We propose a framework to analyze the relationship between the movement features of a wheel gymnast around the mounting phase of Unit 2 of the vault event and execution (E-score) deductions from a machine-learning perspective. We first developed an automation system from a video of a wheel gymnast performing a tuck-front somersault to extract the four frames highlighting its Unit 2 performance of the vault event, such as take-off, pike-mount, the starting point of time on the wheel, and final position before the thrust. We implemented this automation usingrecurrent all-pairs field transforms (RAFT)andXMem, i.e., deep network architectures respectively for optical flow estimation and video object segmentation. We then used a markerless pose-estimation system calledOpenPoseto acquire the coordinates of the gymnast’s body joints, such as shoulders, hips, and knees then calculate the joint angles at the extracted video frames. Finally, we constructed a regression model to estimate the E-score deductions during Unit 2 on the basis of the joint angles using an ensemble learning algorithm calledRandom Forests, with which we could automatically select a small number of features with the nonzero values of feature importances. By applying our framework of markerless motion analysis to videos of male wheel gymnasts performing the vault, we achieved precise estimation of the E-score deductions during Unit 2 with a determination coefficient of 0.79. We found the two movement features of particular importance for them to avoid significant deductions: time on the wheel and angles of knees at the pike-mount position. The selected features well reflected the maturity of the gymnast’s skills related to the motions of riding the wheel, easily noticeable to the judges, and their branching conditions were almost consistent with the general vault regulations.