Innocence Scroll 40% does not work at a 40% passing rate

[Halcyon]

IGN: Halcyon
Job: Night Walker
Job Level: 275
Description of Bug (Explain the bug, How is it done, what should it really be doing? etc. An unclear description will not get the bug fixed):
Innocence Scroll 40%'s obtained from the PQ shop do not work at a 40% success rate. I've shared this belief for a while with many other players, but without providing data, my thoughts of being "unlucky" are pretty much meaningless. As such, I've gathered some data that amounts to around ~600 of these Inno 40's being used, and tracked their pass/fail rates. I've included a screenshot of my findings below, and I think that ~600 trials that converge to a passing rate of ~29.47% gives me confidence to say that although the passing rate of these might not be exactly 30%, it is pretty far from the advertised 40%.

On the topic of this, I don't believe Spell Trace Innocence Scroll 30%'s (5000 Spell Traces) work at 30% either, but I don't have a statistically significant amount of data to prove that just yet.

Thanks!

Screenshot (If Applicable):

https://imgur.com/a/AIfyogL

 

[savagestorm]

I did some statistical analysis on Halcyon's data (with his help), and came up with this:

https://imgur.com/a/S33KCBw

Any stats people, feel free to double check my results, thank you!

 

[Dreams]

Just wanted to say that saying the pvalue is <1% is really understating how unlikely the pass rate is actually 40%.

There's a 0.00002716% chance of getting only 173 passes in 587 attempts if the probability is indeed 40%.

 

[Edyrem]

Still working on MCS-ing my arc hat and the data that l have compiled hope this helps. Will share data once spent another 100 Innocence 40% scroll for better accurate data comparison.

https://imgur.com/a/r0j3pJS

 

[Sensualism]

Just wanted to add this piece of information.

If we plug in this data (p = 0.4, N = 573, x = 173) into a binomial distribution calculator (say this one: https://stattrek.com/online-calculator/binomial.aspx) we can see that the probability of passing less than or equal to 173 scrolls is < 0.000001, i.e. < 0.0001%.

Either Halcyon got incredibly incredibly incredibly unlucky, or there should be some checks to the RNG algorithm used for these scrolls.

If I were to guess, there could be an off by 1 error on the generation of pass/fail rate server side, or the rate is close to 30% and this was just never disclosed to players.

 

[sprooties]

The real question is, what should we do if the problem is real and the server's decoders are aware about it, kept it quite and didn't do anything?

 

[CptSpark]

Here is a simulation for inno scrolls: