# Magnus-Forces Analysis of Pitched-Baseball Trajectories Using YOLOv3-Tiny Deep Learning Algorithm
## 1 Introduction
Multi-angle tracking uses images from multiple angles to reconstruct three-dimensional spatial information to track a baseball. A well-known commercial baseball data analysis software, K Zone [8], which has been used in baseball games, uses three-angle images to track the baseball's location, and it is expensive to build. The literature used TV broadcasting to analyze baseball trajectories from a single perspective [9]. It used a positive frame difference image and morphological operations to filter the background and then used size, shape, compactness, and Kalman filters to filter noise to detect and record baseball flight trajectories. In addition, the literature used a high-speed camera to capture real-time images of the seams on the surface of the baseball and calculated the speed of the baseball through the relative displacement between the seam positions of each image [10]. When performing morphological processing or applying filters, many parameters need to be adjusted individually for different videos. The afterimages produced by broadcasting cameras distort the shape of the baseball, making it difficult to recognize a baseball using shape recognition for circular object detection, such as the Hough transformation [11]. Moreover, when using colors to identify baseballs, each scene has a different light and shadow background, and the color of the baseball on the screen may no longer be pure white, making it necessary to adjust the color mask parameters for different videos. Using deep learning to adjust the chroma, saturation, size, and exposure of each image during training can easily solve the problem of using shape, size, and color to detect the baseball. Furthermore, an optimized deep learning model (increasing the number of training samples) is more accurate for baseball detection. This saves a great amount of adjustment time and cost compared to image recognition optimization. In recent years, a significant amount of research has been conducted on the development of deep learning algorithms [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26]. The You Only Look Once (YOLOO) machine learning object-recognition algorithm developed by [PERSON] and [PERSON] vividly describes the characteristics of the multiple-object-tracking algorithm from input to output using only a single-stage neural network to train and target the image [17; 18]. It overcomes the shortcoming of traditional object detection, that is, individual objects must be trained and detected separately, and simultaneously increases the computing performance considerably. Moreover, many recent studies have adopted YOLOv3 [17; 19; 20; 23; 26], which has the advantages of the previous generation algorithms, an updated multi-scale detection function with a more powerful feature extraction network, and improved accuracy and performance. YOLOv4 [24; 25; 26] utilizes spatial pyramid pooling and a path aggregation network to improve the performance of YOLOv3. However, because the baseball thrown by the pitcher is fast and live-action TV videos like sports and concerts are typically at least 24 fps or more [27], this study used YOLOv3-tiny algorithm to speed up the calculation [18]. While its accuracy is not as high as that of YOLOv3 and YOLOv4, it exhibits high performance and its computing speed is close to the real-time speed of the ball in live-action TV videos [19; 23; 26]. This algorithm is used along with the aerodynamic theory to recognize baseballs and analyze the characteristics of throw points, catch points, and vertical displacements of pitched baseballs from the TV broadcast videos. Eventually, using the ratio of the spin rate and ball speed as a parameter to analyze the pitching state of the pitcher's four-seam fastball in the Nippon Professional Baseball (NPB) and MLB matches for the late break of the pitched baseball due to the Magnus effect. It also provides baseball broadcast units with pitching information of the pitchers to enhance fans' satisfaction while watching the games.