Log5

Log 5 is a formula invented by Bill James[1] to estimate the probability that team A will win a game, based on the true winning percentage of Team A and Team B. It is equivalent to the Bradley-Terry-Luce model used for paired comparisons, the Elo rating system used in chess and the Rasch model used in the analysis of categorical data.[2]

Let be the fraction of games won by team and also let be the fraction of games lost by team . The Log5 estimate for the probability of A defeating B is .

A few notable properties

It may also be conveniently rewritten using the odds ratio[2] as

Here as before .

References

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