Soccer as a Markov process: modelling and estimation of the zonal variation of team strengths
Soccer as a Markov process: modelling and estimation of the zonal variation of team strengths
复制标题
足球作为马尔可夫过程：球队实力区域变化的建模和估计
DOI：
10.1093/imaman/dpab042
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发表时间：
2023
期刊：
影响因子：
--
通讯作者：
Yamamoto K and Yoshimura M.
中科院分区：
文献类型：
--
作者：
Hirotsu N;Inoue K;Yamamoto K and Yoshimura M.
这项研究将足球建模为一个马尔可夫过程。我们将球场离散为九个区域，并根据球所在的球场区域、控球球队和比分来定义马尔可夫过程的状态。对数-线性模型用于表示状态转移。使用对数线性模型，我们不仅根据得分或丢球，而且在考虑球所在的离散区域时，估计球队的实力。我们使用2015赛季日本联赛甲级联赛的逐场数据来说明我们的方法，并描述这个联盟中球队的优势。Sanfrecce广岛就是一个特别的例子。我们确定了对数线性模型的拟合优度。此外，我们在对数线性模型中引入了随机效应，并讨论了状态转移过程的复杂性。我们证明了我们的马尔可夫模型，在九个区域的水平上，提供了一个很好的近似值来估计球队的实力。
This study models soccer as a Markov process. We discretize the pitch into nine zones, and define the states of the Markov process according to the zone of the pitch in which the ball is located, the team in possession and the score. Log-linear models are used to represent state transitions. Using the log-linear models, we estimate team strengths not only with respect to scoring or conceding, but also with respect to gaining or losing possession, while considering the discretized zones in which the ball is located. We use play-by-play data from Japan League Division 1 games in the 2015 season to illustrate our approach, and characterize the strengths of teams in this league. Sanfrecce Hiroshima is used as a particular example. We determine the goodness-of-fit of the log-linear models. Additionally, we introduce random effects into the log-linear models and discuss the complexity of the state transition process. We demonstrate that our Markov model, at the nine-zone level, provides estimates of teams’ strengths to a good approximation.