The more efficient measures use the location of each and every shot on a target within the calculations for the measurement. 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.
In statistics 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. This is especially exasperated by the small sample statistics used by shooters.
In practice there are three options.
(1) The best solution is to avoid this problem in the first place. Shoot few shots per target (i.e. target meaning one POA since some paper targets have more than one POA), 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.
(2) Use a measure that can be done on a target with ragged holes. In general such measures are not as efficient statistical estimators as those which use all the shot positions. Pragmatically ease of use on the range may outweigh the benefit of being able to use less shots to get the same precision.
(3) It may be possible to "salvage" a target with a ragged hole and get at least some notion of the precision.
- (a) If there are a small number of "censored" shots, place them "evenly" inside the hole.
- (b) If the number of censored shots is large, and there is still a reasonable number outside the ragged hole, then a better solution is to:
- - Find the smallest hole such that covers the ragged hole.
- - From n, the number of shots fired, and c the number outside the circle, determine p=(n-c)/n that the radius of CEP(p) for the number of holes censored by the circle.
- - Use the experimental CEP(p) measurement to estimate CEP(50) so that the measurement is repeatable.
Measures On Ragged Holes
The following measures can be made on targets with ragged holes.
- Covering Circle Radius - Smallest circle that covers all the shots
- Diagonal - Conceptualizing the horizontal and vertical range as forming a rectangle on the target, then the measure is the diagonal of the rectangle.
- Extreme Spread - distant between two widest shots
- Figure Of Merit - average of the horizontal and vertical range