This study investigates and quantifies some possible sources affecting the position of impact points of small caliber spin-stabilized projectiles (such as 12.7 mm bullets). A comparative experiment utilizing the control variable method was designed to figure out the influence of tiny eccentric centroids on the projectiles. The study critically analyzes data obtained from characteristic parameter measurements and precision trials. It also combines Sobol’s algorithm with an artificial intelligence algorithm—Adaptive Neuro-Fuzzy Inference Systems (ANFIS)—in order to conduct global sensitivity analysis and determine which parameters were most influential. The results indicate that the impact points of projectiles with an entry angle of 0° deflected to the left to that of projectiles with an entry angle of 90°. The difference of the mean coordinates of impact points was about 12.61 cm at a target range of 200 m. Variance analysis indicated that the entry angle — i.e. the initial position of mass eccentricity — had a notable influence. After global sensitivity analysis, the significance of the effect of mass eccentricity was confirmed again and the most influential factors were determined to be the axial moment and transverse moment of inertia (Izz Iyy), the mass of a projectile (m), the distance between nose and center of mass along the symmetry axis for a projectile (Lm), and the eccentric distance of the centroid (Lr). The results imply that the control scheme by means of modifying mass center (moving mass or mass eccentricity) is promising for designing small-caliber spin-stabilized projectiles.