Cow level Statistics

[Slayersteven]

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 friends9022@yahoo.com or sven00100@yahoo.com, my aim is Sven00100 my msn is sven00100@hotmail.com and my yahoo messenger screen name is friends9022@yahoo.com.

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.

[helvete]

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?

[Slayersteven]

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?
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.

[helvete]

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!!

[Slayersteven]

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!!

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

[ebyworx]

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

[RTB]

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.
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.

[frygia]

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

[krischan]

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.

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.
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.

[krischan]

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.

[Rekk_Dalton]

was the number of players in each game equal?

[FodderCannoned]

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.

[krischan]

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.

[Angel_Dusted]

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:

[FodderCannoned]

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.

[krischan]

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:

[Ax2Grind]

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:

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...

[Rekk_Dalton]

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

[RTB]

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

[Myrakh-2]

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.

[RTB]

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.
It depends on Mlvl.

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

An easy way of counting cows would be to do it in normal and get enough dr to be immune to their physical attack and use a 1 hit kill attack. Then you can count the dead cows.

[Myrakh-2]

An easy way of counting cows would be to do it in normal and get enough dr to be immune to their physical attack and use a 1 hit kill attack. Then you can count the dead cows.

Hm... don't count the dead cows; use an amazon and guided arrow, and count the arrows shot :-) This should be more reliable, since you just start with a full quiver, and when you're empty you know you've killed 250 cows.

[frygia]

Hm... don't count the dead cows; use an amazon and guided arrow, and count the arrows shot :-) This should be more reliable, since you just start with a full quiver, and when you're empty you know you've killed 250 cows.That would make a good example, yes. But since normal cows are not that interesting from gaming point of view, I would prefer to see it done with the hell cows. I know it's more difficult... but if I have patience enough, I will start counting this thing when I do cows alone.

An easy way of doing this test is making a char that would 1-hit kill hell cows on Single Player; it is doable. For statistic's sakes, it would work as well as on bnet, and you can also set the number of players in the game. Doing it on SP is far far faster, and I would use a bowazon with arrows too, provided that I was sure that each guided arrow would for sure kill one cow.

[RTB]

That would make a good example, yes. But since normal cows are not that interesting from gaming point of view, I would prefer to see it done with the hell cows. I know it's more difficult... but if I have patience enough, I will start counting this thing when I do cows alone.
The amount of cows in the normal and hell cows only differs a tiny bit thanks to more boss packs in hell.

An easy way of doing this test is making a char that would 1-hit kill hell cows on Single Player; it is doable. For statistic's sakes, it would work as well as on bnet, and you can also set the number of players in the game. Doing it on SP is far far faster, and I would use a bowazon with arrows too, provided that I was sure that each guided arrow would for sure kill one cow.
Why not mod cows to have 100 life while you're at it?

[krischan]

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...

That sounds like not wanting to believe it, even if it's true (which I doubt BTW). I would be convinced if I can agree to the way this tests have been made and if a trustful person repeats them...

... but if I have patience enough, I will start counting this thing when I do cows alone.

... like that person :D

Killing hell cows with a one-hit attack slowly enough and counting the cows at the same time sounds dangerous. I would accept doing the tests in any difficulty level anyway. However, I think it's pointless to do the tests in single player. The only unknown part of this is the software running on the bnet server. In single player the answer has already been found by checking the disassambled game code and the config files.

BTW, not any guided arrow will kill a cow, even if you do it in a one player normal game. A few will probably hit a wall, so they are gone. However, I expect that the number of GA shots and the number of cows are proportional to each other (i.e. GA shots divided by number of cows is more or less constant if made by the same player with the same enthusiasm).

Another possibility would be killing and counting cows for a fixed amount of time, but it's important to consider that the player does his work with varying enthusiasm, especially if he knows when a full tome was used and depending on if it's the first or the 20th cow run and which player and character it actually is.

These are things not no neglect, so a working test environment could be like this:

1. The tests are made in closed bnet
2. One and only one player does the killing.
3. The player doesn't know which kind of tome has been used to open the portal.
4. 40 cow runs are made with small breaks inbetween and a bigger break after each 5.

There are methods involving hacks, like using MH, making a screenshot right after entering the cow level and then counting the monsters displayed on the map. You can do a variant of this without using any hacks: Enter cows, teleport to the upper left edge of the screen, make a screenshot, tele to lower left, screenshot, tele to lower right, screenshot, tele to upper right, screenshot and then count all cows found on each picture, ignoring that several cows will on two screenshots at the same time. If that teleport pattern isn't possible, the cow level is ignored. If it doesn't matter which kind of tome is used, it will have no influence on the answer to the question this is about.

[Thrugg]

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

Apparently so :) Once upon a time I actually taught a statistics course at college while finishing off my studies, and I'm afraid none of the presented data goes anywhere near supporting the claim the original poster is making.


Full (20) Statistics::
Number: 20
Mean: 65.5 Average number of cows with 20 tp scrolls
Standard Deviation: 6.4031

Base Statistics::
Number: 20
Mean: 55.1 Average with the base TP scrolls
Standard Deviation: 6.5767


The other (outlying) statistics are irrelevant here. The mean and spread (SD) are the only numbers that can determine our hypothesis.

[wrote something here before, found an error in it, re-writing it]

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

Thank you for that :) That has quite brightened my day. Part of teaching the course involved setting and marking the end of semester exams, and if there is one thing I do know with most certainty, it is that people taking stats classes can count things wrong :lol:

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.

Let's not get ahead of ourselves :) Your 20 is usually actually 25 or 30. And it is not the number of samples needed to be that confident, it is the number of samples needed to be able to assume a distrbution is roughly normal (which is required to do a meaningful z-score calculation, otherwise you need to do some much harder maths). Most statistical distributions start to behave like the normal distribution as sample sizes get larger. The number of cows is already roughly normal so it isn't important here, but even if it wasn't 20 would be enough. But it is not an automatic slam dunk on confidence by any means. You always need enough samples to shrink your std dev low enough to get your z-score up where you want it. The std devs quoted are simply too big here.

Sorry.

[Thrugg]

Bugger, I see to have taken longer than the 60 minutes they let you edit posts for. Oh well.

Against my expectations, this data does actually lead to the conclusion presented. It doesn't look like it should but it does :) So, since I am 100% sure that the number of cows in the cow level is not affected by TP scrolls in any way (I mean, really), there must be some other source of error - presumably that the numbers of cows (which are too small by a factor of at least 6, so I am not sure what he was counting or how).

[FodderCannoned]

Bugger, I see to have taken longer than the 60 minutes they let you edit posts for. Oh well.

Against my expectations, this data does actually lead to the conclusion presented. It doesn't look like it should but it does :) So, since I am 100% sure that the number of cows in the cow level is not affected by TP scrolls in any way (I mean, really), there must be some other source of error - presumably that the numbers of cows (which are too small by a factor of at least 6, so I am not sure what he was counting or how).
or that he counted wrong, or just made up data to see if we would believe it, he only did have 1 post. and I realize that my post regarding the minimum is irrelevent regarding actual "statistics" its just was an easy way to demenstrate that there was a definent difference between full TPbook and a TP book with just 1 or 2 scrolls. Hopefully that make sense.

[thegiantturtle]

I think I may do a few runs tonight to see what kind of numbers i get. I'm not promising 30 at each difficulty, but i'm gonna do something (the curiosity is killing me).

My thought for counting cows was to use a barb with no cold damage. I'd try to kill the cows slowly so i could count them, but if a pack swarmed, I'd kill the whole pack, and then count how many bodies i could immediately *hork*. Does that seem like a valid way to go about it, or is their something other than shattering/exploding that would make a COW unhorkable?

[Aerath]

Some items that carry the RIP mod.

Only thing I can think off of the top of my head.

[helvete]

I'd vote for RTB's way. Mod cows to have very little life, and then kill them using guided arrows. That gives the complicated equation of: Arrows gone = Cows killed, at any given time.

...unless you are a hardcore statistic and prefer counting.

[Ax2Grind]

Counting live cows is nearly impossible given they move too much. Counting dead cows is only slightly more possible because of shatter/melting/vaporizing/spooning. Horking may get by this, but I've found certain corpses unhorkable for various reasons.

If you're talking about modding then there's a simple mod that doesn't affect gameplay and could probably already be in the forbidden program: kill count. A counter starts at zero every new game and has two counters, the number you've killed and the number killed in the game. These are the same if playing solo, but it may be faster with more players in the game. Of course, since you normally kill a few creatures before entering the Moo Moo Farm (like while getting the leg) you might have to subtract those (take a reading of the kill counter immediately before entering the red portal), but that's a minor issue.

Outside of that I don't see a reliable way of accurately counting every monster in an area for such a reason as this, which we're pretty sure doesn't involve the quantity of scrolls in a Tome of Town Portal. No other areas in the game are decided such a way, and since the amount of cows doesn't appear to vary much it wouldn't make sense to throw in something like this for one area, especially knowing that it couldn't be detected without cheatin... er, modding.

[krischan]

You actually doesn't have to count the killed cows, but cows in general or something with is equivalent to the number of cows with a high accuracy, e.g. :idea: the amount of gold you find in a complete run.

[Slayersteven]

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...

normally i would agree with you, but the sample test i used, allows for the variance of sample amounts, and in a test like this a sample of 15+ is good enough to come with a conclusion, if there were more possibilities such as runes where it is also weighted, you need a sample that will have at least 5 zods in it. but since i took into account the accuracy of 20 sample size it is still a just case, if i can find my 13 page report i did on this i'll post it, i threw away most of my stuff from school, but i think i might still have that, and for the amount of cows in the level how u see it is in the 60's usually, thats because i took 1/10 of the actual amount of cows and called it a 'herd' since that is approximately the normal herd size in the cow lvl. i would do 1000 tests of it but the time requirement wouldnt be plausable, or justifiable in any manner, since when i was done, the calculations would prolly have changed.

[Slayersteven]

ok, what some of you didnt get in my original message is that a T-statistic test does account for the number of samples taken, it is a worst case 99.993% accuracy of being a difference, which means the 100%-99.993% is the case of accuracy since a 2 sample T-statistic test is based on a normally distributed curve, that being 68-95-99.7 after 3 standard deviations so based on the 2 normal curves of this data, only .007% of it is overlapping, the two major outliers in both cases, as i had 832 cows in a 20 tp once and 721 in a normal, while all others were below this, this spread the distribution and made a slight overlap, without the outliers, the standard deviations shrink and it goes to 100%-99.9992%

[Slayersteven]

was the number of players in each game equal?

I only ever tested the cow level with myself in the game and no others, i am i guess making my conclusion on a 1 person game, not all games, but it also keeps the statistics un-obscured and my data more accurate and verifiable

[Slayersteven]

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.

this would be true of a die, but as i have stated before and will state again, i am only dealing with one outcome, in a number, a die has 20 sides, however, if the die was loaded toward ALL high numbers you could take the average of the rolls and make a conclusion based on the two averages based on their standard deviations and a normal curve, bell's curve.

[Slayersteven]

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.

its well enough explained, you can use my data, i'll also post the actual counts for you, just a sec, afk.

ok, not only are these my samples of counts based on herds from an average herd size counting cows and dividing to make it easier to calculate here are my raw data samples & calculations.

20 scrolls-
67
62
60
61
72
83
59
66
68
59
73
63
65
57
61
64
69
75
62
64

Base-
49
51
52
74
61
53
55
57
44
62
51
53
47
54
57
61
58
49
55
59

Calculations-

Standard Deviation = Square root (((sample size1 - 1)*stand dev.1^2 + (sample size2 - 1)*stand dev.2^2) / (sample size1 + sample size2 - 2)
SD = SqRt (((20 - 1)*6.4^2+(20 - 1)*6.58^2) / (20 + 20 - 2 ))
SD = 6.49

T = (Mean1 - Mean2) / (SD* SqRt(1/sample size1 + 1/sample size2))
T = (65.5 - 55.1 ) / (6.49* SqRt(1/20 + 1/20))
T = 5.067

DF = sample size1 + sample size2 - 2
DF = 38

Based on their curve, which is slightly skewed from normal using 38 degrees of freedom i got a P-Value of .00007 which means that the probability of them being the same is equal to that, meaning the probability of 20 scrolls being larger is = .99993 or 99.993%, and if we took out the outliers and did it based on a normal curve the p value would be .000005 meaning the probability of 20 scrolls being larger would be .999995 or 99.9995 percent but since i am doing it directly off of my data i went with the current curve, and not off of inference.

[Slayersteven]

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...

yep, i'm glad i'm not doing it based on that but on base versus 20, i am only seeing that 20 scrolls makes more cows than the base from the NPC, if you are ambitious u do that, i dont have the time.

[Slayersteven]

That sounds like not wanting to believe it, even if it's true (which I doubt BTW). I would be convinced if I can agree to the way this tests have been made and if a trustful person repeats them...


... like that person :D

Killing hell cows with a one-hit attack slowly enough and counting the cows at the same time sounds dangerous. I would accept doing the tests in any difficulty level anyway. However, I think it's pointless to do the tests in single player. The only unknown part of this is the software running on the bnet server. In single player the answer has already been found by checking the disassambled game code and the config files.

BTW, not any guided arrow will kill a cow, even if you do it in a one player normal game. A few will probably hit a wall, so they are gone. However, I expect that the number of GA shots and the number of cows are proportional to each other (i.e. GA shots divided by number of cows is more or less constant if made by the same player with the same enthusiasm).

Another possibility would be killing and counting cows for a fixed amount of time, but it's important to consider that the player does his work with varying enthusiasm, especially if he knows when a full tome was used and depending on if it's the first or the 20th cow run and which player and character it actually is.

These are things not no neglect, so a working test environment could be like this:

1. The tests are made in closed bnet
2. One and only one player does the killing.
3. The player doesn't know which kind of tome has been used to open the portal.
4. 40 cow runs are made with small breaks inbetween and a bigger break after each 5.

There are methods involving hacks, like using MH, making a screenshot right after entering the cow level and then counting the monsters displayed on the map. You can do a variant of this without using any hacks: Enter cows, teleport to the upper left edge of the screen, make a screenshot, tele to lower left, screenshot, tele to lower right, screenshot, tele to upper right, screenshot and then count all cows found on each picture, ignoring that several cows will on two screenshots at the same time. If that teleport pattern isn't possible, the cow level is ignored. If it doesn't matter which kind of tome is used, it will have no influence on the answer to the question this is about.

i see you know something about statistics, i would have done a double blind experiment, except i had to get this done for stats class on the last day of school, if you'd care to partner up :P ill do another double blind experiment with you, however only involving the base & 20 since i dont have time to do others, i didnt bias myself beforehand, but we could do another test.

[Slayersteven]

Bugger, I see to have taken longer than the 60 minutes they let you edit posts for. Oh well.

Against my expectations, this data does actually lead to the conclusion presented. It doesn't look like it should but it does :) So, since I am 100% sure that the number of cows in the cow level is not affected by TP scrolls in any way (I mean, really), there must be some other source of error - presumably that the numbers of cows (which are too small by a factor of at least 6, so I am not sure what he was counting or how).

its actually too small by a factor of 10 since i divided for simplicity's sake to make the calculations faster, and so that i wouldnt plug in a wrong number when doing calculations. thanks for your help tho.

[Slayersteven]

sorry to everyone that all my responses took so long, i have been busy helping my mom do my brothers grad party, if you have any more questions and you think i'm not answering them fast enough, you can email me at friends9022@yahoo.com thanks everyone.

[RTB]

Got a working kill counter. Will do tests when I have time. First run-through: 551 kills (1 scroll)

[Slayersteven]

Got a working kill counter. Will do tests when I have time. First run-through: 551 kills (1 scroll)

do you have a start & end script so that it only counts kills in the cow lvl cuz we dont want kills that are from trist, or manually subtract those kills, if there are any that is.

[RTB]

It only counts cow kills, and it doesn't matter anyway, since I use a read-only character file. I just load it up, and start killing cows. I make it write-able once per run to switch difficulty levels, so the map seed is just as random as on bnet.

[Slayersteven]

It only counts cow kills, and it doesn't matter anyway, since I use a read-only character file. I just load it up, and start killing cows. I make it write-able once per run to switch difficulty levels, so the map seed is just as random as on bnet.

hey can u send that counter to Friends9022@yahoo.com i'd like to try it out :) thx!!

[RTB]

Or you can download it from here:
D2mod.dll (http://phrozenkeep.it-point.com/forum/dload.php?action=file&file_id=1102)
Kill Counter plugin (http://phrozenkeep.it-point.com/forum/dload.php?action=file&file_id=1268)

It'll take a bit of modding experience to make it work.

[Quietust]

One quick way to kill this theory is to mod the game files to redirect one of the waypoints to point at the Secret Cow Level, allowing you to enter the cow level without ever opening the red portal. In fact, some "Horadric Cube" patch I once downloaded (you know, one of the ones that adds a ton of cube formulas for creating arbitrary items) did exactly this. If it's possible to enter the cow level without creating the red portal, then the number of TP scrolls in the tome used to create the red portal cannot possibly be related to the number of cows in the level (other than it being yet another influence on the random number generator, of which there are plenty already).

[Damric]

mod the cows to make them all uber diablos

easier to count that way

[Ax2Grind]

One quick way to kill this theory is to mod the game files to redirect one of the waypoints to point at the Secret Cow Level, allowing you to enter the cow level without ever opening the red portal. In fact, some "Horadric Cube" patch I once downloaded (you know, one of the ones that adds a ton of cube formulas for creating arbitrary items) did exactly this. If it's possible to enter the cow level without creating the red portal, then the number of TP scrolls in the tome used to create the red portal cannot possibly be related to the number of cows in the level (other than it being yet another influence on the random number generator, of which there are plenty already).

It's possible to make a portal with an empty tome, so if the way the Moo Moo Farm is generated is X + (TPSiT * Y) then whether you enter the level without the formula or with it by way of an empty tome it'll still wind up the same.

I think this has perked RTB interest a bit, and with the kill counter he's going to disprove (or prove) this once and for all.

[dooaag]

Heh.. statistically (if the count, of course.. was simply the actual number/10).. this appears to be all correct. (Minus your degrees of freedom.. I coulda sworn you should've used 19 and not 38.. (Two sample T-Test.. 20 replications total in each.. v = n -1 ... or 19 = 20 - 1) .. But it's been a while since I have messed with much statistics. However.. given the numbers (and my laziness/desire to go to sleep now) I'd assume that it would still be over a 95% confidence interval that there's a difference. I don't feel like doing the calculations myself. Maybe I'll do them tomorrow, if I feel like it.

What I think is funny is the myriad of posts by people on the first two pages which don't have a clue about statistics... I think everyone but one person completely ignored the fact that you said you "took this data and ran a T-test on it" .. much less that they knew what that was. And then went and tried to argue things they knew nothing about. :P Funny.

Moo.

Edit: Well.. apparantly I'm wrong and you're right on degrees of freedom. Maybe I'm getting terms confused. It's been quite a while, after all. :P But yeah. This is completely accurate then.

The only possibility that it is not the case, is of course, if something besides the number of scrolls in the tomes was affecting the number of cows... or... if you were only counting the herds.. if the number of herds vs the number of cows per herd changed due to the number of scrolls as well. (In other words.. to make completely sure it's accurate.. you would need to run tests on that first. Or better yet, run an 3-factor ANOVA on number of herds, number of total cows, and number of scrolls in the tomes.. hehe.. like anyone would want to spend that kinda time on this)

[krischan]

What I think is funny is the myriad of posts by people on the first two pages which don't have a clue about statistics... I think everyone but one person completely ignored the fact that you said you "took this data and ran a T-test on it" .. much less that they knew what that was. And then went and tried to argue things they knew nothing about. :P Funny.

Moo.

Edit: Well.. apparantly I'm wrong and you're right on degrees of freedom. Maybe I'm getting terms confused. It's been quite a while, after all. :P But yeah. This is completely accurate then.
...


I already admitted that I haven't read the first posting carefully. Just like you, I confused a few things, as it's quite a few years ago since I made statistics like these. Perhaps the people who usually post here (which probably includes me) felt offended by reading something they didn't unerstand immediately :uhhuh:

The problem with the first posting was that 99% of all forum members didn't understand it and even for the remaining 1%, it was lacking a lot of information. Sure, this is the statistics forum, but the typical statistical issues are more like "which monster has the greatest chance to drop a SoJ" etc.

For example, it needed a lot of time to find out what exactly has been counted. The first posting also didn't explain in detail how the counting actually took place. These questions are extremely important for others to judge the quality of the data. If it claims to be a kind of scientific research, these questions have to be answered. It's not just knowing about the math, it's about setting up and describing the test conditions in detail, so others can reproduce the test.

[Thrugg]

Just so everyone understands; there is nothing to be proved or disproved here, although perhaps some people who like to believe in superstitions need the information re-inforced. The code that generates the Cow Level does not take any variable in beyond the usual map generation ones (which of course do not include the number of scrolls in the user's tome); also, the code that creates the portal takes a simple boolean "Wirt's leg and tome of TP present?" if so create portal and destroy ingredients, if not, do nothing. At no stage is the contents of the tome looked at.

So what is interesting here is only why Slayersteven's numbers came out showing apparent bias.

It is important to bear in mind when doing statistics that you can often find things that aren't really there. It is very easy to statistically "show" that having lung cancer causes people to smoke, for example.

[helvete]

(...)the code that creates the portal takes a simple boolean "Wirt's leg and tome of TP present?" if so create portal and destroy ingredients, if not, do nothing(...)
The code would have to check if the quest is done (credited king kill) and if baal has been killed at the given difficulty. So the AND? function would have to be slightly bigger, like ""Wirt's leg and tome of TP present?" and "Cow King has not been killed and Baal has been killed?""

[Thrugg]

:P Pick pick pick :)

It does also take a pointer to the player's quest state, the (hidden) Cow King quest is enabled when you kill Baal and disabled if you ever kill the King. You can only create a portal while the quest is enabled, yes.

[Slayersteven]

This may seem like a stupid question to ask, but i dont know the answer so here it goes.. Does anyone know is the actual cow level there before the tome and wirts leg are combined to open the portal, and if there is a mod to use a waypoint to go to it couldnt it simulate a random amount of scrolls or a full or empty tome for the waypoint to it? I dont know the answer its just a question, and has anyone here done checks on substream data and coding to check what the actual code is for the creation or distribution of the cows? Oh also, to how i did take the samples, i didnt count herds, i counted cows and divided by 10 and just named it as a herd, since the herds are spastic and often clumped together counting herds wouldnt work anyways. i think i'll ask my brother (since our other computer crashed and this is the only one we have that can run diablo) if i can download the kill counter onto this computer, and i'll do tests of it on single player (since the map doesnt change and cows couldnt be spawned more scarcely due to the area given for spawning) and i'll run more tests, or one of you could do that and run a t test on it, or give me the raw data and i can try, being as i'm lazy in my old age.. 16.. lol well i hope that brings up more contriversy lol, wow this is an ongoing thread.. hmm well i'll check back here in a couple days probably, maybe more maybe less depending on how my schedule is for basketball, peace out.
-steven

[Slayersteven]

^^^^^^^^^^^^^ I really have to start putting stuff into paragraphs.

[slam]

wow, one of the most interesting threads of late. personal experience has led me to believe that the number of scrolls in the tome does affect number of cows in the level. the times when i am lazy and don't fill it up, the cows are sparse and when i do fill it up, there are so many cows, i am often overwhelmed.

yes, a very indepth statistical analysis i know :)

i'd like to see a thread started with a poll where the options presented are: number of scrolls affect number of cows
number of scrolls does not affect number of cows

i expect the majority of the votes would go to the number of scrolls having no affect on the number of cows. and if slayerstevens finding were proved to be accurate, what fun it would be to prove so many people wrong.

though i obviously know nothing about statistical mathmatics, i see nothing wrong with slayerstevens methods but i am eager to see results using the kill counter.

in the mean time, i'll keep filling up my tome

[Slayersteven]

Ok there is now a poll here, i didnt realize i could add one to this thread so i made a different thread, if you voted there please vote here as well, thanks :D.

[Slayersteven]

Heh.. statistically (if the count, of course.. was simply the actual number/10).. this appears to be all correct. (Minus your degrees of freedom.. I coulda sworn you should've used 19 and not 38.. (Two sample T-Test.. 20 replications total in each.. v = n -1 ... or 19 = 20 - 1) .. But it's been a while since I have messed with much statistics. However.. given the numbers (and my laziness/desire to go to sleep now) I'd assume that it would still be over a 95% confidence interval that there's a difference. I don't feel like doing the calculations myself. Maybe I'll do them tomorrow, if I feel like it.

What I think is funny is the myriad of posts by people on the first two pages which don't have a clue about statistics... I think everyone but one person completely ignored the fact that you said you "took this data and ran a T-test on it" .. much less that they knew what that was. And then went and tried to argue things they knew nothing about. :P Funny.

Moo.


You aren't entirely incorrect, there is another type of t-test that involves 2 different tests of one sample, so you apply two different things to one group of people, like if you had this group of people that shop at both cub & target, how much do they spend at each place? but in this case, its not the same game (since thats impossible) and so in that case instead of taking the combined minus two you take the LOWER of the two, in this case the sampling is equal, minus one, so it would be 19, but in this case the samples are from the same population, which they have to be or it would be biased, but it has two samples, so a two sample t-test, i am not sure what the other one is called though, sorry.

[RTB]

This may seem like a stupid question to ask, but i dont know the answer so here it goes.. Does anyone know is the actual cow level there before the tome and wirts leg are combined to open the portal, and if there is a mod to use a waypoint to go to it couldnt it simulate a random amount of scrolls or a full or empty tome for the waypoint to it? I dont know the answer its just a question, and has anyone here done checks on substream data and coding to check what the actual code is for the creation or distribution of the cows? Oh also, to how i did take the samples, i didnt count herds, i counted cows and divided by 10 and just named it as a herd, since the herds are spastic and often clumped together counting herds wouldnt work anyways.
The map is generated once you enter the red TP. The cows don't spawn until within about 2.5 screens. What I can't remember is whether the cows are already there (but inactive) when you enter the lvl, or that they're only spawned (using the parameters I listed in a previous post) on entering the 2.5 screen distance. First one is more logical.

One cow herd normally consists of 5 - 10 cows, although it may seem bigger, but then it's two (or more) herds spawning very close to eachother.

[Slayersteven]

The map is generated once you enter the red TP. The cows don't spawn until within about 2.5 screens. What I can't remember is whether the cows are already there (but inactive) when you enter the lvl, or that they're only spawned (using the parameters I listed in a previous post) on entering the 2.5 screen distance. First one is more logical.

One cow herd normally consists of 5 - 10 cows, although it may seem bigger, but then it's two (or more) herds spawning very close to eachother.

Yeah counting herds would have been a stupid thing and how i stated it as being herds although i just divided actual count by 10 it sounds like i counted herds so it sounds discreditable, but i see nothing wrong with how i did it, i'm not sure though, and yeah, i wish we knew for sure whether or not the cows were 'placed' on creation of the red portal, because if they're not, then i got a really out of place sample, although it was a fair sample it still has that .003 i think it was percent chance of failure... hmm.. i think i was blabbering again, wow its like 2 - 8 lol on poll..