Acceleration and age in soccer

This paper considers how player acceleration changes in soccer relative to age. A plot of average maximum acceleration versus age is produced. The construction of the plot is based on methods from functional data analysis and the availability of tracking data from the 2019 season of the Chinese Super League. For an individual player, we calculate his maximum acceleration for each single match of the 2019 season. Since the players' maximum accelerations are observed only on a single season instead of their entire careers, we treat them as incomplete functional data, called functional snippets. The average maximum acceleration, i.e., the mean function of the functional snippets rather than full curves is estimated by a local linear smoothing method. The most important observation is that the shape of the acceleration curve closely resembles curves of soccer performance versus age. This observation has implications for predicting future performance since acceleration is more easily and more accurately measured than performance.