Exponential growth combined with exponential decline explains lifetime performance evolution in individual and human species.

The physiological parameters characterizing human capacities (the ability to move, reproduce or perform tasks) evolve with ageing: performance is limited at birth, increases to a maximum and then decreases back to zero at the day of death. Physical and intellectual skills follow such a pattern. Here, we investigate the development of sport and chess performances during the lifetime at two different scales: the individual athletes' careers and the world record by age class in 25 Olympic sports events and in grandmaster chess players. For all data sets, a biphasic development of growth and decline is described by a simple model that accounts for 91.7% of the variance at the individual level and 98.5% of the variance at the species one. The age of performance peak is computed at 26.1 years old for the events studied (26.0 years old for track and field, 21.0 years old for swimming and 31.4 years old for chess). The two processes (growth and decline) are exponential and start at age zero. Both were previously demonstrated to happen in other human and non-human biological functions that evolve with age. They occur at the individual and species levels with a similar pattern, suggesting a scale invariance property.

Success and decline: top 10 tennis players follow a biphasic course.

INTRODUCTION: The victory percentages for tennis players who entered the top 10 women and men rankings show various evolutions related to age and time since 1968. METHODS: The study analyzed the careers of all top 10 players: 97 women (50,933 matches) and 144 men (92,450 matches). For each player, we describe a biphasic performance course. Two generations were compared: the first one (G1), including players who started their professional career before 1985, and the second one (G2), with players starting after 1985. RESULTS: The average career length is 16.1 ± 3.8 yr for the top 10 men and 15.8 ± 4.4 yr for women. Compared with G1 players, G2 players begin earlier (women = 1.3 yr, men = 0.8 yr), but career length remains the same. An exponential model describes the time course of the victory percentage with a great similarity for both genders. Using this equation, the peak victory rate reaches 82.5% at 21.5 yr for number 1 (no. 1) women and 78.5% at 23.7 yr for no. 1 men, showing a greater precocity and earlier decline in women. Finally, the area under the curve shows a potential that is 22.8% (men) to 56.8% (women) larger for the no. 1 players as compared with all other numbers 2-10. CONCLUSIONS: 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.

Athlete atypicity on the edge of human achievement: performances stagnate after the last peak, in 1988.

The growth law for the development of top athletes performances remains unknown in quantifiable sport events. Here we present a growth model for 41351 best performers from 70 track and field (T&F) and swimming events and detail their characteristics over the modern Olympic era. We show that 64% of T&F events no longer improved since 1993, while 47% of swimming events stagnated after 1990, prior to a second progression step starting in 2000. Since then, 100% of swimming events continued to progress.We also provide a measurement of the atypicity for the 3919 best performances (BP) of each year in every event. The secular evolution of this parameter for T&F reveals four peaks; the most recent (1988) followed by a major stagnation. This last peak may correspond to the most recent successful attempt to push forward human physiological limits. No atypicity trend is detected in swimming. The upcoming rarefaction of new records in sport may be delayed by technological innovations, themselves depending upon economical constraints.

Success in developing regions: world records evolution through a geopolitical prism.

A previous analysis of World Records (WR) has revealed the potential limits of human physiology through athletes' personal commitment. The impact of political factors on sports has only been studied through Olympic medals and results. Here we studied 2876 WR from 63 nations in four summer disciplines. We propose three new indicators and show the impact of historical, geographical and economical factors on the regional WR evolution. The south-eastward path of weighted annual barycenter (i.e. the average of country coordinates weighting by the WR number) shows the emergence of East Africa and China in WR archives. Home WR ratio decreased from 79.9% before the second World War to 23.3% in 2008, underlining sports globalization. Annual Cumulative Proportions (ACP, i.e. the cumulative sum of the WR annual rate) highlight the regional rates of progression. For all regions, the mean slope of ACP during the Olympic era is 0.0101, with a maximum between 1950 and 1989 (0.0156). For European countries, this indicator reflects major historical events (slowdown for western countries after 1945, slowdown for eastern countries after 1990). Mean North-American ACP slope is 0.0029 over the century with an acceleration between 1950 and 1989 at 0.0046. Russia takes off in 1935 and slows down in 1988 (0.0038). For Eastern Europe, maximal progression is seen between 1970 and 1989 (0.0045). China starts in 1979 with a maximum between 1990 and 2008 (0.0021), while other regions have largely declined (mean ACP slope for all other countries = 0.0011). A similar trend is observed for the evolution of the 10 best performers. The national analysis of WR reveals a precise and quantifiable link between the sport performances of a country, its historical or geopolitical context, and its steps of development.