Non-Centered Chi Distributions as Models for Fair Assessment in Sports Performance

Puig Castro, D., Coronado Ferrer, A., Castro Palacio, J. C., Fernández de Córdoba, P., Ortigosa, N., & Sánchez Pérez, E. A. (2025). Non-Centered Chi Distributions as Models for Fair Assessment in Sports Performance. Symmetry, 17(7), 1039. https://doi.org/10.3390/sym17071039

symmetry-17-01039

Abstract:

Some stochastic phenomena that appear in real-world processes and satisfy some similar characteristics can be effectively modeled using functions based on variants of the chi distribution. In this paper, we extend the use of the uncentered chi distribution to the assessment of sports performance, focusing on its ability to characterize the physical fitness of athletes. The generating functions, constructed from individual test data assumed to follow a Gaussian distribution, provide a basis for creating a fitness index. In addition, we propose a methodology to rank athletes based on their performance in specific physical tests. Drawing on parallels with thermodynamic systems, such as the behavior of particles in an ideal gas, we explore the suitability of the (non-centered) chi distribution for modeling sports data. Simulations and real examples are presented that demonstrate the robustness of this approach.