Doing the maths: Grian's failure at getting a mending book
lots of talk about maths and probabilities below the cut! but there's a graph and simple explanation at the end if you want to get the gist of it and are bad at maths.
(I am still young and learning maths, critique/advice always welcomed)
What are the odds of getting a mending book in Minecraft?
(I am assuming Grian has been doing all his fishing with Luck of the Sea 3)
The probability of a mending book is actually a bit annoying to estimate. The Minecraft Wiki lists fishing up an enchanted book as 1.9% chance. This is for ANY enchanted book. The Minecraft wiki talks about how the chance of an enchantment being selected is calculated. Mending has a weight of 2. Using the table, mending has a probability of 2/135.
However, Grian is looking for any book with mending, not just a pure mending book. Additional enchantments are calculated in a different way, involving RNG, which means it won't be as easy to model. Due to this reason, I'll just be using the odds for a pure mending book throughout.
TLDR: a mending book has a 0.028..% chance (2/135*0.019*100)
Grian's Data
According to this screenshot, Grian has used a fishing rod 5679 times. This number may not be fully accurate, as it includes the times he's fished other players, rather than just fished for items, but it is a good estimate.
To help visualise this data, with a median waiting time between catches of 17.5 seconds, Grian has spent over 20 hours fishing so far! He may have a problem.
Is this statistically significant?
Hypothesis testing (p-value approach):
H0: p = 19/67500 (the null hypothesis - he has no mending books because of chance)
H1: p < 19/67500 (the alternate hypothesis - he has no mending books due to different odds)
5679 trials, 0 mending books
X ~ B(5679, 19/67500) (binomial distribution, 5679 tries with a probability of a mending book being 19/67500, where X is the number of mending books)
p(X=0) (what is the probability the number of mending books being 0)
p = 0.2021473392
Now, the point at which data becomes significant is subjective. For instance, you *could* get a million heads in a row flipping a coin, it's not impossible, but at a certain point, you can begin to say "okay there's something not normal about this". For this approach, the closer the p-value is to 0, the more evidence there is against the null hypothesis . The p-value here is far above a significance level of 0.01, or 0.05, or 0.1. There isn't a clear line between significant/non-significant, but this is answer is quite a bit far from 0
With this, I cannot reject the null hypothesis.
Personal conclusion: this is not statistically significant, Grian is just unlucky.
Are other values statistically significant?
Gem's proposed 9000: results in a p-value of 0.079... more significant than Grian's number but I don't imagine Mojang would be too concerned. As said though, it's all subjective.
I am bad at maths, what does all this mean?
Here is a graph, showing what number of mending books you might have after 5679 tries. The height of the bar represents the probability of getting that amount. The numbers at the top are the (rounded) numbers I used in my calculation
The pink column is 0 mending books - like what Grian has! As you can see, it is less likely than getting 1 or 2 books, but not too uncommon to happen.
End conclusion: Grian has bad luck. Like, not as hilariously bad as he thinks, but still bad. If he keeps going, chances are he will get a mending book, but I think he should probably stop fishing because at this point he has a problem.
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They could have solved this sooner if any of them bothered to look at a calendar
Hear me out
Ninjago doesn't have the best track record with dates (Wu's lifetime...) and I don't expect DR to be any better at it. But rewatching the season I realized the fact that when Lloyd narrates, he mentions being "alone for weeks" and, in the carnival, recalls not being around many people in a while, nailing down how he was secluded to the monastery during those weeks he woke up alone. This is fine, typical Lloyd behavior, just that when Nya encounters Cole, he says years.
Lloyd has no reason to lie, he doesn't have to make it seem like he was less time around so if he is not lying, and he truly was weeks alone, while Cole spends years lost after the merge? What happened?
And Nya and Kai! Kai woke up early enough, and in the bounty! to be able to map and travel a big part of the new land and try to find his way back, we don't know his side, but considering he pretty much arrived and then left again, had he entered the monastery before? I do believe he was longer out, awake and traveling. Nya also mentions having traveled before encountering the cranglings-- and she was on foot, she's resilient and strong, but for how long can you travel unknown terrain without a vehicle and survive it.
The idea of time getting messed up is plausible, other than reality coming undone and messing up every physics law-Cole is hanging out with what seems to be a kid formling, whose realm is confirmed to move differently time-wise, how could two different time progressions reacted to each other? How did that affect dates? Growing rates? So interesting.
I want to know if dr is planning on going somewhere with this, if not, then it'll be one more concept I'll rotate in my brain like a skewer, its such an interesting concept to me
Its also free trauma for the ninja! Win-Win
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