The primary aim of this research is to provide a significant addition to the existing body of knowledge by presenting a new probability model called the weighted sine generalized Rayleigh (WSG-Rayleigh) distribution. This initiative aims to enhance data modeling capabilities and techniques for better decision-making across various applied fields. The WSG-Rayleigh is derived from integrating the generalized Rayleigh distribution with a previously developed trigonometric approach. In addition to the presentation of specific distributional functions and visual representations, various properties are established for the WSG-Rayleigh distribution. Additionally, the approach for estimating parameters and the simulation studies associated with the WSG-Rayleigh distribution are also incorporated. Ultimately, the practical applications of the WSG-Rayleigh distribution are sufficiently examined through an analysis of two distinct data sets, each representing a particular field of study. The initial application centers on physical education. The second application highlights sports sciences. A quantitative assessment is conducted to contrast the WSG-Rayleigh distribution with several notable modifications of the Rayleigh distribution. Through several assessment methods, we find that the WSG-Rayleigh distribution is the most efficient for data modeling in the examined application across these two domains.