Steven Sanderson explains the concept of an odds ratio:
Imagine a loan officer flipping a coin to decide whether to approve your loan. Odds ratios tell you how much more likely one factor (like your income) makes the “heads” (approval) side appear compared to another (like your student status).
In logistic regression, odds ratios compare the odds of an event (loan default, in our case) for two groups defined by a specific variable. They’re like multipliers: greater than 1 means something increases the chances of default, while less than 1 means it decreases them.
As for why, we use odds ratios because it’s hard to track and interpret changes in probabilities directly, at least when you’re thinking small numbers.