To obtain a comparative standard value for the measurement data of the pitcher’s ball speed and spin rate, this study used 30 home-game videos of the Fukuoka Softbank HAWKS baseball team, including real-time displays of the ball speed and spin rate by the Fox Networks Group. The testing videos of the pitched baseballs included four-seam fastballs, forkballs, and change-up balls. This automatic measurement and analysis system of pitched-baseball trajectories showed the pitch angle, speed, spin rate, vertical movement, and other information of the flying baseball in real time. Moreover, this study made a numerical comparison of the measurement results with the ball speed and spin rate provided by the broadcasting unit, and the related automatic measurement results are shown in
Figure 8,
Figure 9 and
Figure 10 and
Table 3. In
Figure 8,
Figure 9 and
Figure 10, the measurement results of this study are shown in the upper left corner, and the measurement results of the broadcast unit are shown in the lower right corner. The trajectories and the coordinates of the throw point and catch point of the pitched baseball are represented for four-seam fastball, forkball, and change-up ball in
Figure 8,
Figure 9 and
Figure 10, respectively. The three bounding boxes with classification confidences and coordinates of the ball by YOLOv3-tiny in the trajectory of pitched baseball are depicted in
Figure 8,
Figure 9 and
Figure 10, respectively. Most values of classification confidence in this study are close to 100%. However, the worst classification confidence of 69.1% is presented in
Figure 10, because the ball was flying between a red billboard and green grass when the ball in the video was recognized. According to the measurement results in
Table 3, this algorithm accurately recorded the trajectory of the ball. The average error of the measured ball speed was 1.88% with a standard deviation of 1.16, and the average error of the measured spin rate was 7.51% with a standard deviation of 4.33.
According to Equation (15), the ball speed estimation method in this study is related to the number of frames per second (fps) of the video. The test video in this study was at 30 fps, and the single-frame interval was 0.0334 s. Errors between the measured ball speed and the actual ball speed are due to the minimum measurement resolution of the time parameter in the denominator of Equation (15). In addition, the spin rate estimation using Equation (14) and the pitch angle have a significant correlation. The detection of the ball at the moment of the pitcher’s throw can easily cause a sensing error, which causes an error in the calculation of the pitch angle, ultimately leading to an error between the measured spin rate and the actual spin rate. In addition, as seen from the measured results in
Table 3, the ball speeds of the four-seam fastballs are in the range of 145–154 km/h, and the spin rates are the highest among the three pitch types, ranging from 2082 to 2477 rpm. Moreover, the Magnus displacements are between 0.64 and 0.72 m in the upward direction. The ball speeds of the forkballs are between 134 and 144 km/h, the spin rates are between 976 and 1515 rpm, and the Magnus displacements are between 0.45 and 0.58 m in the upward direction, which were the smallest among the three pitch types. Due to the downward displacement caused by air resistance and gravity, a small Magnus displacement results in a large downward displacement of the forkball. Finally, for the change-up ball, the ball speeds are between 133 and 138 km/h (slowest among the three pitch types), the spin rates are between 1539 and 2009 rpm, and the Magnus displacements are between 0.59 and 0.69 m in the upward direction. 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 Magnus 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 (Manabu Mima), as shown in
Table 4. Manabu Mima 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 Manabu Mima increases in the four-seam fastballs from the 27th to 48th ball, which also means that the late break of this pitcher decreases. According to the actual game situation of the 27th to 48th ball (in the third inning), Manabu Mima lost three points in this inning. Additionally, this study analyzed the MLB matches on 14 and 18 April 2022, respectively, as shown in
Table 5 and
Table 6. Shohei Ohtani (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 Shohei Ohtani increases in the four-seam fastballs from the 10th to the 36th ball and after the 62nd ball, which also means that the late break of this pitcher decreases. According to the actual game situations of the 10th to 36th ball (in the second inning) and the 62th to 70th ball (in the fourth inning), Shohei Ohtani lost four and two points in the second and fourth innings, respectively. In the match on 18 April 2022, Clayton Kershaw (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. According to the results in
Table 6, this parameter for Clayton Kershaw increases in the four-seam fastballs from the 59th to 81se ball, which also means that the late break of this pitcher decreases. According to the actual game situation of the 59th to 81st ball (from the fifth to sixth innings), Clayton Kershaw lost one and three points in the fifth and sixth innings, respectively. Therefore, it was verified through the parameter of the spin rate to ball speed ratio that the late break of the pitcher became smaller, thereby reducing the power of pitching.