Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball

Area of Science:

• Statistics
• Machine Learning
• Sports Analytics

Background:

• Regularized multinomial regression is commonly used for multi-category outcome prediction.
• Ridge penalty is a standard regularization technique, but may not fully leverage response category structures.
• Existing methods may not optimally capture complex relationships in high-dimensional categorical data.

Purpose of the Study:

• To propose and evaluate the nuclear norm penalty as an alternative to the ridge penalty for regularized multinomial regression.
• To develop a method (NPMR) that leverages underlying structure among response categories for improved prediction accuracy.
• To apply NPMR to predict outcome probabilities in Major League Baseball (MLB) based on batter-pitcher matchups.

Main Methods:

• The study proposes nuclear penalized multinomial regression (NPMR), a convex relaxation of reduced-rank multinomial regression.
• The nuclear norm penalty is utilized to incorporate and leverage the structure among response categories.
• The method is applied to analyze Major League Baseball play-by-play data.

Main Results:

• NPMR demonstrates the ability to leverage underlying structure among response categories for enhanced prediction.
• Application to MLB data shows NPMR's effectiveness in predicting outcome probabilities based on batter-pitcher matchups.
• The interpretation of results aligns with subject-area expertise and reveals novel player differentiators.

Conclusions:

• Nuclear norm penalty offers a promising alternative to ridge penalty in regularized multinomial regression.
• NPMR provides a powerful tool for predictive modeling in complex categorical data, particularly in sports analytics.
• The method yields interpretable results and advances understanding of factors influencing player performance and outcomes.