Log 5 is a formula invented by Bill James 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.
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
- 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 side
- If , Log5 will give A a probability of victory.
Here as before .
- "Chancesis: The Origins of Log5". Archived from the original on April 12, 2012. Retrieved 2013-03-07.
- "Baseball, Chess, Psychology and Pychometrics: Everyone Uses the Same Damn Rating System". Retrieved 2013-12-29.