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A technique to determine the fastest age-adjusted masters marathon world records

View Article: PubMed Central - PubMed

ABSTRACT

Introduction/purpose: This study’s purpose was to develop and employ a technique to determine the fastest masters marathon world records (WR), ages 35–79 years, adjusted for age (WRadj).

Methods: From single-age WR data, a best-fit polynomial curve (WRpred1) was developed for the larger age range of 29–80 years for women and 30–80 years for men to improve curve stability in the 35–79 years range. Due to the relatively large degree of data scatter about the curve and the resultant age bias in favor of older runners, a subsample was constituted consisting of those with the lowest WR/WRpred1 ratio within each five-year age group (N = 11). A new polynomial best-fit curve (WRpred2) was developed from this subsample to become the standard against which WR would be compared across age. WRadj was computed from WR/WRpred2 for all runners, 35–79 years, from which the top ten fastest were then determined.

Results: The WRpred2 model reduced data scatter and eliminated the age bias. Tatyana Pozdniakova, 50 years, WR = 2:31:05, WRadj = 2:12:40; and Ed Whitlock, 73 years, WR = 2:54:48, WRadj = 1:59:57, had the fastest WRadj for women and men, respectively.

Conclusions: This technique of iterative curve-fitting may be an optimal way of determining the fastest masters WRadj and may also be useful in better understanding the upper limits of human performance by age.

No MeSH data available.


Marathon world records by age. Best-fit curves (WRpred) are 2nd order polynomials
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Fig1: Marathon world records by age. Best-fit curves (WRpred) are 2nd order polynomials

Mentions: In Fig. 1, the scatterplots of age versus WR for the 11 age groups, data points exhibited the expected scatter above and below the best-fit curve (WRpred1) particularly among the oldest runners. Since largest percent distance below the curve corresponded to the fastest WRadj then visual inspection of Fig. 1 suggested a bias in favor of older younger runners in the determination of the fastest WRadj for either sex. Pearson correlation coefficients of age versus WR/WRpred1 for the 20 lowest ratios of each sex confirmed the bias (r = 0.56 for women and 0.53 for men, p < 0.01 for both). The same correlation coefficients for age versus WR/WRpred2, however, suggested reduction of the bias (r = 0.09 for women and 0.33 for men, p > 0.10 for both). The 20 lowest ratios were used because the scatter below the curve is where increasing age would be associated with faster WRadj in WRpred1—where the bias matters (i.e., bias amongst the slowest WRadj is inconsequential). Above the curve, where the slower WRadj holders are, one would expect WRadj would be slower with increasing age. To include all WR holders would cancel out the correlations to essentially zero. As expected, the subsample’s WRpred2 fit improved from WRpred1 (R2 = 0.990 vs. 0.916 for women and 0.992 vs. 0.901 for men, p < 0.001 for both). The equations for WRpred2 were:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\text{Women}}&{:}\,{\text{WRpred2}} = 0.0.0000308562\, \times \,{\text{Age}}^{2} - 0.0018125288 \\ & \quad \times \,{\text{Age}}\, + \,0.121203508 \\ \end{aligned}$$\end{document}Women:WRpred2=0.0.0000308562×Age2-0.0018125288×Age+0.1212035082\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\text{Men:}}\,{\text{WRpred2}} & = 0.0000137573\, \times \,{\text{Age}}^{2} - 0.0005140915 \\ & \quad \times \,{\text{Age}}\, + \,0.0879275237 \\ \end{aligned}$$\end{document}Men:WRpred2=0.0000137573×Age2-0.0005140915×Age+0.0879275237The large number of decimal places was necessary for the precision of the WRpred2 curves, especially with the characteristic exponents. As expected, due to the mandatory selection of the lowest WR/WRpred1 values within each age group, the largest age gaps with no data points were 9 years, each occurring only once within each sex. Fig. 1


A technique to determine the fastest age-adjusted masters marathon world records
Marathon world records by age. Best-fit curves (WRpred) are 2nd order polynomials
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5016493&req=5

Fig1: Marathon world records by age. Best-fit curves (WRpred) are 2nd order polynomials
Mentions: In Fig. 1, the scatterplots of age versus WR for the 11 age groups, data points exhibited the expected scatter above and below the best-fit curve (WRpred1) particularly among the oldest runners. Since largest percent distance below the curve corresponded to the fastest WRadj then visual inspection of Fig. 1 suggested a bias in favor of older younger runners in the determination of the fastest WRadj for either sex. Pearson correlation coefficients of age versus WR/WRpred1 for the 20 lowest ratios of each sex confirmed the bias (r = 0.56 for women and 0.53 for men, p < 0.01 for both). The same correlation coefficients for age versus WR/WRpred2, however, suggested reduction of the bias (r = 0.09 for women and 0.33 for men, p > 0.10 for both). The 20 lowest ratios were used because the scatter below the curve is where increasing age would be associated with faster WRadj in WRpred1—where the bias matters (i.e., bias amongst the slowest WRadj is inconsequential). Above the curve, where the slower WRadj holders are, one would expect WRadj would be slower with increasing age. To include all WR holders would cancel out the correlations to essentially zero. As expected, the subsample’s WRpred2 fit improved from WRpred1 (R2 = 0.990 vs. 0.916 for women and 0.992 vs. 0.901 for men, p < 0.001 for both). The equations for WRpred2 were:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\text{Women}}&{:}\,{\text{WRpred2}} = 0.0.0000308562\, \times \,{\text{Age}}^{2} - 0.0018125288 \\ & \quad \times \,{\text{Age}}\, + \,0.121203508 \\ \end{aligned}$$\end{document}Women:WRpred2=0.0.0000308562×Age2-0.0018125288×Age+0.1212035082\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} {\text{Men:}}\,{\text{WRpred2}} & = 0.0000137573\, \times \,{\text{Age}}^{2} - 0.0005140915 \\ & \quad \times \,{\text{Age}}\, + \,0.0879275237 \\ \end{aligned}$$\end{document}Men:WRpred2=0.0000137573×Age2-0.0005140915×Age+0.0879275237The large number of decimal places was necessary for the precision of the WRpred2 curves, especially with the characteristic exponents. As expected, due to the mandatory selection of the lowest WR/WRpred1 values within each age group, the largest age gaps with no data points were 9 years, each occurring only once within each sex. Fig. 1

View Article: PubMed Central - PubMed

ABSTRACT

Introduction/purpose: This study&rsquo;s purpose was to develop and employ a technique to determine the fastest masters marathon world records (WR), ages 35&ndash;79&nbsp;years, adjusted for age (WRadj).

Methods: From single-age WR data, a best-fit polynomial curve (WRpred1) was developed for the larger age range of 29&ndash;80&nbsp;years for women and 30&ndash;80&nbsp;years for men to improve curve stability in the 35&ndash;79&nbsp;years range. Due to the relatively large degree of data scatter about the curve and the resultant age bias in favor of older runners, a subsample was constituted consisting of those with the lowest WR/WRpred1 ratio within each five-year age group (N&nbsp;=&nbsp;11). A new polynomial best-fit curve (WRpred2) was developed from this subsample to become the standard against which WR would be compared across age. WRadj was computed from WR/WRpred2 for all runners, 35&ndash;79&nbsp;years, from which the top ten fastest were then determined.

Results: The WRpred2 model reduced data scatter and eliminated the age bias. Tatyana Pozdniakova, 50&nbsp;years, WR&nbsp;=&nbsp;2:31:05, WRadj&nbsp;=&nbsp;2:12:40; and Ed Whitlock, 73&nbsp;years, WR&nbsp;=&nbsp;2:54:48, WRadj&nbsp;=&nbsp;1:59:57, had the fastest WRadj for women and men, respectively.

Conclusions: This technique of iterative curve-fitting may be an optimal way of determining the fastest masters WRadj and may also be useful in better understanding the upper limits of human performance by age.

No MeSH data available.