Rocketman,
My knowledge of the Rayleigh Distribution is a bit vague, admittedly. However, if my understanding of the distribution is in any way correct, shotgun patterns at distance tend not to follow such distributions, especially in the cases of tighter chokes. As "Gough Thomas" points out, shotgun patterns tend to "trumpet out" as they approach their maximum extended ranges. The distribution remains intact for both choke effect and distance (time of flight). The trumpet shape swept by the pattern is caused by the forward veocity of the shot slowing at a higher proportional rate than the sideways velocity. However, the pattern will retain a Rayleigh disribution no matter the distance of capture or the choke effect. A pattern captured close to the muzzle will be very "spikey" (lots of shot near the pattern centerline) when plotted and one captured at long range (for a shotgun) will plot quite flat (most of the shot having moved away from the centerline). In both cases, the % of shot in any given band of the pattern can be predicted by the Rayleigh distribution.[/color
My comments were based on 80% patterns at 40 yards. I assumed that this would have been understood. Yes, all loads will pattern 80% at some distances and heavier shot charges will have more pellets in their 80% patterns than lighter shot charges will. So what? [color:#FF0000]If one wishes to shoot a given pattern density at a given range with a given shot load, then choke effect must be used as the control. A lighter shot load will require more choke, which means smaller pattern diameter.
I guess my attempt to make my point was unclear. Smaller pattern percentages DO NOT necessarily indicate smaller pattern diameters. Zutz demonstrates this fact when he compared modified and full choke patterns and "Gough Thomas" takes this to comparisons between IC and FC patterns. Differences between patterns thrown by various chokes are very often differences in the densities of pattern cores rather than pattern diameters. This conclusion is the result of incomplete pattern analysis. A valid statistical analysis will show that all patterns follow the Rayleigh distribution which means that diameter will vary as will the "spikeyness" of the pattern. There is not core, per sey.
[Full disclosure: My computation of the relative pattern per centages for 3/4 ounce loads should have been 53.33%, not 60%. To extend my analysis, if 85% patterns are used as a baseline, 1-ounce loads "score" 75.55%, 7/8-ounce loads "score" 66.11%, and 3/4-ounce loads "score" 63.75%, relative to 1 1/8-ounce loads.]
There is not a "core" to patterns? Really? This would be news to a whole lot of shooters who patterned their guns and were able to detect and analyze often large variations in pattern center density. Yep, really. "Core" implies a zone with a different distribution than the annular ring around the "core." The highest number of shot per square inch is at the centerline of the pattern and varies with distance from the muzzle (time of flight), number of shot (shot size, shot load), and choke effect. The shot per area varies according to the stated Rayleigh distribution as you move out in diameter. The "aiming error" comment is accurate.
