Odds

Definition

Odds is the probability of success $\pi$ divided by the probability of failure $(1-\pi )$:

$$\text{odds}=\frac{\pi }{1-\pi }$$

Interpretation

$\text{odds}=4$ can be interpreted as:

• “The odds of success are $4$ to $1$”
• “Success are $4$ times more likely than failure”

Remark

• The odds are nonnegative.
• Value greater than $1.0$ means a success is more likely than a failure.
• $\text{odds}=4.0$ means success is 4 times more likely than failure.
• $\pi =\frac{\text{odds}}{\text{odds}+1}$
• In econometrics, the logarithm of odds is called logit