The role of intrinsic dimension in high-resolution player tracking data - Insights in basketball

Following the introduction of high-resolution player tracking technology, a new range of statistical analysis has emerged in sports, specifically in basketball. However, such high dimensional data are often challenging for statistical inference and decision making. In this article, we employ a state-of-theart Bayesian mixture model that allows the estimation of heterogeneous s (ID) within a dataset, and we propose some theoretical enhancements. Informally, the ID can be seen as an indicator of complexity and dependence of the data at hand, and it is usually assumed unique. Our method provides the capacity to reveal valuable insights about the hidden dynamics of sports interactions in space and time, which helps to translate complex patterns into more coherent statistics. The application of this technique is illustrated using NBA basketball players’ tracking data, allowing effective classification and clustering. In movement data, the analysis identified key stages of offensive actions such as creating space for passing, preparation/shooting, and following through, which are relevant for invasion sports. We found that the ID value spikes, reaching a peak between 4 and 8 seconds, in the offensive part of the court, after which it declines. In shot charts, we obtained groups of shots that produce substantially higher and lower successes. Overall, game-winners tend to have a larger intrinsic dimension, indicative of greater unpredictability and unique shot placements. Similarly, we found higher ID values in plays when the score margin is smaller rather than larger. The exploitation of these results can bring clear strategic advantages in sports games.