Log5, the Logit Link and Bradley-Terry

In the late 1970’s Bill James, now a famous baseball writer and historian, was working night shifts a security guard at a pork and beans cannery. He, much like us, was interested in building a model to predict the probability that one team would beat another team given the relative qualities of the two teams. James reasoned that with: $p_{a,b}$ defined as the probability that Team A will beat team B, $p_a$ as Team A’s *true* winning percentage (the probability that they would beat an average team) and, $p_b$ as Team B’s *true* winning percentage, the following six statements **must be true**: 1. $p_{a,a} = 0.5$ (note that this rule concerns two teams of equal quality not a team playing itself) 2. $p_{a,.5} = a$ 3. If $a > b$…

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