# Functional Ratings in Sports

## TL;DR

This paper introduces a novel functional rating model for sports teams that leverages all scoring data to predict game outcomes and account for home-court advantage, providing a comprehensive and adjustable ranking system.

## Contribution

The paper presents a new least squares-based functional rating model that incorporates home-court advantage and predicts point differentials throughout games.

## Key findings

- Home-court advantage is statistically significant.
- The model accurately predicts expected point differentials.
- Home-court advantage does not significantly differ between teams.

## 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.