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Xmas Cracker Research Project!

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Finance
Apr Gold Premier Club Member 2012

Finance

Posts: 55,945Emerald Posts by user Forum Profile RuneMetrics Profile
I decided to take a Bayesian approach to the partyhat analysis. Suppose that, before partyhats were released, we thought that each color will be equally likely. We can represent that belief as a "prior distribution" by using a Dirichlet distribution with parameters (1,1,1,1,1,1) corresponding to the 6 colors (purple, yellow, green, red, white, blue).

The nice thing about Dirichlet distributions is that we can update our beliefs about the probabilities of each partyhat by simply adding to the corresponding parameters when a particular color is observed. For example, if we observe 1 purple partyhat, our new distribution becomes (1+1, 1, 1, 1, 1, 1) = (2, 1, 1, 1, 1, 1).

Based on Shuttleduck's 1337 observations, we therefore have a Dirichlet distribution parameterized by (104, 322, 194, 322, 263, 138). Here's what that looks like for each partyhat:

Purple


Yellow


Green


Red


White


Blue


In Bayesian analysis, we can construct "credible sets" that have a much more natural interpretation than frequentist confidence intervals. For each color, there is a 95% probability that the true partyhat drop rate falls into the following intervals:

Purple: 6.4% to 9.2%
Yellow: 21.7% to 26.3%
Green: 12.6% to 16.4%
Red: 21.7% to 26.3%
White: 17.5% to 21.7%
Blue: 8.7% to 12.0%
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16-Mar-2018 18:28:39 - Last edited on 16-Mar-2018 18:38:36 by Finance

Sea King
Feb Member 2019

Sea King

Posts: 6,812Rune Posts by user Forum Profile RuneMetrics Profile
"fr3sh princ" got blue partyhat from pulling cracker just now. If you are willing to chuck your most precious possessions like phats because someone said words like crashing/dying/quitting and then find yourself unable to rebuy for what you sold for, then you don't deserve to own a phat.

15-Jul-2018 17:11:01

Sea King
Feb Member 2019

Sea King

Posts: 6,812Rune Posts by user Forum Profile RuneMetrics Profile
last week, scary time got white from pulling his cracker. If you are willing to chuck your most precious possessions like phats because someone said words like crashing/dying/quitting and then find yourself unable to rebuy for what you sold for, then you don't deserve to own a phat.

15-Jul-2018 17:11:24

dafda1111111

dafda1111111

Posts: 172Iron Posts by user Forum Profile RuneMetrics Profile
Check out the pull rarity rates on the official RS Wiki page for Christmas Cracker confirmed by jmod:

Blue partyhat (15/128)
Green partyhat (20/128)
Purple partyhat (10/128)
Red partyhat (32/128)
White partyhat (23/128)
Yellow partyhat (28/128)

31-May-2019 05:31:16

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