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 (and if you grouped the shot according to distance from the center of impact, counted the shot in each grouping, and plotted the result, you would see a basic Normal distribution). 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?
No, but it does, however, show that it is very, very difficult to eyeball pattern density. The Rayleigh/Normal distribution (your choice as they are very similar)is durable for the flight of the pattern. Both predict much higher density at the core than at the fringe. Ever see someone make a seemingly imposible long range shots with more than usual frequency? It is quite amazing how far the center, the very center, of an open choke will retain lethal density. So, what was happening? The tubes were giving less choke effect. Simple as that.
DDA
SRH
