# Magnus-Forces Analysis of Pitched-Baseball Trajectories Using YOLOv3-Tiny Deep Learning Algorithm
## 5 Conclusions  
In this study, pitched-baseball characteristics were analyzed to observe the effects of Magnus force on a pitched-baseball trajectory from TV broadcast videos using the aerodynamic theory. Moreover, an automatic measurement and analysis system was established by YOLOv3-tiny for the pitched-baseball trajectories, speeds, and spin rates. Finally, a system was used to automatically present pitching data, such as the throw point, catch point, pitch angle, ball speed, spin rate, vertical displacement, and ball trajectory on the screen. According to the results of 30 testing videos of pitched baseballs, this system fully grasped the baseball trajectories, throw points, catch points, and vertical displacements. The average errors of the measured ball speeds and spin rates were 1.88% and 7.51%, respectively, compared to the values of the ball speeds and spin rates provided by the TV broadcast. In addition, this study used the ratio of the spin rate to the ball speed as a parameter to analyze the pitching state of the pitcher's four-seam fastballs. It can be seen from the results of the NPB and MLB matches that when this parameter increased, the Magnus displacement of the ball also increased, thereby decreasing its late break. As a result, the spin rate to ball speed ratio verified that \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Number of Pitches** & **1** & **7** & **19** & **24** & **32** & **41** & **53** & **59** & **66** & **77** & **81** \\ \hline Speed (km/h) & 144 & 144 & 145 & 145 & 144 & 146 & 146 & 143 & 145 & 143 \\ Spin rate (rpm) & 2377 & 2395 & 2398 & 2370 & 2310 & 2344 & 2351 & 2352 & 2426 & 2432 & 2467 \\ Spin/speed & 16.56 & 16.58 & 16.54 & 16.35 & 16.01 & 16.06 & 16.15 & 16.50 & 16.77 & 16.96 & 17.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Pitching state analysis of four-seam fastballs by [PERSON]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Number of Pitches** & **4** & **7** & **9** & **27** & **31** & **32** & **35** & **36** & **48** & **49** & **58** \\ \hline Speed (km/h) & 144 & 147 & 146 & 147 & 145 & 146 & 143 & 143 & 137 & 147 & 143 \\ Spin rate (rpm) & 2398 & 2241 & 2357 & 2219 & 2313 & 2386 & 2415 & 2486 & 2495 & 2441 & 2284 \\ Spin/speed & 16.65 & 15.24 & 16.14 & 15.10 & 15.95 & 16.34 & 16.89 & 17.38 & 18.21 & 16.61 & 15.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Pitching state analysis of four-seam fastballs by [PERSON]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Number of Pitches** & **1** & **10** & **13** & **16** & **26** & **36** & **50** & **55** & **62** & **63** & **64** \\ \hline Speed (km/h) & 155 & 158 & 157 & 154 & 157 & 158 & 154 & 157 & 158 & 153 & 154 \\ Spin rate (rpm) & 2157 & 2377 & 2373 & 2395 & 2378 & 2357 & 2189 & 2216 & 2350 & 2220 & 2228 \\ Spin/speed & 13.93 & 15.01 & 15.15 & 15.59 & 15.12 & 14.96 & 14.22 & 14.10 & 14.87 & 14.47 & 14.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Pitching state analysis of four-seam fastballs by [PERSON]. the late break of the pitcher became smaller, and thus the power of pitching reduced. Using this system, pitching information in the baseball game was easily obtained and recorded for further discussion. The system developed in this study provides scientific pitching data to improve the performance of baseball pitchers. Conceptualization, B.-J.W. ; methodology, B.-J.W., C.-R.C., C.-W.L. and Y.-C.Z. ; software, B.-J.W., C.-R.C., C.-W.L. and Y.-C.Z. ; validation, B.-J.W., C.-R.C., C.-W.L. and Y.-C.Z. ; formal analysis, B.-J.W. ; investigation, B.-J.W. ; resources, B.-J.W. ; data curation, B.-J.W., C.-R.C., C.-W.L. and Y.-C.Z. ; writing--original draft preparation, B.-J.W. ; writing--review and editing, B.-J.W. ; visualization, B.-J.W. ; supervision, B.-J.W. ; project administration, B.-J.W. ; funding acquisition, B.-J.W. All authors have read and agreed to the published version of the manuscript.