Nonparametric Statistics and Sports Analytics

在过去的几十年里，记录和存储的数据量和种类出现了巨大的爆炸性增长。这对现代数据分析的前沿问题的类型和复杂性产生了很大的影响，不仅在科学的所有领域，而且在其他重要的应用领域，包括体育分析。特别是，我对足球分析非常感兴趣，因为现在可以获得完整的事件数据(球门时间和球员、球门射门等)。跟踪数据(每个球员和球在球场上的位置在非常精细的时间尺度上，比如每十分之一秒)开始可用。因此，每个游戏的海量数据集都会被获得，并且必须经过仔细的处理才能提取有用的信息。至关重要的是，使用所有可用的数据，并通过监控球员和团队行为的能力，可以更好地了解游戏的各个阶段和团队战略。球员的行为和教练的决定也可以被客观地评估。拟议研究方案的总体目标是开发统计工具来协助完成这些任务。其中一套工具与统计深度的概念有关。一般来说，深度函数是对一个对象在一组其他相似对象中的中心程度的度量，从而允许人们对一组复杂对象进行“排序”。例如，这一概念在异常值检测和分类中很有用，这两项任务是统计学习的核心。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，并为移动对象、轨迹和与体育分析相关的其他类型的数据开发深度。对上述任务有用的第二套工具与平滑估计的概念有关，特别是与构建携带关于手头问题的重要信息而同时做出尽可能少的技术假设有关的曲线有关。与足球分析相关的简单例子是得分率，即球队失去对球的控制的可能性，作为当前比赛情况的函数。拟议方案的第二个主要目标是研究这样的方法，特别是考虑到球员或团队的战略。最后，通过这项提议引入的方法将可用于国际比赛，特别是加拿大的国家队。在未来，这些球队应该在很大程度上依赖于高级分析：他们在球员组成中看到的变异性，以及他们相对较短的准备时间，导致了重要事件的发生，迫使教练迅速调整他们的策略。顺便说一句，开发的技术还将大大增强统计学家分析移动物体和复杂轨迹的工具箱，鉴于全球定位系统数据的可用性增加，这可能有助于许多其他研究领域。

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.