[Deleste] I could not find evidence that Dereste's Gasha is manipulating probability.

Do you guys do Dereste? I have recorded all my daily tax payments since July 30, 2016. It's one of the only two smartphone apps I'm paying for (the other is COMIC FUZ).

And speaking of social games, it is a stochastic operation. Is Dereste's Gasha really reliable? (Spoilers in the title)

I'm a math amateur, so maybe something is wrong. In that case, someone should kindly tell you in the comments.

Probability survey for 2019-2020

This time, I would like to investigate the tax payments for the two years of 2019 and 2020.

Dereste's Gasha has an appearance rate of SSR3%, SR10%, and R87%. I want SSR, so I don't care about anything else and think of it as a binomial distribution with a success rate of 3%.

So, first of all, we will aggregate the tax payment results. The counting method is simply = COUNTIF (C: C," SSR ") in Excel.

2019

2020

The number of sheets in 2020 has increased dramatically due to the introduction of Memorial Gasha on September 27, 2019. The tax paid in two years was 2076. By the way, the amount of tax paid is about 60 yen per sheet, so ……………… Oops, don't think about it any more.

By the way, both 2019 and 2020 are far from 3%. It can happen that the number of trials is small. However, if you increase the number of trials, it should approach 3% as much as possible. This time, I've drawn 1000 sheets, but it's a lot off, but isn't this enough to converge? Or is something happening behind the scenes?

The survey method uses P value. If you look it up, you will find strange words such as the null hypothesis and test statistic, which makes it difficult to understand, but roughly speaking, it is the rate at which assumptions are likely to occur. The P-value is calculated assuming that the SSR appearance rate is 3%, and if the result is less than 0.01, the first assumption is incorrect, that is, the SSR appearance rate is not 3%. is. There seems to be a story like Iro Iro that the P value doesn't mean anything, but I'm not sure, so I don't care.

Now, what is the likely rate? I have 10 consecutive SSRs drawn (probability 1.68%) during Derefes (SSR appearance rate is 6%), but this P value is 0.018. It's a fairly low value, but it's not impossible.

Then, will it happen that 6 SSRs appear after 20 consecutive draws? The ratio is 10 stations, which is the same as 3 SSRs, so it seems no wonder that it actually happens. However, when I asked for the P-value, it was 0.00087, which was clearly unnatural. In this way, even if the ratio is the same, the P value will differ depending on the number of trials.

However, when I actually try it, I feel that the P value when the number of trials is small is unreliable. For example, there are 10 SSRs 4 (probability 0.19%) and 5 (probability 0.014%), but the P value of 4 SSRs is 0.0020, and 5 The P value of the sheet is 0.00015. As a more extreme example, the P-value is 0.0036 when only two Gashas are pulled and both become SSRs. Based on these results, the null hypothesis that the SSR appearance rate is 6% is rejected, and theoretically, the SSR appearance probability is not 6%.

But if it's about 10 stations, there are many people who turn it, so it's no wonder it happens. Probably the difference between when the measurement is started until the result is obtained and when the measurement is started after the result is obtained, but there is something about the reliability of the P value when the number of trials is small. Is it?

Oops, it's a long way off, but this time we're calculating nearly 1000 trials. If this is the case, there is no problem considering that the reliability of the P value is quite high.

import scipy.stats as stats

print ("2019:%s" % stats.binom_test(31, 880, 0.03))
print ("2020:%s" % stats.binom_test(34, 1196, 0.03))

The P-value for 2019 was 0.37 and the P-value for 2020 was 0.87. All of them are much higher than 0.01, which means that the number of appearances is not unnatural at all.

As a result, the SSR appearance rate of Dereste has not been manipulated, or at least it has not been manipulated to reveal it.

What is the probability of a limited SSR appearing?

By the way, there are roughly three types of Dereste SSRs. They are called permanent, limited, and festival limited, respectively.

Permanent SSRs are the most common SSRs, and once provided, they can always appear in subsequent Gashas.

Limited SSRs will only appear for a week or so after they are newly added. After that period, it is basically not available after that. It may reappear in the form of a reprint a year or a few years later, but if you want to get it later, you have to wait for that time.

The festival limit is also limited, but this will appear during an event called Cinderella Fes, which is held once every few months and the probability of SSR appearance is doubled to 6%. Therefore, although it is called a limited edition, it is relatively easy to obtain.

From the above, it seems that there is not much point in manipulating the constant and festival limits. In other words, there is a suspicion that the appearance of limited SSRs is particularly narrowed down. Squeeze the appearance rate of only specific characters It's a common story to turn Gasha.

It's difficult to verify this, or I can't prove it. I'm not a heavy-charger, and basically I only spin Gasha at Cinderella Festival, so I don't have a limited number of Gasha trials.

This year, I happened to be spinning a limited edition Gasha called Pure Bridal Gasha that swear love in June 2020, so let's check it using the results. Since the number of trials is 300, I don't think it is very reliable in terms of reliability.

In this Gasha, the appearance probability is high for the three limited characters newly introduced here, and each is 0.4%. And the remaining SSR 202 types have a fierce probability of 1.8% in total. If you draw 300, you will get 1.2 pickups on average, and 5.4 non-pickup SSRs, for a total of 9 pickups. Of course, the probability is not so simple, and the number of trials is too small in the first place, so it is normal for 300 to pick up 0.

So here is the result of drawing 300 sheets.

The acquired SSR is as follows.

import scipy.stats as stats

print ("Pure Bridal Gasha who swear love:%s" % stats.binom_test(9, 300, 0.03))

The P value is 1.0, the maximum value. 9 SSRs in 300 stations is completely in the center of the expected value.

In addition, 5 of the 9 pickups. The P-value for acquiring 5 pickups is 0.42, which is also within the range that can be afforded. Or rather, I've taken all three types of pickups, so rather than narrowing down the appearance rate, it's upswing.

From the above, the result is that the appearance probability of the limited SSR is not manipulated, or at least in the Pure Bridal Gasha who swear love, the appearance probability is not manipulated. Among the limited SSRs, there is a possibility that the probability is set small only for [Eternal My Love] Mizuki Kawashima, but when it comes to that, the number of trials is too short and a meaningful value can be given. There will be no.

By the way, the probability of getting 3 types of pickups in 300 stations is 34%, the probability of not getting any pickups is 2.6%, and the probability of not getting any SSR itself is 0.01%. How should I calculate the P-value to get one or more pickups each?

Conclusion

The result is that both tax payments and limited Gasha Pure Bridal Gasha that swear love have not been stochastic, or at least not enlightened. It cannot be said that "there is no injustice in all Gasha", but it is possible that it is "almost unlikely".

bonus

So far, I wrote in advance, but when I turned the 300-series Gasha on 2021/01/04 (that is, today), a great downswing occurred.

It's a normal sight with an SSR rate of 3%, but this was actually a derefes period when the SSR appearance rate doubled to 6%. The P value is 0.051, which is close to the lower limit of the allowable range. This is terrible. I mean, this is an SSR rate of 3%. It must be so. I grabbed the proof that it didn't work![^ 1]

[^ 1]: It's not proof that it doesn't work.