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On the ranking of test match batsmen

机译：关于考级板球运动员的排名

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摘要

Ranking sportsmen whose careers took place in different eras is often a contentious issue and the topic of much debate. We focus on cricket and examine what conclusions may be drawn about the ranking of test batsmen by using data on batting scores from the first test in 1877 onwards. The overlapping nature of playing careers is exploited to form a bridge from past to present so that all players can be compared simultaneously, rather than just relative to their contemporaries. The natural variation in runs scored by a batsman is modelled by an additive log-linear model with year, age and cricket-specific components used to extract the innate ability of an individual cricketer. Incomplete innings are handled via censoring and a zero-inflated component is incorporated in the model to allow for an excess of frailty at the start of an innings. The innings-by-innings variation of runs scored by each batsman leads to uncertainty in their ranking position. A Bayesian approach is used to fit the model and realizations from the posterior distribution are obtained by deploying a Markov chain Monte Carlo algorithm. Posterior summaries of innate player ability are then used to assess uncertainty in ranking position and this is contrasted with rankings determined via the posterior mean runs scored. Posterior predictive checks show that the model provides a reasonably accurate description of runs scored.
机译：对职业生涯发生在不同时代的运动员进行排名通常是一个有争议的问题，也是许多争论的话题。我们将重点放在板球上，并通过使用从1877年开始进行的第一次测试的击球得分数据，来检验关于测试击球手排名的结论。游戏职业的重叠性质被利用来架起从过去到现在的桥梁，以便可以同时比较所有玩家，而不仅仅是相对于其同时代的玩家。击球手得分的自然变化是通过加法对数线性模型建模的，该模型具有年，年龄和板球特定组件，用于提取单个板球运动员的先天能力。不完整的局通过检查来处理，并且模型中包含了零膨胀的组件，以允许局开始时虚弱过多。每个击球手得分的局间变化会导致其排名位置的不确定性。使用贝叶斯方法拟合模型，并通过部署马尔可夫链蒙特卡洛算法从后验分布中获得实现。然后使用先天性球员能力的后验总结来评估排名位置的不确定性，这与通过得分后验均值确定的排名形成对比。后验预测检查表明，该模型对计分的运行提供了合理准确的描述。

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