标题： 足球中控球与最高速度之间的相互作用：耐力因素 显示英文标题

标题： Interplay between pitch control and top speed in soccer: The stamina factor

摘要： 本研究探讨了足球比赛中球员速度与控球能力之间的相互作用。我们提出了一种新的场地控制算法，该算法量化了球员在球场任意位置获得控球权的概率。我们的模型通过测量比赛中的表现并为每位球员分配特定的最快速度来考虑球员速度的异质性。然后，我们将基于我们方法得出的场地控制百分比与经典模型（假设所有球员具有相同的最快速度）的结果进行比较，并分析不同角色球员（后卫、中场和前锋）的结果。我们的发现揭示了球员最快速度与其累积场地控制之间存在正相关关系，某些球员从这种关系中受益更多。然而，这种正相关关系受到球员在球队中角色的限制，尽管不是最快的球员，但后卫实现了最高的累积场地控制。此外，我们的方法支持团队层面的分析，识别哪些球队能从球员最快速度中获得最大的优势，并扩展到对比赛上半场和下半场的比较。我们的模型还能够探索顶级速度的变化如何影响个体和团队层面的场地控制。为此，我们引入了一个耐力因子，该参数调整球员的最快速度。我们发现耐力因子对场地控制的影响遵循对数函数，缩放因子量化了速度增加带来的潜在好处。有趣的是，耐力因子对场地控制的影响因球员位置而异。总体而言，我们的方法为哪些球队或球员可能从身体表现的改进中获益最多提供了有价值的见解。 显示英文摘要

摘要： In this study, we investigate the interplay between player speed and ball control in soccer. We present a novel pitch control algorithm that quantifies the probability of a player gaining possession at any location on the field. Our model accounts for the heterogeneity of player speeds by measuring performance during matches and assigning each player a specific top speed. We then compare the pitch control percentages derived from our approach with those from classical models, which assume uniform top speeds for all players, and analyze the results across different player roles (defenders, midfielders, and forwards). Our findings reveal a positive correlation between a player's top speed and their accumulated pitch control, with certain players benefiting more from this relationship. However, this positive correlation is constrained by the role of the player in the team, with defenders achieving the highest accumulated pitch control despite not being the fastest. Furthermore, our methodology supports team-level analysis, identifying which teams gain the greatest advantage from their players' top speeds, and extends to comparisons between the first and second halves of matches. Our model also enables exploration of how changes in top speed may affect pitch control at both the individual and team levels. To facilitate this, we introduce the stamina factor, a parameter that adjusts a player's top speed. We find that the impact of the stamina factor on pitch control follows a logarithmic function, with the scaling factor quantifying the potential benefits of increased speed. Interestingly, the influence of the stamina factor varies significantly by player position. Overall, our approach provides valuable insights into which teams or players could benefit most from improvements in physical performance.