I really like the way you have gone about doing this. You literally know the percentage of shots which land within a 3" group. This kind of information is extremely useful for analysis. Given you have 50% probablity of landing in a 3" group with any given shot. Do you have any idea what the probability of getting a 3" group is? I think alot folks may surmise its pretty close to 50%. But it isn't. Its alot less than that.

You have 50% probablity of landing the first shot in a 3" group.

To get two in a row the probability is 50% for each shot so the Probability P2 = .50 x .50 = .25 or 25 % This basically means that if you tried 4 times you would get two consequetive shotin a 3" group in only one of those four groups. How about 3?

P3 = .5 x .5 x .5= .125 or 12.5 % which means if you try 20 times to get a 3 shots in a 3" group, you will succeed 2 times out of 20 attempts, half of the time, and 3 times out of 20attempts the other half.

In order to geta 3 shot group at 3"half the time, you must put80 percent of your shots inside the 3" group.

Its easy to get frustrated with group sizes when you don't understand what going into making them. There are factors beyond your control, which contribute and add to the uncertainty of POI. Don't make too much of any particular 3 shot group. If 100% of your shots were inside the 6" group, then you knowwhatyou're maximum range for hunting is. You simply plan your hunt to take advantage of your skills at less than 100 yards where your maximum miss is acceptable. Study the movements and signs of your gameand give yourself the opportunity of a high probability shot.

Meanwhile, one continues with the obsession of shrinking group sizes.