Related papers: The Bradley--Terry condition is $L_1$--testable
The Bradley-Terry model has previously been used in both Bayesian and frequentist interpretations to evaluate the strengths of sports teams based on win-loss game results. It has also been extended to handle additional possible results such…
Prediction and modelling of competitive sports outcomes has received much recent attention, especially from the Bayesian statistics and machine learning communities. In the real world setting of outcome prediction, the seminal \'{E}l\H{o}…
The seminal Bradley-Terry model exhibits transitivity, i.e., the property that the probabilities of player A beating B and B beating C give the probability of A beating C, with these probabilities determined by a skill parameter for each…
This paper deals with the estimation of the unknown distribution of hidden random variables from the observation of pairwise comparisons between these variables. This problem is inspired by recent developments on Bradley-Terry models in…
In the Bradley-Terry model for paired comparisons, and its extensions to include order effects and ties, the maximum likelihood estimates of probabilities of certain outcomes can be 0 or 1 under certain data configurations. This poses…
We consider a Bradley-Terry model in random environment where each player faces each other once. More precisely the strengths of the players are assumed to be random and we study the influence of their distributions on the asymptotic number…
The rating of items based on pairwise comparisons has been a topic of statistical investigation for many decades. Numerous approaches have been proposed. One of the best known is the Bradley-Terry model. This paper seeks to assemble and…
The Bradley-Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behaviour, chess…
PageRank and the Bradley-Terry model are competing approaches to ranking entities such as teams in sports tournaments or journals in citation networks. The Bradley-Terry model is a classical statistical method for ranking based on paired…
The Bradley-Terry model assigns probabilities for the outcome of paired comparison experiments based on strength parameters associated with the objects being compared. We consider different proposed choices of prior parameter distributions…
A common problem faced in statistical inference is drawing conclusions from paired comparisons, in which two objects compete and one is declared the victor. A probabilistic approach to such a problem is the Bradley-Terry model, first…
Ranking problems based on pairwise comparisons, such as those arising in online gaming, often involve a large pool of items to order. In these situations, the gap in performance between any two items can be significant, and the smallest and…
Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model and its variants have been widely used to do so. The…
The Bradley-Terry (BT) model is a common and successful practice in reward modeling for Large Language Model (LLM) alignment. However, it remains unclear why this model -- originally developed for multi-player stochastic game matching --…
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…
We propose a time-varying generalization of the Bradley-Terry model that allows for nonparametric modeling of dynamic global rankings of distinct teams. We develop a novel estimator that relies on kernel smoothing to pre-process the…
We propose a general framework for statistical inference on the overall strengths of players in pairwise comparisons, allowing for potential shifts in the covariate distribution. These covariates capture important contextual information…
Pairwise comparison data are widely used to infer latent rankings in areas such as sports, social choice, and machine learning. The Bradley-Terry model provides a foundational probabilistic framework but inherently assumes transitive…
We present a theoretical analysis of the Elo rating system, a popular method for ranking skills of players in an online setting. In particular, we study Elo under the Bradley--Terry--Luce model and, using techniques from Markov chain…
We study the ranking of individuals, teams, or objects, based on pairwise comparisons between them, using the Bradley-Terry model. Estimates of rankings within this model are commonly made using a simple iterative algorithm first introduced…