Applied Sciences: Physical Fitness and Performance
As running performances continue to improve, the limits to human performance remain the subject of much debate. The perceived reduction in the prevalence of record-breaking performance over recent years further fuels this debate, leading to a dichotomy of opinion between those who believe that we are close to the limits of human performance and others who believe that we have a considerable reserve in capacity. The importance of gender in this debate centers on the possible convergence of male and female performances. A number of studies have attempted to offer evidence for this debate. However, care is warranted in interpreting previous studies that have reported running performance predictions due to a number of methodological shortfalls in data collection and analysis.
Whipp and Ward (7), employing a simple linear regression model to predict running speed, stated that women marathon runners would run as fast as men in 1998, predicting a performance convergence at 2 h 1:59 min. It must be noted, however, that world marathon records for females did not exist before the late 1970s. Indeed, women's marathon did not feature as an Olympic discipline until the 1984 Los Angeles Olympics. This relatively recent involvement of women in the Marathon (men's records dating back to 1906) leaves a comparison of male and female marathon times somewhat tenuous.
In a more recent study, Tatem et al. (6) also employed simple linear regression to analyze male and female 100-m running times and predicted that women would run as fast as men in the year 2156 with a convergent running time of 8.079 s. A number of confounding variables exist when examining 100-m performances including the move from handheld to electronic timing and technological advancements including track surfaces in the mid-1960s. A further confounding influence is the rapid acceleration of world record times for women during the 1970s likely associated with the institutionalized approach to sports training, particularly in the former Eastern block. In particular, the significant performance gains observed during this period may be associated with the alleged systematic doping of athletes in these regimes. Whereas systematic doping may have played a significant ergogenic role in female athlete performance, the effect of doping was less obvious inmale athletes as anabolic agents were the principal form of doping during this period.
However, it is the use of linear regression modeling that results in potentially the greatest source of error in the evidence presented by Whipp and Ward (7) and Tatem et al. (6). Both use linear regression, but the former models world record running speeds whereas the latter uses world record running times. Clearly both models cannot be correct. For example, if relationship between world record speed and year was linear, given by speed = a + b·year (where a and b are the intercept and slope parameters, respectively), then world record times must follow a hyperbolic curve of the form, time = distance/speed = distance/(a + b·year). Furthermore, these conflicting models suggest that there are no limits to the speed at which humans can travel. Indeed, the linear model proposed by Tatem et al. suggests that at some time in the distant future, humans will run negative world record times. Clearly the use of linear regression to model world records is questionable and, as such, should be treated with some caution.
Hence, the purpose of the present study was to determine whether a more biologically sound and statistically robust nonlinear (flattened S-shaped) logistic curve could provide a superior fit to both men's and women's established world records across a range of running distances, compared to linear regression models. We would argue that the logistic curve is better able to reflect the learning curve that established world-record running performances would appear to have followed during the 20th century (probably due to advances in training, nutrition, science, and technology). Assuming that the logistic curves are better able to fit these world records, the upper running-speed limits will provide evidence to support or refute previous research that women will eventually run faster then men (6,7).
Given that future projected athletic world-record running times cannot continue to decline ad infinitum (i.e., becoming negative), and speeds are known to be more symmetric, normally distributed, and more linearly related to other variables (1,2,4), all world record times were converted to average running speed (m·s−1). Careful inspection of running speed world records over the 20th century suggest a rise in world-record running speeds that follow a flattened S-shaped curve similar to the logistic curve (3). A logistic curve to model world-record running speeds as a function of date (as the predictor variable) is given by
where min and max are the minimum and maximum predicted asymptotic world-record running speeds, b describes the rate at which the world-record running speeds accelerated during the 20th century, and y is the centered year that this acceleration was greatest.
The logistic model (equation 1) was fitted to all the world-record running speeds from 800 m to the marathon for men, and 800 m and 1500 m for women, using the nonlinear least-squares regression program as implemented in SPSS (see Appendixfor the adopted SPSS syntax file).
The men and women's 800-m and 1500-m running-speed world records recorded during 20th century, plus the fitted logistic curves are given in Figs. 1 and 2, respectively.
The fitted logistic curves parameters (estimated using the SPSS nonlinear regression analysis) for men and women's running speed world records are given in Table 1. Note that by comparing the estimates with twice their standard errors, all parameters are significant. For comparative purposes, the explained variance (R2) and SD about the fitted logistic (four parameters) and linear models (two parameters) are given in Table 2, together with the significance of the additional variance explained by the two additional parameters (obtained by separating/partitioning the explained variance from the logistic and linear models using ANOVA).
The men's mile, 5000-m, 10,000-m, and marathon running-speed world records recorded during 20th century, plus the corresponding fitted logistic curves are given in Figure 3.
Finally, a summary of current world records and future predicted peak running world records (the upper asymptotic limits) from 800 m to the marathon for men and 800 m and 1500 m for women are given in Table 3 (Note that the current women's 1500-m world record would appear to have reached its peak asymptote¡)
Previous research has fitted linear models to describe the rise in world-record running speeds or the decline in world record times over the past 20th century (6,7). These models imply that either world-record times will continue to decline ad infinitum (i.e., eventually become negative) (6) or that world-record running speeds will continue to rise (7), suggesting there are no limits to athletic running performances. However, in the present study, a more biologically sound logistic, flattened S-shaped curve was fitted to the middle- and long-distance world-record running speeds of both male and female athletes. All the four-parameter logistic models (with the exception of the men's 800-m logistic model) fitted the data significantly better than the two-parameter linear models. The logistic curves suggest that there are indeed limits to human running performance (see Table 3 for predicted asymptotic speeds and times).
For male athletes, it appears that the limits to performance have not been reached, and while the difference between current and predicted world record times are variable between events, the percentages of differences are similar between distances: 1.1% (1.3 s) for the 800 m to 1.4% (2.9 s) for the 1500 m, 1.9% (4.1 s) for the mile, 3.3% (25.3 s) for the 5000 m, 0.7% (9.4 s) for the 10,000 m, and 1.1% (1 min 15.6 s) for the marathon. These data suggest that male runners are close to maximum running speed.
Examination of the logistic curves' beta values b and centered year for male runners at each distance demonstrates the period of greatest gain (acceleration) in world record performances occurred from the late 1940s to the mid-1960s. This period coincides with a shift in attitudes to a more professional approach to training and competition as evidenced by the introduction of professional coaches and the use of coaching and sport science (5). In addition, the globalization of sport during this period resulted in an increased participation and the inclusion of a number of the key running nations, that is, middle Africans. Note that world records of new events such as women's pole vault are still going through this acceleration phase, as evidenced by the pole-vault world record being broken six times in 2004. However, because these pole-vault world records were recorded only recently and are relatively sparse, these data were not be included in the present analyses.
The relatively slow improvement in men's world record times in the early 1900s is likely due to the Victorians who codified athletics under the AAA and imposed a strictly amateur ethos surrounding athletic participation limiting sport primarily to the middle classes. Indeed, there is evidence to suggest professional athletes ran considerably faster times before the imposed amateur regulations; however, these records were not recognized by the AAA when official record keeping began in the early 1900s (5).
Data for female athletes present a slightly different picture. It would appear that female 1500-m runners have reached the limit to performance. Care is warranted in this conclusion, however, due to the late inclusion of female athletes in this event (1967). This postulation is supported by the year of greatest acceleration in world-record times (beta value) occurring in the early 1970s. Despite the late inclusion of female athletes in the 1500 m, the world record of 3 min 52.47 s set in 1980 was only broken in 1993 in a time of 3 min 50.46 s, a record that stands 12 yr after being set, offering support for the notion that female 1500-m runners are unlikely to run faster. Previous authors (6,7) might be forgiven for speculating that women will run faster than men due to women's world records reaching the steeper acceleration phase of the flattened S-shaped curve more recently than men (see Figs. 1 and 2).
Based on the evidence presented above, it would appear that there are limits to human athletic performance and given their lower peak running speed asymptotes, it is clear that female athletes are unlikely to run middle and long distance events faster than men. The consequences of reaching the limits of human athletic performance undoubtedly have social ramifications for both the athletic, scientific, and general populations. In a quest to attain faster times linked to commercial reward, the athletic and scientific community may continue to explore greater performance gains through the use of pharmacology and the evolving science of gene doping. For spectators of athletic events, the impact of attaining the limits to human performance may be less profound. As was observed with the changes in Javelin design in the 1990s and the subsequent reduction in the world record by approximately 30%, spectators continue to be thrilled by these gladiator-like contests between the world's greatest athletes irrespective of performance in relation to world records.
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* Nonlinear regression.
MODEL PROGRAM MIN = 5 MAX=7 B=0.04 Y=1950.
COMPUTE PRED_ = min+(max-min)*exp(b*(date-y))/(1+exp(b*(date-y))).
/OUTFILE = ’C:
/CRITERIA SSCONVERGENCE 1E-8 PCON 1E-8.
Keywords:©2005The American College of Sports Medicine
LOGISTIC CURVE; NONLINEAR REGRESSION; RUNNING SPEEDS; MIDDLE- AND LONG DISTANCE