## Statistical survey shows that the claimed Lupin-drawing probability may be inauthentic

FORUMWe've done a statistical survey for all three Lupin-associated summons, trying to examine if the true probabilities match what the official claims by collecting large amount of data from players. The three summons are: Lupin-guaranteed pickup summon(3%), Lupin pickup summon(1%), and Lupin-Ophois pickup summon(0.75%). This survey only investigated Lupin drawing situation, meaning the probabilities refer only to the drawing probabilities for Lupin itself. Samples were collected mainly from players from gamer.com.tw and a non-official line group. As of [00:30 06/14] , the result showed as following:

Obviously, all three empirical probabilities are significantly lower than the corresponding official-claimed probability, especially that of Lupin-Ophois summon. Let's interpret this by statistical method and see how impossible this could happen if we assume the claimed probability is true (to be concise, calculation is neglected, while any number presented can be calculated from the statistical result above.) 1. Lupin-guaranteed pickup summon The empirical probability lies outside of the 68.4% confidence interval, and it is below the lower bound of the confidence interval. The normal distribution is symmetrical, so if assuming the official-claimed probability is true, then the possibility that one gets the result of what we see in the survey would be (100%-68.4%)/2=15.8% (which is the outlier on lower half side of 0.4789 z-scores.) 2. Lupin pickup summon The empirical probability lies outside of the 86.9% confidence interval, and it is below the lower bound of the confidence interval. If assuming the official-claimed probability is true, then the possibility that one gets the result of what we see in the survey would be (100%-86.9%)/2=6.55% (which is the outlier on lower half side of 1.1217 z-scores.) 3. Lupin-Ophois pickup summon The empirical probability lies outside of the 93.7% confidence interval, and it is below the lower bound of the confidence interval. If assuming the official-claimed probability is true, then the possibility that one gets the result of what we see in the survey would be (100%-93.7%)/2=3.15% (which is the outlier on lower half side of 1.5301 z-scores.) With the three results combined, one can calculate the possibility that the three empirical probabilities are coincidentally low to the extent of what we see in the survey: 15.8%*6.55%*3.15%=0.0326%. This means if conducting such a survey (with more than 25k samples) 3067 times, one could expect only once to obtain such a disappointing result. This implies it is extremely likely that the Lupin-drawing probabilities claimed by the official are inauthentic.

The result and raw data of the statistcs can be found in this google sheet

https://docs.google.com/spreadsheets/d/16PamVX0SFiQ6sZZc-gZYqsMEAtudEj1OI1zLe0GN3M4/edit?usp=drivesdkSample size looks pretty small. What was your reason to call it a "large amount of data"?

How was the data falsification being prevented?Exactly what I was wondering! More or less at least ;) only 4060 samples for 0.7 pickup banner to speak of a significant result?..

Overall I appreciate the effort and I think being critical is a good thing. I hope the guys keep up the good work and we see more statistics like that in the near future.Good question.

CI is a function of N_s (sample size), and also depends on confidence level(CL). In order to prove that the difference between the claimed probability (P) and results of the survey (p') is meaningful, one needs to prove the difference is not within the margin of error, which can be represented by CI. So, one would hope to increase N_s and thus narrow down CI until p' lies outside of CI. In this case, N_s is large enough when p' lies outside of CI with a high CL, high enough such that one could conclude how unlikely the survey result p' would happen. In other words, how high a CL with which one finds p' outside CI already reflects how large enough the N_s is.

In the case of P being authentic, p' should remain inside of the margin of error, and gets closer and closer to P as N_s gets larger (and thus MOE narrower.) One would increase N_s until (P-p') is satisfyingly small and thus P being authentic could be concluded.Can't believe your claims, if this moot post accurately showed how you choose to present everything about the subject.

And I can't invest enough effort and polish into logical arguments over moot (the abominable bad design is a problem) in order to potentially be convinced the foray into the hypothesis testing here had merits.For the guys do not have enough statistic knowledge, you can learn from https://en.wikipedia.org/wiki/Statistical_hypothesis_testing

While I applaud the effort, and the 0.75% banner likely has something funny goin' on, the only issue is it relies on player self-reports and the validity of such reports is hard to determine. Especially considering most of the participants I'd imagine are biased to think it was rigged already.

Also, isn't it illegal for them to lie about gacha rates? it just seems they have a lot to lose for questionable gains it bring to the table. But I guess companies have done worse than this for smaller gains.got 1 Lupin after more than 70K cristals soooo seems legit....

Why would they lie? Sounds like a bunch of people who were unlucky got together to "confirm" that their luck couldn't be THAT bad, so obviously the game is "cheating".

Nope, it was not like what you thought. If you ask our community, I am usually the luckier one. I have been thinking about conducting such a survey for a long time, but had not done so until Lupin, who is so strong that many gamers planned to put all of their diamonds in, by which I would have enough samples. And I started this survey in the begging when the summons were just on, before I even did a draw (you can check the time in the google sheet.)

you know this sounds like something you cut & pasted out of a text book not likely to be used in an accredited statistics class.

who did these physical calculations and there's a proof of work needed to even begin to validate any of this.

it this is to be taken seriously and not as your personal opinion which could be flawed? someone should cite the individual(s) for using their work as to avoid plagiarism.

The entire 2nd to last paragraph uses verbiage to that of a text book or thesis statement.I am glad you feel my writing is like transcribed from a textbook. I would regard that as a compliment. But I wrote all of this based on my own knowledge and calculation. I don't see the point to cite anything, because only basic concepts are involved in this post. No one would regard using basic concepts in any discipline as plagiarism.

I am sorry my writing seems rigid or formal, or whatever you perceived. I am not an English native speaker, and may not be able to use English as casually as you guys do. My writing style just shows how I had been trained as a doctor in physics.

As mentioned in the post, the main calculation were neglected, because I thought no one here would really care about the calculation process, except for those who knows statistics. But any who knows basic statistics can understand what I am saying and easily check the correctness of the numbers (based on survey result I present in the figure), so there is no point to show calculation here. And most importantly, I am too lazy to do so, I don't even know how to use LaTex in moot. So I choose to make it concise, after all, I am not writing a paper, am I?

I did the same thing for all three summons, hence of course the later part would seem kind of repeated.nice effort but pointless overall tho

companies including gaming devs will allways do things like this to increse profits just because if they try to make profits on same level legaly (make things more expencive ) that would turn away most customers, and they most likely to just ignore such research.

And sad part is u will NEVER convince majority that manipulations take place... no matter how much evidence u bring they will always find something to answer to it , there is lots of reasons for it : fanboying, unwilling to belive in worst , wish to bash on victims (ppl who get screwed by such manipulations) etc..

Best thing u can do rly is either accept it and play by their rules or vote with ur money and dont play such games where such manipulations possible1. The 2020 U.S. Presidential Election was not stolen

2. Hydroxychloroquine is ineffective against COVID-19

3. Lupin rates were not rigged (probably)

Here’s what’s interesting to me: of the communities for this game — Discord, Reddit, Moot — this community is the only one where the belief that the Lupin rates were nerfed feels like a prevalent theory among the people. Why? While I don’t personally believe that this is true, the only thing that separates Moot from the others is that there is the possibility of moderators in disguise here. Lack of trust is extremely toxic to a community, and it’s sad, really: Moot is becoming the conspiracy theory land of the DC communities.

Is there any merit to the nerfed Lupin rates? Maybe. But I think that the big concern is a general lack of trust caused by (1) increase in boss difficulty without prior communication to the community, and (2) the Moot intern in disguise. I mean, we’d be fools to place our trust into the game so soon if we knew this information.

I don’t think that the Lupin rate theory really progresses existing concerns; in fact, it sort of muddies it up. I think the focus of mods should be generating trust (honestly, this is super super hard) and I do think that some of the onus is on leadership here to make it less toxic and more helpful. Moot is the least reliable community for game-related information (to me, at least) and that sucks.The stats are right, you are not guaranteed lupin you have a higher chance for lupin. Make sure you read the banner.

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