Functional Ratings in Sports

Abstract: In this paper, we present a new model for ranking sports teams. Our model uses all scoring data from all games to produce a functional rating by the method of least squares. The functional rating can be interpreted as a teams average point differential adjusted for strength of schedule. Using two team's functional ratings we can predict the expected point differential at any time in the game. We looked at three variations of our model accounting for home-court advantage in different ways. We use the 2018-2019 NCAA Division 1 men's college basketball season to test the models and determined that home-court advantage is statistically important but does not differ between teams.