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?
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asked May 19, 2015 at 8:10
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2 Answers
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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.
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$\begingroup$ I think the odds of a horse who has a 66% chance of winning would be 1/2 , meaning you get your bet back plus 1/2 the bet. What you describe above is a probability 33% horse, get bet back plus 2x the bet. Essentially you should always get 1.0 when you figure the payout. So a 1/2 horse wins 66% of the time so .66 + .66 * 1/2 = 1.0 and .33 + .33 * 2/1 = 1.0 for a 33% chance horse. Just as a sanity check, it makes sense a 66% horse pays less than even money and that a 33% chance horse pays better than even money. $\endgroup$ Commented Aug 16, 2021 at 8:40
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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.
