Challenges and Models for the Analysis of Functional Data in Sports

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With new developments in sports technology, data are recorded continuously on a large-scale over finer and finer grids. For example, detailed player tracking data captures the two-dimensional coordinates of all players and the ball during each play at a rate up to 30 Hz. Functional data analysis (FDA) is an increasingly useful tool for analyzing such data. More generally, FDA deals with the analysis and theory of functions, surfaces, or any multidimensional functions. The theme of my research program is the development of new statistical models and methods to analyze spatio-temporal data and large-scale and complex functional data in sports. The first long-term objective of my research program is to develop novel and practical FDA methods to analyze spatio-temporal data in sports. We will study spatio-temporal tracking data and event data. Event data are chronological records of well-defined match events, such as passes, shots, and fouls, and are recorded with timestamps. The research program will provide a series of novel developments. For example, a conventional method for analyzing spatio-temporal data in sports is to discretize the playing area into subdivisions, construct an intensity matrix by counting the number of events in each region and apply matrix factorization on the intensity matrix. In our research, we assume a continuous and smooth intensity function and we aim to develop novel FDA methods for estimating the intensity function and simultaneously achieve a low-rank structure. We expect to discover a spatial representation from the low-rank structure and provide sports insights such as the offensive and defensive roles of players. We will also propose regression models that involve spatial functional objects and develop regularization methods for dimension reduction. The large-scale and complex functional data in modern sports introduce both computational and statistical modelling challenges. The second long-term objective of my research program is to propose a collection of interpretable FDA models to accommodate the large-scale and complex functional data in sports. For instance, we will develop subsampling-based functional regression models. Another example is that we will propose a multiresolution approach to cluster large-scale spatial functional data. The research theme is expected to establish frameworks for analyzing a variety of large-scale and complex functional data in sports and simultaneously develop more flexible yet interpretable FDA models to gain insights into different types of sports. We have connections to national and provincial Canadian sports organizations and we expect the proposed research program is useful in providing a competitive advantage to Canadian sports teams and individual players. The proposed objectives will be of interest to researchers in the field of sports analytics. At the same time, the proposed FDA models also have many applications in natural sciences and other scientific areas.