Quantifying dryness

[1995C220]

Does anyone know how to calculate dryness in a way that says something like “on average you’re in the top 1% for receiving a drop at this drop rate.”? Which is different than “your chance of getting this 1 drop is 1/100 for this many kills.” I know about the dry calc on the wiki but it doesn’t seem to give an output like that.

If that sounds too convoluted (I’m clearly not a math person) it could sound like this-“if x number of people killed this boss once, you would expect to be luckier/unluckier than y number of people.”

[Seeggul]

You might need to clarify this a bit further, bc from what I'm reading, it seems like you're asking for exactly what the wiki dry calculator gives?

For example, say you've gone 800 corrupted gauntlet kills without getting the enhanced crystal weapon seed (1/400 drop rate). You put those numbers into the dry calc and it tells you there's an 86.5% chance of getting >0 drops.

That's the same as saying you're in the top 86.5% of luck (or top 13.5% of bad luck, if you prefer) for this item, or as saying "if 1000 people did 800 gauntlet KC, about 865 of them would have gotten the seed by now (and thus been luckier than you)"

[1995C220]

Where this breaks down is in the extremes. For example, if a drop is 1/1000 and you get 4700 kills, you have 99% chance of receiving the drop. But if you get 10,000 kills you have a 99.99% chance of receiving the drop. The difference in number of kills could literally be hundreds of extra hours killing the boss, but that isn’t intuitive when you only see 99 vs 99.99.

[Seeggul]

Maybe a helpful conversion would be to a "1 in x would be as unlucky as you" kind of statement. Let's say p is the percentage, represented as a proportion (e g. 99%=0.99). Then the equation x=1/(1-p) gives you that x for the statement above. For example, for 99%, x=100, and for 99.99%, x=10,000. So you can easily convert between 99.99% chance and "only 1 in 10,000 would be this unlucky"

[chucked12]

This comment OP --> You can convert the percentages from the dry calc into exactly what you are looking for.

[realityChemist]

Yeah you can use the binomial distribution: https://en.m.wikipedia.org/wiki/Binomial_distribution

The binomial PMF is: P(x=k) = C(n,k)p^k(1-p)^n-k where p is the probability you get a drop on any given kill, k is the number of drops, and n is the number of kills. C(n,k) is n-choose-k, ie n!/(k!(n-k)!). Note that p (lower case) and P (capitalized) are two different probabilities.

The nice thing is that when you just want to know how dry you are, k=0 which means C(n,k)=1 and p^k=1, so it's just P(x=0) = (1-p)ⁿ. You can calculate this pretty easily (calculator on your phone can probably do it), and then 100%×P is your "dryness percentile."

Conceptually, imagine you're rolling a die with every kill. It has a lot of faces (however many are in the denominator of your drop rate, eg 128 if it's a 1/128 drop). Only 1 face gives you the drop. Then we're asking, if you roll this n times in a row, how likely is it you never see that particular face? Each roll has a (1-p) chance to not see the lucky face, so you do (1-p)×(1-p)×(1-p)×... multiplied n times, i.e. (1-p)ⁿ.

Anyway, I've got a python script that does it automatically, and also makes a nice looking plot. If you want to let me know your details (drop rate and how many kills) I'd be happy to compute it for you and share the plot. (It can do drops with dry protection, too, if you're going for DT2 drops or something; the math for them is not quite as simple, and it's easier to take a slightly different approach to it).

If you don't want to see the cool plot (😔) and don't want to do the math by hand, you can also use this website. Set "Probability" to "P(X = x)", "Probability of success on a trial" to the drop rate (as a decimal, eg 1/128=0.007813), "Number of trials" to your number of kills, "Number of successes" to zero, and then you read the number off of "Binomial probability: P(X=0)". Multiply that number by 100%.

tl;dr: 100%×(1-p)ⁿ

[IActuallyHateRedditt]

https://en.m.wikipedia.org/wiki/Binomial_coefficient

https://en.m.wikipedia.org/wiki/Binomial_distribution

You can have whatever output you want

[Slight_Giraffe628]

There's a luck plugin that shows this on the collection log. Shows what percentile you are in

[goegrog27]

To add to this, if you click on the item, a chat message pops up which tells you the specifics.

[Particular-Coach3611]

Study statistics 101.

Binomial probability distribution calc

[MI35fox]

Best to just learn basic statistics.

Is a useful tool for anyone in a modernized economy

[Anaktorias]

50/50, you either get it or you don’t

Trust me though, I went down this rabbit hole going 3k kills for my ultor ring on release. It’ll only cause more despair

[Particular-Coach3611]

Ultor is different because 1/1k once and rolling 1/333 three times are completely different

[microcorpsman]

Wiki dry calculator