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This site explains and demonstrates the statistics which can be used to analyze the precision of weapons systems as demonstrated by their projectile impact points on a two dimensional target. The general situation would be for a weapon firing a single projectile at a target perpendicular to the line of sight, like target shooting with a rifle or pistol. The wiki will discuss some factors of ballistics, but it is not intended to address all the nuances of internal, external, or terminal ballistics. Rather, the focus is primarily on the analysis of the precision of the whole weapon system which can be observed directly by the relative impact points on a target. Some effort will be made to explore the precision of weapons subsystems.
High level topics, which are good places to start exploring the site, include:
- What is Precision?: An important explanation of the difference between precision and accuracy as the terms are used in statistics.
- Describing Precision: Units, terms, and relationships
- Precision Models: Statistical approaches for efficient estimation and inference of precision
- Prior Art: Reviews of past efforts to address this question
- FAQ
Synopsis
When testing a gun, shooter, and/or ammunition the most popular measure is Extreme Spread or "group size" of a sample of target shots. However Extreme Spread must be used with care since it is frequently and easily abused. As with all measures, the single best measurement is meaningless in isolation. The proper statistical estimator would be the "average" (aka expected value) of the measurement.
Another consideration is that some measures, such as Extreme Spread, change value when there are more shots in a group. Measures that have such a dependency will be called variant target measures in this wiki. Measures for which the values do not change with the number of shots in a group, like Circular Error Probable or Mean Radius, will be called invariant target measures in this wiki. For invariant measures as the number of shots on a target increases, rather than the measurement value changing the precision of the measurement improves. Of course for both variant and invariant target measurements the experimental error can also be decreased by shooting more targets and calculating an average measurement over the targets as opposed to trying to make a measurement on a single target more precise.
Furthermore, by first making assumptions about the inherent shot dispersion, then it is possible to use theoretical models to estimate measurements and their precision. The distributions are of two basic types. If the expected values and the expected precision factor for the measurements depend on distributions which have a closed-form expression then the values can be calculated to a desired precision via a deterministic algorithm in polynomial time. If the values don't have a distribution with a closed form expression then they are estimated via a Monte Carlo technique, which is a nondeterministic algorithm and requires non-polynomial time to reach a desired 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.
