C26. Bradley–Terry

Topic: Paired comparisons, and how far a fit is from the data · more questions on this topic
‹ Q34 C29 ›

What is the Bradley–Terry model for a head-to-head contest with no ties?

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Definitions/notation. For a contest with no ties, assign real-valued log-abilities \lambda_j; the model specifies \mathbb{P}(j\text{ beats }k)=e^{\lambda_j}/(e^{\lambda_j}+e^{\lambda_k}), equivalently odds e^{\lambda_j-\lambda_k}. Only ability differences are identifiable, so a reference such as \lambda_1=0 is needed.