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

In particular:

Synopsis

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 must be used with care since it is 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.

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 how many sighter shots you should take.
  • 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.