橄榄球联盟建模的马尔可夫链方法
A Markov Chain Approach to Modeling Rugby Union
- University of Virginia（弗吉尼亚大学）
- University of Pennsylvania（宾夕法尼亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种基于马尔可夫链的橄榄球联盟建模方法，通过有限状态空间和转移概率估计，实现比赛轨迹分析及获胜概率预测，并经校准验证具有竞争力。
AI中文摘要：
橄榄球联盟的连续比赛、可变长度的控球权以及多种得分结果使其难以用标准方法建模。我们提出一个马尔可夫链框架，将橄榄球联盟表示为关于比分差、剩余时间和球场位置的有限状态空间，转移概率根据历史比赛数据估计。所得模型支持对比赛轨迹的模拟和分析，包括从任意给定状态出发的获胜概率和期望得分估计。我们通过校准分析以及与仅预测最终结果的模型进行比较来验证该模型。我们的状态空间方法产生了校准良好、具有竞争力的估计，同时还能够分析比赛如何在状态之间演变。
英文摘要：
Rugby Union's continuous play, variable-length possessions, and multiple scoring outcomes make it difficult to model with standard approaches. We present a Markov Chain framework that represents Rugby Union as a finite state space over score differential, remaining time, and pitch location, with transition probabilities estimated from historical match data. The resulting model supports simulation and analysis of in-game trajectories, including win probability and expected point estimates from any given state. We validate the model through calibration analysis and comparison to models that predict only final outcomes. Our state-space approach produces well-calibrated, competitive estimates while additionally enabling analysis of how games evolve between states.
