2024 SPECIAL EDITION

AUTHORS

Ethan Seung, Harvard-Westlake School
John Xu, Harvard-Westlake School
Ryder Katz, Harvard-Westlake School
Mason Wetzstein, Harvard-Westlake School
Michael Barr, Harvard-Westlake School

ABSTRACT

This study presents a novel approach to evaluating soccer team strength and calculating win probabilities given any two matchups of soccer teams in the fictional North American Soccer League (NSL), whose data is provided for the Wharton High School Data Science Competition. Traditional win-loss metrics have many limitations, like failing to account for the strength of schedule, margin of victory, and home-field advantage. Thus, we developed a Whole-History Rating (WHR) model adapted from Rémi Coulom that incorporates expected goals (xG) and accounts for home-field advantage, overcoming the sequencing issues inherent in single-pass Elo systems. Using a dataset of 476 NSL games, we implemented a multi-pass system for iterative rating adjustments and employed Bayesian inference to develop probability distributions for team ratings.

The model was optimized using Nelder-Mead optimization, achieving a root mean square error (RMSE) of 0.346 when tested against a held-out dataset. Key findings include a significant home-field advantage constant of 32.3 rating points and identifying the top four teams based on the optimized ratings. The model’s strengths lie in its order-independent nature, use of expected goals as a performance metric and continuous updating of all team ratings. Limitations and areas for future work include refining the expected goals metric to account for elite player performance and developing a dynamic home-field advantage factor that considers time zone differences. This research provides a more nuanced and accurate method for evaluating team strength and forecasting game outcomes in soccer leagues around the world.