Here's why hard node shard farming seems unfair

Qleak

Occasionally someone will make some sort of claim basically assuming that shard drop rates are normally distributed. Under certain assumptions it may be nearly normal, but if the shard drop rate is approximately p=1/3 you'd need at least 15 trials (np and n(1-p) greater than 5 criteria) to get a roughly good normal approximation.

So without further delay I'll give you some accurate histograms of what to expect.

Farming 3 tries a day:


Farming 6 tries a day:


Farming 9 tries a day:



Notice these are all positively skewed, that means you should expect the number of shards dropped to be in the lower end of the range.

Does anybody have any good estimates for the gear drop rate?

Lower p will give the graph more positive skew for larger n.

Edit: (Note there are assumptions that these are iid Bernoulli trials with p=1/3)

Here's the weekly distribution for farming one hard node for a week:



And 2 hard nodes for a week:



Note the normal approximation to binomial works pretty well for these. Make sure to do your continuity correction.

oofalong

this is a great piece of work. So how many people have gone 9/9?

Qleak

oofalong wrote: »

this is a great piece of work. So how many people have gone 9/9?

I'd expect a fairly good probability of 9/9 by a player on some day. Thousands of players have played for months it's only ~ 1/20k

Qleak

I added some histograms for the weekly distribution for one and two hard nodes to the original post.

IsaacieOscarie

Jesus

oofalong

Qleak wrote: »

oofalong wrote: »

this is a great piece of work. So how many people have gone 9/9?

I'd expect a fairly good probability of 9/9 by a player on some day. Thousands of players have played for months it's only ~ 1/20k

I would too given the likelihood of the outcome. Still, my observation was more the psychological side of this, which is: people remember the negative experiences and complain about it rather than celebrating their success.

I like the weekly histograms as well.

HanSkywalker

This is really informative. Thank you.

Qeltar

Good writeup.
I know all this. And yet when I go 0/6 on Anakin's endless shard grinding I still want to pitch my phone through a window.

WilliamRickard

This is a great bit of statistics here, thank you. I have been trying to find something like this for a while !! It is positively skewed since p=0.3, when p=0.5 you get the normal distribution. My findings are that 0.13<p<0.25. I think the 0.13 is a pretty bad estimate as my sample size was only 42 attempts but the 0.25 is pretty good as my sample size was 118.

Many people seem to forget that the system is memory-less, they fall into the gamblers fallacy!

Qleak

WilliamRickard wrote: »

My findings are that 0.13<p<0.25.

For the shard drop rate or the gear?