Bayesian Enhanced Stacking Method Integrating Multi-Model Advantages and its Application in Olympic Medal Prediction

Abstract

The Olympic medal tally serves as a key indicator for measuring a nation's comprehensive athletic strength, and accurate prediction holds significant importance for sports resource allocation and strategic planning. This study utilizes historical data from 163 countries/regions across Summer Olympics from 1896 to 2024. First, K-means clustering is employed to categorize participating nations into high, medium, and low medal-winning groups based on their performance levels, addressing data heterogeneity. Subsequently, we propose the Bayesian Enhanced Stacking Model (BESM). This model integrates three base learners-LightGBM, Attention-LSTM, and Bayesian Negative Binomial Regression-to capture nonlinear features, long-term temporal dependencies, and count data distribution characteristics, respectively. At the meta-learning layer, Bayesian Linear Regression enables adaptive weight allocation and uncertainty quantification. Systematic comparisons against mainstream models (SARIMA, Prophet, Random Forest, XGBoost, CNN) evaluated performance using MAE, RMSE, NB_Deviance, and SMAPE. Results demonstrate BESM's superiority across all groups: achieving the best performance on at least one metric in 88.5% of cases within the low-tier group (statistically significant, p<0.0001); demonstrated strong overall adaptability in the medium-medal group; and achieved the best SMAPE (33.3%) in the high-medal group. Traditional models exhibited pronounced group dependency and unstable performance. This study validates BESM's effectiveness in handling heterogeneous, sparse sports data, providing an accurate and reliable solution for Olympic medal prediction and national sports strategy formulation.