Estimating flight trajectories of breaking balls from four-seam fastballs

It is widely acknowledged that understanding the physical mechanics of the flight trajectories of four-seam fastballs and breaking balls is crucial for players and coaches to enhance pitching performance. The characteristics of the flight trajectories of four-seam fastballs and breaking balls have been revealed; however, the relationship between them has not been examined. Here, we show the characteristics of the flight trajectory of breaking balls from the four-seam fastballs. We found that the direction of the deviation of the curveballs could be generally predicted from that of the four-seam fastballs. We also found that the limits of the deviation of the sliders can be determined from the direction of the deviation of the four-seam fastball. This study revealed the deviation of the breaking ball from the four-seam fastballs, which clearly showed the differences in the characteristics between curveballs and sliders. This study moved forward with the description of the physical properties of each pitch type and allowed us to obtain valuable insights and practical implications.