Bradley–Terry model

The Bradley–Terry model is a probability model for the outcome of pairwise comparisons between items, teams, or objects. Given a pair of items i and j drawn from some population, it estimates the probability that the pairwise comparison i > j turns out true, as

where p_i 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, p_i might represent the skill of a team in a sports tournament and

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Source: Wikipedia