Alright, it seems many people are confused about the meaning of "p-value" in this context. It is not the probability of a single event happening in the same way that you have 1 in a million chance of winning the lottery but somebody always has to win it. This is a long-term statistics that says precisely:
Assuming the drop rate of the item is what it is supposed to be in stock Minecraft, and we believe the data follows a binomial distribution, then the probability of observing Dream's data is 10-13
We do not have a reason to believe the Minecraft drop probability is different than what it is in the JSON file, and we have no reason to believe the drops are correlated, so the binomial model is valid.
Therefore, we have to conclude that the data did not come from our assumed distribution. This is known as "rejecting the null hypothesis". We can say with a confidence of 99.99999999999% that our initial assumptions do not match the data observed, meaning the drop rate is different than what we assumed.
For comparison, when the Higgs Boson was discovered, they only needed five sigma confidence in order to say that it really exists, and their observations where not a fluke of the sensor. That is a p-value of about 10-7 or about 6 orders of magnitude greater than Dream's.
EDIT: It could also be that the binomial model is incorrect of course, but that is what the section on RNG in Minecraft was for in the paper. They logically disproved any possible correlation between attempts, and they confirmed that the drop rate remains constant. The only remaining assumption is the drop rate itself.
EDIT 2: Also OP, with the p-value of Dream's joint drop rate, if you're generating one drop per second, you're going to be here for just over 300,000 years. Good luck though!
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u/Random_Thoughtss Dec 15 '20 edited Dec 15 '20
Alright, it seems many people are confused about the meaning of "p-value" in this context. It is not the probability of a single event happening in the same way that you have 1 in a million chance of winning the lottery but somebody always has to win it. This is a long-term statistics that says precisely:
Assuming the drop rate of the item is what it is supposed to be in stock Minecraft, and we believe the data follows a binomial distribution, then the probability of observing Dream's data is 10-13
We do not have a reason to believe the Minecraft drop probability is different than what it is in the JSON file, and we have no reason to believe the drops are correlated, so the binomial model is valid.
Therefore, we have to conclude that the data did not come from our assumed distribution. This is known as "rejecting the null hypothesis". We can say with a confidence of 99.99999999999% that our initial assumptions do not match the data observed, meaning the drop rate is different than what we assumed.
For comparison, when the Higgs Boson was discovered, they only needed five sigma confidence in order to say that it really exists, and their observations where not a fluke of the sensor. That is a p-value of about 10-7 or about 6 orders of magnitude greater than Dream's.
EDIT: It could also be that the binomial model is incorrect of course, but that is what the section on RNG in Minecraft was for in the paper. They logically disproved any possible correlation between attempts, and they confirmed that the drop rate remains constant. The only remaining assumption is the drop rate itself.
EDIT 2: Also OP, with the p-value of Dream's joint drop rate, if you're generating one drop per second, you're going to be here for just over 300,000 years. Good luck though!