Drop Theory Experiment

OK. I should be able to get online sometime around 7:30; I'm meeting some other friends around 8pm, but that should be enough time.

Feel free to send a PM with your in-game name (since it can't be Sentinel

^^^^^

This is wrong, it shouldn't be X1-X2 but (X1+X2)/2, i.e. the sample mean. Assuming your calculations for the interval are right (my memory of confidence intervals are pretty much gone, so I googled the term and found no formula matching your own, but whatever), you get an interval of confidence of:

0.625 +/- 0.27... or 0.355 < x < 0.895

Which would tend to indicate that the gathered sample does not, in fact, hint at a non normal distribution.

The sample size was not 40 but 20 (i.e. 20 battles total). From this site:

So not necessarily.

Not in this case, apparently.

The theory of drops has always intrigued me - it would be better if ANet would simply tell us =P

A few other things I would like to note:

Concerning chests, I think the person that opens it have a higher chance of getting an item from the chest. That, or the theory of proximity comes into play here. For me, it always seems that the person that opens the chest gets at least one item - but I am always open to the theory of complete randomness, since its hard to rule that out.

An example is the first quest in FoW, the clearing of the tower by beating that Shadow Beast. After killing it, a chest appears, usually with purple armor of some type.

The other strange thing about drops, is that there is a certain theme that may exist. On some runs, you might get a string of bows, or you will get a ton of blue items that have similar mods or wands that have similar elemental properties. Again, I won't rule out the existence of 'coincidence'.

This 'theory' is more prevalent on runs of FoW. Two of the main item drops there: the Chaos axe and Shadow Shields. On one run, I may get 5-6 Chaos axes! Same with shields. And my party member will get none. On other runs, I may not even get one Chaos Axe/SSheilds, when a party member gets a string of them.

Then comes the factor of enemies stop dropping loot, which Anet seemingly introduced a few updates ago (June 15th I believe).



Although they say this only happen when you "rejoin the current map". It would be terrible to find out that the 'game' sees you as doing FoW ventures over and over, and therefore stops you from getting more Chaos Axes and other special items.

You would be correct, however I'm not trying to calculate a mean there with X1-X2, rather I'm testing that the difference between two means is zero. Hence they should not be divided by two, I want the ACTUAL difference, not half the difference. Sorry, I may be wrong about some of what I posted, but that's not it

Again, I'm not averaging the means here. You average the means when you're trying to use repeated sampling as your technique. In this case, I'm testing the difference between means. The sample size is indeed 40.

Thanks for the attitude. I don't mind being wrong but when you fail to read my post and then give me attitude I don't think it's terribly good form.

-Diomedes

For the record here, you just made things much worse for yourself. Since I'm taking the difference between means, if there was NO difference, then zero would be inside the 95 % confidence interval. Mine came close to zero, but yours just got much further from zero. I think the key here is that you haven't read my post carefully enough to see what I'm trying to calculate. Instead, as you said, you typed, "confidence interval" into google. Sorry, sometimes understanding math takes more than a google search.

-Diomedes

Just to throw my experience in, I do solo tanking for 5/6man Underworld smite groups on most nights if we have favor. Usually the casters are just on the edge of my aggro range while the mobs are surrounding me. It seems like my item drops are about evenly distributed at 1/5 or 1/6 share, maybe slightly less. Sometimes I do some minor smiting, but not quite the damage that the ele nukers are doing. Sometimes I don't smite and just concentrate on tanking.

This leads me to believe that drops are mostly random and maybe slightly damage based, although not much if at all.

I would have done a simple Chi Square.

_________Far_____Near____Total
Dropped___8_______17______25
No Drop___12______3_______15
Total _____20______20______40

while expected would be:
_________Far_____Near____Total
Dropped__12.5____12.5_____25
No Drop___7.5_____7.5_____15
Total______20_____20______40

So:

Chi^2 = (17-12.5)^2/12.5 + (8-12.5)^2/12.5 + (3-7.5)^2/7.5 + (12-7.5)^2/7.5

thus Chi^2 = 8.64, df=1

Making it significant at alpha<0.005

In other words, if the drops aren't affected by proximity, the chance of getting the drops recorded randomly is < 0.005, or less than one in 200. The only assumption that the chi-square test makes is that these trials are independent. However, givin that the same spells weren't used and such, and that there are tons of other factors involved (how the presence of your character closer to the target affects the damage distribution on other players, how you affect their ability to do damage, where you employed more single/aoEspells, total damage attributed to you and to other players...) I'd say it's tough to come to a real conclusion, though there is no doubt that whatever happened between those two situations, some factor or combination of factors, including change in proximity, caused there to be a change in drops.

You failed to mention one key factor: the value of each item dropped. I'd gladly take 8 good drops to 17 junky drops...

No. I assumed you were computing your interval right but had made some mistake when computing what I assumed you wanted to be the mean. My formulation implied that both assumed populations where compatible with a normal distribution according to the traditional use of intervals of confidence. Since this isn't the case and I don't care enough to calculate the interval (I play a warrior, hehe), disregard my post.

Sometimes, but very rarely. This basic high-school statistics stuff doesn't. I'll preempt any insinuations on my mathematical background by noting that I'm a grad student in image processing, so, yeah, it's been a while since I made use of stats exensively (Bayes Theorem excepted), but any misunderstanding on my part definitely stems not from my own inability but rather from a lack of clarity in your presentation, IMO.

"You failed to mention one key factor: the value of each item dropped. I'd gladly take 8 good drops to 17 junky drops..."

How does this matter? If drop system is random, then it doesn't mean "less items = better items". Personally, I don't believe half of these "theories". As a Monk, I might sometimes *not* heal at all, if the battle is easy, and I still get the drop. Only this that is *certainly* true, is that if you're too far away, you will not get the drop.

.. I was under the impression that code couldn't account for a true random--and, in fact, that there has to be a degree of 'method' to it.

Just use Chi-square. It's very good with problems like this, as it has very easy to interpret results - it simply says that the two (or more) conditions aren't independent - that is, there exist factors associated with being close or far that changes the number of drops. The assumption is simply that there isn't such a difference, and alpha<0.005 is 10 times the alpha needed for publication in most journals.

Well, in this type of situation the difference is academic. It wouldn't have any effect - it's like claiming that die rolls aren't truly random because the thrower will tend to release the die on similar angles, and that the facing of the die pre-launch on a given throw will influence the next throw - possibly, but it is a minute effect if any. It only really matters when you are having issues with picking seeds - the actual numbers are generated by a formula, and if you know the seed and the formula used you could predict the rolls, hence they aren't random, but since it isn't the "randomness" that's important, but that it distributes things with equal odds in non-visible patterns it isn't really a problem.

Chi-square... I have vague memories of sleeping through that. No, I saw your post on page 2, and, yeah, I guess it would appear from this (albeit limited) sample that drops aren't completely random. I'll drop by again to see what tonight's experiment finds out.

what is defined as far distance?

being within spell casting range of killing things? ie within danger circle?



only asking because I want to do same test using only 2 players

- I have 2 computers, 2 accts

Diomedes,

Define near(N) and far(F)...lol....and how in the world you know what the frequency for N and F are. Are those numbers (.85 and .4) assumptions?? Or you know them for a fact.

Because, if they are guesstimates..well..I need to say no more...:-)


JoDaimonds,

<-----ING (the W one)

Sent.-

He's using the figures provided by Uldrath in the original post.

I know then since the OP posted them, go back and read his post, then my post, it'll make more sense. I was going to use N and F from then on as subscripts but I can't do that given the tools available to me on this forum.


-Diomedes

I'm fine with using Chi^2, I used the other method since I figured it'd be more intuitive to follow. Given the reaction that I got however, perhaps your way is far better (it's at least, a lot easier to calculate). However I agree with what you've posted, there are other factors that probably need to be accounted for. I'll try to repeat the experiment farming flesh golems with two people. I've noticed that you can stick one person up front for all the enemies to group around and have the second person cast AoEs fairly easily. As the groups of flesh golems are fairly constant, I think this experiment can be done by entering and exiting the area repeatedly and just killing the same first two groups over and over.

I'm sure that if there is a drop formula, it does probably involve more than just distance, but I think a person can make a good attempt to remove the other factors.


-Diomedes

It has to involve more than distance, otherwise warriors would get far more drops than anyone else (except possibly the odd caster "tank", hehe), assuming the warriors do their job and shield the casters from the brunt of the mobs. This hasn't been my experience, i.e. I never noticed any bias in my favor when it came to drops.

theres 3 different distances to take into account


- melee distance

- spell casting distance, which is the same as danger circle

- peripheral distance
(only rangers and healers can be outside the monsters danger circle and yet still affect combat)