College Football Bowl Game Model

Random Walk Model

The first is a random walk model (i.e. Google Page Rank). The idea of the random walk model is to imagine a network where each node (point) represents a team. There is a one-way edge between two teams if they played a game, and the direction of the path points toward the winning team. Assume you begin the walk at a random node and begin travelling along the edges randomly. A team's ranking is the probability that you are located at that team's node after a very long time. The idea of the Google Page Rank algorithm is that if you add a little more randomness -- a small probability of moving from any node to any other node -- then this limiting probability is well determined.

I weight the graph's edges by the score differential. I tried applying various functions to the score differential as well as the score differential scaled by the winning team's score. An idiosyncrasy of the random walk model is that it rewards teams that beat other teams with very few losses, even when that team had mediocre results through the season. To compensate for this quirk, I used a large Google constant, that is I made the small probability of moving from any node to any other node quite a bit larger than the default value.

Regression Model

The second is a regression model where each game is an observation. The teams participating in the game are the features, and I arbitrarily assign one team to be team one and the other to be team two. The value of team one is +1 and the value of team two is -1 for each game. The difference in score (team one score less team two score) is the label. One advantage of the regression model is that it was very simple to do model selection using cross-validation. I used L2 regularization and determined the amount of regularization through cross-validation.