I don't completely understand the Rayleigh distribution thing. I understand the concept, I think. But consider that, years ago, I took a Remington barrel, with fixed choke, and shot numerous patterns with it using several different loads. All exhibited the same type pattern that we are used to seeing-- a hot, dense core with decreasing density as the you approached the edge of the pattern. Then, I had the barrel threaded for screw-ins and tested a particular maker's choke tubes in it. The distribution changed markedly, with all constrictions I tried of that brand's tubes, .005", .010" and .015", as I recall. The patterns were all significantly less dense at the core, with those pellets being distributed more toward the edge, i.e., while the fringe of the patterns were still less dense than the core, the difference was not nearly so marked as with the fixed choke, previously. The overall pattern size was consistent with the fixed choke pattern, choke for choke, just different distribution.
Does this contradict the Rayleigh distribution, or no?
SRH