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Conceived and designed the experiments: AS A. Marc FD JFT. Performed the experiments: AS A. Marc JS. Analyzed the data: AS A. Marc A. Marck JS GB. Contributed reagents/materials/analysis tools: AH MD GB. Wrote the paper: AS A. Marc A. Marck FD JS MD JFT. This manuscript was critically revised for intellectual content by all co-authors.

The purpose of this study is to investigate the association between anthropometric characteristics and performance in all track and field running events and assess Body Mass Index (BMI) as a relevant performance indicator. Data of mass, height, BMI and speed were collected for the top 100 international men athletes in track events from 100 m to marathon for the 1996–2011 seasons, and analyzed by decile of performance. Speed is significantly associated with mass (r = 0.71) and BMI (r = 0.71) in world-class runners and moderately with height (r = 0.39). Athletes, on average were continuously lighter and smaller with distance increments. In track and field, speed continuously increases with BMI. In each event, performances are organized through physique gradients. «Lighter and smaller is better» in endurance events but «heavier and taller is better» for sprints. When performance increases, BMI variability progressively tightens, but it is always centered around a distance-specific optimum. Running speed is organized through biometric gradients, which both drives and are driven by performance optimization. The highest performance level is associated with narrower biometric intervals. Through BMI indicators, diversity is possible for sprints whereas for long distance events, there is a more restrictive aspect in terms of physique. BMI is a relevant indicator, which allows for a clear differentiation of athletes' capacities between each discipline and level of performance in the fields of human possibilities.

In general, nature tends to increase diversity and complexity ^{−2}, and for the 10 best performers of all time a BMI range between 17.5 and 20.7 kg.m^{−2}. Following the example of energy contribution from the aerobic to anaerobic mechanisms in different running distance

Data of mass, height, BMI, and speed were collected for each international male athlete among the top 100 rankings of eight running events: 100 m, 200 m, 400 m, 800 m, 1500 m, 3000 m, 10.000 m and marathon during the 1996–2011 seasons. This represents 12,800 annual-performers and 3,852 different athletes. Height and mass values were coincided with each individual's best performance by year. All of the data was collected from the website

Data was organized according to four types of distributions.

First, the distribution of all athletes by distance was organized according to their BMI to identify potential morphological gradients.

Secondly, by deciles of speed: the first decile represents the 160 best performers of the discipline and the last decile represents the 160 slowest performers for a total of 1,600 annual-performers by distance (Top 100 in 16 years). We compared data of mass, height and BMI according to race distances and performance deciles.

The third organization of data was by percentage of performance: we stratified athletes BMI, by distance treated by the percentage of the best performances during the study period (1996–2011).

Lastly, the fourth by density: distributions of all BMI points by running events were presented according to speed. In order to investigate these distributions, we partitioned the BMI points of all athletes according to running events depending on performance percentage over a mesh M. Let _{i}, Y_{j}_{X} = 1600) and _{Y} = 1600). The density of athletes' BMI was estimated over the nodes of _{i}_{j}_{i}), min(Y_{i}). Upper boundaries [Ux; Uy] were defined as the smallest integer that is not less than max(X_{i}), max(Y_{i}). Note that in our case, the difference of the boundaries of the athletes BMI dimension

The numbers of nodes in the _{x}_{y}

M was set as a homogeneous mesh, such that each node was separated by the value

Such that the maximum possible distance between two nodes did not exceed _{Y}

For the estimation of the density, the number of athletes' BMI performance _{j}

For choosing the best representation of the density and in order to avoid information loss due to an inadequate resolution of the mesh, we set the value of

All of the data was reported as means ± standard deviation. Associations between the subjects' physique (height, mass and BMI), and speed were examined using the Pearson product-moment correlation coefficient. Differences in anthropometrics and speed of the different track and field running events were compared using one-way analysis of variance test (ANOVA). Comparisons of the different track and field groups were performed using Bonferroni's Multiple Comparison Test. The level of significance was set at p = 0.05. Statistical analyzes were realized with the software Statistica 7.1 and Matlab 7.13.

This study is designed and monitored by the IRMES (Institut de Recherche bio-Médicale et d'Epidémiologie du Sport) scientific committee. It uses a research protocol qualified as non-interventional, in which ‘…all acts are performed in a normal manner, without any supplemental or unusual procedure of diagnosis or monitoring.’ (Article L1121–1 of the French Public Health Code). According to the law, its approval therefore did not fall under the responsibility of a committee for the protection of persons (CPP), it does not require informed consent from individual athletes.

Speed is significantly associated with mass (r = 0.71) and BMI (r = 0.71) but moderately with height (r = 0.39). The ANOVA test shows significant differences among events for height (excluding 10,000 m

The mean mass of athletes by decile and discipline continuously increases with speed (

Black circles show the 200

The mean height of athletes by decile and discipline also depends on speed (

First decile athletes from marathon to 800 m are lighter than their counterparts in lower deciles. Conversely, a break occurs in sprints (400 m, 200 m and 100 m), where the most successful athletes (from the first decile) have a gradient tending towards a higher mass. Thus, the fastest athletes in sprints are heavier while the lighter athletes are the most effective in long distances. Like mass, athletes of the first deciles from marathon to 800 m are shorter than their counterparts in the lowest deciles. In contrast for sprints, a break occurs as well for the most successful athletes who they display a progressively taller height.

^{−2} for the 100 m, 23 kg.m^{−2} for the 200 m, 23–22 kg.m^{−2} for the 400 m, 21 kg.m^{−2} for 800 m and 1500 m and 20 kg.m^{−2} for the 3000 m, 10 000 m and marathon. Long distances are distributed according to a peak while, 100 m 400 m have a plateau with range of BMI.

Each curve links points representing the percentage of athletes per 1 BMI unit for each event.

^{−2} to 100 m: 23.3±1.67 kg.m^{−2}.

Black circles show the 200 m athletes ordered by decile.

Exact data and density function are shown in ^{−2}; when performance level reaches 98–99%, BMI ranges from 20.1 to 20.9 kg.m^{−2}. And we observed the same differences across all of the events. We also observed an offset of the majority of the points (red density) towards lower BMI from sprint events to long and middle distance. For the 10,000 m and marathon, like the best performers, the greatest numbers of points (red density) are centered on an optimum interval between 19–20 kg.m^{−2}.

To the left: Exact data of athletes' BMI distribution. To the right, athletes' BMI are represented by a density function. At the left end points are more visible to the right central density of greater number of athletes appears more clearly. (Fig. 4A 100 m, Fig. 4B 800 m, Fig. 4C 10 000 m and Fig. 4D marathon).

The present study shows that biometric parameters are ordered in a consistent self-organization between sprint and long distance. Physique optimal range for performance across the full continuum of event specializations events emerge in an organized structural basis. Consequently, this study is the first to reveal morphological optimization on the entire spectrum of track events and the relevance of BMI as performance indicator.

We also find that between 1996 to 2011 seasons, mean mass and height of the best athletes of sprint events (100 m to 400 m) are bigger (BMI and mass) than those of middle and long distance (800 m to marathon). This confirms the trends observed in track and field history

As distance progressively decreases from marathon to 400 m, the runners gradually become taller, in accordance with the literature

Similarly to height, as the distance progressively decreases from marathon to 100 m, runners gradually become heavier. This redefines mass as a key requirement for speed

Smaller sized runners also draw another benefit of their morphologies for long distances. There is a strong relationship between distance and heat-exchange characteristics. Heat production/dissipation ratio becomes increasingly important as running distance increase

Links between performance and morphology are strengthened by gradient of size within each discipline. Not only sprinters are heavier than their long and middle distances counterparts but within their distance, the fastest athletes are also heavier. This confirms the trend observed by Khosla

Like energetic progressive contribution from the aerobic to anaerobic mechanisms

A consistent trend of increasing BMI with speed was observed with distance running performance, in accordance with previous studies showing positive effect between BMI and performance

Event differences, from the marathon to 100 m, create patterns of divergent BMI and optimal body type. As performance increases it can be observed that the spectrum of BMI narrows into a more optimal area. Our study shows a reduction in variability of BMI with performance increments, where the best athletes are attracted to optimum interval. For an athlete, being away from optimum probably negatively affects his performance. Moreover, a major part of the 10,000 m and marathon athletes are also centered around an optimum interval (19–20 kg.m^{−2}) respectively, as shown by Marc et al

Locomotion is one of the major functions in life. Previous studies have suggested that the relationship between maximum relative running speed and body mass follow a curvilinear function

This study emphasizes mass, height and BMI as key requirements for speed. It allows for the identification of optimal physiques according to track and field events. BMI and mass are better indicators than height. However, BMI is preferred because it allows for the combination of both contributions. It appears to be a useful indicator in the categorization of elite athletes. Over time, physiological, physical and biomechanical constraints generated morphologies adapted to each race, a trend reinforced by performance gradients within each discipline. As a result there is a narrowing range around an optimal BMI for each event, where best athletes are “attracted”. Our study also reveals a possibility of larger organization induced by BMI range in diversity and complexity increase system.

The authors thank Guy Ontanon sprint coach at the French Federation of track and fields for proofreading the manuscript and providing valuable critique and advice. The authors thank INSEP teams for their full support.