I believe I have found a mathematic explanation for the phenomenon.
There is a linear relationship between distance and impressiveness of group size, where distance increases impressiveness also increases. Expressed as a formula where impressiveness is expressed as a function of x and mx is the slope of increasing distance, the equation would be:
f(x) = mx + b
Following this, there is a secondary effect with a strong exponential curve. Once we have solve for the f(x) impressiveness factor, we can calculate the likelihood that the underlying group size would be verbally recounted to others. As you can see, with the factors of increasing distance and decreasing size there is a rapidly increasing incidence of "bullseye summarization", or BS for short.
Combine this aggregate auditory data that the average shooter encounters with the underlying experiential knowledge that is the basis for all shooting and reloading practices, and we have a solid foundation with which to calculate the direct relationship between distance and the resulting group size in minutes of angle.
m = (y_2 - y_1) / (x_2 - x_1)
The net result gives us concrete proof that the phenomon is indeed true.
Mr. Litz, can I please have my prize?