Assessment of the performance of a player in any sport is very much needed to determine the ranking of players and make a solid team with the best players. Besides these, fans, journalists, sports persons, and sports councils often analyse the performances of current and retired players to identify the best players of all time. Here, we study the performance of all-time top batters in one-day cricket using physics-based statistical methods. The batters are selected in this study who possess either higher total runs or a high number of centuries. It is found that the total runs increases linearly with the innings number at the later stage of the batter carrier, and the runs rate estimated from the linear regression analysis also increases linearly with the average runs. The probability of non-scoring innings is found to be a negligibly small number (i.e., $\leq 0.1$ ) for each batter. Furthermore, based on innings-wise runs, we have computed the six-dimensional probability distribution vector for each player. Two components of the probability distribution vector vary linearly with average runs. The component representing the probability of scoring runs less than 50 linearly decreases with the average runs. In contrast, the probability of scoring runs greater than or equal to 100 and less than 150 linearly increases with the average runs. We have also estimated the entropy to assess the diversity of a player. Interestingly, the entropy varies linearly with the average runs, giving rise to two clusters corresponding to the old and recent players. Furthermore, the angle between two probability vectors is calculated for each pair of players to measure the similarities among the players. It is found that some of the players are almost identical to each other.

翻译：在任何体育项目中，评估运动员的表现对于确定运动员排名和组建由最佳运动员组成的坚实团队至关重要。除此之外，球迷、记者、体育人士和体育理事会也经常分析现役和退役运动员的表现，以识别有史以来最优秀的运动员。本文中，我们采用基于物理学的统计方法，研究了单日板球赛中历史顶尖击球手的表现。本研究选取了那些总得分较高或拥有大量百分杆的击球手。研究发现，在击球手职业生涯的后期阶段，总得分随局数线性增加，并且通过线性回归分析估计的得分率也随平均得分线性增加。对于每位击球手，未得分局数的概率被发现是一个可忽略的小数（即 $\leq 0.1$）。此外，基于每局得分，我们计算了每位运动员的六维概率分布向量。概率分布向量的两个分量随平均得分线性变化。代表得分低于50分的概率分量随平均得分线性减少。相反，得分大于或等于100分且小于150分的概率随平均得分线性增加。我们还估计了熵以评估运动员表现的多样性。有趣的是，熵随平均得分线性变化，从而形成了对应于老一代和近期运动员的两个聚类。此外，我们计算了每对运动员之间的概率向量夹角，以衡量运动员之间的相似性。结果发现，部分运动员彼此之间几乎完全相同。