Marksmanship's probabilities ?

Hi all !

While chatting in a live game, I was told Marksmanship uses a true random distribution, while I was telling them it was a PRD, with the most obvious effect being to change the frequency of 2+ Marksmanship procs in a row.

Having some doubts, I decided to launch the Demo Hero thing, get an Axe with some Hearts and armor, while I kept pummeling him with my level 6 Drow Ranger with 700 attack speed thanks to multiple Moon Shards, opening the combat log and manually reading the damage instances on 30-second periods to identify which ones were Markmanship procs. While I forgot to count the number of 30-second periods I checked, I did count how many time periods I had when I made the first measurements, so the total number of attacks, N1, could be approximated as 617-618. The number of Marksmanship procs in this case was N = 121, and the number of instances where 2 procs happened on 2 consecutive attacks was x = 12. As expected, N =~ 0.2*N1, but x/N =~ 0.1.

To get more accurate probabilities, I did some more measurements, and ended up with N = 342 and x = 30. Note no strings of 3 or more Markmanship procs in a row were detected. So why do these numbers matter ?

If Marksmanship followed a true random distribution, one would expect x to tend to 0.2*N, which is obviously not the case with my measurements. If it followed the PRD as known in Dota 2, it should have a C =~ 0.055704042949781851858398652 for a nominal probability p = 0.2, and since a Marksmanship proc should reset the probability for a proc on the next attack to the base value C, this should result in x tending to C*N1. But that's not the case either.

If you play a bit with this binomial probability calculator, you'd realize the cumulative probabilities P(X <= x), either with the constant p = 0.2 for true randomness or with C =~ 0.0557 for normal PRD, would give values very far from 0.5, meaning they'd be such edge cases it's way more likely the null hypotheses that Markmanship follows true randomness or normal PRD are incorrect and therefore some other model of probability distribution is afoot.

So is Marksmanship intentionally programmed differently from normal PRD, or is there some bug ?

Also, is it possible to have the possibility to export the combat logs in some text files for easier reading ?

See you