Place holder

[Cheshire]

This is a temporary place holder for a conversation i had on the TC which I think would actually help people playing DC (especailly once i take the time to properally write it out).

The topic is, how are weapon stats determined in DC but not in technical programming terms... this is in border statistic terms)

Cheshire> I plotted the stats of the DSJ vs. # of DSJs at that stat
<gr_8scorpio> ok
<Evil_D> sleepy time for me, pease oit everyone.
<Cheshire> and it is a normal distribution but it is centered to the left ("skewed to the left" i believe is the correct term for it)
<gr_8scorpio> good nite evil d
<Brykk> night D.
<gr_8scorpio> ok
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<Cheshire> so, if weapon stats are still determined the way I think they are
<gr_8scorpio> ok
<Cheshire> the game picks a "random" integer but it has to follow the skewed distrubition
<Cheshire> so i would guess the integers are weighted or something
<gr_8scorpio> ok
<Cheshire> to have a better grasp of how it works, i would need to be able to read the code of the game, which I can't understand
<Brykk> i'm out. later all.
|<-- Brykk has left www.freejavachat.com (Quit: Brykk)
<Cheshire> another piece of information I got from making DSJs
<Cheshire> the "50/50 point" is at the 1.1 tier
<Cheshire> meaning you have ~50% chance of a weapon being at the 1.1 tier or lower stat
<Cheshire> and you have a ~50% chance of the weapons being 1.1 tier or higher
<Cheshire> the actual chance of getting a 1.1 tier is ~18%
<Cheshire> and getting a 1.0 tier is approx 20%
<gr_8scorpio> ok so that means you have a better chance of gettin a teir 1.0
<Cheshire> yea
<Cheshire> 1.0 tier DSJ is a 80d
<Cheshire> 1.0 tier SAC is a 140a
<gr_8scorpio> so should i make less more often then?
<Cheshire> that is where the "random" bit i was talking about comes in
<gr_8scorpio> ok
<gr_8scorpio> makes sense
<Cheshire> random because it "randomly" picks a stat, but the amount of that particular stat is choses is random
<Cheshire> sorry if i'm not making sense
<Cheshire> i'm tired and should be in bed
<gr_8scorpio> you are
<gr_8scorpio> i understand
<Cheshire> actually, i'm going to keep going because I'm going to C/P this and make a write up on weapon stats
<Cheshire> an example of this happening, would be one of those wheels you spin at a fair
<gr_8scorpio> ok
<Cheshire> you spin the wheel and it eventually stops at number
<gr_8scorpio> uh huh
<Cheshire> there's the crappy prize which most people win because it is the one with the highest frequency on the wheel
<gr_8scorpio> yea right
<Cheshire> then there is the better prize, which is not as common on the wheel
<Cheshire> etc
<gr_8scorpio> i got you
<Cheshire> until you have the grand prize which only once on the wheel
<Cheshire> *which is
<gr_8scorpio> which would be like the 248dsj
<Cheshire> ya
<Cheshire> now imagine you spun the wheel a thousand times and kept track of all the results
<Cheshire> the distribution of the prize versus the number of times it came out, would be quasi-normal, but skewed to the left
<gr_8scorpio> yea makes since but if you spin that wheel enough eventually u'd get the bigg prize once
<Cheshire> this is the same situation with DC and weapon stats
<Cheshire> ...or at least, that is my understanding of it
<gr_8scorpio> i know it took me 3yrs to get a SG
<gr_8scorpio> but a week to get a CWT
<Cheshire> silvers are harder because they simply are harder to find
<Cheshire> so with silvers, it would be as if the wheel had several "blank" slots on it
<Cheshire> which would represent reg glads
<Cheshire> for example, CSB
<Cheshire> people know the value of 100 is associated with the CSB in the code
<Cheshire> they don't know what it exactly means, but if that means the chance of getting a CSB is 1 in 100
<gr_8scorpio> hmmm could be
<Cheshire> then on our wheel, for ever CSB on the wheel, there are 100 SB
<gr_8scorpio> and one CSB
<Cheshire> yup
<gr_8scorpio> i wish i knew the ratios like on CSB
<Cheshire> and if my distribution on DSJ is correct for all or nearly all weapons
<gr_8scorpio> but my thoughts are is that 1 and 100 if you make them or everyone on dc makes them
<Cheshire> then for every 1.3 tier CSB on the wheel, there are 20 1.0 tier CSB and then there are 2100+ SBs

[Loth Emnati]

Hi Chesh, and everybody else. I will take the chance to repost a few old threads that are about to fall off the boards various places:

http://p082.ezboard.com/Item-Drops--how ... D=24.topic
LordXod-01-25-03

How drop quality is calculated:

The notation [0..3] means a random number in the range 0-3 (it could be 0,1,2, or 3).

skew(50) works as follows:
Start with a value of 0. Select a random number between 0 and 99. If it is less than 50, then add 1 to the value and try again by selecting another random number. If it is equal to or greater than 50, quit. Notice that this is an unbounded value. There is no upper limit on weapon power, just a statistical probability that it won't get too high. For instance, the probability of getting a skew value of 8 or greater is 1/256.

A number is calculated as follows:
7 + [0..3] + [0..3] + skew(50)

This number is applied to each of the items base stats as follows (base stats are listed at the end of this post):
If the stat is >= 0: stat = (stat * number) / 10
If the stat is < 0: stat = (stat *10) / number

Notice that the lowest an item can be is 70% of its base stats. As I indicated above there is no upper limit on an item because of the skew function.

For example, if you find a +115a+46s gladius, then the number calculated was 23.

DSJ works just like that. In an old thread at SOIA, Mandrayk made almost 1000 DSJ's and noted their quality:

http://sick-of-it-all.agony.de/thread.php?threadid=15978&sid=

Madrayk 10-07-06

I am making up to 2k DSJ's (if i have the stamina)

after making i'll list the quantities of each i make, I'll also note any that come with stuff (bless, lucky, panic, guild skills etc...)

(currently made 500)

M

(i'll post here the results b4 the end of the night)

OK I thought I made 1000 DSJ, seems i only made 973 OR I can't count (well i failed my uni degree in maths so Meh)

Def / qty / %age
56 / 30 / 3.08
64 / 77 / 7.91
72 / 145 / 14.90
80 / 177/ 18.19
88 / 197 / 20.25
96 / 156 / 16.03
104 / 103 / 10.59
112 / 29 / 2.98
120 / 25 / 2.57
128 / 17 / 1.75
136 / 10/ 1.03
144 / 2 / 0.21
152 / 4 / 0.41
160 / 0 / 0.00
168 / 1 / 0.10

40 had scroll effects
14 had rare effects
7 had guild skills

The two things correlate very well, and small errors are probably due to too few data points



Edit: uhmm.. what I was trying to say, is that we do indeed understand DSJ drops very well. They strictly follow the skewed binomail distribution ;D - and the succes rates are terrible.

We still don't know what the correlation numbers in the weapon.txt does.

2nd edit: The graphs shows percentage along the y-axis and the dropvalue that LordXod talks about along x.

[Guest]

couple o' quick things:

Can you explain the skew more? I'm a bit confused about the +1 and then pick another number... to me, sounds like it is an never ending loop if you keep hitting under 50.

I have a better understanding of the correlation number is due to my "CSB Project" (check it out =P)

I also made a nice distrubition graph of the DSJs i've made (over 2k now) what equation did you use to make the theory line?

[Guest]

btw, it's me, chesh =P

[Loth Emnati]

statistics is the worst kind of math, so I have no fancy tricks up my sleave.

Divide the probability into two kinds. P(x)=SUM[A(y)B(z)], x=7+y+z,
First the random [0...3]'s, which I will call A(y)
They generate a pyramid distribution. Each entry has a chance of 1/16 to appear
0: (0,0)
1: (1,0),(0,1)
2: (0,2),(2,0),(1,1)
3: (0,3),(3,0),(2,1),(1,2)
4: (1,3),(3,1),(2,2)
5: (2,3),(3,2)
6: (3,3)

so, A(0)=1/16, A(1)=2/16, A(2)=3/16...A(6)=1/16

The skew function is a very general "flip a coin" function, and yes, if you keep hitting under 50, then you'll get something incredible. That is why there is no weapon max.

B(z)=1/2^(z+1)

Then I put the numbers into a spreadsheat and multiplied them together. For instance
P(10)=A(0)B(3)+A(1)B(2)+A(2)B(1)+A(3)B(0)=1/16*1/16+2/16*1/8+3/16*1/4+4/16*1/2=0.1914

This seems tedious, but there is a trick . After P(13), all A y values [0-6] are considered for every x, which simplifies things
P(13+x)=A(0)*1/2^(x+7)+A(1)*1/2^(x+6)+A(2)*1/2^(x+5)+A(3)*1/2^(x+4)+A(4)*1/2^(x+3)+A(5)*1/2^(x+2)+A(6)*1/2^(x+1)=P(13)*1/2^x

That brings us to one of the nice conclusions; For weapons above tier 1.3, the chance of getting a weapon of the next tier is exactly halfed for every step.

Edit: I intended to post something about the droprates in the CSB project thread, but it slipped my mind, and I thought you were trying to explain the drop numbers in the txt files. I would suggest that you hunt easier pray. Perhaps gladiators. They appear all the time and has nice drops. Alternatively, if someone is fighting Evil Fred, it should be fairly easy to go through the usual routine, and when done, count the numbers of used quest and compare to the amount of loot. (given that you don't die)

[Cheshire]

First things first:






Now before I show you how lost I am at your intermediate steps, tell me this:

Lets call: P= 7 + [0..3] + [0..3] + skew(50)
(which is what I think you did)

For the skew, the first "roll", if you get below a 50, then P looks like:

P= 7 + [0..3] + [0..3] + 1 + skew(50) , correct?


But as soon as it hits a number that is 50 or greater, it stops and returns a zero... so if on the 2nd roll it gets >=50, P looks like:

P= 7 + [0..3] + [0..3] + 1 + 0 ?

[Loth Emnati]

uhmm. P is for propability. So P(10) means the propability to get a roll of 10

Edit:
The skew function is a flip a coin function. The rules are, if you flip get head, you add 1 to the value, and if you don't.. well, then you stop.

So, stopping with the first flip, has a probaility of 50%, while stopping after the second flip (adds 1) is 25%, and so on.

Your data compared to the theory looks like this:

[Cheshire]

cool, btw, the data i posted is just for the first 1k i made, i have numbers for (i think) another 2k jackets that i never added to that excel sheet.

Would you care for me to add it, or can we agree that the observed distribution is the same as the theory?

[Loth Emnati]

If you care to count them, then I'd gladly plot the data.. It's no biggy. And yes it kind of looks like the data correlates with the theory. I like the way the two data lines intersect on the theory line.

[Guest]

wow man u guys go deep lol i was lost reading the chat thingy lol

[Curulan]

I've been off my game about this lately, but I would like to say that Cheshire's calc sheet does match the previous consensus that a Tier 1 (base stats) item will drop about 80% of the time. (100% - 0.199601)

Also, would you please stop misspelling "probability" as "propability"? It makes this old math geek cringe.

[Cheshire]

That is my old plus new(er) data together. I thought i had kept track of more DSJs than that... but apparently i slacked off =P


Curu... what do you mean with "...a Tier 1 (base stats) item will drop about 80% of the time. (100% - 0.199601)"

My data says that a tier 1.0 will drop 20% of the time, not 80%.

[Curulan]

You're right. I confused myself. I was subtracting the distribution from 100 to get a percentage.