PD
Member
|
@Primate Murder: Thanks for posting, I get to bump this now :P The contests are finally over! I have some interesting analysis to do for sure, and will momentarily update the post as the last increment of data comes in. Final numbers: (Raw numbers, includes people outside the top 200) Top: 50: 19,668,590,982 Gold, (Currently 18,435,050,000 Gold, +6.7%) 100: 9,076,284,602 Gold, (Currently 6,577,700,000 Gold, +38.0%) 150: 5,143,165,178 Gold, (Currently 3,926,501,000 Gold, +30.9%) Total: 4,399,706,134,889 Gold (Currently 3,039,816,782,600 Gold, +46.1%) So I missed pretty badly because it turns out there were quite a few people who could have been on the top ranks, but chose not to participate for reasons unknown. Although it's still surprising to me at least that I managed to predict the top 50 cutoff within 10%. However if we chose to exclude the people who were outside the top 200, it looks more like this... Top: 50: 18,832,321,493 Gold, (Currently 18,435,050,000 Gold, +2.15%) 100: 7,452,011,560 Gold, (Currently 6,577,700,000 Gold, +13.3%) 150: 4,465,420,126 Gold, (Currently 3,926,501,000 Gold, +13.7%) Total: 3,703,814,178,982 Gold (Currently 3,039,816,782,600 Gold, +21.8%) Still not perfect, but MUCH closer to within predicted range. Regardless this predictive model did much better than I expected it to all things considered how simplistic the analysis was. In reality though I failed to account how people were actually trending much more minimalistically than maximimally. There are two things to understand. First let's for now call this first thing the Propensity Ratio, or: Currently Donated Amount / Possible Donated Amount Where a ratio of 1 means perfectly spending all your possible gold, and 0 meaning you spent nothing. Running this amongst the Top 50 finishers, we get something like this: Average Propensity Ratio: ~.83 (or 83%) Median Propensity Ratio: ~.90 (or 90%) On the surface, it sounds like most people gave it their all, but let's use the Safety Ratio as another thing: Currently Donated Amount / Minimum Cutoff The lower the ratio, the less "Safe" you decided to play. That said: Average Safety Ratio: 1.60 (60%) Median Safety Ratio: 1.19 (19%) Averages skewed by the top, but the Median tells a very different story - That most people actually donated "just enough" to make their cutoffs. And you can see this empirically in the behaviors of the top 50 where the separation between the 50 and 25 was a mere 3 billion gold. So with all that being said, this was quite an interesting contest - at least for me because I learned quite a lot (and I'm sure others have learned quite a lot as well). Going forward I have some ideas about how to deal with all of this variable behavior - perhaps running this as a Monte Carlo Simulation and accounting for a wide vareity of behaviors that people exhibit (IE, if people donate maximally, minimally, and a aggregate with a probability distribution of all simulated outcomes). Though this is too much math for me today, maybe next time this will all be a real possibility. All said, I managed to hit over 350 Billion at the end thanks to getting lucky with the receipts as well as playing with no effort spared. After I get all my remaining receipts I am probably going to take a break for a good while as I have exerted myself far beyond what is reasonable. EDIT: Shutting down the app for now. May bring it back in the future but for now it has served its purpose.
< Message edited by PD -- 2/1/2022 1:35:11 >
|