The Odds of an Event

Many of the statistical methods for the analysis of binary outcome variables are based on the odds of an event, rather than on its probability.

The Odds of event A are defined as the probability that A does happen divided by the probability that it does not happen:

Odds (A= prob (A happens) / prob (A does not happen) = prob (A) / 1- prob (A)

Since 1- prob (A) is the probability that A does not happen. By manipulating this equation, it is also possible to express the probability in terms of the odds:

Prob (A) = Odds (A) / 1+ Odds (A)

Thus it is possible to derive the odds from the probability and vice versa.

It can be seen that while probabilities must lie between o and 1, odds can take any value between o and infinity .

Thus the odds are always bigger than the probability (since 1- prob (A) is less than one).