I'm a PhD in Stats and Data Science who has no life. Here's why I think Dream didn't cheat

Posting on a PCA because I don't want my profile exposed to haters.

Basically, all this drama has shown me that many people don't understand basic statistics. Lots of people are throwing around the "1 in 7.5 trillion" figure as if it is surely statistically significant or implies causality on its own. So, let's explore this.

I downloaded all the information the mods used to run my own tests. All calculations below were made in R Studio Markdown. Let's get into it:

I'm sure you've heard of the Law of Large Numbers. They make a reference to it in their video. Basically, as the number of observations grows infinitely large, the sample mean will converge to the population mean. This is just jargon that means, if you flip a coin twice, getting heads 100% of the time is not unlikely, but the more you flip it, that number will grow closer and closer to the true probability, 50%.

Was the sample size of Dream's speedruns enough to apply the Law of Large Numbers and assume that Dream's luck was actually 1 in 7.5million? Absolutely not. BUT, it is still a huge number, so it seems inconceivable.

According to a simple Two-Tailed T test I ran on the mod's numbers, we would expect to see Dream's pearl chances .02% of the time given that the actual pearl trade chance is 8.4%. That's 2/10000, or 1/50000. Much less, right? This is because we have accounted for the standard error. Still, its very lucky. So...

The next test I ran was an GRET regression with a boot-strapping mechanism that accounts for the the Thomason effect. Essentially, this determines whether a perceived anomaly, had the greatest outliers in the data still occurred, could be explained by the Thomasson effect. The Thomasson effect is, in Grahag's words: When a Random Event Xi is standardized to a binomial distribution, the outliers will be standardized at a rate equal to ln(Var^2+E[X]) due to a standard error bias.

Basically, imagine you are playing basketball and you are deciding whether or not to put on a cup, because last time you accidentally got hit in the testes, and you're not sure if that was an anomaly or if its a serious possibility. Bit of a ridiculous example, I know, but this is how I learned it-- London profs are a different breed. If you took your last 100 games and somehow knew the probability that you would get him in the nards at any given moment and applied it to a standard deviation by what we call "standardizing the distribution," the outliers (farthest data points from the sample mean) would be underrepresented. You fix this by removing the outliers and adding them in post.

If you don't understand this, it's fine. What you need to know is that after running this regression, the coefficient on B3*.084 was greater than 1. This means that any probability derived from the data is insignificant at the 99% confidence level, when outliers are properly standardized. AKA, the 1/7.5 trillion number is complete BS. The true number I got when I ran a LR was 1/98, only slightly better than Illumina.

Finally, just for shits and giggles, I made a mechanism to test if Minecraft is as random as it claims to be. You can easily test this with another T-test. I had my wife beat the game 300 times in a row overnight and log her rates on every drop. Turns out, minecraft's RNG might not be independent. This means, that if you got a blaze rod on the last drop, you will be slightly more or slightly less likely to get another one the next time you kill a blaze. However, this requires more study.

Anyway, that's what I discovered.