A D-2 distance–accuracy law of human throwing: theory and experiments in pétanque shooting

We present an experimental and theoretical study of accuracy in pétanque shooting. Field measurements across distances and targets size (boule and jack) show that the probability of a direct hit exhibits an inverse–square dependence on distance. This distance–accuracy law holds for elite men, elite women, juniors and for amateurs alike, revealing a robust human characteristic of throwing. A minimal physical model accounts for these trends by separating three elements—geometry, style (the coupled choice of release angle and speed), and execution variability (shot-to-shot reproducibility). Within this framework the inverse–square dependence emerges naturally, while the prefactor reflects skill and target size, yielding interpretable metrics for performance and training.