# Magnus-Forces Analysis of Pitched-Baseball Trajectories Using YOLOv3-Tiny Deep Learning Algorithm
## 4 Results and Discussion
From Table 3 and Equation (13) it is clear that the smaller the Magnus displacement of the ball, the larger the longitudinal displacement when the ball reaches home base. This also means that there is a larger late break. According to Equations (10)-(12), the Magnus displacement is related not only to the physical parameters of the baseball, but also, more importantly, to the pitch angle, ball speed, and spin rate. Therefore, according to the Magnus displacements, ball speeds, spin rates listed in Table 3, and a least-square fitting algorithm from IEEE Standards [33], the curve-fitting equation between the Magnus displacement and ball speed was obtained with a coefficient of determination (R2) of 0.30. Furthermore, the curve-fitting equation between the Magnus displacement and spin rate was also obtained with an R2 of 0.71, showing a positive correlation between the Magnus displacement and spin rate. As the pitching skill of every pitcher is different, the spin rate of the ball may be different for different pitchers even for the same pitch types and ball speed. Therefore, in this study, the spin rate was divided by the ball speed, and the curve fitting of this ratio was done with the [PERSON] displacement. The curve-fitting equation [33] between the Magnus displacement and the ratio of the spin rate to the ball speed was obtained with an R2 of 0.78. Compared to the spin rate alone, the ratio of the spin rate to the ball speed was found to be more positively correlated with the Magnus displacement. For this reason, this ratio was a more effective parameter for analyzing the late break of the pitcher. This study analyzed the Nippon Professional Baseball (NPB) match between the Tohoku Rakuten Golden Eagles and the Fukuoka Softbank HAWKS baseball team on 6 October 2019. Furthermore, this technology was used to analyze the pitching state of the four-seam fastball of the starting pitcher ([PERSON]), as shown in Table 4. [PERSON] pitched a total of four innings in this game using 62 balls. The speeds of his four-seam fastballs were between 137 and 147 km/h, and the spin rates were between 2219 and 2495 rpm. The parameter of the spin rate to ball speed ratio was between 15.10 and 18.21. According to the results of the previous discussion, the smaller this parameter, the larger the late break phenomenon. Therefore, according to the results in Table 4, this parameter for [PERSON] increases in the four-seam fastballs from the 27 th to 48 th ball, which also means that the late break of this pitcher decreases. According to the actual game situation of the 27 th to 48 th ball (in the third inning), [PERSON] lost three points in this inning. Additionally, this study analyzed the MLB matches on 14 and 18 April 2022, respectively, as shown in Tables 5 and 6. [PERSON] (the starting pitcher of the Los Angeles Angels baseball team) pitched a total of 3.2 innings in this game using 70 balls in the match on 14 April 2022. The speeds of his four-seam fastballs were between 154 and 158 km/h, and the spin rates were between 2157 and 2395 rpm. The parameter of the spin rate to ball speed ratio was between 13.93 and 15.59. According to the results in Table 5, this parameter for [PERSON] increases in the four-seam fastballs from the 10 th to the 36 th ball and after the 62 nd ball, which also means that the late break of this pitcher decreases. According to the actual game situations of the 10 th to 36 th ball (in the second inning) and the 62 th to 70 th ball (in the fourth inning), [PERSON] lost four and two points in the second and fourth innings, respectively. In the match on 18 April 2022, [PERSON] (the starting pitcher of the Los Angeles Dodgers baseball team) pitched a total of 5 innings in this game using 87 balls. The speeds of his four-seam fastballs were between 143 and 146 km/h, and the spin rates were between 2310 and 2467 rpm. The parameter of the spin rate to ball speed ratio was between 16.01 and 17.23.