发表机构
Brigham Young University; Teamworks Innovations, Inc.（杨百翰大学; Teamworks创新有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过与大学网球队开展实验，结合贝叶斯两阶段马尔可夫决策过程，研究网球发球的陈述、实际与最优瞄准策略，发现最优第二发球更保守，实际发球中心接近最优值。
AI 中文摘要
我们研究网球运动员在选定的Wide或T区域内应将发球瞄准何处。瞄准发球区边界附近会使发球更难被接回，但会增加失误（fault）概率，形成取决于运动员执行误差的权衡。普通比赛数据因未观测到运动员的预期目标，对执行误差的信息有限。因此我们与杨百翰大学男子网球队成员开展实验：每位运动员确定其认为最优的目标并标记在场地，随后向每个目标反复发球，我们记录精确的弹跳位置。基于这些数据，我们在考虑网接触导致的发球删失（censored）后，估计运动员特定的发球分布，再将其与估计的得分奖励曲面结合，构建具有连续空间动作空间的贝叶斯两阶段马尔可夫决策过程。我们发现，在所有运动员-区域组合中，估计的最优第二发球目标比第一发球目标更保守，这与先前理论一致；同时，运动员的陈述目标通常比最优目标更具攻击性，但其实际发球中心比陈述目标更保守，且明显更接近估计的最优值。
英文摘要
We study how a player's execution error affects the optimal location at which to aim a serve in tennis. Aiming near the service-box boundaries makes a serve harder to return but increases the probability of a fault, creating a trade-off that depends on the player's execution error. Match-play data provide limited information about execution error because players' intended targets are unobserved. We conducted an experiment with Brigham Young University men's tennis players in which players explicitly identified targets they believed to be optimal for their serves. Players then served repeatedly toward their chosen targets, and we recorded the bounce locations. Using these data, we estimate player-specific execution error via a Bayesian hierarchical model that accounts for serves censored by net contact. These distributions define the transition dynamics of a two-period Markov decision process (MDP) representing a point in tennis, where the decision variables are the first- and second-serve aim locations. We solve the MDP for each posterior draw of the execution error distributions, yielding a posterior distribution over each player's optimal aim location. We find that players' stated targets are generally more aggressive than optimal, whereas their realized serve centers are more conservative and markedly closer to the optima.
Comments22 pages, 11 figures
