Functional Ratings in Sports

Competing Process Hazard Function Models for Player Ratings in Ice Hockey

Evaluating the overall ability of players in the National Hockey League (NHL) is a difficult task. Existing methods such as the famous "plus/minus" statistic have many shortcomings. Standard linear regression methods work well when player substitutions are relatively uncommon and scoring events are relatively common, such as in basketball, but as neither of these conditions exists for hockey, we use an approach that embraces the unique characteristics of the sport. We model the scoring rate for each team as its own semi-Markov process, with hazard functions for each process that depend on the …

Bayesian GARCH Modeling of Functional Sports Data

The use of statistical methods in sport analytics has gained a rapidly growing interest over the last decade, and nowadays is common practice. In particular, the interest in understanding and predicting an athlete's performance throughout his/her career is motivated by the need to evaluate the efficacy of training programs, anticipate fatigue to prevent injuries and detect unexpected of disproportionate increases in performance that might be indicative of doping. Moreover, fast evolving data gathering technologies require up to date modelling techniques that adapt to the distinctive features o…

Are Multilevel functional models the next step in sports biomechanics and wearable technology? A case study of Knee Biomechanics patterns in typical training sessions of recreational runners

This paper illustrates how multilevel functional models can detect and characterize biomechanical changes along different sport training sessions. Our analysis focuses on the relevant cases to identify differences in knee biomechanics in recreational runners during low and high-intensity exercise sessions with the same energy expenditure by recording $20$ steps. To do so, we review the existing literature of multilevel models, and then, we propose a new hypothesis test to look at the changes between different levels of the multilevel model as low and high-intensity training sessions. We also e…

Space-Time VON CRAMM: Evaluating Decision-Making in Tennis with Variational generatiON of Complete Resolution Arcs via Mixture Modeling

Sports tracking data are the high-resolution spatiotemporal observations of a competitive event. The growing collection of these data in professional sport allows us to address a fundamental problem of modern sport: how to attribute value to individual actions? Taking advantage of the smoothness of ball and player movement in tennis, we present a functional data framework for estimating expected shot value (ESV) in continuous time. Our approach is a three-step recipe: 1) a generative model for a full-resolution functional representation of ball and player trajectories using an infinite Bayesia…

增强共情准确性：惩罚函数对齐方法以纠正实时情绪感知中的时间错位

Enhancing Empathic Accuracy: Penalized Functional Alignment Method to Correct Temporal Misalignment in Real-time Emotional Perception

针对共情准确性评估中时间错位问题，提出基于平方根速度框架和正则化约束的对齐方法，通过约束动态规划实现高效对齐，在模拟和真实数据上优于传统方法。

A Skellam Regression Model for Quantifying Positional Value in Soccer

Soccer is undeniably the most popular sport world-wide and everyone from general managers and coaching staff to fans and media are interested in evaluating players' performance. Metrics applied successfully in other sports, such as the (adjusted) +/- that allows for division of credit among a basketball team's players, exhibit several challenges when applied to soccer due to severe co-linearities. Recently, a number of player evaluation metrics have been developed utilizing optical tracking data, but they are based on proprietary data. In this work, our objective is to develop an open framewor…

Universal temporal features of rankings in competitive sports and games

Many complex phenomena, from the selection of traits in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which may eventually lead to stratified structures such as the wealth distribution worldwide. However, it is still unclear whether the road to hierarchical complexity is determined by the particularities of each phenomena, or if there are universal mechanisms of stratification common to many systems. Human sports and games, with their (varied but simplified) rules…

信用评级：对资本结构的异质性影响

Credit Ratings: Heterogeneous Effect on Capital Structure

本文利用双重机器学习检验信用评级对杠杆率的异质性因果效应，发现拥有评级总体提升杠杆率，但该效应因具体评级和微调级别而呈现从负到正的渐进异质性变化。

NFL选秀建模：损失函数分析

NFL Draft Modelling: Loss Functional Analysis

本文提出基于范数损失函数和Weibull分布的NFL选秀权估值框架，用于评估选秀交易的公平性与效率，并揭示激进与保守策略之间的权衡。