Success and Decline

Abstract

Tennis players in the top 10 show a biphasic career. Women reach their highest level earlier than men, consistent with their more precocious biological development. For the current generation, the peak performance tends toward a younger age than the first generation. We show how to precisely quantify and compare tennis performances using indicators that follow the trends of development and aging and demonstrate that precocity does not provide a larger victory potential.

An integrative modeling approach to the age-performance relationship in mammals at the cellular scale

“…Many studies describe the decline in locomotor speed, perceptual or cognitive functions, components of memory, reaction time, nerve conduction speed, muscular strength and flexibility, and other traits, and show that experimental investigations are valuable because they provide information about the dynamics of changes during the lifespan. In particular aging effects are studied in human sporting events 9,11,12,22,25,40 where it is non-linear with time and has a declining curved shape. The extension of such research to other species may also help in identifying the common physiological and biological features that are responsible for this decline 4,26 .…”

“…Moore’s equation has been frequently used to describe changes in physical or cognitive performance with aging 10,25,27 . A difference between Moore’s equation and the model presented herein is the additional parameter t d that corresponds to an explicit time of death, where the decreasing process reaches 0.…”

“…pain, fatigue) from several different chronic conditions after the fifth decade of life 24 . The rate of physical decline in aging adults has been studied in various disciplines 10–12,25 and is now regarded as a hallmark of the aging process 4,26 , and serves as a key indicator of diminishing quality of life while remaining a predictor of physical disability and other morbidities 4 . Justice et al .…”

“…He showed that the age-related changes of top physical performance in 15 running and two throwing events exhibit an inverted-U pattern that can be described using a single equation based on two non-linear functions:where a , b , c , d are four positive constants and P ( t ) is the performance value at age t . Equation (1) can be accurately applied to existing datasets in a variety of species 10,25,26 for a number of different individual athletic or cognitive capacities despite inter-individual variability 10,25 . Other studies have used second-order polynomial equations to fit the pattern 9 ; however, the age-performance relationship is consistently reported to be asymmetrical, with an ‘early’ ( i .…”

“…e . before mid lifespan) age of peak performance 10,25–27 , meaning that quadratic functions, such as second order polynomials, provide a poor estimate of the age of peak performance.…”