack ^ Y)} * { (1-chance of double attack) ^ (X - Y)} ]




Odds of a given number of misses out of a given number of hits assuming 95% accuracy:

I am only going to list the calculations for the three hit situation so that you can see I am not making up the rest of the numbers off the top of my head. The 6 hit ones take a while to type out and there is no good keyboard convention for writing powers. Again please feel free to check the numbers.

3 Hits:

0 miss = 1 * 0.95 * 0.95 * 0.95 = 0.8574 = 85.74%
1 miss = 3 * 0.95 * 0.95 * 0.05 = 0.1354 = 13.54%
2 miss = 3 * 0.95 * 0.05 * 0.05 = 0.0071 = 0.71%
3 miss = 1 * 0.05 * 0.05 * 0.05 = 0.0001 = 0.01%

4 Hits:

0 miss = 81.45%
1 miss = 17.15%
2 miss = 1.35%
3 miss = 0.05%
4 miss = 0.0006%

5 Hits:

0 miss = 77.38%
1 miss = 20.36%
2 miss = 2.14%
3 miss = 0.11%
4 miss = 0.0003%
5 miss = 0.00003%

6 Hits:

0 miss = 73.51%
1 miss = 23.21%
2 miss = 3.05%
3 miss = 0.21%
4 miss = 0.008%
5 miss = 0.0002%
6 miss = 0.000002%

EDIT: Edited the first two equations because I had been monumentally stupid, I knew something was bugging me about them. They are fixed now.

[Armando]

Re: Test: Double Attack during WS

I've gotten as much as 18% TP on rampages on my WAR/NIN, and it actually happens quite often thanks to my Double Attack merits + gear.
I average 6 TP a swing I believe with DW2, so that's 12 base, so 4 more swings since it's a 5-hit WS boosts that to 16. There's your proof right there; Double Attack can and does proc on both hands.

I don't doubt it. There's only two problems with that, though:
1) It can still be written off as the "once per hand" theory since you're dual wielding
2) "Screenshot or it didn't happen."
Not that I don't appreciate the testimony, mind you. Just that I want to conduct tests that can't possibly be thrown into question. It's about time we really knew for sure what's the deal with Double Attack/Triple Attack.

Also, I occasionally swing 4 times in an attack round. I've never ever seen rampage return more than 18%, so I'm going to bet that you can only DA once per hand.

You can't do more than 8 hits. I've read that this cap applies to attack rounds as well; supposedly, if you were to dual wield Kraken + Octave, you wouldn't be able to swing more than 8 times between both weapons.

Saren: Wow. Many, many thanks. If I did the math right, the odds of Fast Blade getting a single Double Attack are 18%. Of those theoretical 18 3-hit Fast Blades I should've gotten out of the 100 I did, 81.45% of them should show up as 3 hits (i.e. no misses), which is 14.661. The 15 Fast Blades we can confirm as being 3-hits matches that number pretty closely.

One question, though:

Chance = [X! / {Y! * (X-Y)!}] * [ {(Chance of Double Attack ^ Y)} * { (1-chance of double attack) ^ (X - Y)} ]

What's with the exclamation marks?

[Feenicks]

Re: Test: Double Attack during WS

The exclamation mark is the symbol for the factorial function. Bascially,

X! = 1 x 2 x 3 x 4 x 5 ... up to X

So 4! = 1x2x3x4 = 24

[LyonheartLakshmi]

Re: Test: Double Attack during WS

One question, though: What's with the exclamation marks?

That's notation for "factorial", where...

X! = X * (X - 1) * (X - 2) * ... * 2 * 1

So 5! (read "5 factorial") is 5 * 4 * 3 * 2 * 1 = 120.

[Malacite]

Re: Test: Double Attack during WS

I don't have FRAPS so I can't take pics with the chat log up or make videos.

[Saren]

Re: Test: Double Attack during WS

Uhmm…….I have more.


Asusmptions:

• The chance of getting a DA on every single hit of a multi-hit weapon skill is 10% no matter how many DA activations have previously occured
• The chance of a successful hit is 95% on every single hit of a multi-hit weaponskill including DA hits.
• Weapon class/specific weapons do not affect chance to DA or multi DA

I was thinking about this last night and about including the accuracy percentages and what that would do to your success case percentages. There is also this neat statistical thing which for this type of test is fantastically useful:

Average number of attempts required for success = 1 / (probability of a success)

So I ran your numbers this morning and the problem is that if you are doing 200 tests using various weapon skills then your chances of a successful test case are very small.


2 Hit WS:

Chance of 2 DA = 1 * 0.1 * 0.1 = 0.01

The chance of 4 hits ( i.e two double attacks on a two hit weapon skill) having no misses is 0.8145 (from the previous numbers I gave)

So the chance of 2DA and no misses on those 4 hits = 0.0081 or 0.81%

Using the formula above for the average number of tries required for a successful test case, gives you 123.46. This means that you would need, on average, 124 tries before you saw the result you are looking for. As a general rule of thumb to test something like this 4* the average number of tries required is fairly safe. 2 * is o.k. but you can’t be as sure and the more tests you do the better really. Proving statistically that something isn’t true, to a reasonable degree of surety, is hard. Assuming you want to be safe that means you are approaching 500 test cases have to be fails before you can be fairly sure you are wrong, if you use a 2 hit WS.

Put in other terms, if you did 100 fast blades you would only have about a 20% chance of seeing what you are looking for so, if you only did 100 and you got no successes, it wouldn't be that suprising.



It gets better though. As the number of hits in the weapon skill (before DA) increases so do your chances of seeing two or more DAs with all their hits connecting. The stats for this gets a bit long winded so I thought I would skip most of the calculation side of it out.

Disclaimer: The chance for success that I will be giving you is slightly lower than the true value because I ignored cases like a 4 hit weapon skill getting 3DA procs but only 2 of them (still enough to be of interest for your theory) having no misses in them for the sake of simplicity. Since the chance of 3 DAs on a 4 hit weapon skill is pretty small (0.36%) and the chance of 3 DAs on a 4 hit weapon skill where only one of the DAs has a miss in it (so it appears as a regular non DA hit) is even smaller, it’s a negligible difference. Also, my giving lower chances for success means that you are doing a few more tests than strictly required by the numbers not a few less so it won’t adversely harm your test accuracy if you do the number of tests I will be suggesting.

I also ignored cases where you have 2 DA procs on a 3 hit WS, the 4 DA hits all connect but the non DA hit misses again for simplicity but also because I don't know how you are counting these hits and how accurate you can be. Are you able to count every attack whether it connects or not for example? I haven't any experience with double attack on my own character to see what it looks like. The difference in the numbers is again small and again I am lowering the sucecss percentage doing it this way, which increases the number of test cases so not exactly a bad thing but I can't say that the probabilities I am giving you cover every possible situation your test covers.

3 Hit WS:

Chance of 2 DA (resulting in 5 possible hits) = 0.027
Chance of 3 DA (resulting in 6 possible hits) = 0.001

Chance of no miss on 5 hits = 0.7783
Chance of no miss on 6 hits = 0.7351

So:

Probability of a 2 DA, 3 hit WS where all 5 hits connect = 0.021
Probability of a 3 DA, 3 hit WS where all 6 hits connect = 0.00074
Probability of a 2+ DA, 3 hit WS where all hits connect = 0.0217 (or 2.17%)

This means that you would expect on average to have to WS 46.08 times before you had a 2 or 3 DA weapon skill where none of the hits missed. This reduces your rough number of test cases to be fairly sure to 188 three hit weapon skills, which is a lot better than 500.

4 hit WS:

Chance of 2DA (resulting in 6 possible hits) = 0.0486
Chance of 3 DA (resulting in 7 possible hits) = 0.0036
Chance of 4 DA (resulting in 8 possible hits) = 0.0001

Chance of no miss on 6 hits = 0.7351
Chance of no miss on 7 hits = 0.6983
Chance of no miss on 8 hits = 0.6634

So:

Probability of a 2 DA, 4 hit WS where all 6 hits connect = 0.0357
Probability of a 3 DA, 4 hit WS where all 7 hits connect = 0.0025
Probability of a 4 DA, 4 hit WS where all 8 hits connect = 0.00007
Probability of a 2+ DA, 4 hit WS where all hits connect = 0.0383 (or 3.83%)

This means your average number of tries before success goes down to 26.13 which in turn reduces your number of test cases before you can be fairly sure you are wrong if you get no successes to 108, say 110-120 just to be on the safe side. You can get really complicated with testing if you want to be absolutely sure but unless you have a lot of time on your hands, 100-150 repetitions of the same 4 hit weapon skill gives you a good chance of detecting a success if there is going to be one.

If you can find a 5 hit WS the number of test cases to be sure goes down again.


Sorry for the length, if there are any questions/corrections on this please let me know and I hope it helps.

[Armando]

Re: Test: Double Attack during WS

Feenicks, Lionheart, thanks for clearing that up. Malacite, don't worry about it ^^ Saren, thanks again. That was extremely helpful. I didn't realize the number of trials needed to say for sure that Double Attack can't kick in twice on the same WS when single-wielding would drop so dramatically when increasing the number of hits on the WS. I'll get started on Vorpal Blade next weekend, and Lmnop has Rampage (5 hits.) It shouldn't be too long for those to yield results.

[Celeal]

Re: Test: Double Attack during WS

EDIT: Oh, yeah, I almost forgot. Anyone here really good at statistics? I'd like to know the correct way of calculating the odds of an X hit WS getting a single Double Attack, the odds of missing a certain number of hits out of 3, 4, 5, or 6 consecutive hits at 95% acc (to have an idea of how many Double Attacked Fast Blades/Raging Rushes/Vorpal Blades would look like a lower-hit WS.)

I am not a math person, but I would list the possible output for Fast Blade. (Hopefully it may help)

The following are the symbol for the chart:

1 = One hit landed on the mob during multi-hit WS.
0 = One miss on the mob during multi-hit WS.
X = Double Attack does NOT trigger during that hit.

Note: I include both Shield Break (single hit WS) and Fast Blade (2-hit WS) just for reference.

Shield Break:
1st hit double attack after 1st hit
------- ---------------------------
0 ..... X ...................... (missed 1st hit w/o double attack)
1 ..... X ...................... (one hit w/o double attack)
0 ..... 0 ...................... (missed 1st hit and missed double attack)
1 ..... 0 ...................... (one hit and missed double attack)
0 ..... 1 ...................... (1st hit missed but double attack landed)
1 ..... 1 ...................... (one hit and double attack landed)

Fast Blade:
1st D.A. 2nd D.A.
--- ---- --- ----
0.. X... 0.. X
0.. X... 1.. X
0.. X... 0.. 0
0.. X... 0.. 1
0.. X... 1.. 0
0.. X... 1.. 1
1.. X... 0.. X
1.. X... 1.. X
1.. X... 0.. 0
1.. X... 0.. 1
1.. X... 1.. 0
1.. X... 1.. 1
0.. 1... 0.. X
0.. 1... 1.. X
0.. 1... 0.. 0
0.. 1... 0.. 1
0.. 1... 1.. 0
0.. 1... 1.. 1
1.. 0... 0.. X
1.. 0... 1.. X
1.. 0... 0.. 0
1.. 0... 0.. 1
1.. 0... 1.. 0
1.. 0... 1.. 1
1.. 1... 0.. X
1.. 1... 1.. X
1.. 1... 0.. 0
1.. 1... 0.. 1
1.. 1... 1.. 0
1.. 1... 1.. 1

[Malacite]

Re: Test: Double Attack during WS

Well, if you really want to fully test this you need;

1) A WAR with full DA merits and every last bit of DA Gear
2) A COR with Fighter's Roll up on an 11


I've had a COR roll an 11 before and rampage still wouldn't go higher than 18TP returned =/

[Saren]

Re: Test: Double Attack during WS

Apologies in advance, this is long and a bit ranty. I am probably about to be pedantic (not that you can tell I am a maths person or anything) but it annoys me when people are flip about the amount of work that goes into these sorts of tests. Armando and lmnop are working hard for this data and they are taking sensible levels of precautions to make sure their data is good and free from likely related variables.

Well, if you really want to fully test this you need;

1) A WAR with full DA merits and every last bit of DA Gear
2) A COR with Fighter's Roll up on an 11


I've had a COR roll an 11 before and rampage still wouldn't go higher than 18TP returned =/

The rate of Double Attack if you can be sure that you are boosting just the rate at which it kicks in and nothing else (and you don't go under your 95% accuracy cap) would be useful but only for reducing the number of tests you would have to do and probably not by as many as you might think. Having capped accuracy on the mob you are testing against has a more noticeable effect because it maximises your chances of getting a successful result you can see (i.e one with no misses) as opposed to more results. The chance of missing one hit out of two (i.e making the double attack that proced look like an ordinary attack) is 4.7% at 95% accuracy but rises to 9% (almost double) if you go down to 90% accuracy. That means that a 5% drop in accuracy potentially makes you miss, on average, an extra 5 sucessful results (on top of the 5 you are already missing because of the accuracy cap) out of every 100 which given that you are searchin for something that’s occurring less than 5% of the time, really hurts.

You need to control your test conditions extreemly carefully and change things one thing at a time. If you don't know exactly what affect something has when you are testing like this, you do not use it because you could be introducing unqualified variables.

I had a quick look a DA gear and there was 'Enhances Double Attack' gear 'Double attack +X%' gear and 'Double Attack +' gear. Do you know what the difference is between the actual effects those have is because I don't. One could (and probably does) affect the rate at which DA occurs, one could make multiple double attacks more likely, on could increase the damage of attacks a Double attack procs on. Are you absolutely sure that Double attack merits just increase the rate at which Double attack activates and nothing else? If the test was done the way you are suggesting it were done then you would have absolutely know way of knowing if the results you found would hold for any player who wasn’t wearing exactly the same gear as you, using the same food, with the same cor roll value on and with the same number of merits.


If you wanted to fully test Armando's hypothesis you would need to start at 1 on the following list and work your way through until you got a successful result:

1. Do the 150 four hit weapon skills on sword all on the same mob (in the same area to avoid level variation as a variable)
2. Do the 200 three hit weapon skills on sword on the mob you used for 1
3. Do the 500 two hit weapon skills on sword on the mob you used for 1
4. Perform the relevant number of tests on every single multi hit weapon skill in the game going through each class one at a time again on the mob you used for 1
5. Repeat 1-4 using as much 'Enhances Double Attack' gear/food that gave no other double attack related boost and still allowed you to keep your capped 95% accuracy.
6. Repeat 1-4 using as much 'Double Attack +X%' gear/food that gave no other double attack related boost while still allowing you to keep your capped 95% accuracy.
7. Repeat 1-4 using as much 'Double Attack +X' gear/food that gave no other double attack related boost and still allowed you to keep your capped 95% accuracy.
8. Repeat 1-4 with a constant score of fighters Roll
9. Repeat 1-8 using /nin and dual wielding and looking for 3+ activations on a weapon skill.
10. Repeat 1-9 on the same mob class that you used for 1 but at different level ranges
11. repeat 1-10 on at least 4 different mobs from different mob family classes.


There are several reasons to do 1-3. It’s possible that certain WS could allow 2+ DAs to occur and some don’t. It could be possible that the more hits on the weapon skill the less likely a DA is to occur. The reason you do 4 is to take into account the weapon class. It’s possible that certain weapons allow 2+ DA on a multi hit single wield weapon skill and some don’t.

The reason you do 5-7 is because it’s possible that one of the different types of gears function is to allow or also allows the occurrence of 2+ DA activations on a single wield, multi-hit weapon skill and to see if any of those gear effects interacts with any of the previous variables changed to allow 2+ DA activations on a single wield, multi-hit weapon skill.

The reason you do 8 is to find out if Cor’s roll allows a success or Cors roll interacting with any of the previous variables allows a success. The reason you do 9 is to see if dual wield allows a success or dual wield interacting with any of the previous variables allows a success. 10 and 11 are to make your results independent of the mob you are fighting against.

If you went through all of that and had no successful incident of DAing more than once per however many hands you are using on a multi hit weapon skill then you can be 99% sure that it’s not possible to (notice not 100%).

Practically speaking no one in their right mind would test like this. Using some common sense your list would be much much shorter and would almost certainly be as valid but if you are talking proof the above list pretty much constitutes it. For full proofs everything you could possible vary is a variable until you have proved it isn’t including things that common sense is telling you are almost certainly not related to what you are doing.

[Malacite]

Re: Test: Double Attack during WS

There's nothing wrong with piling on as much +DA as you can get.

Just use sushi and +accuracy in every other slot where you can't boost DA.

[Lmnop]

Re: Test: Double Attack during WS

Still, with your full DA (and likely Brutal), feel free to do some tests for Rampage single-wielded. All data is good data, assuming you capture all the right information.

It would be nice to first and foremost, prove that you can DA multiple times on a single WS with the same hand.

[Macht]

Re: Test: Double Attack during WS

There is one thing about this theory you forgot.

What if the 1st hit misses and doesn't proc Double Attack but the second hit does. Then that means it should be possible to see a TP result of 2. Then what if the 1st hit misses and it does proc Double Attack and second hits and procs, then you should get a TP result of 3. With how frequent I've had double attack proc and even had it proc for each hand when dual wielding out of 100 hits I have to say the current data doesn't look promising that you'll see any different then the statement you are trying to debunk.

Well to put it easier should be able to see:

1st miss 1 DA miss 2nd hit 2 DA hit = 2 TP
1st miss 1 DA hit 2nd miss 2 DA hit = 2 TP
1st miss 1 DA hit 2nd hit 2 DA miss = 2 TP
1st miss 1 DA hit 2nd hit 2 DA hit = 3 TP

The theory may of been true that double attack proc'd for each hit when multi-hits returned the same TP per hit, but since that change it's questionable. So really all you should have to look for is a WS that is a 2 hit one were the first misses but the other potential 3, if your theory is right, do hit. It should then result in TP return of 3. If you ever see that happen even just once then it proves your theory right.

From looking at it you would think there should be a decent number of 2 TP returns if the second hit were to proc a double attack with the first one missing. Hell you would think at least 1 of those 6 were the first missed would produce at least a 2 TP. Just from that one being absent starts to make it questionable to me that 4 hits will proc from a 2 hit WS, though it also makes a curious proposition that the DA in a WS will only have a chance of proc'ing if the 1st attack hits. Which kind of indicates that the second hit is ignored for the potential of DA happening.