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Cow level Statistics

Discussion in 'Theorycrafting and Statistics' started by Slayersteven, May 28, 2005.

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  1. Slayersteven

    Slayersteven IncGamers Member

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    Cow level Statistics

    For mathematics (Statistics) i had to do a final project, a statistical inference, i happened to do it on the cow level and whether or not the amount of scrolls in a tome affect the amount of cows in the level.

    Here is a 5 point summary + of each sample, base is the number u buy from the merchants or npc's in the tome, 1-4 scrolls, and full is 20 scrolls.

    Data Summary

    Full (20) Statistics::

    Number: 20
    Mean: 65.5
    Standard Deviation: 6.4031
    Minimum: 57
    Quartile 1: 61
    Median: 64
    Quartile 3: 68.5
    Maximum: 83

    Base Statistics::

    Number: 20
    Mean: 55.1
    Standard Deviation: 6.5767
    Minimum: 44
    Quartile 1: 51
    Median: 54.5
    Quartile 3: 58.5
    Maximum: 74

    I then conducted a two-sample T-Statistic test, to find the probability that my null (or base) hypothesis was true stating that the amount of cows created by both were equal against the probability that the amount of cows created by a full tome were greater.

    the probability of the null being correct was = 0.007%,
    the probability of the other being correct was = 99.993%

    Normally a statistic only has to be proven at the 95% confidence interval. so i concluded at the 99.993% confidence interval, which means that 99.993% of the time, at this difference in statistics this will represent the entire population, that having a full tome causes more cows to be present in the cow level, rejecting except for a 7 / 100,000 chance that the tome full and with base in it are equal.

    If you have any questions for me, my email is [email protected] or [email protected], my aim is Sven00100 my msn is [email protected] and my yahoo messenger screen name is [email protected].

    Since i was not bias beforehand, and random game names were used, on USEAST ladder, this is a random sample, granted a simple random sample (SRS) is impossible since the games aren't pre-existing, but its next best, hopefully this defers disputes about this topic, as i've had many people telling me it both ways.

    Simply put, i am almost positive that a full tome is better used for more cows in the secret cow level.

    -Steven W.
     
  2. helvete

    helvete IncGamers Member

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    Well, it wouldn't be impossible that number of scrolls in the tome is part of the map seeding for cows? Or would it? Because in Single Player games, I think the map stays the same, even though I'm far from sure about it. But conducting such tests on SP should be easy, shouldn't it?
     
  3. Slayersteven

    Slayersteven IncGamers Member

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    no its not impossible for the seeding of cows to happen from the tome, the map stays the same on 1 player, but my thoery is that the monsters there, and possibly other places arent spawned until someone goes to that area, so until u make the cow level, unlocking it, the cows arent there, so as not to cause extra lag.
     
  4. helvete

    helvete IncGamers Member

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    Sometimes, cows, even the king, spawn on top of the red portal. That's sort of annoying, especially for amas and necros..

    The magic number of scrolls in the tome for this to happen must be 13, and if it's friday as well, the king spawns on the portal!!
     
  5. Slayersteven

    Slayersteven IncGamers Member

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    If you're trying to discredit me, please do so justly, with either a flaw in my experiment, or a counter-experiment. conducting the same test.
    thank you
    -steven
     
  6. ebyworx

    ebyworx IncGamers Member

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    wouldn't the only way to test this be to count the cows?
     
  7. RTB

    RTB IncGamers Member

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    That's not a theory, it's a fact. The spawning of monsters happens about 2.5 screens away from a character, using a density value from levels.txt (three columns total, one for each difficulty level), actual size of the level(which is controlled by two columns in levels.txt: SizeX, SizeY, and that three times, one for each difficulty level), and two columns in monstats.txt: MinGrp and MaxGrp. The values in these columns control how many monsters of a certain type appear at one spawn spot. Some monsters also have minions (Shamans, Overseers, Unravelers, etc) and in that case two other columns (PartyMin and PartyMax) are used for deciding how many minions spawn. Lastly, there's the map seed.
    In theory, the number of scrolls in the tome could affect the amount of cows in the cow lvl too, but it's still a myth to me.

    What I'm missing from your otherwise nice statistical analysis is how you counted the cows. The amount of cows seems really low too.

    20 runs seems too small an amount for an analysis on something with this many variables.

    IMHO a chance of 99.993% won't be not enough to prove something in a game where odds much worse can happen. The legitly spawning of items like perfect Goldstrike Arches and Zod runes for example.
     
  8. frygia

    frygia IncGamers Member

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    I believe that the (20) means the number of scrolls, RTB. For this to be trustable, I would say that a sample would have to be on the 1000's...
     
  9. krischan

    krischan Europe Trade Moderator

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    I think that a few things are missing in your analysis. To make statistics about this, you have to make a list of the number of cows for your created cow levels. That list can be used to make e.g. a histogram of the numbers of cow levels with the number of cows being within a certain range, e.g. 3x 201-210 cows, 10x 211-220 cows etc. If you made enough cow runs, you can make a proposal about the kind of distribution. I guess a Gaussian distribution will be a good approximation (the square of a Gaussian distribution might perhaps be better). For that kind of distribution you can make statements about standard deviation etc. and if the standard deviation (which is the average difference between the average number of cows and the actual number of cows BTW) of your distribution is equal to the Gaussian standard deviation with a certain accuracy (99.9993% in your case), you can regard your proposed distribution as statistically proven well enough for the standard you set up - but only with respect to standard deviation. I might not remember details about other things to consider, I admit.

    However, to make a statement about the accuracy of your standard deviation being 99.9993% accurate, you have to do tens of thousands of cow levels and count the cows, else it might just be pure incidence. For example, if you do just two cow runs, you can calculate the average number of cows x=(value1+value2)/2 and the standard deviation (|x-value1|+|x-value2|)/2. It's not that improbable that you exactly hit the standard deviation with these two values.

    A chance of something being 99.993% accurate is something different than a chance of something being 100-99.993%

    For example, it would be wrong to say "The chance for a monster to drop an elite unique is 100-99.993%, i.e. it's a good approximation to say it's never going to happen." (I made these numbers up). In the reverse case, it doesn't really matter if something happens 99993 times or 100000, as long as those 7 incidents are unimportant for you. Regarding the number of cows in the cow level, it won't be important if you actually got 99993 cows instead of 100000.
     
  10. krischan

    krischan Europe Trade Moderator

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    Hmm, after reading the whole again, it seems I missed the point of the whole. It's not how the distribution of the number of cows is, but simply how many cows there typically are. That means, everything I wrote before I quoted RTB is nonsense and can be ignored :rolleyes:

    Anyway, you need more than 20 countings of the number of cows for being 99.993% accurate.
     
  11. Rekk_Dalton

    Rekk_Dalton IncGamers Member

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    was the number of players in each game equal?
     
  12. FodderCannoned

    FodderCannoned IncGamers Member

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    I know 20 tests seems like it may be too small, but it isn't, 20 tests is the usual number done in statistics. I have taken a couple stats courses myself in college and everything seems alright, it is still hard to believe that something as trivial as the number of scrolls in the book would affect the number of cows though. I also would like to see 20 more results done for each of 1 scroll, and 20, I may do this, but I don't have any characters right now where i haven't killed the king, maybe my bowazon, i will have to check.
     
  13. krischan

    krischan Europe Trade Moderator

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    If I roll a die e.g. to see if it's "loaded", 20 tries are far too less. Of course, the number of cows in the cow level is the result of dozens of such die rolls, but for being 99.993% accurate, you still need far more than 20 tests.
     
  14. Angel_Dusted

    Angel_Dusted IncGamers Member

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    You know, I hate to be unproductive to the post and to infringe upon your intellectual tirade, but I just have to comment upon how savvy and interesting this post is in comparison to almost every other sample out there.

    To summarize: You be smart. :thumbsup:
     
  15. FodderCannoned

    FodderCannoned IncGamers Member

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    Ok I will explain why his data is right, although it has been 2 years since i have taken a stats course.

    Full (20) Statistics::

    Number: 20
    Mean: 65.5 Average number of cows with 20 tp scrolls
    Standard Deviation: 6.4031
    Minimum: 57
    Quartile 1: 61
    Median: 64
    Quartile 3: 68.5
    Maximum: 83

    Base Statistics::

    Number: 20
    Mean: 55.1 Average with the base TP scrolls
    Standard Deviation: 6.5767
    Minimum: 44
    Quartile 1: 51
    Median: 54.5
    Quartile 3: 58.5
    Maximum: 74


    The minimum that you get with the 20 tp scrolls is higher still than the average that you get with base. This is the easyest way to tell that the amount of TP scrolls plays a major difference. hmm, explaining this is harder than i thought, can you explain it better slayersteven.


    As long as he counted the number of cows right, and i don't see why someone taking a stats class would ever count wrong, I garantee that number of scrolls affects the number of cows, thanks slayer, I will now always use 20 tp scrolls thanks to you. Also do you mind if i use your data elsewhere?


    edit
    also you don't need more than 20 tests to do this type of statistical analysis. It may seem like you do, but it has been proven over and over again by great mathmaticians for centuries that 20 is enough.
     
  16. krischan

    krischan Europe Trade Moderator

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    I'm missing a complete description of how the counting actually took place.

    There are several hundreds of cows in the cow level, so whatever has been counted, it cannot be the total number of cows.

    As anybody can reproduce that, it should be possible to get a second, independent analysis. However, it sounds like a lot of work, so I won't do it :lol:
     
  17. Ax2Grind

    Ax2Grind IncGamers Member

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    Doubt I ever will

    That's 20 tests of twenty-one different amounts of scrolls in a tome; 420 tests and an accurate accounting would start to satisfy me. Would love to see those numbers...
     
  18. Rekk_Dalton

    Rekk_Dalton IncGamers Member

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    i still want to know how many players were in each game, he hasn't answered that question. There are FAR more cows in an 8 player game than a 1 player game
     
  19. RTB

    RTB IncGamers Member

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    AFAIK the number of monsters that spawn in a lvl does not depend on player count.
     
  20. Myrakh-2

    Myrakh-2 IncGamers Member

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    For the number of cows...

    Does exp depend on mlvl? Because if it doesn't, one could just count the bosses (assuming they give more exp than normal cows), subtract that from the total exp gained, and determine the number of cows from the exp gained.

    Won't work if minions give more exp, though.... and you can't count the minions.
     

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