Ragged holes
Throughout the rest of this site we assume that we can measure the location of each and every shot on a target. It is possible -- and with larger shot groups and/or more precise rifles increasingly likely -- that the target will exhibit a "ragged hole" into which one or more shots has disappeared.
This is known as a "center-censored" sample. A detailed explanation and discussion of the problem is here, but presently no good mathematical solutions have come up.
In practice, given a target with a ragged hole and a small number of "censored" shots, it is probably adequate to place them evenly inside the hole. If the number of censored shots is large a better solution is to:
- Set p = proportion of shots that were censored.
- Find the smallest sigma such that CEP(p) covers the ragged hole.
The best solution is to avoid this problem in the first place: Shoot no more than three rounds per target, and then aggregate them into a data set. Software to automate this process exists, e.g.,
- OnTarget Target Data System - uses coded target sheets that can be scanned to automatically aggregate one shot per aiming point.
Another easy and powerful approach is to use Brent Danielson's clever 2-shot method of generating and analyzing data.