The Technoid Takes Gauss…


Your new Holland and Holland sporting clays gun was specially choked in England by a famed necromancer of that black art. You paid extra, but you got the best. You are certain that its patterns will be superior to the old Mossberg lurking in the back window of your pickup truck. Well- ‘taint necessarily so. This is deep stuff, so pull on your boots and step in with the Technoid.

You see, shotgun patterns, Holland’s and Mossberg’s together, are Gaussian in nature. Carl Gauss was a late eighteenth century German mathematician who contributed greatly to the knowledge of the bell shaped curve, also called a ‘normal’ distribution. Most succinctly, he showed that certain seemingly separate random processes, when taken as a group, act in a predictable manner. This predictable manner is called a ‘normal’ distribution and is mathematically and graphically expressed as a bell shaped curve.

So, what does it mean to us as shooters? At the end of the nineteenth century a French ballistician named JournÇe was doing some work for the French army. He noted that when many rifle bullets were fired at a single target, the highest percentage hit near the center and then the hits became fewer and fewer as the distance from the center increased. Careful analysis of many such targets showed that the bullet distributions mathematically followed Gauss’s bell shaped curve and produced a ‘normal’ distribution. This was significant because it meant that such seemingly random clusters of bullet holes were regularly obeying unyielding mathematical laws when taken as a group. It meant that statistically JournÇe could predict performance of groups of bullets. Although each bullet fired was a random event, together their group performance was predictable.

Cut to the 1970s. Mid-western graduate students Oberfell and Thompson wrote a scientific book on shotgun patterning, which has been considered a leader in the field for the past twenty years. In it they went to extremes to calculate the difference between good patterns and bad patterns based on the number of 5″ holes in the pellet spread. They attempted to show that proper load development and choking could result in a shot pattern with a more even distribution and fewer holes, even though the total percentage of shot in the circle was unchanged. They felt that one 60% pattern could be better than another 60% pattern because shotgun pellets worked in concert with each other. There was sort of a group influence, as opposed to JournÇe’s bullets randomly functioning as individuals.

Recently, shotgun ballisticians on both sides of the Atlantic (Messrs. Lowery, Giblin and Brindle) have concluded that the shot pellets, once well clear of the barrel, act independently- like JournÇe’s bullets. Each pellet is on its own and subject only to the higher law of the bell shaped curve. Oberfell and Thompson’s idea that there is a repeatable group harmonic is rejected. This means that no matter what you do, if you shoot enough patterns with the same total pellet count in each pattern (that is important), the number of 5″ holes (pellet distribution) will even out and follow a bell shaped curve ‘normal’ distribution. There is no such thing as a consistently high quality or low quality pattern just as long as they all have the same number of pellets in the same sized circle.

For example, let us say that you find a load and choke combination from your Mossberg which produces a 60% pattern at 40 yards. You then shoot 100 patterns. Then you find a choke and load combination (same pellet count) which shoots a 60% pattern from a high quality, custom choked gun. You shoot 100 patterns. If you compare those 200 patterns, you will find that the custom choked gun produces 60% patterns which are no better or worse than the 60% patterns produced by the cheaper gun. They will both follow the normal distribution of the bell shaped curve and the number of 5″ voids will average out equally from both guns.

If all 60% patterns of the same pellet count and in the same circle average the same number of holes in the long run, does this mean that there is no difference between low quality chokes and cheap shotshells as opposed to the good stuff? Not hardly. There is a big difference. Custom chokes and high quality shotshells are worth it because they enable you to achieve a certain pattern percentage performance which may be totally unobtainable with inferior equipment.

Good chokes and good shot may achieve a 60% pattern with a .020″ (modified) choke. Cheap chokes and shot may require .035″ (full) choke to reach that performance. At this stage the patterns would be mathematically equal, both following the same bell shaped curve.

Now look at the next step and suppose you want a 70% pattern. The good choke/good shot combination can achieve 70% by using somewhat more constriction. The cheap choke/cheap shot cannot achieve that number by any means. The difference between good and bad has just emerged. The bell shaped curve no longer applies because the poor equipment cannot deliver the basic percentage required.

The equipment quality difference becomes even more pronounced when shot string on a crossing target is considered because that makes it even harder to produce a pattern of a given percentage. That bell curve equality only applies when each shotgun can achieve the same percentage and the cheap stuff often cannot achieve the high percentages.

So what is the bottom line? There is no statistical difference in patterns of the same percentage, regardless of which shotgun produced them. There is no point in counting holes in the pattern, just count the pellets in the shot load and then in the circle. Cheap chokes and shotshells can be made to equal the performance of good equipment up to a certain distance. At longer range good equipment wins out.

Junior Technoids- At Ease! Take off the boots, you are now clear of the bovine remnants.

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One Response to The Technoid Takes Gauss…

  1. Doug kubosh says:

    Pretty deep, considering most will never pattern their gun but will have all kinds of opinions on different ammo, chokes, barrel length, etc. Does it matter to most if they are right or wrong? Not really if they smile when they shoot. And, reality most prefer a good looking gun even if the 500 Mossberg patterns better.

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