Krampus Sack Drop Rate Analysis

[WillPwn4Food]

Hey guys,

I know how frustrating it can be to acquire a krampus sack, so I bothered to do the math. Wow, getting a drop is even more unlikely you'd expect. You'd think that at a 1% drop chance, killing 100 krampuses would essentially guarantee you a drop. Not according to the math. Here's a table showing the first 100 krampuses by increments of ten and then probability increments of about 5% thereafter:     

Here's a graph of the cumulative probabilities going out to almost a 99% chance of getting at least one drop:

A quick explanation of what these numbers mean. Whether you have already killed 100 krampuses or 0 krampuses, the probability of a drop on the next kill is the same 1%. The graph and table can be interpreted as this: "Regardless of how many krampuses you have killed up to some point, if you proceed to kill X more krampuses, you have a Y% chance of getting a drop from at least one of them."

If you care to know how the math works, I have detailed the method below. The probability of getting a drop on the:

1st Krampus = .01

2nd Krampus = .99*.01 = .0099

3rd Krampus = (.99^2)*.01 = .009801

4th Krampus = (.99^3)*.01= .00970299

etc.

Taking the 4th Krampus example, there is a .99 probability for getting nothing the first krampus, .99 for nothing on the second, .99 for nothing on the third, and .01 for getting the sack on the fourth. If we combine the instances of getting the first, second, third, or fourth to drop, we add the individual probabilities together to find the cumulative probability of getting at least one sack between our first and fourth kill, which is .03940399. So in general, summing individual probabilities up to the nth krampus kill gives the cumulative probability of getting at least one drop for killing n krampuses.

Good luck, everyone! Your farming party will need it!

[Mudley]

In my opinion, the drop rate should be something in between 5 and 10% to be even worth the effort.

[WillPwn4Food]

2 hours ago, Mudley said:

In my opinion, the drop rate should be something in between 5 and 10% to be even worth the effort.

I ran my R code and at different drop rate chances (right column) and recorded the amount of krampuses killed required to get a 50%, 75%, and 99% cumulative chance of getting at least one drop:

This topic isn't about making things easier but since we're talking about it now, I think if Klei were to change anything, moving the drop rate to about 2.5% could make getting one a lot more realistic. It would be about a 50/50 split whether you get a sack or not after killing about 30 krampuses, and you'd very likely get one for killing a couple more than 50. 

[Mudley]

@WillPwn4Food I was just giving a little opinion of mine, really nice effort of you making all of this.

[HutGenerator]

Nice analysis.

Take krampus sack as a lottery or something. I got one at day 600 but the second i got at day 700. Fyi i just kill gloomer every fullmoon, not much effort wasted actually.

[Arlesienne]

1% per each attempt. Dice have no memory, remember.

[cezarica]

A similar and less stressful/painful way to test the 1% would be finding a gear in tumbleweeds as it has the same 1% chance as the sack from Krampus.

My personal record is that once found 4 gears in a row, while most of the time I spend from one to a few days chasing tumbleweeds in hopes of finding a gear for an ice box. Either way you look at things, 1% is still 1% chance and even after 100, 200 or even 500 one could be very unlucky and still not find any.

On a couple of occasions found a Orange Gem that has a 0.02% chance or a Purple Gem with  0.01% chance like once or twice if recall correctly. On the other hand, a couple of times found a rabbit, a mole, a spider or even a damn frog or bee with a 0.1% but no gear.

Will put your probability to the test in finding a gear later on when will get home.

Edit: According to the wiki apart gears the following items also share the same 1%: petals, Gord's knot, beefalo wool, berries, blueprint, dark petals, hardened rubber bung, hound's tooth, stinger, foliage, silk, butterfly wings, rope, cut reeds and seed.

[Arlesienne]

Please. Every attempt is unique. I keep getting rubber bungs. It changes nothing in regard to your problem. There can be no recipe for getting the sack or anything for sure.

Except through the console. Or a mod that makes it craftable. Here, I said it. I just see all those calculations that take your time and effort, but are not useful in the game. Sorry. It is human to believe there is a pattern, but it is a cognitive fallacy.

[Muche]

I had no idea that probabilities and statistics could be such controversial subjects.

[Mudley]

26 minutes ago, Muche said:

I had no idea that probabilities and statistics could be such controversial subjects.

You have no idea, pal.

[Arlesienne]

52 minutes ago, Muche said:

I had no idea that probabilities and statistics could be such controversial subjects.

 

26 minutes ago, Mudley said:

You have no idea, pal.

Odd, right? Because all theory is here and technically the situation is crystal-clear.

On a general note, the chance of getting the sack is outrageously low given the efforts some make to get it. One out of one hundred...

I wish it was a one-in-a-million chance. I like the 9/10 probability :).

[JohaneBrote]

The odds are actually 50/50. You either get it, or you don't.