There are some ideas that help us see the world more clearly. For example, the idea that a flipped coin has no memory of past events helps us realize that a recent string of heads does not increase the likelihood of tails (if the coin-flipping is done fairly). Thinking in predictors is one of those ideas that can make complex problems a little easier to think about.



This post is an introduction to how to visualize predictive power in the simplest case, where the outcome we want to know about only has two values. Examples include predicting first year student retention, student graduation, and applicants enrolling after being admitted. Having only two outcomes means there are only two possible predictions in a particular case--we predict that the outcome is one or the other of the two possibilities.



Let's suppose that you want to predict which of the new first-year students will return for their second fall. Suppose for a moment that I have a crystal ball and know the answer for ea…