I made a habit of recording events of resurrection of the Dragon Soul and Infernal King in PvP battles for the past couple of weeks. So, my total is 75 TDS/IK encounters. The number is probably insufficient to make reliable conclusions but I just got bored and 3 weeks is quite a long time. For statistical calculations, I used real-statistics plugin for Excel 2010. For simulation, I used Excel which has the same Mersenne-Twister pRNG as GoW.
So, I compared actual results and simulation to see whether they come from some uniform random distribution.
Actual data had 24 resurrections including 5 double resurrections. I did not have triple or higher resurrections. So, the percentage is around 32% which might be fairly close to 25% expected.
Simulated data had 20 resurrections. Percentage is 26.7% which is a bit closer to expected 25%.
I then used Runs test (some people call it Wald–Wolfowitz runs test, details are here https://en.wikipedia.org/wiki/Wald–Wolfowitz_runs_test and here http://www.real-statistics.com/non-parametric-tests/one-sample-runs-test/ ) to check whether the data come from a random sample.
So, actual gathered data had z-stat value of 1.99 and P value of 0.047. Simulated data had much lower z-stat value 0.1 and P value of 0.92. For those who cannot be bothered to read the math and understand what it means and whether it is applicable: P value less than 0.05 means that hypothesis that the runs are random is rejected which means that the actual data are not random at more than 95% probability. While simulated data are perfectly random. It seems that the test might not be powerful enough with only 75 data points. Chi-squared test of sufficient power around 0.8 might require something around 400 points. But the difference between actual data and simulated data is quite staggering, so I presume that just based on this, sample size is sufficient.
I’m not sure if it means anything. Mostly because the runs for actual data are not sequential and the simulated data runs are sequential. However, since the actual data are derived from a larger set of apparently sequential random data, the actual data might be random although not necessarily.
I can post the numbers if somebody wants to take a look. And yes, I have some professional background in statistics.
Strictly speaking, the only real thing that can be concluded is that my simulation is not adequate. However, it is random according to runs test and is obtained using the same pRNG as GoW.
Ask some questions and I’ll try to answer to the best of my abilities. I’m also running some other tests, and they are not black and white, statistics is never black and white, apart from few clear cases.