Ranking Teams with Optimization

Here’s a fun exercise. Remember back in high school calculus when you would find the peak of a curve by setting its derivative to zero? That’s a basic example of mathematical optimization. Regression is another, more complicated form of optimization. In regression we want to fit a line or curve so that the difference between the predicted values and the observed values is minimized. Simply put, optimization is finding either the maximum or minimum of a function, subject to a list of constraints.

Optimization is the hidden science behind much of the world around us. It’s how airlines know how to schedule routes, how politicians gerrymander districts, and how companies plan advertising campaigns. It’s also how sports leagues manage to build schedules to accommodate a dizzying myriad of requirements. Optimization is why we had to suffer through the Titans-Jaguars game Thursday night.

Let’s say we want to find the best-fitting set of team ratings that would explain the game outcomes so far in the season. What we can do is start out with an assumed set of team ratings. Anything is fine, but let’s start with a rating of zero points for every team. Then we can list each game and its net score result (home score – visitor score - 3). We’ll subtract 3 because that’s the value of home field.

Read more: Ranking Teams with Optimization