Not very. But I'd be interested to see such an equation. That's always a good place to start and then work backwards from.
Sorry, I thought I was zeroing in on you wish. Would you restate it for me, please?
There is no such equation, to my knowledge. However, Dr. Jones's analysis program seems able to calculate a pattern's lethal/effective diameter based on one known pattern (10 samples) at a particular distance (yardage). The program also requires target susceptible area and number of hits for a lethal dose. And, you need to pick a required probability of a target break. Once you understand the shape and size of the effective diameter volume, you arrive at aiming error of the shooter as an input.
Lot of information in the above. It doesn't tell you how a pattern develops, but it does tell you how it performs.
Let me know if I am doing any good or if it is time for me sigh off.
DDA