Maximum likelihood estimation for the Bradley-Terry model when some teams are combined or restructured

概要

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In two player competitions, the Bradley-Terry model is a well-known probability model. This model shows that the propability that player i wins is the power of player i divided by the power of player i plus the power of player j in the battle between player i and player j. When “players" mean baseball, soccer, or football teams, some teams might be combined or restructured in next season.In this paper we discuss the maximum likelihood estimation of the power of each team for this problem. Obtaining the MLE by using iterative scaling procedures is also discussed.