Optimization of Sports Team Management Based on Bayesian Dynamic Weights and Entropy-Weighted TOPSIS

Abstract

Aiming at the coupling problems of dynamic multi-objective decision-making, multi-dimensional asset valuation and structural risk transmission in professional sports team management, this paper constructs an integrated algorithm framework integrating Bayesian online learning, entropy-weighted TOPSIS and graph theory clustering. At the dynamic decision-making level, a three-objective optimization function including competitive performance, financial return and risk exposure is established, the Bayesian weight update mechanism (learning rate η=0.05) is used to realize the adaptive adjustment of strategy priority, and the Monte Carlo simulation (1000 iterations) is combined to calculate the value at risk and the value at risk at 95% confidence level, and the convergence test shows that the utility function increases by 18.7% within 10 weeks. At the level of player valuation, a multi-dimensional evaluation system containing 7 on-field indicators, 3 commercial factors and injury risk coefficients is constructed, and the entropy weight method is used to objectively determine the index weight (information entropy redundancy). <0.12), the player ranking is completed by calculating the relative closeness of TOPSIS, and the optimal resource allocation is solved in combination with linear programming, and the balanced strategy of "40% of the draft + 40% of free signing + 20% of the trade" is realized under the constraints of the salary cap, and the expected win rate is increased by 5.2%. At the level of league expansion impact analysis, a team association network is constructed based on graph theory, K-means clustering (contour coefficient 0.73) is used to quantify the market overlap index, and a revenue dilution function and talent dispersion model are established, which shows that the new adjacent teams will cause an annual revenue loss of 5.6–7.2 million US dollars, and the talent dilution index reaches 0.15, according to which a hierarchical buffer strategy can recover about 20% of the potential loss. The sensitivity analysis verifies that the key parameters (learning rate, injury reduction coefficient, geographical weight) maintain a stable model output within the ±20% fluctuation range, and the cross-verification shows that the coupling error of each module is less than 6.8%. Experimental results show that the integrated algorithm framework can provide quantitative decision support for management, and improve the three dimensions of strategic adaptability, asset allocation efficiency and risk forward-looking by 23%, 17% and 31% compared with traditional methods, respectively.