Odds and Probability

Lead Author(s): Jeff Martin, MD

Odds = Probability of an Event


Odds are most simply calculated as the number of events divided by the number of non-events.


The formal way to describe the odds is as the probability of the event divided by the probability of the non-event.

So odds are the ratio of two fractions: So the formula for odds is p / (1 - p).

Since both fractions have the number of subjects in the denominator,

Probability and Odds

If event occurs 1 of 5 times, probability = 0.2 Out of 5 times, 1 time will be the event and 4 times will be the non-event, odds = 0.25 Calculating the odds without the number of subjects:

Calculating Probability Given Odds

To calculate probability given the odds:

Odds versus Probability

Odds is less intuitive than probability (probably wouldn't say "my odds of dying are 1/4")

No less legitimate mathematically, just not so easily understood

Also important because the log odds of the outcome is given by the coefficient of a predictor in a logistic regression