Nonparametric Statistics and Sports Analytics

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The last few decades have seen a tremendous explosion in the amount and variety of data that is being recorded and stored. This has had a big influence on the types and complexity of problems at the forefront of modern data analysis in all areas of Science, but also in other important areas of application, including Sports Analytics. In particular, I'm very interested in soccer analytics where it is now possible to get complete event data (time and players involved in goals, shots on goal, etc.) and where tracking data (position on the field of each player and of the ball at a very fine time-scale, like every tenth of a second) is starting to be available. Immense data sets for each game played are thus obtained and have to be carefully processed to extract useful information. Crucially, using all the available data and with the ability of monitoring player and team behavior, one can better understand the phases of the game and team strategy. Player actions and coaching decisions can also be objectively evaluated. The broad goal of the proposed research program is to develop statistical tools to assist with these tasks. One such set of tools is related to the concept of statistical depth. Generally speaking, a depth function is a measure of how central an object is within a set of other similar objects, thus allowing one to "order" a set of complex objects. This concept is useful, for instance, in outlier detection and classification, two tasks at the heart of statistical learning. The first main objective of the proposed research program is to further study existing concepts of statistical depth and develop depths for moving objects, trajectories and other types of data relevant to Sports Analytics. A second set of tools that can be useful for the above tasks is related to the concept of smooth estimation, especially with the construction of curves that carry important information about a problem at hand while making as few technical assumptions as possible. Simple examples relevant to soccer analytics are scoring rates, or the probability of a team losing control of the ball, as a function of the current game situation. The second main objective of the proposed program is to study such methodologies, especially accounting for player or team strategy. Finally, the methodologies introduced through this proposal will be transferable to international competition and, in particular, to Canada's national teams. In the future, these teams should rely heavily on high-level analytics as they become available: the variability they see in player composition and the relatively short preparation time they have leading to important events forces coaches to quickly adapt their strategy. Incidentally, the developed techniques will also greatly enhance the statistician's toolbox for the analysis of moving objects and complex trajectories, which has the potential to contribute to many other fields of research given the increased availability of GPS data.