The Bradley-Terry model is widely used for the analysis of pairwise comparison data and, in essence, produces a ranking of the items under comparison. We embed the Bradley-Terry model within a stochastic block model, allowing items to cluster. The resulting Bradley-Terry SBM (BT-SBM) ranks clusters so that items within a cluster share the same tied rank. We develop a fully Bayesian specification in which all quantities-the number of blocks, their strengths, and item assignments-are jointly learned via a fast Gibbs sampler derived through a Thurstonian data augmentation. Despite its efficiency, the sampler yields coherent and interpretable posterior summaries for all model components. Our motivating application analyzes men's tennis results from ATP tournaments over the seasons 2000-2022. We find that the top 100 players can be broadly partitioned into three or four tiers in most seasons. Moreover, the size of the strongest tier was small from the mid-2000s to 2018 and has increased since, providing evidence that men's tennis has become more competitive in recent years.

翻译：布拉德利-特里模型广泛用于成对比较数据分析，其核心功能是生成被比较对象的排序。我们将布拉德利-特里模型嵌入随机分块模型中，允许对象进行聚类。由此产生的布拉德利-特里随机分块模型（BT-SBM）对聚类进行排序，使得同一聚类内的对象共享相同的并列排名。我们建立了完整的贝叶斯框架，通过基于瑟斯顿数据增强推导的快速吉布斯采样器，联合学习所有参数——包括分块数量、分块强度及对象分配。尽管采样效率高，该采样器能为所有模型组件提供连贯且可解释的后验摘要。我们的应用实例分析了2000-2022赛季ATP巡回赛男子网球比赛结果。研究发现，在大多数赛季中，前100名选手可大致划分为三至四个层级。此外，最强层级规模在2000年代中期至2018年间较小，此后持续扩大，这为男子网球近年竞争日趋激烈提供了实证依据。