With the rapid development of the AMOS model, it provides new ideas for the construction research of sports statistical index systems. This paper firstly measures the level of sports development based on the current situation of the construction of a sports statistical index system, and the sports statistical index system is scored by the comprehensive index method. Secondly, it identifies for SEM model and AMOS model and establishes the sports statistical index system based on the AMOS model. Finally, it was verified that the dimensional division of the PE model and variable indexes were reasonable, and the relationship between latent variables was defended on the basis of variable index calculation and utility analysis. The results show that student expectations have the greatest positive total impact on students’ perceived value with a value of 0.58274, that student expectations have the greatest indirect impact on students, and that the indirect impact is close to its direct effect impact with a value of 0.26845, that the total impact on students ranks second with a value of 0.66374, and that student expectations have an indirect impact on student complaints and student loyalty through one and more intermediate variables. Thus, it shows that the AMOS model can effectively solve the problem of constructing a sports statistical index system and promote the development and innovation of research on constructing a sports statistical index system.