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Project Partyhat

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Shuttleduck

Shuttleduck

Posts: 4,346Adamant Posts by user Forum Profile RuneMetrics Profile
This is the final writeup of the “Xmas Cracker Research Project!” (QFC: 17-18-35-63828458) that I designed and led from late June 2012 into early July 2012.
The project was an attempt to discover the exact probabilities of obtaining each color partyhat from a Christmas cracker. The project was conducted with as strict of adherence to the scientific method as possible on RuneScape. The process was recorded and released for public viewing. The results for the partyhat probabilities are statistically significant with low margin of error and high confidence. (It is quite possible we have obtained the exact probabilities.) Secondary item probabilities are not statistically significant and have a high margin of error with low confidence, however they still yield interesting results that suggest the assumed-accurate documented history on popular fansites concerning Christmas Crackers is completely inaccurate and/or fabricated.
Procedure “In a nutshell”:
1. Purchase christmas crackers on RuneScape live.
2. Duplicate 1,337 crackers on beta.
3. Pop all 1,337 crackers on beta.
4. Collect data and combine with trusted data from others that chose to help.
5. Analyze data in Microsoft excel and report conclusions.
Video recording of the popping procedure can be found on YouTube. (You should be able to find it easily.) There is an original video by me of the original footage. There is also a summarized version of the video posted by a well known rs video maker.

20-Aug-2012 23:04:24 - Last edited on 20-Aug-2012 23:15:07 by Shuttleduck

Shuttleduck

Shuttleduck

Posts: 4,346Adamant Posts by user Forum Profile RuneMetrics Profile
By combining the 1,337 pulls with a few hundred more pulls from the other contributors, we obtained the following data:

Total - 2189
Red - 546
Yellow - 465
White - 399
Green - 375
Blue - 243
Purple- 161

Plugging this data into Excel revealed a very interesting result. It's linear! (With the exception of green) Remove the green data point and you can fit a line with an r^2 value of .999. It's undeniable. Partyhat rarities are based on a linear function. Green is the odd one out. This led us to believe that the following are more than likely the EXACT probabilities:

Purple: 7.50%
Blue: 11.00%
Green: 17.00%
White: 18.00%
Yellow: 21.50%
Red: 25.00%

Interesting results considering the current price tier on RuneScape live. Sure, we all know about the dupe. But, based on Kaitniek's documenting of the event, it seems like crackers were the main focus rather than partyhats. (Search around in random places for “Cracker Party by ARC” for a primary source documenting the dupe. There is also another source out there which can no longer be obtained. Unfortunately, I have no way of sharing it on these forums.) Even if they had focused on purples, they're just so rare that chances are the AutoRune crew didn't dupe enough to make them the most common. Personally, I believe purple became the most common, if it is, as a result of Jagex haphazardly removing masses of partyhats from the game after the dupe.
Interestingly enough, the price tier on RuneScape classic follows the rarity tier we discovered from popping the crackers. This means that, more than likely, the majority of players transferred their partyhats from classic to RS2. More crackers were then cracked on classic over time allowing a partyhat market relatively uninfluenced by the duplication to develop.

20-Aug-2012 23:04:31 - Last edited on 20-Aug-2012 23:15:46 by Shuttleduck

Shuttleduck

Shuttleduck

Posts: 4,346Adamant Posts by user Forum Profile RuneMetrics Profile
But there’s still a significant question. Why does green not follow the linear trend? I'm not 100% sure, but here's my speculation on it:

I remember reading once that a Jagex Mod had confirmed they were planning on releasing a black partyhat but scrapped it because it wasn't "festive" enough. If this is true, it could explain why green doesn't fit the trendline. If not including the black was a last minute decision, it's quite possible that Jagex just severely adjusted the probability on green as a quick fix. This would have meant a small change for the other color partyhats too.
EDIT: It may be that it's impossible to fit 6 points on a line adding up to 1. If this is the case, that would also explain why green doesn't fit the trend and would render the black partyhat theory rather baseless. I'm too busy to look into this now; but when I have the time, I'll see if I can prove whether the 6 points can add up to 1.

~~~~~~

20-Aug-2012 23:04:35 - Last edited on 24-Oct-2012 03:53:44 by Shuttleduck

Shuttleduck

Shuttleduck

Posts: 4,346Adamant Posts by user Forum Profile RuneMetrics Profile
Other items.

Unfortunately, other items were only logged on my 1,337 portion of the project. The other contributors did not log them. Here are the results:

Spinach Roll: 166
Holy Symbol: 114
Silver Bar: 177
Black Dagger: 55
Gold Ring: 96
Chocolate Bar: 254
Chocolate Cake: 154
Noted Iron x5: 157
Silk: 110
Law Rune: 53
Nothing: 1 (Likely an error. Perhaps a spinach roll or choco bar was consumed?)

We did not collect enough data to determine whether the probabilities are based on a function of sorts.

20-Aug-2012 23:04:43 - Last edited on 20-Aug-2012 23:07:37 by Shuttleduck

Shuttleduck

Shuttleduck

Posts: 4,346Adamant Posts by user Forum Profile RuneMetrics Profile
An interesting result though is that we received NO rune items, dragon items, or coins from the Christmas crackers. None of the contributors did. This means that either these items are INCREDIBLY rare, or they just don't exist inside of crackers. Is it possible that the community deluded themselves into thinking these rare and pricey items were inside of the crackers just from flight of fancy? Perhaps. Or maybe those who have written some of the most popular articles on the history of RuneScape used poor sources and/or had distorted memories.

Anyways, that's all. Hope you all found this interesting!
~Shuttle
Note: Proper credit to those involved with the project can be found in the original video I posted on Youtube.

20-Aug-2012 23:04:47 - Last edited on 20-Aug-2012 23:07:55 by Shuttleduck

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