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Log5 is a method of estimating the probability that team A will win a game against team B, based on the odds ratio between the estimated winning probability of Team A and Team B against a larger set of teams.

Let and be the average winning probabilities of team A and B and let be the probability of team A winning over team B, then we have the following odds ratio equation

One can then solve

The name Log5 is due to Bill James[1] but the method of using odds ratios in this way dates back much farther. This is in effect a logistic rating model and is therefore 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]

The following notable properties exist:

  • If , Log5 will give A a 100% chance of victory.
  • If , Log5 will give A a 0% chance of victory.
  • If , Log5 will give each team a 50% chance of victory.
  • If , Log5 will give A a probability of victory.
  • If , Log5 will give A a chance of victory.

Additional applications [edit]

In addition to head-to-head winning probability, a general formula can be applied to calculate head-to-head probability of outcomes such as batting average in baseball.[3]

Sticking with our batting average example, let be the batter's batting average (probability of getting a hit), and let be the pitcher's batting average against (probability of allowing a hit). Let be the league-wide batting average (probability of anyone getting a hit) and let be the probability of batter B getting a hit against pitcher P.

Or, simplified as


  1. ^ "Chancesis: The Origins of Log5". Archived from the original on April 12, 2012. Retrieved 2013-03-07.
  2. ^ "Baseball, Chess, Psychology and Pychometrics: Everyone Uses the Same Damn Rating System". Retrieved 2013-12-29.
  3. ^ "A Short Digression into Log5". The Hardball Times. 2005-11-23. Retrieved 2023-02-25.