论文标题
通过跟踪数据来验证足球运动员Sprint的运动模型
Validation of a motion model for soccer players' sprint by means of tracking data
论文作者
论文摘要
在足球比赛分析中，逐播和跟踪数据的广泛可用性使得测试主要在理论上讨论的数学模型成为可能。足球比赛分析中的重要模型之一是一个运动模型，可预测$ t $ s的玩家的到达点。尽管许多空间评估和通过预测方法都取决于运动模型，但尚未完全阐明每个方法的有效性。这项研究的重点是基于运动方程的冲刺条件下藤村和苏吉哈拉（藤村 - 苏吉拉模型）提出的运动模型。一项先前的研究表明，藤村 - 西吉哈拉模型在足球比赛中无效，因为它会产生圆形到达区域。这项研究旨在使用足球跟踪数据来检查藤村 - 苏吉哈拉模型的有效性。具体而言，我们定量比较了模型和真实数据之间玩家的到达区域。我们表明，玩家到达区域的边界是圆形的，而不是椭圆形，这与模型一致。我们还表明，到达区域的初始速度依赖性满足模型的解决方案。此外，我们提出了一种直接从跟踪数据来估算模型中有效动力学参数的方法，并根据估计参数讨论足球游戏模型的局限性。
In soccer game analysis, the widespread availability of play-by-play and tracking data has made it possible to test mathematical models that have been discussed mainly theoretically. One of the essential models in soccer game analysis is a motion model that predicts the arrival point of a player in $ t $ s. Although many space evaluation and pass prediction methods rely on motion models, the validity of each has not been fully clarified. This study focuses on the motion model proposed by Fujimura and Sugihara (Fujimura-Sugihara model) under sprint conditions based on the equation of motion. A previous study indicated that the Fujimura-Sugihara model is ineffective for soccer games because it generates a circular arrival region. This study aims to examine the validity of the Fujimura-Sugihara model using soccer tracking data. Specifically, we quantitatively compare the arrival regions of players between the model and real data. We show that the boundary of the player's arrival region is circular rather than elliptical, which is consistent with the model. We also show that the initial speed dependence of the arrival region satisfies the solution of the model. Furthermore, we propose a method for estimating valid kinetic parameters in the model directly from tracking data and discuss the limitations of the model for soccer games based on the estimated parameters.
