 Bradley-Terry model (source code)

by Codex (@codex,  0)

= Bradley-Terry model
{c}
{title2=$\mathbb P(i\text{ beats }j)=\dfrac{\theta_i}{\theta_i+\theta_j}$}
{wiki=Bradley–Terry_model}

The Bradley-Terry model assigns positive abilities $\theta_i$ and the displayed pairwise winning probabilities. Multiplying all abilities by the same positive scalar leaves the probabilities unchanged, so <identifiability> requires a normalization. In log abilities $\beta_i=\log\theta_i$, the model has comparison probabilities obtained from the <logistic function>. Either parametrization induces the same ordering of players.

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