The Bradley–Terry model is a probabilistic model used in statistics to analyze paired comparisons between items, such as in tournaments, ranking systems, or voting situations. The model is particularly useful in scenarios where the objective is to determine the relative strengths or preferences of different items based on the outcomes of pairwise contests.
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The Bradley-Terry model assigns positive abilities and the displayed pairwise winning probabilities. Multiplying all abilities by the same positive scalar leaves the probabilities unchanged, so identifiability requires a normalization. In log abilities , the model has comparison probabilities obtained from the logistic function. Either parametrization induces the same ordering of players.