Back in the '80s, Bill James introduced the Log5 method to find the probability that Team A will defeat Team B, based on Team A's and Team B's winning percentages. Later, with the help of a colleague, he expanded on the formula to account for an average other than .500 (an average winning percentage), so the formula could be used to find the probability of any kind of match-up - batting average, on-base percentage, free throw percentage - where the league average is something other than .500.
-
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 used for, paired comparisons,Elo rating system used in chess, and the Rasch model used in the analysis of categorical data.
Let Pi be the fraction of games won by team i and also let qi = 1 - Pi, be the fraction of games lost by team i.
A few notable properties exist:
If Pa = 1, Log5 will always give A a 100% chance of victory.
If Pa = 0, Log5 will always give A a 0% chance of victory.
If Pa = Pb, Log5 will always return a 50% chance of victory for either team.
If Pa = 1/2, Log5 will give Aa 1 - Pb, probability of victory.
It may also be conveniently rewritten using the odds ratio as PA,B/qA,B = PA/qA xqB/PB.
Here as before qA,B = 1 - PA,B
Thank you for coming to our cache. BYOP