The following is an analysis of a set of HM rapter farm data set. A sample of 80 runs was taken with the following summary statistics:
Variable N N* Mean StDev
Kills 80 0 32.150 2.159
Grog 80 0 2.363 1.478
Golds 80 0 0.5125 0.7955
AS Recharge 80 0 0.8750 0.3328
Kills is how many rapters were killed, grog is how many grog dropped, golds is how many golds dropped and AS recharge is how many times the Air of Superiority rechared after the boss was killed. As you can see the average number of kills per run was 32.15 and grog were about 2.36.
The following is a plot of the Grog drop over time for this series of 80 runs. The black line is the proportion of grog drop and the red line is the statistical control limits (the upper one varies slightly based on number of kills), so it shows a relatively stable process with an average grog drop rate of 7.35% per kill.
Grog Drop Rate
Based on this series of data the95% confidence interval for the grog drop rate is [0.063695, 0.084256] with the average rate at 0.0735.
Test and CI for One Proportion
Sample X N Sample p 95% CI
1 189 2572 0.073484 (0.063695, 0.084256)
The following plots shows that for any particular run the grog drop vs probability for a 33 Kill run. The black line is the cummulative probability and the red line probability density (point estimate). It shows the likelihood of drops of any particular run of 33 kills and shows that the most kills per run to expect is 7 and it is not that unusual to get 0.
For Golds, including, Black Dye the following shows the drop proportion of the series of 80 runs:
The gold contorl chart above shows some unusual points, 8 and 11, which may suggest that the process may have been unstable during that time, (possibly a data error), or the estimate of gold drop rate is incorrect.
The 95% confidence interval for gold drops is show below with the most likey estimate as 0.0159 (~1.6%).
Test and CI for One Proportion
Sample X N Sample p 95% CI
1 41 2572 0.015941 (0.011463, 0.021564)
The following is the probability plot, given this estimated drop rate and a run of 33 rapters.
So based on the data I have gathered for golds the most likely event for a single run of 33 kills, would be 0 at about 58% of the time. Getting 1 or less golds for a run of 33 kills is about 90% likely. Getting a gold drop of 4 and 5 or more in one run is very unlikely.
So these are the facts I have thoroughly gathered. In God we trust the rest bring data.
Here's my data:
