I am analyzing monte carlo generated data of the paths of some particles. For each event, the path is (nearly) random except that the probability of the angle of deflection at each interaction point increases with distance traveled. I am considering different parameters to use for descriptive statistics.
One interesting point would be "how curly the track is" in some average sense. While I could calculate the angular displacement at each interaction point, I'm not sure I really want to get that detailed. On the other hand, I already have an algorithm for total displacement and track length and could easily take the ratio. It seems reasonable that the "more curly" a track is, the smaller the ratio of displacement to track length should be (generally speaking).
While this "feels" right, I have taken enough math to know that feeling is a poor guide for truth. So, my question is
Is the ratio of the displacement from start to finish along a drunkard's walk characteristic of the angle of deflection at any turn along the path and, if so, how good of an approximation is it?