Advancing NFL win prediction: from Pythagorean formulas to machine learning algorithms

This study evaluates the predictive performance of traditional and machine learning-based models in forecasting NFL team winning percentages over a 21-season dataset (2003-2023). Specifically, we compare the Pythagorean expectation formula-commonly used in sports analytics-with Random Forest regression and a feedforward Neural Network model. Using key performance indicators such as points scored, points allowed, turnovers, rushing and passing efficiency, and penalties, the machine learning models demonstrate superior predictive accuracy. The Neural Network model achieved the highest performance (MAE = 0.052, RMSE = 0.064, <i>R</i> ² = 0.891), followed by the Random Forest model, both of which significantly outperformed the Pythagorean method. Feature importance analysis using SHAP values identifies points scored and points allowed as the most influential predictors, supplemented by margin of victory, turnovers, and offensive efficiency metrics. These findings underscore the limitations of fixed-formula models and highlight the flexibility and robustness of data-driven approaches. The study offers practical implications for analysts, coaches, and sports management professionals seeking to optimize strategic decisions and competitive performance. Ultimately, the integration of advanced machine learning models provides a powerful tool for enhancing decision-making processes across the NFL landscape.