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.