## Thursday, February 09, 2006

### Translate "odds"

Odds are a technical term that is often used in horse or car racing. It refers to the ratio p/(1-p) where p is the probability of success. So for instance, a 1:3 odds of winning is equivalent to a probability of 0.25 of winning.

What I found odd is that the term "odds" in this meaning does not exist in most languages! Usually, the closest you can get is "proabbility" or "chance". I first realized it when I tried to translate to Hebrew. Then, students who speak other languages (Spanish, Russian, Chinese) said that is the case in other languates as well.

Odds are important in data mining because the are the basis of logistic regression, a very popular classification method. Say we want to predict the probability that a customer will default on a loan, using information on historic transactions, demographics, etc. A logistic regression models the odds of defaulting as an exponential function of the predictors (or, equivalently, the log-odds are writted as a linear function of the predictors). The interpretation of coefficients in a logistic model are usually in terms of odds (e.g., "single customers are on average 1.5 times more likely to default than married customers, all else equal".)

A frequent terminological error when it comes to odds: Sometimes odds are referred to as "odds ratios". This is a mistake that probably comes from the fact that odds are a ratio (of probabilities). But in fact, an odds ratio is a ratio of odds. These are used to compare the odds of two groups. For example, if we compare the loan defaulting odds of males and females (e.g., via a "Gender" predictor in the logistic regression), then we have an odds ratio.

Does anyone know of a language that does have the term "odds"?