Gaussian Patterns


Dear Larry:

You asked, “…you continue to refer to patterns as Gaussian,…”” Where is your proof of this very doubtful theory?”

Your question is just right. Everyone should always ask for proof of theories. In this case the short answer is that the proof is in the pudding, or rather, in the pattern data. But since short answers aren’t any fun, bear with me while I expand on this.

When I first started my study of shot patterns quite a few years ago and put together the SPRED model (or theory), which is Gaussian-based, I thought initially that I was the first one to discover that shot patterns followed the Gaussian distribution. After doing more homework, however, I found that the idea had been around since the 1920s, when a French artillery expert named Journee started writing about it. Subsequently, Ed Lowry, John Brindle, and Roger Giblin extended the theory to shotgun patterns. My focus has been on extending the practical applications of this concept with Choke Chooser(tm) and other products.

OK, back to your question: where is our proof? The proof is in the shotgun pattern data sets that have accumulated over the years. If you were sitting here with me, I could show you several batches of data which I think would convince you. It’s harder to do via email, but let me try. I started with some of my own pattern data, then went on to that of Oberfell and Thompson (O&T). The strange thing about O&T is that all the pattern data in their book follow the Gaussian model extremely closely, yet they never explicitly recognized it. They just made no attempts to apply theory. The closest they came was to say that the data “appear to follow the laws of probability”. Loosely translated, that means the Gaussian model.

Another excellent data set comes from the pattern tests performed and published by American Rifleman. With assistance from others, I’ve compiled 21 years of Rifleman data, from 1978 to 1998, consisting of over 300 high-quality data points in all. I plotted these and compared them with the Gaussian model. Again, the agreement is truly remarkable. I’m planning to publish some of these comparisons soon.

Additional, but less convincing, support for the theory comes from statistical reasoning. The Gaussian distribution occurs extensively in nature. That’s why another name for it is the “normal” distribution. After studying these phenomena, theoreticians (i.e., Herr Gauss and others) were able to show the following, probably the most important axiom in the entire field of statistics: data that are influenced by many small and unrelated random effects are approximately normally distributed.

This explains why the normal or Gaussian distribution is everywhere: stock market fluctuations, student weights, daily maximum temperatures, SAT scores, and yes, shot patterns. In the latter case, the travel of each pellet is independently and randomly influenced by numerous small effects: air turbulence, temperature fluctuations, aerodynamic forces on pellet flat spots, and many others.

See, the long answer really is a lot more fun, right?

Best regards and happy shooting,

Warren Johnson

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