Which probability formula to use?

Two are provided:

odds / ( 1 + odds) and

1 / (1 + odds)

The second one uses this formula essentially:


If i get a standard logistic regression, I’m not sure how to find out probability. The first one would be to work out the model using the provided coefficients, then exp the outcome, and then do odds / (1 + odds).

The second one would be to work out the model, multiply it by minus, then exp the outcome, and then do 1 / (1 + odds)

Pr(rolling 6 on a dice with 6 faces) = 1/6
Odds rolling 6 = 1/5 = 0.2

Prob = odds / (1 + odds) = 0.2 / (1 + 0.2) = 0.2 / 1.2 = 1/6 prob for rolling a six

Prob = 1 / (1+ odds) = 1 / (1 +0.2) = 1 / 1.2 = 5/6 prob AGAINST rolling a six


Thanks, that makes sense, but as an example I had a question that asked me the probability of a winning fund, and it used the second example instead of the first, even though I didn’t want the ‘against’ probability.

There is a separate table with coefficients and independent variable means, but I don’t understand why I have to use this formula which does 1 / 1 + odds, instead of doing a regression that looks like this (and using this formula):

ln(p/1-p) = b0 + b1X1 + …

Sorry I don’t really understand what you are asking.

I can’ t make any comments on questions without seeing all the questions and answers

Note the second formula has e^ (negative odds)
There is a minus sign in front of the regression equation.

My algebra is not up to the task but I believe this explains the perceived inconsistancy.

about 5 mins in he shows the equation of the probabilities and odds (but no algebraic proof)


Thank you! Makes much more sense than before!