Value functions are used in sports applications to determine the optimal action players should employ. However, most literature implicitly assumes that the player can perform the prescribed action with known and fixed probability of success. The effect of varying this probability or, equivalently, "execution error" in implementing an action (e.g., hitting a tennis ball to a specific location on the court) on the design of optimal strategies, has received limited attention. In this paper, we develop a novel modeling framework based on Markov reward processes and Markov decision processes to investigate how execution error impacts a player's value function and strategy in tennis. We power our models with hundreds of millions of simulated tennis shots with 3D ball and 2D player tracking data. We find that optimal shot selection strategies in tennis become more conservative as execution error grows, and that having perfect execution with the empirical shot selection strategy is roughly equivalent to choosing one or two optimal shots with average execution error. We find that execution error on backhand shots is more costly than on forehand shots, and that optimal shot selection on a serve return is more valuable than on any other shot, over all values of execution error.
翻译:然而,大多数文献暗含地假定玩家可以执行已知和固定成功概率的指定动作。在设计最佳战略时,这种概率或等效的“执行错误”对执行某种动作的影响各不相同(例如,打网球到法庭上某个特定地点),在设计最佳战略时,这种效果得到的关注有限。在本文件中,我们根据Markov奖赏程序和Markov决定程序开发了一个新型示范框架,以调查执行错误如何影响玩家的数值功能和网球策略。我们用3D球和2D玩家跟踪数据以数以亿计的模拟网球射击模型为模型提供动力。我们发现,在网球中的最佳射击选择策略随着执行错误的增长而变得更加保守,与实验射击选择策略的完美执行大致相当于选择一或两场最佳射击,平均执行错误。我们发现,反射手射击的执行错误比前针射击的成本要高,对服务回报的最佳射击选择比任何其他射击的价值都要高。