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Frequently in sporting competitions it is desirable to compare teams based onrecords of varying schedule strength. Methods have been developed for sportswhere the result outcomes are win, draw, or loss. In this paper those ideas areextended to account for any finite multiple outcome result set. Aprinciple-based motivation is supplied and an implementation presented formodern rugby union, where bonus points are awarded for losing within a certainscore margin and for scoring a certain number of tries. A number of variantsare discussed including the constraining assumptions that are implied by each.The model is applied to assess the current rules of the Daily Mail Trophy, anational schools tournament in England and Wales.

Retrodictive Modelling of Modern Rugby Union: Extension of Bradley-Terry to Multiple Outcomes