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One of the simplest and most common power ranking models is known as the Bradley-Terry-Luce model , which is equivalent to other famous models such the logistic model and the Elo rating system . I'll be referring to "teams" here, but of course the same ideas apply to any two-participant game. Let me clarify what I mean when I use the term "power ranking". A power ranking supplies not only a ranking of teams, but also provides numbers that may be used to estimate the probabilities of various outcomes were two particular teams to play a match. In the BTL power ranking system we assume the teams have some latent (hidden/unknown) "strength" Ri, and that the probability of i beating j is RiRi+Rj. Note that each Ri is assumed to be strictly positive. Where does this model structure come from? Here are three reasonable constraints for a power ranking model: If Ri and Rj have equal strength, the probabil...