Don,
If there was no wad, I would agree with your math. But the pellets exit together.
If you look at the photography, They do not begin to separate until nearly 6" from the muzzle. At 12" the column is deformed.
Add in the fact that some pellets are compressed, thus deforming them and changing their co-efficient. The wad, hardness of the shot and any buffering material all play a role. Given that, I believe that a mathematically pristine Rayleigh distribution is impacted. The theory at least assumes all components of the distribution to be equal. In practice an allowance is always made for reality.
The pellets do not impact the plane of the target simultaneously. Not just because of the length of the column, but also because of minor variations in velocity and ballistic co-efficient. This becomes obvious to the shotgunner at the patterning board.
Pete
