Shot distribution in target archery, with application to arrow selection.

This article investigates the statistical distribution of shot placements in target archery, concluding that the radial distance \( R \) from the target center follows a Rayleigh distribution more accurately than the previously assumed half-normal distribution. Using a large dataset of over 220,000 shots from diverse subpopulations—including compound and recurve archers, males and females, indoor and outdoor settings, and varying skill levels—the study confirms that the Rayleigh distribution fits well across these groups, with only scale parameters varying. The research develops a predictive model for archery performance under World Archery rules, incorporating arrow shaft diameter to quantify its impact on expected qualification scores and match-winning probabilities. Results indicate significant benefits in selecting the maximum allowed arrow diameter for indoor archery, with improvements in expected scores and match-winning odds evident across skill levels and bow types, though the magnitude of benefits differs between recurve and compound archery. The study emphasizes that accurate modeling of shot distribution is crucial for reliable performance predictions and equipment selection.