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This site explains and demonstrates statistics for analyzing the precision of guns.

In particular:


When testing a gun, shooter, and/or ammunition the most popular measure is Extreme Spread or "size" of a sample target group. However, as we will illustrate throughout this site, Extreme Spread is not only a statistically inefficient measure but also one frequently and easily abused.

We advocate for size-invariant measures like Circular Error Probable or Mean Radius. The expected value of these does not change with the number of shots on target. Instead taking more shots serves only to reduce the statistical error in our measurement.

Since shooting large samples on a single target risks developing ragged holes where data points are lost, there are three recommended approaches to efficiently build data sets for estimating precision. These are explained in more detail in Measuring Tools:

  1. Use Danielson's 2-shot method: Fire two shots per target and use calipers to measure their distance from each other. This provides two samples per target with radius r = spread / 2.
  2. Fire one shot per target. Manually overlay them or use software like OnTarget Target Data System to automatically aggregate them into a single sample group.
  3. Use a logging electronic target. (Not yet widely available.)

Furthermore, if we assume that the inherent shot dispersion is free of directional bias then we can use closed-form expressions to calculate and analyze precision.

Examples of the application of these methods and tools include:

  • Determining the likelihood of a hit on a particular target by a zeroed shooting system.
  • Comparing the inherent precision of different shooting systems.
  • Determining which ammunition shoots better in a particular gun.