# Nonlinear age effects on basketball player performance: insights from Kolmogorov–Arnold Networks in NBA data

## TL;DR

This paper uses a new machine learning model to show how NBA player performance changes nonlinearly with age, revealing different patterns for young, prime, and veteran players.

## Contribution

A novel interpretable machine learning framework using Kolmogorov–Arnold Networks to model nonlinear age-performance dynamics in basketball.

## Key findings

- KAN outperforms other models in predicting performance across age groups with the lowest MAE and RMSE.
- Youth performance is driven by volatile, interacting variables, while Prime performance is stabilized by key metrics like points and rebounds.
- Veteran performance shows a ceiling effect and diminishing returns, converging on a few core variables.

## Abstract

This study utilizes 2,786 NBA player–season samples from 2019 to 2024 to develop a nonlinear modeling approach based on Kolmogorov–Arnold Networks (KAN), applied to modeling the relationship between player age and basketball performance. A novel modeling framework is proposed, integrating interpretable machine learning with age-group-specific feature analysis, aiming to systematically reveal the nonlinear dynamics and transitional mechanisms of performance evolution across age.

Fantasy Points is used as the unified performance metric, and players are categorized into three age groups: Youth (19–23 years), Prime (24–30 years), and Veteran (31–40 years). The KAN model is tuned via Bayesian optimization and evaluated using five-fold cross-validation. Its performance is systematically compared against mainstream models, including Multilayer Perceptron (MLP), XGBoost, Random Forest, and Linear Regression.

Results show that KAN achieves the lowest MAE and RMSE across all age groups, with the best or near-best R² values. In the youth group, the model achieves MAE = 0.089, RMSE = 0.115, and R² = 0.986, significantly outperforming all baseline models. Further response function analysis reveals nonlinear structural features in the age–performance relationship. Attribution results indicate that youth performance is driven by multiple interacting variables with strong and volatile marginal effects; in Prime, performance stabilizes and is dominated by key metrics such as points (PTS), assists (AST), and rebounds (REB); in Veteran, performance converges on a few core variables, with a “ceiling effect” and diminishing marginal returns.

Using a KAN-based nonlinear framework, we reveal the age-group-specific evolution of basketball performance with age, offering new methodological insights for career management, training optimization, and intelligent decision-making in professional sports.