XII. Accuracy

C. Miscellaneous

5. Group Size Analysis Methods

by Jim Ristow c/o Recreational Software, Inc. (rsi@sedona.net)

This article was edited from software documentation to explain various ways to measure targets and how they are best used. Some of the measurements are tedious to take manually but may be calculated quickly with computer software capable of digitizing and analyzing targets.

Group Size Analysis Methods

Maximum Spread
The Maximum Spread (also called group diameter or extreme spread) is simply the distance between the centers of the two most widely dispersed shots in a group. This is the most common method used to describe group size because it is the easiest measurement to take. Unfortunately it only considers two shots in the result so an otherwise tight group of 10 shots with one "flyer" can produce results similar to a widely dispersed two shot group. For bench rest shooters who are capable of putting five shots in one hole it is a valid measure; but for the rest of us, or for handgun shooting it does not provide a "statistically significant" number for comparing targets.
String Measurement
This is an old method still used to determine a shooter's skill at hitting a target. It assumes the point of aim is always the desired point of impact and is simply the sum of the distances from the point of aim to each bullet hole. Originally a string was used to gather the distances, hence the name. It is still a valid measure of total error relative to the aim point. String Measurements however cannot be used to analyze sight settings because it only measures the magnitude of error, not the direction of error. It is also not a useful measure of group size because a tight group located away from the Bullseye will produce a large String Measurement.
Average Group Radius
The average of the distances from the statistical group center (not the aim point) to each shot is the Average Group Radius. It accurately reflects how far a typical shot will impact from the aim point with a well sighted arm. This measure is the best indicator of group size or firearm performance because flyers have less impact on the result so it provides a "statistically significant" number for comparing a series of targets or groups. Unfortunately it is difficult to calculate manually. Unlike a String Measurement, the Average Group Radius does not assume the point of aim is the desired impact point, so sighting error is not a factor in the result. Average Group Radius can therefore be used to compare group sizes when the impact point is intentionally high (rifle sighted for maximum point blank range and shooting high at 100 yards). It is also the best measure for evaluating the overall accuracy of loads. Magazine articles using Average Group Radius indicate the writer has taken care to provide readers with statistically significant data, but you should be careful not to compare it to the more common Maximum Spread.

Error Analysis Methods

Vertical & Horizontal Spread
The Horizontal and Vertical Spread of a group is simply the greatest distance between shots on the vertical or horizontal plane. This contrasts with the Maximum Spread which can be at any angle across the group. This measurement is understood by most shooters, easy to make, and can be used to help detect load and mechanical problems or "pulling" by the shooter. If the Vertical or Horizontal Spread is significantly larger and shots are well dispersed, it is called "stringing". A cross wind will obviously disperse shots horizontally. Vertical stringing may be caused by irregular powder charges and detonation problems (inconsistent ignition due to variations in primer pocket depth or primer thickness). Improper crimping, bullet inconsistencies or other loading problems usually result in larger overall group sizes, and not "stringing" in any particular direction. A loose gun sight, or broken scope may also cause stringing.
Average Vertical & Horizontal Error
The Average Horizontal and Vertical Error is the average of errors on the Vertical and Horizontal plane from the group's statistical center. This is a much better measure for detecting errors than Vert./Hor. Spread because the shot data is averaged to reduce the influence of "flyers". If the goal is to track "pulling" by the shooter over time or to isolate problems, then the Average Vertical & Horizontal Error is a better measurement for comparing a series of targets.
Maximum Shot Radius
The Maximum Shot Radius (or maximum group radius) is the distance from a group's statistical center to the center of the most distant hole. It really only indicates how far from the group center the worst shot should fall and is not a good indicator of overall performance. On a target where shots are evenly dispersed, this measurement will be about 1/2 the Maximum Spread and larger than the Average Group Radius. It is best used to quantify the worst shot in a series of targets.
Maximum Shot Radius Compared To Average Group Radius
The Maximum Shot Radius should be only slightly larger than the Average Group Radius. A big difference between these measures is another indication of shooter error or a bad load.
Average Elevation and Windage Error
The Average Elevation and Windage Errors compare a group's statistical center to the point of aim. It accurately indicates where the group center is located (or average shot impacted) with a set of vertical and horizontal dimensions. The two measurements show how well the firearm is sighted to hit the Bullseye and can be used to adjust sights if the results are converted to Minutes of Angle.

To view a graphic that visually maps a target with these measurements enter http://rsi.sedona.net/Samples/TA.html; or to pass on comments and questions contact:
Jim Ristow c/o Recreational Software, Inc.
rsi@sedona.net
http://rsi.sedona.net