The logit function is just a mapping from non-log prob space to log odds space. It’s the odds formula wrapped in a natural logarithm. In one way, it’s not “doin

The logit function is just a mapping from non-log prob space to log odds space. It’s the odds formula wrapped in a natural logarithm. In one way, it’s not “doing” much of anything. It’s not the journey, it’s the destination. Why hang out in log odds space? Well, it’s a bigger space. It’s [-inf, inf], which is bigger than the [0, inf] of odds and the [0, 1] of prob. Odds space means you can multiply without normalizing. Log space means you multiply by adding. And being a natural log means you’re good to go when you start doing calculus and the like. You can also cover a huge range of probabilities in a small range of numbers. -21 to 21 covers 1 in a billion to 1 - (1 in a billion).