Bradley–Terry model
The Bradley–Terry model is a probability model that can predict the outcome of a comparison. Given a pair of individuals i and j drawn from some population, it estimates the probability that the pairwise comparison i > j turns out true, as
where pi is a positive real-valued score assigned to individual i. The comparison i > j can be read as "i is preferred to j", "i ranks higher than j", or "i beats j", depending on the application.
For example, pi may represent the skill of a team in a sports tournament, estimated from the number of times i has won a match. then represents the probability that i will win a match against j. Another example used to explain the model's purpose is that of scoring products in a certain category by quality. While it's hard for a person to draft a direct ranking of (many) brands of wine, it may be feasible to compare a sample of pairs of wines and say, for each pair, which one is better. The Bradley–Terry model can then be used to derive a full ranking.
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