Tamid, this s a very good question. Unfortunately, the answer is complex. Fortunately, Dr. A C. Jones addressed this question in his book "Sporting Shotgun Performance." You can get an intuitive idea of performance/pattern comparisons by "eye-ball integration" of patterns. However, it would be more worthwhile to use the shotgun insights program to generate statistically valid data.
Briefly, patterns have a Rayleigh distribution (you can use a normal distribution with only a small loss of accuracy) from muzzle until the shot hits the ground. That said, pattern can be calculated up and down the range once it is established. The fly in the ointment is that the diameter of the effective area of the pattern blooms for some distance (influenced by choke) and then withers as the number of pellets becomes insufficient to cover the ever expanding pattern area.
The expansion is not a log function. The following estimate is not too far off: 10 yds to 20 yds - double, 20 yds to 30 yds -double, 30 yds to 40 yds - 1.5X, and 40 yds to 50 yds - 1.5X. Keep in mind that this does not give you effective diameter, rather linear area.
Hope that helps some.
DDA
