Video analysis and mathematical reconstruction of three-point shot trajectories in Basketball: Validation through physical modeling

Three-point shooting accuracy has become increasingly critical in modern basketball, yet comprehensive biomechanical analysis remains prohibitively expensive and inaccessible for most training programs. Kinovea, a free open-source video analysis software, offers a promising alternative but requires rigorous validation against established biomechanical principles. This study aimed to validate Kinovea's measurement reliability for shooting kinematics, verify measurement consistency with parabolic motion physics, and identify kinematic parameters that discriminate successful from missed shots. Eight competitive U18 male basketball players performed 34 three-point shots from the wing position at regulation distance (7.24 m). Shots were filmed at 60 fps using high-definition cameras positioned perpendicular to the shooting plane. Ball trajectories were manually tracked frame-by-frame using Kinovea 0.9.5 software. Four kinematic parameters were extracted: projection angle (θ), initial velocity (v₀), maximum trajectory height (h_max), and foot orientation. Trajectories were mathematically modeled using classical projectile motion equations. Between-group comparisons employed independent t-tests with Cohen's d effect size calculations. Of the 34 shots analyzed, 14 were successful (41.2%) and 20 were missed (58.8%). Maximum trajectory height emerged as the sole discriminating parameter between successful and missed shots: successful shots reached 5.94 ± 0.27 m compared to 5.71 ± 0.37 m for missed shots, representing a 23 cm difference (p = 0.059, d = +0.68, medium effect). In stark contrast, projection angle showed no difference (57.18° vs. 57.00°, p = 0.810, d = +0.08), nor did initial velocity (9.07 m/s vs. 9.08 m/s, p = 0.894, d = -0.05). The parabolic trajectory model provided consistent mathematical reconstruction of observed trajectories, validating the simplified physics approach.