Football with Linear Algebra
Predict NFL playoffs using Linear Algebra
[Full Writeup]
Partner: Eric Gan
This was a course project from when I took Matrix Algebra at CMU in 2019. The main goal of this project was to take data from the regular season of the NFL and predict the playoffs be computing rankings for each team.
Implementation
We employed two main strategies:

In the first, we try to find rankings of teams, such that for every game between teams i and j, the difference between team i’s score and team j’s score is equal to their difference in ranking. This method didn’t work well at first, but after taking all nonzero terms in our matrix and making them small values 10^(15) it was very efficient. We surmise that this is because we were able to increase the stability of the matrix through perturbation<

In the next method, we created a matrix that is 32 by 32, such that every entry Aij is equal to the total number of points scored by team i against team j, with some normalization. Next, we tried to find some strength vector S such that, when multiplying A by S, we get a vector proportional to S. This becomes an equation where we can use eigenvalues and eigenvectors to find a solution. It worked better than a naive version of strategy 1, but worse than the perturbed values.