Quote:
Originally Posted by whosnext
The log5 method was developed/derived to answer questions like this.
Answer = [.75 - (.75*.20)] / [.75 + .20 - (2*.75*.20)]
= .60 / .65
= .923
I googled Log5 and found this :
Is this the same formula just written in a different way ?
Seems different to me. Which one is correct ?
The “5″ in “log5″ and a More General Formulation
The “5″ part of “log5″ was in reference to the fact that teams were being compared to .500, the average winning percentage. But when we’re dealing with individual matchups, the league average isn’t always .500 (for a batter/pitcher matchup to estimate the probability of a hit, we would need to use the league-wide batting average). To deal with this we need to add another term to the formula representing the league average probability (or odds).
In the odds ratio formulation, this is easy. We just divide by the league average odds (Odds_{LG}). When the league average probability is .500, the odds are \{.500}{(1 - .500)} = 1, so the term can be omitted without consequence.
OddsRatio_{AvB} = {Odds_A}/{Odds_B}}/{Odds_{LG}}
Converting this to a probability, we have what I find to be the clearest formulation of the generalized log5 formula:
p_{AvB} = {Odds_A}/{Odds_A + (Odds_B * Odds_{LG})}
Last edited by dantheman_05; 01-28-2018 at 02:08 PM.