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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_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 exist:

  • If , Log5 will always give A a 100% chance of victory.
  • If , Log5 will always give A a 0% chance of victory.
  • If , Log5 will always return a 50% chance of victory for either team.
  • If , Log5 will give A a probability of victory.

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

Here as before .


  1. ^ "Chancesis: The Origins of Log5". Archived from the original on April 12, 2012. Retrieved 2013-03-07. CS1 maint: discouraged parameter (link)
  2. ^ a b "Baseball, Chess, Psychology and Pychometrics: Everyone Uses the Same Damn Rating System". Retrieved 2013-12-29. CS1 maint: discouraged parameter (link)