Shot distribution in target archery, with application to arrow selection

Abstract

This work examines the distribution of shots in target archery. In previous work, based on a small sample size, it was concluded that the radial distance [Formula: see text] from the centre of the target to the point of impact had a half-normal distribution. In this work, with a very large sample size, we find that [Formula: see text] follows a Rayleigh distribution very closely, and that only varying the scale, this holds for subpopulations of interest: compound, recurve, male, female, indoors, outdoors and from intermediate to elite skill level. The importance and utility of an accurate statistical model of shot distribution is demonstrated by developing a model of the expected increase in qualification score due to arrow diameter, and the probability of winning head-to-head matches, conducted under World Archery rules. It is concluded that the choice of shot distribution has a significant impact on the accuracy of predictive models of archery performance and that shot distribution is accurately characterized by the Rayleigh distribution. It is found that there are substantial benefits in selecting the maximum permitted arrows shaft diameter, for indoor archery. The benefits vary with archer skill level but are not confined to elite archers.