# Leslie 1993

# Leslie, 1993, *Is "Group Size" the Best Measure of Accuracy?*

*Is "Group Size" the Best Measure of Accuracy?*, John "Jack" E. Leslie III, 1993.

Abstract:

- Extreme Spread: Maximum distance between any two shots in group. Notes that this effectively only uses two data points.
- Figure of Merit (FoM): Average of the maximum horizontal group spread and the maximum vertical group spread. This uses only 2-4 data points depending on the group. Like Diagonal, FoM becomes more efficient than Extreme Spread for larger group sizes.
- Mean Radius: Average distance to center of group for all shots.
- Radial Standard Deviation: Sqrt (Horizontal Variance + Vertical Variance).
- Found military using RSD and Mean Radius as early a 1918.

His Monte Carlo analysis shows sample RSD to be most efficient predictor of precision, followed closely by Mean Radius. I.e., they can distinguish between loads of different inherent precision more accurately and using fewer sample shots than the other measures.

Note that, like Grubbs, Leslie estimates MR by sampling the mean of radii. This is less efficient than using the Rayleigh estimator on the radii, and than computing MR based on the sample Rayleigh parameter. The latter process is equally and maximally efficient for all invariant measures that are products of the Rayleigh parameter σ.

# Corrections

Ref 3 should be **Stephen** not Steven, and **Mosin-Nagant** not Moisin-Nagant