AI 中文总结
该研究通过贝叶斯动态布拉德利-特里模型分析网球比赛数据，发现三巨头时代的特殊之处在于三名球员长期占据顶尖位置，而非球员个人实力远超历史选手。
AI 中文摘要
在2003年至2023年举办的81项大满贯赛事中，有66项冠军由三名球员夺得，这一时代被广泛认为是网球历史上最具统治力的时期。评估这一时期的特殊性需要比较从未直接交过手的球员，因此所有比较都需通过他们各自面对的对手来进行。我们通过三个维度衡量统治力：球员在其所处时代的选手中领先的程度、同时处于领先位置的球员数量，以及他们保持领先的时长——其中时长通过固定窗口的平均值计算，而非连续的连胜纪录，因为当连胜纪录背后的实力本身被估计时，连胜纪录是不稳定的。球员实力来自贝叶斯动态布拉德利-特里状态空间模型，统治力通过超出高阈值的情况来表征。将该模型应用于1968年至2025年间进行的197926场比赛后发现，仅德约科维奇在峰值实力上与其他选手拉开差距，而费德勒和纳达尔与博格、麦肯罗、伦德尔无法区分。近期时期的独特之处并非其最佳球员的实力有多高，而是有三名球员同时处于顶尖位置的时长：在其鼎盛时期，三名球员至少在五分之四的周数里占据前三位置，而过去最强的可比十年中，前三位置由四名球员分享。更显著的异常之处在于：1990年起的12年间，网球实力分布的上尾不仅无人占据，还被压缩了。
英文摘要
Three players won 66 of the 81 Grand Slam titles contested between 2003 and 2023, and their era is widely held to be the most dominant in the history of tennis. Assessing it means comparing players who never met, so that every comparison passes through the opponents each did face. We measure dominance by how far a player stands above the field of his own day, how many stand there at once, and how long they remain, the last through averages over fixed windows rather than through unbroken runs, which are unstable when the strengths beneath them are themselves estimated. Strengths come from a Bayesian dynamic Bradley-Terry state space model, and dominance is characterized through exceedances of a high threshold. Applied to 197,926 matches played between 1968 and 2025, only Djokovic separates from the field on peak strength, Federer and Nadal being indistinguishable from Borg, McEnroe and Lendl. What distinguishes the recent period is not how high its best players stood but how long three of them stood there together. At its height three players held a top-three position in at least four fifths of all weeks, where in the strongest comparable decade of the past those positions were shared among four. The sharper anomaly lies between: for twelve years from 1990 the upper tail was not merely unoccupied but compressed.
