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This site explains and demonstrates statistics for analyzing the precision of projectile weapons firing a single projectile on a vertical target within the line of sight. A good example would be target shooting with a rifle or pistol. Such weapons as shotguns, mortars, and ballistic missiles would have some similar characteristics, but also have factors that are neglected in the discussions and measurements.
High level topics, which are good places to start exploring the site, include:
- What is Precision?
- 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 target group. However Extreme Spread must be used with care since it is frequently and easily abused. As with all measures, the "best" measurement obtained is meaningless. The proper statistical estimator is an average measurement of some sort. In other words, on average what would the expected value of the measurement be?
Another consideration is that some measures, such as Extreme Spread, changes value when there are more shots in a group. Measures which have such a dependency are variant measures. There are other measures which are invariant measures, like Circular Error Probable or Mean Radius, for which the expected values do not change with the number of shots in a group. Instead having more shots in a group decreases the statistical error of measurement efficiently. Of course the error of either type of measurement can also be decreased by shooting more groups.
Furthermore, by first making assumptions about the inherent shot dispersion, then it is possible to use theoretical distributions 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 has a closed-form expression, then the values can be calculated using an algorithm of some sort. If the values don't have a distribution with a closed form expression, then they can be simulated via Monte Carlo sampling. Using a modern computer allows either type to be analyzed easily.
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.
