Did I miss something regarding Crit WSes?

[Max™]

Was in a retarded debate on gfaqs and got myself a little baffled over the math.

Comparing the Perdu parses vs my Rampager parses, and calling the Perdu crit rate 13%, and Rampager 19%, I was "informed" that over a dumbed down sample of 33 WSes and 99 hits, you'd land roughly 13 Crits with Perdu and 19 with Rampager.

Assuming a non-crit for both axes is in the 200-250 Dmg range, and a Crit is in the 350-400 Dmg range, I wound up getting an average damage over said 33 hypothetical WSes of like 750 for Rampager with 19 Crits, and 800 for Perdu with 13 Crits.

Yet, when I multiply the crit rate by the WS hit count (3 in this simplified case) for 39% and 57%, I get an average WS damage for Rampager right around 1000 Dmg, and 950 for Perdu.

Which, matches up with parses I've found for both axes.

Is there some strange thing in the math that I'm not seeing that would explain only getting a 13%/19% WS Crit rate yet produce WS averages almost exactly the same as those seen from parses?

The big boost of Rampager, and Claymore Grip, that I saw anyway, was adding that 6/9% Crit rate to each hit, for +18/27% WS Crits.

I took 200-250 non-Crit x the non-Crit hits + 350-400 x the Crit hits /33.

250 x 87 + 400 x 13 = 26,950 /33 = 816
250 x 61 + 400 x 39 = 30,850 /33 = 934

230 x 81 + 390 x 19 = 26,040 /33 = 789
230 x 43 + 390 x 57 = 32,120 /33 = 973

Keep in mind my eyes dislike numbers, and that I cheated with a calculator some to make sure I was doing it right, but that LOOKS correct to me, did I screw up something majorly here?

If so, how did I get such accurate WS averages to the parsed WS averages? I started from the 250/400, 230/390 range assumption, not from the parsed averages backwards.

[Ferien]

Assuming no DA, 100% acc, and using your assumed numbers as the averages (Perdu numbers first, Rampager second)

melee crit rate		13%	19%			
						
hits in ws		3				
						
dmg if 0:		600  -  750				
dmg if 1:		750  -  900				
dmg if 2:		900  -  1050				
dmg if 3:		1050 -  1200				
										
chance at 0		0.658503	0.531441		
chance at 1		0.295191	0.373977		
chance at 2		0.044109	0.087723		
chance at 3		0.002197	0.006859		
		
Perdu        Rampager
low end
395.1018     318.8646
221.39325    280.48275
39.6981      78.9507
2.30685      7.20195
658.5        685.5

high end
493.87725    398.58075
265.6719     336.5793
46.31445     92.10915
2.6364       8.2308
808.5        835.5

Adjust for DA and the numbers fall pretty much where you see your averages. Assume non-capped acc and Perdu comes closer, and adjust for 2% extra DA from Perdu and it edges a little closer as well. Realistically, they're probably dead even.

[Mugekuge]

2 minuet, 116 dex, i think 105 str on gear, perdu/pole strap, war/sam, not being able to use hasso too much:

http://docs.google.com/Doc?id=dgdr6nsq_8cf8746d4

[Therin]

Completely anecdotal I know, but I've been using Rampager and I just switched to Perdu since I just got enough IS to get it, and already I can notice what APPEARS to be a pretty large increase in my damage. Maybe I'm just terribly unlucky with Rampager. ;P

[shaddix]

i don't like rampager because of low base damage and i'm kind of meh about it since crits are not as spectacular as they are for 1h. I'm a huge fan of perdu

[Max™]

I left out the chances for doubles, since I also left out the chances for misses, and it sort of roughly evens out in theory at least.

Not sure where the extra 2% DA's for Perdu would come from, since I'd use the same grip with either setup for this comparison.

Crits during WS are kind of spectacular for 2hers still, going from a 200-300 Dmg hit to a 350-400+ Dmg hit isn't a big deal?

I gotta get a good parsed merit with 2 Brds though, cause I've done the same WS avg as that parse Muge just posted with 1 Brd, Min/Mad.


Also: regarding Perdu seeming to give a bigger jump, thats the thing about eyeball parses, I didn't believe Rampager did as well as it does, because it does more for the bottom end of the WS range it seems.

When I swap to Byakko's to test, it always seems like the first 4 or 5 WSes I hit a big 1600-2000 Dmg kablammo in there, but then it swings down just as far.

[Max™]

So after having some voodoo-mathologists correct me, I see that it should be 34% and 47% WS Crit rate between the 13%/19% melee rates, but it works either way.

So, here's some numbers I drummed up, feel free to pick it apart, but I THINK I did it all correctly, though I was being nice with assuming the flat 2.5 pDif for both instead of the actual range it would fall into. It was just to simplify the math.

Being generous, 5 Acc will give 2~3% Acc, 10 Att isn't going to raise your pDif by 1.0 6% of the time, and 9 base Dmg added to 100+ after fStr still has to be multiplied by your pDif roll.

Think I worked out my TP gear fStr to be something like 10 or 11 before food/hasso, 12~13 after, so Dmg 97~100 for Rampager vs 106~109 for Perdu.

Let's go with 100/109
Assume you're hitting a 2.5 pDif roll to simplify, after level correction, that's like 207~ for a normal melee hit Rampager, and 226~ for Perdu.

With 3.25 Crit cap and level correction again (though I think that fStr is a bit low actually) it's 269 Rampager crit, 292 Perdu crit.

I'm assuming (cause I'm still a little confused how that 34%/47% number got produced, honestly) that this next bit works, but I'm sure it will be corrected.

19,662 87 Perdu swings
3,796 13 Perdu Crits
23,458 Dmg 100 Swings

16,767 81 Ramp swings
5,111 19 Ramp crits
21,878 Dmg 100 Swings

1,580 Dmg to make up

Every 5 Swings = 1 WS (which then counts towards the next part of the 6 hit)
So 20 WSes in that 100 Swings

19,000 Dmg from 20 Perdu WSes (950 Avg)
21,000 Dmg from 20 Ramp WSes (1050 Avg)

400~ Dmg in the lead for Rampager, being nice and giving the Perdu about the average it should hit with the gear I WS in with Rampager and know does 1050 Avg, min/min, meat, etc.

Now I'm sure this will be picked apart, and the accuracy will be factored in, the DA rate, etc, but I figured since the DA would be the same for both, and Acc with the gear I have now floats in the 92-94% Range as is, so 5 Acc isn't going to be a significant boost except against lurkers and whatnot, when flashes are factored in and all that then the Perdu will reduce the WS lead to null basically.

It wouldn't be an overwhelming win either way, as I've long suspected, the parses agree with me, and roughing out the math without favoring either side other than assuming Lolibri camp in the acc factor, they should be equal.

The better your gear/acc/att is to start with, the less Perdu will do for you, and the reverse is true.

Looking at it like this, I'd probably have to parse Perdu vs Rampager at sepulcher camp and see how they both fared there, but at Colibri it should be a wash really.

[Ferien]

Parse below is /NIN with Rampager+Claymore. Songs were March x2, Minuet, Madrigal. Only 5 merits in Great Axe and no Fort Torque, so only 286 skill. Gear, as you can see, isn't spectacular, but it's better than most WARs I've had the...pleasure...of xping with.
http://i170.photobucket.com/albums/u...ffxi/WARTP.pnghttp://i170.photobucket.com/albums/u...ffxi/WARWS.png

http://docs.google.com/Doc?id=dfxtmqbb_3dvpzznz4

Low/Avg/Hi for melee and crit were 98/163.8/237 and 182/270.3/311. The 2075 WS in there was a 2x DA with Mighty Strikes up (I'm convinced MS massively increases your ws DA rate, that shit's been happening to me since level 40). I tried not to kill mobs with ws, but it happens.

Statistics 101, or How To Know You've Spent Too Much Time On This Game:
As for the math stuff that's confusing you, remember, it's a 19% chance to crit each hit, independently of the next. It's a binomial distribution (since this has 3 hits, it's a³+3a²b+3ab²+b³, where a and b are the probabilities of non-crit and crit). Mean is np, where n is the number of trials (hits in ws) and p is the probability of success (crit). Mean for 19% crit rate (Rampager+Claymore) is 0.57 crits/ws, where 13% (Perdu/Clay) is 0.39 and 10% is 0.30.

Of course, you need more terms because of the chance of DA, especially since it's not negligible (hi2u 22% DA rate, more if you believe that AF2 pants are more than 1%). Also, you need to adjust for accuracy (which should be completely distributive since the value for a miss is 0).

[Max™]

You need more Dex in that WS build, Berk +1, Haidate (I'm assuming you've had no luck on kitty pants), Nhands (probably the same problem) or hell, hume RSE hands would probably do better than the -5 Dex on Pallas's, you'd lose 6 Str but gain 8 Dex.

Still, getting 980 with such a low Dex build kind of proves my point.

Also: I was getting 39% for 13% crit and 57% for 19%, but on lolgfaqs they said something about you have to figure the probability of it not happening, and then work from there, didn't make a whole lot more sense, but they seemed sure of it.

I'm quite pleased with my WS getup atm, Askar head would be a nice boost too it though.

[Rampager][Claymore] [_] [Bomb core]
[Uni cap] [Snow gorget] [Brutal] [Hollow]
[Berk +1] [Nhands] [Flame] [Rajas]
[Forager's] [Warwolf] [Haidate] [Nfeet]

Pretty sure with the same buffs, I could push that 980 up to 1050-1100, I'll be meriting like gangbusters soon so I'll try to get a good dual brd parse with my current gear.

I sub in Warrior's mask/Nbody in my LoRsh macro (the initial WS swap button has a /echo <hpp> <hp> HP, and I can swap between the two in my WS page if I get cured/hit as Im about to ws) and wind up with 71+41 Str (43 Low hp macro), 68+40 Dex (39 Low hp macro) figure since I got the uni hat for fashion, may as well use the darned thing.

I hate to say it, but I'd only use Are's for choppahrizing and steel cyclone/jump macros unless I had a Bravura, and in that case I'd probably want Askar body for 6 hit.

[Ferien]

Yea, I know I do. Problem is I haven't done sky in years and until very recently (like, last week) couldn't fit it into my schedule. Hence, no kittypants or n.hands. My dumb ass also took E.Hands over N.Head back when I did HNM, and never had the opportunity to fix it so I'm screwed there, too. Elvaan, so no-go on Hume RSE, lol.

As for Ares, meh. I've heard all of the arguments against using it, and as it stands now, cold dead hands etc. I use Hauby when I need the accuracy, and as it stands now I don't have enough DEX for +5 to make a shit of a difference, so for now I choose spikes. At least it matches the Rampager.

[Max™]

Yeah, I'm just an acc/dex whore.

That is still really wicked seeing such a low Dex build pushing 980 basically just from the crit +%.

[Mugekuge]

You guys are going to make me use seals to get a rampager lol, i want to try it and see how it works, my avg on hits on that last parse was : 98 / 176,9 / 248 compared to 98/163.8/237 of Ferien that's 13 damage less in average but probably with increase of critical hits % it closes the difference, other is first parse i posted in other section i was /nin where my avg was around 950, this last parse i went /sam and had 2 brd, but no /cor (like on that first parse) and my ws avg was 1010, and i barely could use hasso.

But yea Rampager looks nice, base damage isn't that low to make a big difference compared with perdu, according to these results.

[Beckwin]

Here's the math from "lolgfaqs" (by vegetaken)

You want the probability of it happening *at least* once.

Let's figure the *opposite* probability of it not happening at all.

If it happens 13% of the time, then it won't happen 87% of the time.

For it to *not* happen 3 times would be:
0.87 x 0.87 x 0.87 = 0.658503

Therefore the probability that it does happen at least once is 1 minus this:
1 - 0.658503

= 0.341497

Answer:
34% (not 39%)

Using the coins, if you were to toss a coin two times, you would have a 100% chance of getting at least one head. You can see that this logic is incorrect, because you could easily toss two tails. Additionally, if you tossed the coin *three* times you would have a 150% probability. :-D.

The correct probability of getting at least one head after 2 tosses is:
1 - 0.5 x 0.5
= 1 - 0.25
= 0.75
= 75%

The probability of getting at least one head after 3 tosses is:
1 - 0.5 x 0.5 x 0.5
= 1 - 0.125
= 0.875
= 87.5%

This number gets closer and closer to 100% with more tosses but won't ever reach it because there is always the *slight* possibility you get a string of tails on every toss.

Math is far from my forte, but Ferien the problem with your method is that you can have a probability/rate/whatever that exceeds 100% when we know that very little in DD mechanics in this game is 100%. If it does add up how you think it does, there'd have to be some kind of cap on crit rate.

[Max™]

30%~

Except for mighty strikes naturally.

[Ferien]

The only thing they calculated there was the probability of having a 0-crit RR. It's accounted for in my math (look at the first reply, where I gave the probability of 0, 1, 2, and 3). Also, it's not a 39% probability of getting a crit in the ws, it's an expected value of 0.39 crits per ws. Two different numbers. They're right, the "probability of critting at least once" is 34%, but like I said in my post, the "mean crits per ws" is 0.39. In the coinflip example, in one throw the expected number of heads is 0.5, in 2 throws it's 1.0, in 3 it's 1.5. This is only a mean, this does not mean the probability of getting one or more heads is 150% (the probability of that is ( 1 - (Ptails^3) = 1 - (0.5^3) = 1 - 0.125 = 0.875 ).

To try to explain the math a little more, the mean of a binomial is represented by np (it simply is, take it as fact, google or search the cheatsheet in the back of a stats textbook), where n represents the number of trials and p represents the probability of success. In this instance, we have 1 WS with 3 trials, so n is 3 trials/ws. p is the average critrate, or 0.13 crits/trial. Expected value becomes 0.39 crits/ws. In 99 trials (or 33 WSes), the mean is 99 * 0.39 = 38.61, meaning that in 99 swings in 33 WSes, you will see, on average, 38.61 critical hits.

The chance of at least one crit in n trials is 1 - (Pnocrit ^ n), and is completely different. For 33 WS, we get 1 - (Pnocrit ^ 99) = 1 - 1.02898E-06 = 0.9999999, meaning there is a 99.999% chance of seeing at least one critical hit in 33 WSes. This number is also completely useless.

Basically, someone at gfaqs wasn't paying attention in their stats class. Run this stuff by them and see what they say, you'll either stump them and make them flame you, or they'll realize they were wrong. Mean, Average, and certainly Probability can not be used interchangeably in Statistics.

TL;DR: They're right, the probability of critting at least once is 34.15%. However, since you can crit more than once, the Expected number of crits per ws is 0.39. Also, 0.39 IS NOT AND CANNOT BE a percentage. It is a final value, representing total successes, and in this case can only be described as 0.39 crits per ws.

Edit: Just realized it's a lot easier to explain if I just call it Expected Value instead of Mean.

[Beckwin]

Ok, I get what you're saying. Easy for terms to get mixed up I guess. However over at gfaqs it was Max's "39% chance to crit" that was being scrutinized, not the expected number of crits per ws. I had previously accounted for the expected crits when I broke it down over a number of WS hits to demonstrate that 6% is still 6% (13% of 100 = 13, 39% of 33.33 = 13, etc), and other posters came in with the 34% figure for the actual chance to crit.

What I'm saying is that in 100 WS swings of RR (call it 33 ws, we'll have DA and misses pretty much wash eachother out), a Rampager gets you 6 more critical hits. We can be generous and say that those crits yield an extra 1,200 damage for the Rampager. Divide that over 33 weaponskills and you end up with 36 tacked on to the Rampager's "base" (no crit bonus) WS average. That figure is nowhere near the +150 Max initially claimed that Rampager has on Perdu for ws average, and doesn't even take into account the superior dmg/att/acc stats on Perdu, and again is fairly generous (your crit hits on WS are doing 400 dmg each). Even if we notch up to 4 hits per ws, it's only a +48 to the Rampager average.

See what I'm getting at?

[Ferien]

Oh yea. I have no opinion either way in the argument, as I'm not even close to the IS for Perdu yet, I was just doing the math for Max and posting the parse. I did notice a massive boost to my average WS damage vs Rune when Rampager finally broke though, which was quite obviously due to the extra 9% Crit (I use Pole Strap with my other Great Axes, and Rune has 1 more base DMG than Rampager). It didn't change the highs or the lows, but really skewed the curve to the highs, which I know is the argument Max has always made. The only real way to tell is to have numbers for exactly even situations, and we'll probably end up concluding that, like everything else, shit is situational.

[Max™]

It didn't change the highs or the lows, but really skewed the curve to the highs, which I know is the argument Max has always made.

Exactly, that 6% doesn't give a huge jump in damage, it just acts as a safety net which Perdu lacks.

Perdu you're going to jump up and down and up and down, highest highs, but you get lows to balance them out.

Rampager doesn't give the same highs, but it really kills the lows, so it seems like you can always count on your damage falling right in the middle range.

As for not seeing how it could parse like that, check his WS setup a bit up the page, far from an ideal build... still puts up 980 WS avg, stack on the dex so you get closer and closer to capping the crit rate (I probably have closer to 24% crit rate for each hit, between the swap to Claymore lately, and the 108 Dex during WS) which helps both axes naturally, as Muge's 1012 Perdu parse in a 116 Dex build shows.

The catch being, I've done the same average and higher with less dex, more str, and fewer buffs, and missing a bit of gear I have now I've done a 1047 WS avg at mjsp in the pit, skoffins, mamools, puks, flash, all that noise.

Like I said on gfaqs, the better your gear overall, the less of a boon 5 acc, 10 att will be, which brings it down to 9 base Dmg vs 6% Crits.

Little to no-buff situation? Perdu will shine.
2 Brd's, decked gear, good meat, the Rampager comes into it's own.

Thought of a good way to explain the better average WS.

Perdu: 1, 2, 3, 4, 5
Ramp: 2, 3, 3, 4, 4

That's how my Byakko's feels against the Rampager, and honestly, Perdu is just a HQ2 Byakko's axe, which is inferior to both options ultimately.