冰球运动员评分的竞争过程风险函数模型
Competing Process Hazard Function Models for Player Ratings in Ice Hockey
摘要：
评估国家曲棍球联盟（NHL）球员的整体能力是一项艰巨的任务。现有的方法，如著名的“加/减”统计有很多缺点。标准线性回归方法适用于球员换人相对少见且得分事件相对常见的情况，例如篮球，但由于曲棍球不存在这些条件，因此我们使用包含该运动独特特征的方法。我们将每支球队的得分率建模为自己的半马尔可夫过程，每个过程的风险函数取决于冰上的球员。这种方法产生进攻和防守球员能力评级，考虑到队友和对手的质量，比赛情况和其他期望的因素，这些因素本身对比赛结果有意义的解释。此外，由于该模型中的参数数量可能相当大，因此我们根据感兴趣的问题使用两种不同的收缩方法：完全贝叶斯分层模型，根据玩家位置部分汇集参数，以及惩罚极大似然估计，以选择数量较少的参数，这些参数与平均值有很大不同。我们将该模型应用于所有五对五（全强度）的情况下，在五个NHL赛季的比赛。
英文摘要：
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 players on the ice. This method yields offensive and defensive player ability ratings which take into account quality of teammates and opponents, the game situation, and other desired factors, that themselves have a meaningful interpretation in terms of game outcomes. Additionally, since the number of parameters in this model can be quite large, we make use of two different shrinkage methods depending on the question of interest: full Bayesian hierarchical models that partially pool parameters according to player position, and penalized maximum likelihood estimation to select a smaller number of parameters that stand out as being substantially different from average. We apply the model to all five-on-five (full-strength) situations for games in five NHL seasons.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
