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 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 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.
HerrmannEE. Exterior ballistics. Annapolis, MD: U.S. Naval Institute, 1935.
2.
GrubbsFE. On the distribution of the radial standard deviation. Ann Math Stat1944; 15(1): 75–81.
3.
ChewVBoyceR. Distribution of badial error in the bivariate elliptical normal distribution. Technometrics1962; 4(1): 138.
4.
HoytRS. Probability functions for the modulus and angle of the normal complex variate. Bell Syst Tech J1947; 26(2): 318–359.
5.
Nakagami M. The m-distribution—a general formula of intensity distribution of rapid fading. In:Statistical methods in radio wave propagation. Elsevier, 1960, pp.3–36.
ParkJL. Modelling archers’ scores at different distances to quantify score loss due to equipment selection and technique errors. Proc IMechE, Part P: J Sports Engineering and Technology2014; 228(4): 250–258.
8.
ParkJL. The relative performance levels of archers in ranking rounds and matches. Proc IMechE, Part P: J Sports Engineering and Technology2020; 235(1): 29–35.
ParkJLLarvenJE. Analysis of scores and arrow grouping at major international archery competitions. Proc IMechE, Part P: J Sports Engineering and Technology2014; 228(2): 86–94.
