Since the first thread got locked (another COVID conversation casualty) Rocketman & I have PMed specifically on the pattern efficiency question and he’s shared some excellent insight. With a green light from Dave and an OK from RM, I’ve “continued” the thread and am posting his insights.
“The real definition must include vulnerable area (in square inches) of the target, number of hits of "X" size shot to constitute a lethal dose, a predetermined distance, and a patterning plate. The "target (plate) " can capture the pattern prior to applying the "target." We are not dealing with POI. The target can include a center of one vulnerable area (X sq. in.) and each concentric circle after the center must contain eight times "X" areas divided into single "X" segments. Looks sorta like the center is an undivided pie and each ring thereafter is donut segments. You now look for the largest ring where the eight segments average a lethal dose. Count the shot inside that diameter and divide by the number of shot in the load and multiply by 100 and presto alakazam you have the efficiency. Repeat ten times and actually know something statistically reliable.”
“By the way, most of the claims of magic patterns are rooted in the wide variability of patterns to pattern. Two or three are useful for point of aim/point of impact. Not so for statistical understanding of true pattern performance. It takes ten (or more). Jones's automation of pattern analysis makes this reasonable to actually do; shoot pattern, electronically/digitally photo pattern, feed photo into computer program, repeat nine more times, run analysis program based on ten patterns, and consider the correlation of real life pattern to desired pattern.
Pellets are distributed according to a Rayleigh distribution (there are many statistical distributions based on differing conditions). Rayleigh is based on no/zero probability of any single pellet hitting dead center of the pattern. The normal distribution/bell curve is the most usually assumed for patterns. The variability from pattern to pattern makes the difference between Rayleigh and normal relatively moot. Bear in mind that theoretical/statistical distributions are predictions of future events. In the case of the pattern, the distribution predicts the probability of distance from center pellets will land. Unfortunately the pellets are unaware of said prediction. Fortunately they follow the prediction closely enough for it to be useful.
I have read/heard that "old time" barrel makers made adjustments to choke profile based on single patterns and including said pattern as proof of the barrel's choke. Now, that sounds an awful lot to me like shooting patterns until you get the one you want.”
“Throughout the majority of the stories is a recurring theme of McManus's lifelong love of hunting and fishing—which is mostly an excuse to just enjoy the outdoors, often in good company. Most of his friends likewise enjoy hunting and fishing, even if they aren't particularly good at it. McManus, in his stories, has a certain amount of disgruntlement for people who take great pleasure in the minutiae of various sports (such as encyclopediac knowledge of firearms calibers and ballistics). He refers to firearms enthusiasts as 'gun nuts' and treats their excited sharing of the fine points of ballistic arcs and grain sizes as something to be endured to get on a good hunting trip.” Wikipedia
Actually, by a robust statistical method. The number of samples is determined from variability of the data and the level of confidence desired. Nine would have yielded lower confidence, 12 higher, and 21 very high. The lower the variability the fewer the samples needed for a given confidence. Rifle shooters fire various numbers of shots per group depending on the confidence they are looking for. A three shot group may be fine for a hunting rifle, but is just getting started for a bench rest gun. Rifle groups are also Rayleigh distributions. You could correctly think of a shotgun pattern as a "500 shot" (however many pellets the shell contained) group.
Copyright (c) 1993 - 2021 doublegunshop.com. All rights reserved. doublegunshop.com - Bloomfield, NY 14469. USA These materials are provided by doublegunshop.com as a service to its customers and may be used for informational purposes only. doublegunshop.com assumes no responsibility for errors or omissions in these materials. THESE MATERIALS ARE PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANT-ABILITY, FITNESS FOR A PARTICULAR PURPOSE, OR NON-INFRINGEMENT. doublegunshop.com further does not warrant the accuracy or completeness of the information, text, graphics, links or other items contained within these materials. doublegunshop.com shall not be liable for any special, indirect, incidental, or consequential damages, including without limitation, lost revenues or lost profits, which may result from the use of these materials. doublegunshop.com may make changes to these materials, or to the products described therein, at any time without notice. doublegunshop.com makes no commitment to update the information contained herein. This is a public un-moderated forum participate at your own risk.
Note: The posting of Copyrighted material on this forum is prohibited without
prior written consent of the Copyright holder. For specifics on Copyright Law and
restrictions refer to: http://www.copyright.gov/laws/ - doublegunshop.com will not monitor nor will they be held liable for copyright violations presented on the BBS which is an open and un-moderated public forum.