Stan Pope wrote:...the cluster of cars which rank near the median tend to "stay close to where they started racing." Some oscillation is expected since the original distribution of racers was not homogeneous.
I might have also said that they tend to "end up
close to where they started."
Stan Pope wrote:Since the original locations of those median-bunch cars are randomly distributed around the ring, there is no "central location" about which the median-bunch cars gravitate.
Yes, it seems that one might be able to make conclusions based only on how far away one traveled from their starting location.
Stan Pope wrote:Since the "ring" method does not tend to cause head-to-head races between similarly matched cars, it is probably slower at ranking the cars than would the original terminated line of tracks.
Probably. It would be an interesting thing to simulate.
The distribution of race scores might also be an interesting data set for analysis. Might the outcome resemble the results of something like a Galton box
and have a predictable distribution? Could race officials thereby detect cheating by a statistical hypothesis test of the distribution of scores? For example, one might expect that ~1/2 the cars end up toward the right of their original location, and ~1/2 end up toward the left. This would not necessarily identify individual cheaters, but it might suggest anomalous activity within the population of race outcomes, say, if the population of scores were highly asymmetrical.