We know what happens if you are slowest or fastest. If you are dead center then you would not have a reason (would you?) to expect one event to happen more often then the other. Not complicating things without cause, I wonder: have you ruled out the (too?) obvious answer a that if you have passed j people and been passed by k then the best estimate (absent other information) is that you are faster than $\frac{j}{j+k}$ of the other runners and slower than ${k}{j+k}$. \frac{k}{j+k}$. With assumptions on the distributions maybe one could say more. Under some assumptions you could infer things by how long it has been since any passings happened, or by how quickly the relative frequency converges, but I'll assume that you run blindfolded and at some stage are stopped and told "over the course of you run you passed j and were passed by k. I wonder if it helps conceptually to renormalize relative to your speed and say that you are a stationary observer next to a track, people have been scattered on it in random positions, some go clockwise and some counterclockwise according to some distribution which maybe be biased in one direction (and maybe with various speeds).Given that you observe j going counterclockwise and k going clockwise... 1 We know what happens if you are slowest or fastest. If you are dead center then you would not have a reason (would you?) to expect one event to happen more often then the other. Not complicating things without cause, I wonder: have you ruled out the (too?) obvious answer a that if you have passed j people and been passed by k then the best estimate (absent other information) is that you are faster than$\frac{j}{j+k}$of the other runners and slower than${k}{j+k}\$. With assumptions on the distributions maybe one could say more.