Mathematical Modeling Analysis of the Performance Evolution Along the Career-Span of Male Swimmers (Análise da Evolução da Carreira Desportiva de Nadadores do Sexo Masculino Utilizando a Modelação Matemática)

The aim of the present study was to analyze the curves of performance evolution along the career-span of male swimmers, trough mathematical modeling procedures. The sample comprised a series of data with a total of 13.360 observations. These data corresponded to the national rankings over the past four years for all age categories in 25m swimming pools. Mathematical procedures were applied to the data following three steps: i) calculation of the optimal age for the best performance; ii) calculation of the performance evolution along the career-span for 100m, 200m, and 400m events; iii) modeling of the curves of performance evolution along the career-span with the inclusion of the optimal age for best performance as a constraint. The results have shown that, in Portugal, the male swimmers tend to achieve their best performances sooner for the largest distances events: 21.97 ± 0.72 for 100m; 20.66 ± 0.68 for 200m; 20.66 ± 0.52 for 400m). The mathematical function of the performance evolution presented a non-linear behavior with two peaks (between 11-12 and 13-14 years and between 15-16 and 16-17 years of age). In Portugal, the systematic training of swimmers aiming top performances begins usually between 9-11 years of age. Therefore, the results of the present study draw attention to the urgency of: i) structure of the training process respecting the individual growth and maturation processes; ii) reflection upon the orientation of training loads and their magnitude; iii) implementation of measures to promote and organize the sport according to the specificity of the training process. The adoption of the aforementioned policies may help to predict the performance evolution of swimmers based on mathematical models such as the model presented on this study