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Conceived and designed the experiments: OH GB JT XJ. Performed the experiments: GB JT VT NE. Analyzed the data: GB VT MT SE. Contributed reagents/materials/analysis tools: GB MT SE. Wrote the paper: GB JT.

The authors have declared that no competing interests exist.

World records (WR) in sports illustrate the ultimate expression of human integrated muscle biology, through speed or strength performances. Analysis and prediction of man's physiological boundaries in sports and impact of external (historical or environmental) conditions on WR occurrence are subject to scientific controversy. Based on the analysis of 3263 WR established for all quantifiable official contests since the first Olympic Games, we show here that WR progression rate follows a piecewise exponential decaying pattern with very high accuracy (mean adjusted ^{2}

Olympic Games were reintroduced in 1896 by Pierre de Coubertin. One hundred and eleven years later, world record collection shows the progression of human performance as elite athletes periodically pushed back the frontiers of “ultra-physiology”. This unplanned experiment could have been written as the phenotypic maximization of present human genotype under the pressure of regulated competition

A. Women 400 m freestyle (swimming) with biexponential decaying curve, adjusted _{i}^{2}_{ii}^{2}_{i}^{2}_{ii}^{2}_{i}^{2}_{ii}^{2}_{i}^{2}_{ii}^{2}_{iii}^{2}_{iv}^{2}

We conducted a qualitative and quantitative analysis of 3263 WR in all 147 measurable Olympic events from five disciplines

Two indicators were introduced in order to describe WR. Because the WR number established each year also depends on the number of events, we defined factor ^{th} best performance as compared to the ^{th} value:_{t}

WR series for each event were fitted by the function

Where Δ_{WR}_{i,j}_{f,j}_{i,j}_{f,j}_{j}_{j}_{i,j}_{f,j}_{i,j}.

A procedure based on the best adjusted ^{2}^{2}

For each event, this piecewise exponential decaying model provides successive periods. A period refers to a time slot defined by a group of consecutive WR, following a rupture of incline. During the period _{j}_{j}_{i}) and final (WR_{f}) records to

The initial progression range is given by

For chronometric events (WR_{i}>WR_{f}): _{i}<WR_{f}):

This presentation also allows for a comparison of each record as a percentage of the estimated asymptotic value.

Data set used for prediction was reduced to 125 events. From the 22 discarded events, two resulted from javelin weight change and 20 referred to weight lifting: 9 Clean and Press events were removed from official list in 1972 (

Coefficients of equation (5) are calculated for the last period of each event through LMA. The result is used to estimate the year ^{th} of a second on the 100m (and about 4s on a marathon or 100g in weight lifting disciplines).

Credibility interval is computed using a simulation method of Monte Carlo

We used the 2.5th percentile, median and 97.5th percentile to produce the prediction errors for the estimated year at 99.95% and the estimated WR asymptotic values. The credibility interval

Chronometric events represent 58% of the data set (swimming, track, cycling, speed skating) with a decreasing tendency of WR values; 42% are non chronometric events (field, weight lifting) with increasing WR values.

Factor _{wwI}_{wwII}

Exact numbers (black dots) are filtered with a 60 Hz second order low pass butterworth filter (black curve). World wars show major impact on _{wwI}_{wwII}

_{t}

This decrease is representative of the growing difficulty to improve previously established WR values.

Using the best adjusted ^{2}^{2}

We predicted the asymptotic value of each record, using the inverse function of equation (3) on the last period of 125 exploitable events (

Results are sampled by decades. Half of the asymptotic records will be established in 2027, and 90% in 2068.

The proposed piecewise exponential decaying model, describing momentary expansion in a finite context, suggests a major global fading of WR progression. During an initial phase of rapid improvement, interrupted by two major events (^{2}

Recently introduced events, such as women weight lifting starting in 1998 (

Historical circumstances and WR evolution are closely linked: the impact of world wars results in two delays (_{wwII}_{wwI}

Individual or team doping strategies have been used throughout the Olympic era, and state controlled protocols were developed since 1970 ^{th} century

Major international rule changes, new technologies or gene profiling have also been tested in sport

In summary, an epidemiological analysis of sport performances demonstrates that WR progression follows a piecewise exponential decaying pattern, altered by historical events. Results point out that in 2007, WR have reached 99% of their asymptotic value. Present conditions prevailing for the next 20 years, half of all WR won't be improved by more than 0.05%. As compared to the positivism triumphing at the time Coubertin inspired Olympic renewal, the present analysis emphasizes the ineluctable rarefaction of the quantifiable proofs of human physiological progression.

Evolution of cumulative annual number of records. The growth of WR is altered by the two world wars, and is slowing down since 1988.

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Evolution of cumulative annual number of events with official WR. In 1972, 9 weight-lifting events were discarded from Olympic event list; 14 women weight lifting events were introduced in 1998.

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Adjusted r^{2} values for the 363 periods showing no variation over the modern Olympic era (Linear model: F(1,361) = 1.268, P = 0.261) and a mean value of 0.91±0.08.

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Evolution of b': this parameter increases (Linear model: F(1,145) = 106.7, P<0.001) during the Olympic era, such that recently introduced events will reach their asymptote faster than early XXth century contests.

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Table of predicted WR asymptotic value, year of the 99.95% limit, credibility intervals and period number per event. Women and men are respectively symbolized by (W) and (M). C&J are Clean and Jerk weight lifting events. Two versions of the Track women 100 m are presented, version 1 includes the last WR, version 2 leaves it out.

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This article is dedicated to Loic Leferme's memory. We thank Dr Robin Choudhury and Pr Zahi A. Fayad for careful reviews. We thank the INSEP teams for their full support.