Log5
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_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 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 as
Here as before.
