Warsoul mats for the mathematicians

Ishmah - Sanctuary
Ishmah - Sanctuary Posts: 192 Arc User
edited April 2010 in General Discussion
According to http://pwi.perfectworld.com/advinfo/ultimate , the probability to create a Warsoul: Avalokites Fragment using Perfect Stones (100 per attempt) is 2.22%.

Now, after 400 attempts, and only having created one fragment, I am beginning to not believe the probability advertised. The warsoul npc does not give a probability like he does for some other mats.

For the mathematicians, how unlikely is a result of 1/400? I was hoping to be at about 8/400 (given a perfect distribution).

Has anyone else documented their results for creating warsoul fragments?
Post edited by Ishmah - Sanctuary on

Comments

  • DrazoThePsy - Dreamweaver
    DrazoThePsy - Dreamweaver Posts: 1,167 Arc User
    edited April 2010
    Since the chance is reset each and every time you try, it'll be very difficult to get an accurate answer (same as how the chances of, for example, rolling a six three times in a row on a fair six sided dice is not actually 3/18). But I'm sure there is at least one person around here who can give a more accurate answer/explanation.

    But since (and especially since) the game seems to not have a realistic randomisation system, it'll impossible unless you had knowledge to the core server code. It's how some people could go through hundreds of ____ packs and get hardly anything worthy while some get as many valuable items as luck tokens. Also in the snake isle race, sometimes you get bombarded by the stuns and slow-downs and hardly get any speed-ups, while sometimes it's vice-versa.

    In other words, the game is rigged. b:chuckle
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  • Brigid - Harshlands
    Brigid - Harshlands Posts: 1,332 Arc User
    edited April 2010
    Ishmah - Sanctuary wrote: »
    According to http://pwi.perfectworld.com/advinfo/ultimate , the probability to create a Warsoul: Avalokites Fragment using Perfect Stones (100 per attempt) is 2.22%.

    Now, after 400 attempts, and only having created one fragment, I am beginning to not believe the probability advertised. The warsoul npc does not give a probability like he does for some other mats.

    For the mathematicians, how unlikely is a result of 1/400? I was hoping to be at about 8/400 (given a perfect distribution).

    Has anyone else documented their results for creating warsoul fragments?

    Assuming a true random distribution, I believe the odds of getting exactly one success in 400 tries is about 0.0011, or a bit over a tenth of a percent. If you include the odds of getting no successes, it's 0.0012 or so. In other words, if the system is actually random, you came out on the wrong end of something like 800-to-1 odds.
  • Asterelle - Sanctuary_1381265973
    Asterelle - Sanctuary_1381265973 Posts: 7,881 Arc User
    edited April 2010
    Assuming it is random the probability p_k of k success out of n trials with probability p is:

    p_k = p^k * (1-p)^(n-k) * (n choose k)

    For you the probability to get exactly 1 success is
    http://www.google.com/search?hl=en&q=0.022+^1+*+(1-.022)^399*+(400+choose+1)
    0.12%

    Edit: ninja'd
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  • Ishmah - Sanctuary
    Ishmah - Sanctuary Posts: 192 Arc User
    edited April 2010
    Thx for replies Drazo & Brigid.

    Now, has anyone else documented their attempts to make warsoul fragments using mats other than chips?
  • Quarka - Heavens Tear
    Quarka - Heavens Tear Posts: 92 Arc User
    edited April 2010
    What you are mostly interested is in 0 successes in 400 tries which is:
    0.01258963592609844246368404271195%

    So AT LEAST 1 success in 400 tries is:
    99.987410364073901557536315957288%

    I believe games don't really work to their probabilities and what we think they mean.
    Edit: oops I see now


    At least 2 successes would have been:
    99.77%.
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  • Asheera - Raging Tide
    Asheera - Raging Tide Posts: 830 Arc User
    edited April 2010
    Random numbers generated on the computer are not purely random but pseudo random. You start with a random seed which you might think is a 'random' number but it just gets it from the system clock or something - at the time of server start I believe.

    Then every action etc who uses some random input will trigger that function. This function will take the previous random number (at start you have the seed), and use some weird formula on it to change it 'randomly', and you get the generated value as output and will also be stored as the last new random value generated for next trigger.

    So thing is it's not totally random just pseudo... sometimes it may work to be very very randomly since the random value is change every time a random action is done, in all categories. So you may trigger a random number on a damage hit, and after that on an animation or something, then another hit etc.

    I don't know the formula but I find it a bit funny game usually generates closer numbers in a row - usually when I get crit I get LOTS of crits, etc. Also have a friend wizard who has low crit rate (arcane build) and said same thing, with an absurd low chance to crit, so very unlikely to trigger but still... when he crits, he crits many times he said, if he has short interval of casting of course.
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  • Michael_Dark - Lost City
    Michael_Dark - Lost City Posts: 9,091 Arc User
    edited April 2010
    Ishmah - Sanctuary wrote: »
    Now, after 400 attempts, and only having created one fragment, I am beginning to not believe the probability advertised. The warsoul npc does not give a probability like he does for some other mats.

    Just like packs, it's pure luck. Some people are just more lucky than others when attempting to do things involving % chances. One of my friends got I think 8 fragments from about 100 attempts.

    I won't attempt it cause my luck is pure ****.
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  • Thelas_Carr - Sanctuary
    Thelas_Carr - Sanctuary Posts: 448 Arc User
    edited April 2010
    Ishmah - Sanctuary wrote: »
    For the mathematicians, how unlikely is a result of 1/400? I was hoping to be at about 8/400 (given a perfect distribution).
    Binomial distribution function so chance of what you call "perfect" is only 50%... 8/400 wtih an expected p = 2.22% is a 53% chance of occurence; 6/400 is 78% chance; 4/400 is 94.28% chance; 2/400 is 99.36% chance; 1/400 is 99.87% chance. Seems you had some bad luck, but not out of the realm of possibility.

    In Excel use 1 - BinomDist(r, n, p, TRUE)

    Where r is number of successes (numerator), n is number of trials (denominator), and p is expected successs rate (e.g., 0.0222).
  • Ishmah - Sanctuary
    Ishmah - Sanctuary Posts: 192 Arc User
    edited April 2010
    Asheera - Raging Tide wrote: »
    Random numbers generated on the computer are not purely random but pseudo random. You start with a random seed which you might think is a 'random' number but it just gets it from the system clock or something - at the time of server start I believe.

    Then every action etc who uses some random input will trigger that function. This function will take the previous random number (at start you have the seed), and use some weird formula on it to change it 'randomly', and you get the generated value as output and will also be stored as the last new random value generated for next trigger.

    So thing is it's not totally random just pseudo... sometimes it may work to be very very randomly since the random value is change every time a random action is done, in all categories. So you may trigger a random number on a damage hit, and after that on an animation or something, then another hit etc.

    I don't know the formula but I find it a bit funny game usually generates closer numbers in a row - usually when I get crit I get LOTS of crits, etc. Also have a friend wizard who has low crit rate (arcane build) and said same thing, with an absurd low chance to crit, so very unlikely to trigger but still... when he crits, he crits many times he said, if he has short interval of casting of course.

    Are you suggesting then, that rather than selecting to make 100 items in one hit, to actually make each one seperately, thereby generating a new timestamp for each?
    Thelas_Carr - Sanctuary wrote: »
    Binomial distribution function so chance of what you call "perfect" is only 50%... 8/400 wtih an expected p = 2.22% is a 53% chance of occurence; 6/400 is 78% chance; 4/400 is 94.28% chance; 2/400 is 99.36% chance; 1/400 is 99.87% chance. Seems you had some bad luck, but not out of the realm of possibility.

    In Excel use 1 - BinomDist(r, n, p, TRUE)

    Where r is number of successes (numerator), n is number of trials (denominator), and p is expected successs rate (e.g., 0.0222).

    Thanks for the Excel tip.

    My results are now 2/600 (1/400 + 0/100 + 1/100)

    This would suggest to me that the percentage advertised of 2.22% (to make a warsoul frag using 100 perfect stones) is incorrect.
  • Ishmah - Sanctuary
    Ishmah - Sanctuary Posts: 192 Arc User
    edited April 2010
    1/400
    0/100
    1/100
    1/100

    =BINOMDIST(3, 700, 0.0222, TRUE) gives 0.000121079 = 0.01% chance.

    Still in 'realm of possibilities'?

    No way advertised probability of 2.22% is true. b:angry
  • Asheera - Raging Tide
    Asheera - Raging Tide Posts: 830 Arc User
    edited April 2010
    Ishmah - Sanctuary wrote: »
    Are you suggesting then, that rather than selecting to make 100 items in one hit, to actually make each one seperately, thereby generating a new timestamp for each?
    Based on my experience so far I do suggest to wait a bit if it fails too much in a row instead of making more, as random numbers would probably be around same. Likewise if it works, I do suggest (based on crits most of time) to make many attempts in a short period after (until it starts to fail a lot again)

    But... just speculation based on my own experience here it could work differently
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  • Solandri - Heavens Tear
    Solandri - Heavens Tear Posts: 2,843 Arc User
    edited April 2010
    Ishmah - Sanctuary wrote: »
    1/400
    0/100
    1/100
    1/100

    =BINOMDIST(3, 700, 0.0222, TRUE) gives 0.000121079 = 0.01% chance.

    Still in 'realm of possibilities'?

    No way advertised probability of 2.22% is true. b:angry
    The TRUE in the last term of BINOMDIST gives a cumulative. That is, 0.01% is the chance of getting 0, 1, 2, or 3 successes out of 700 trials. It is the correct way to analyze what's going on here, but I thought that should be made clear. If you wanted to know the chance to get exactly 3 successes (no more, no less), you'd set the term to FALSE.

    Early in the game, I farmed FB29, FB39, and FB51 for molds. Based on the drop rate I saw, I think they just reduced the chances of a boss to drop a mold to 1/10th what's published in pwdatabase. If you assume they did the same thing here and the chance for success is actually 0.222%:

    =BINOMDIST(3, 700, 0.00222, TRUE) = 0.927611 = 92.76%

    Or put another way, your 3/700 sample gives a 0.43% success rate with a margin of error of +/-0.32% with a 99% confidence interval. That means statistically, there's a 99% chance that the true success rate is somewhere between 0.11%-0.75%. 3 success is kind of a low sample to really trust this conclusion though.
  • Desdemonaaa - Lost City
    Desdemonaaa - Lost City Posts: 98 Arc User
    edited April 2010
    b:faint

    i'll go sit in the corner & let the grown ups talk b:shocked
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  • Ishmah - Sanctuary
    Ishmah - Sanctuary Posts: 192 Arc User
    edited April 2010
    Solandri - Heavens Tear wrote: »
    .... 3 success is kind of a low sample to really trust this conclusion though.

    You would base the success rate alone, rather than the size of the sample pool?

    Solandri - Heavens Tear wrote: »
    Early in the game, I farmed FB29, FB39, and FB51 for molds. Based on the drop rate I saw, If you assume they did the same thing here and the chance for success is actually...

    I do believe they have dropped the success rate.

    IF they have done so I don't have a problem with it. I DO have a problem with them stating the probability is 2.22% on the official site http://pwi.perfectworld.com/advinfo/ultimate . I am not referring to pwdatabase.com


    Edit:

    I suppose my real question is, if I did not know the probability of making this item, how many attempts would it take to get a fairly accurate idea of it? 100? 1,000? 10,000?

    For example, when tossing a coin, how many trials would it take to have a fairly accurate idea that the probability falls withing a 40% - 60% range?

    By the same token, how many attempts would it take to be farily certain of an event having a 2-3% chance? Waht about a 1-2% chance? Is my sample pool of 700 attempts adequate to be reasonably certain that the probability of making a warsoul frag from perfect stones is in fact NOT 2.22%?
  • Solandri - Heavens Tear
    Solandri - Heavens Tear Posts: 2,843 Arc User
    edited April 2010
    Ishmah - Sanctuary wrote: »
    I suppose my real question is, if I did not know the probability of making this item, how many attempts would it take to get a fairly accurate idea of it? 100? 1,000? 10,000?

    For example, when tossing a coin, how many trials would it take to have a fairly accurate idea that the probability falls withing a 40% - 60% range?
    Standard margin of error calculation for a binary (yes/no) event is:

    standard error = sqrt[ (p)*(1-p) / n ]
    p = observed probability
    n = total samples

    margin of error = 0.98 * standard error for a 95% confidence interval
    margin of error = 1.29 * standard error for a 99% confidence interval

    For a coin toss, assuming your observed sample shows p=50%, you want the margin of error to be +/- 10%. From there it's simple algebra:

    0.1 = 0.98*sqrt(0.5*0.5/n)
    n = 24 for a 95% confidence interval
    (i.e. if you took numerous samples of 24 coin flips, on average 95% of them would be in the 40%-60% range)

    0.1 = 1.29*sqrt(0.5*0.5/n)
    n = 42 for a 99% confidence interval
    (i.e. if you took numerous samples of 42 coin flips, on average 99% of them would be in the 40%-60% range)

    However, the problem in this case is that you only have 3 successes. This margin of error stuff does not work so well when p is very close to 0 or 1.

    Going up or down by one success changes the observed probability to 0.57% or 0.29%.
    Going up or down by two successes changes the observed probability to 0.71% or 0.14%.

    These are very close to exceeding the calculated margin of error (0.11% - 0.75%). So I'd be really uncomfortable drawing a conclusion at this point. A couple lucky rolls of the dice can skew your observed results dramatically.
    By the same token, how many attempts would it take to be farily certain of an event having a 2-3% chance? Waht about a 1-2% chance? Is my sample pool of 700 attempts adequate to be reasonably certain that the probability of making a warsoul frag from perfect stones is in fact NOT 2.22%?
    That is something which goes beyond the scope of what I would want to type up. It's called hypothesis testing, and there are lots of different ways to do it.

    http://en.wikipedia.org/wiki/Statistical_hypothesis_testing

    In this case the simplest way to do it is to start with the hypothesis that the real probability is 2.22%. Then you use BINOMDIST to calculate the odds of getting 3/700 (or 2/700 or 1/700 or 0/700) if the actual success rate were 2.22%. As you've already calculated, the chances of your observed results happening are 0.01%. So it's exceedingly unlikely that the 2.22% figure is right.

    Thus endeth the statistics lesson.

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