板球运动中连续个人最佳成绩之间的间隔分布：数据与模型
Gap distributions between successive personal bests in cricket: Data and Models
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中文总结 AI 辅助
本研究针对板球运动员连续个人最佳得分的间隔分布展开，发现其符合截断幂律而非经典理论的普适分布，证实职业生涯时间演化对纪录出现有关键影响，揭示了非平稳路径依赖系统中纪录统计的变化规律。
中文摘要 AI 辅助
连续的个人最佳表现为运动员职业生涯的进步提供了一种天然的衡量标准。经典纪录理论预测，对于独立同分布（i.i.d.）序列，存在普适的间隔分布$P(g)\sim 1/g$。然而，体育职业生涯受到学习、年龄增长、能力变化以及外部影响的塑造，这些因素违背了上述假设。我们研究了板球运动中纪录间隔的统计特征，该间隔定义为连续个人最佳得分之间的局数。我们使用从ESPN Cricinfo获取的顶级Test、ODI和T20球员的职业生涯记录进行分析。研究发现，经验分布可以用截断幂律$P(g) \propto g^{-α} e^{-λg}$很好地描述，其中指数的范围为$0.799 \leq α\leq 0.843$。当破坏局数的时间顺序时，这种偏差大部分会消失，这表明职业生涯的演化在塑造纪录出现的过程中起着关键作用。自助法打乱的职业生涯既保留了个人得分分布和职业生涯长度，又消除了时间顺序，其产生的指数显著更大（$α\approx 0.939\text{--}0.979$）。这些发现表明，个人最佳表现的进步过程保留了球员职业生涯时间结构的信息，无法用简单的随机纪录过程完全解释。更广泛地说，它们说明了在非平稳和路径依赖系统中，纪录统计特征是如何被改变的。
英文摘要
Successive personal best performances provide a natural measure of progression in an athlete's career. Classical record theory predicts a universal gap distribution, $P(g)\sim 1/g$, for independent and identically distributed (i.i.d.) sequences. However, sporting careers are shaped by learning, aging, changes in ability, and external influences that violate these assumptions. We investigate the statistics of inter-record gaps, defined as the number of innings between successive personal best scores, in cricket. Using career records of leading Test, ODI, and T20 players obtained from ESPN Cricinfo. We find that the empirical distributions are well described by truncated power law $P(g) \propto g^{-α} e^{-λg}$ with exponents in the range (0.799 $\leq α\leq$ 0.843). Much of this deviation disappears when the temporal ordering of innings is destroyed, indicating that career evolution plays a key role in shaping record occurrence. Bootstrap-shuffled careers, which preserve individual score distributions and career lengths while removing temporal ordering, yield significantly larger exponents ($α\approx 0.939\text{--}0.979$). These findings show that the progression of personal best performances retains information about the temporal organization of a player's career and cannot be fully explained by simple stochastic record processes. More generally, they illustrate how record statistics are altered in nonstationary and path-dependent systems.
