The advanced analysis and research methods of big data will provide theoretical support for the integration of athletes’ talent training. The advanced technological methods of big data will also give full play to the advantages of tapping the potential of talents and actively improve the success rate of grassroots young athletes. This paper proposes an improved Adaptive Particle Swarm Optimization (APSO) algorithm for the optimization of radial basis function (RBF) neural network parameters. The basic structure of RBF neural network is introduced, and the influence of parameters on the performance of RBF neural network is analyzed. The optimization method of RBF neural network parameters is analyzed, and Particle Swarm Optimization (PSO) algorithm is selected as the parameter optimization method of RBF neural network. In addition, an improved APSO algorithm is proposed according to the advantages and disadvantages of PSO and compared with other PSO algorithms. Experimental results show that the improved PSO algorithm has better accuracy. The improved PSO algorithm is applied to the parameter optimization of RBF neural network, and the experimental results prove the superiority of the proposed method. By weighting the second-level indicators, the weights of the second-level indicators of athletes’ competitive ability are in order of skill, athletic quality, psychological ability, and artistic expression. Skills are the main factors that determine the level of competitive ability. Sports quality and psychological ability are important guarantees for supporting the normal performance of skills. Artistic expressiveness is a supplementary factor for competitive ability. The various elements cooperate with each other and interact with each other. The indicators do not exist alone but cooperate with each other to support the formation of the entire athletic ability system. In the content of the competitive ability index of excellent athletes, technical ability is the core, and sports quality, psychological ability, and artistic performance ability ultimately exist to serve the improvement of technical ability. The competition scores of the 100 athletes counted in this article are all above 9.0 points. The difference between APSO-RBF’s action quality scores of 100 athletes and the real value is less than 3%. In terms of movement difficulty, the APSO-RBF evaluated athletes’ scores are close to 1.65 points, which is basically the same as the real value.