Nonparametric Statistics and Sports Analytics

在过去的几十年里，记录和存储的数据的数量和种类都出现了巨大的爆炸式增长。这对所有科学领域的现代数据分析前沿问题的类型和复杂性产生了重大影响，也对包括体育分析在内的其他重要应用领域产生了影响。特别是，我对足球分析非常感兴趣，现在可以获得完整的事件数据（时间和参与进球的球员，射门等）以及跟踪数据（每个球员和球在非常精细的时间尺度上的位置，比如每十分之一秒）开始可用。因此，每个游戏的大量数据集都被获得，必须仔细处理以提取有用的信息。最重要的是，使用所有可用的数据并监控玩家和团队行为的能力，你可以更好地理解游戏的阶段和团队策略。玩家的行动和教练的决定也可以被客观地评估。拟议研究计划的总体目标是开发统计工具来协助完成这些任务。其中一组工具与统计深度的概念有关。一般来说，深度函数是衡量一个对象在一组其他类似对象中的中心位置，从而允许人们对一组复杂对象进行“排序”。例如，这个概念在离群值检测和分类中是有用的，这是统计学习的两个核心任务。拟议研究计划的第一个主要目标是进一步研究现有的统计深度概念，并为运动物体、轨迹和其他与体育分析相关的数据类型开发深度。对上述任务有用的第二组工具与平滑估计的概念有关，特别是与曲线的构造有关，这些曲线携带有关手头问题的重要信息，同时尽可能少地进行技术假设。与足球分析相关的简单例子是得分率，或者球队失去对球的控制的概率，作为当前比赛情况的函数。该计划的第二个主要目标是研究这些方法，特别是考虑球员或球队的战略。最后，通过这项建议采用的方法将适用于国际比赛，特别是适用于加拿大的国家队。在未来，这些团队应该在很大程度上依赖于高水平的分析：他们在球员组成中看到的变化，以及他们在重要赛事中相对较短的准备时间，迫使教练迅速调整他们的策略。顺便提一下，发展起来的技术也将大大增强统计学家分析运动物体和复杂轨迹的工具箱，鉴于GPS数据的可用性增加，这有可能为许多其他研究领域做出贡献。

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.