Odds Ratio

Odds : ratio of Probability(occurring an event) over Probability(not occurring an event)

odds = p / (1-p)

Odds Ratio (OR): The odds ratio is a measure of effect size [1], describing the strength of association or non-independence between two binary data values.

Mathematical definition in terms of group-wise odds : Odds ratio is the ratio of the odds of an event occurring in one group to the odds of it occurring in another group. If the probabilities of the event in each of the groups are p1 (first group) and p2 (second group), then

OR = {p1/(1-p1)} / {p2/(1-p2)}

OR = 1 : The event occurs in both groups equally.
OR > 1 : The event is more likely to occur in first group.
OR < 1 : The event is more likely to occur in second group.

There are other types of mathematical definition in different contexts which are found here.

[1] Effect Size : In statistics, an effect size is a measure of the strength of the relationship between two variables in a statistical population.