# Odds vs probability in logistic regression

I am going through Trevor Hastie's Classification Techniques.

Its says Odds are traditionally used instead of probabilities in horse-racing.

I still don't understand how they relate more naturally to the correct betting strategy?

## 2 Answers

It's not that they relate more naturally to the correct betting strategy per se, it's that they're much more easily interpretable while on the horse track.

Consider the following example: the probability of horse A to win is 66% percent. In conventional odds notation, this is represented as a 2:1 bet, which is very easily interpretable as a £2 win for each £1 bet, if the horse does win. For the layman, the 66% probability does not lend itself so easily to interpretation in terms of potential winnings.

In a logistic regression model, odds ratio provide a more coherent solution as compared to probabilities. Odds ratio represent the constant effect of an independent variable on a dependent variable. Here, being constant means that this ratio does not change with a change in the independent (predictor) variable. Odds ratio in this sense provide a much easier way of comprehending the marginal effects.