This best-fit iterative method demonstrates a statistically sound and replicable technique to determine not only the fastest WRadj but to rank order all WR holders by WRadj as well. The key innovation is determining WRadj using a standard curve that more closely conforms to the upper limits of performance among master’s runners by using only the fastest WR/WRpred1 ratios within each age group. Figure 2 provides a graphic representation of the effects of the technique: the revised best-fit curve shifts down and to the right thus capturing the “fastest of the fastest” age-adjusted marathoners. With one data point for each age group constituting the scatterplot, the resulting best-fit curve is less likely to be influenced by outliers than the convex hull method.
As expected, the convex hull method, applied to the present data, yielded seven data points for each sex, which contributed to large spaces between certain points: 14 and 15 years for women and 11 and 14 years for men. In terms of ordinal ranking of WRadj for women, both methods included the three of the same marathoners but the rankings were different for each ranking, 1st through 5th. For men, both methods shared the same four marathoners but rankings were different for two places. Furthermore, an example difference for each sex between the two models was calculated. For women, the top-ranked WRadj woman (50 years) in the present iterative model, was 99 s faster than the second place woman (77 years), whereas the convex hull indicated that the 77 years woman was 6 s faster than the 50 years woman—an overall difference of 105 s. The first and second-ranked WRadj man (73 and 35 years in both methods) had an advantage of 63 s with the convex hull model and 80 s with the present model—a difference of 17 s. From these analyses, one cannot conclude that one model is more valid than the other. However, because the present iterative method included all seven of the convex hull data points and four additional for each sex, one might conclude that the present model exhibited more precision and less effects of outliers than that of the convex hull.
Another relevant characteristic of this iterative methodology was that the key metric for WRadj was a ratio of WR/WRpred2. This meant that the selection of the 11 subjects of the subsample was also based on the same corresponding ratio, WR/WRpred1, not the fastest WR, within each masters age category. The importance of this distinction can be illustrated with an example. Among women 45–49 years, the fastest WR was 2:29:08 (45 years, WR/WRpred1 ratio = 1.0234) yet the lowest ratio in that age group corresponded to a 49 years woman whose WR was 2:35:49 (WR/WRpred1ratio = 0.9644). The 45 years woman’s ratio indicated that her WR was actually slower than that predicted by the WRpred1 curve. In fact, the 49 years old woman actually earned second place among all women WR holders for her WRadj of 2:13:30, compared with that of the 45 years runner, 2:21:22.
Another advantage of this technique was that it selected the fastest among the entire sample of WR holders from ages 35–79, not just from the subsample of fastest WRadj within each age category. To do the latter would have omitted the women’s 4th and 5th and the men’s 2nd, 8th, 9th and 10th place finishers from Table 1. The only utility of the subsample was to establish WRpred2, the “bar” against which all WR holders would be evaluated.
Perhaps peculiar is the finding that the slope of the curve is quite sensitive to age differences. For example, Tatyana Pozdniakova’s 1st place (Table 1) 2:31:05 at age 50 actually shows a faster WRadj than that of her 2:30:17 performance at age 49. In this case, 1 year of age difference contributed to an actual difference of 48 s but a predicted difference of 108 s. Therefore, her performance at 50 years yielded a lower WR/WRpred ratio—the very ratio used to rank WRadj among WR holders. Figure 2 depicts this phenomenon in that the data point at 50 years is slightly lower below the line than that of 49 years.
A useful characteristic of the WRpred2 standard curve (Eq. 1) is that it can be used to compare any masters marathon performances of recreational runners. Instead of using WR, one can use actual marathon run time (MRT) to compute the ratio, MRT/WRpred2, with smaller number indicating faster age-adjusted performance. Furthermore, unlike the ratio employed in the WMA standards, the present method is empirically and algorithmically determined, not by a best-guess method upon which WMA standards appear to be based.
Since the common unit of measure for both sexes is variance from the predicted WR, the WR/WRpred2 ratio can be used to compare male with female WR performances. Important to note is the fact that the WR/WRpred2 ratio is appropriate for between-sex comparison, not WRadj. The latter factors in the predicted open WR within each sex. In the present study, for example, Tatyana Pozdniakova (50 years, WR = 2:31:05, WRadj = 2:12:40), the fastest WRadj for women; had a smaller ratio than Ed Whitlock, her male counterpart (73 years, WR = 2:54:48, WRadj = 1:59:57), at 0.9740 and 0.9813, respectively. This suggests that Ms. Pozdniakova has the fastest age-adjusted marathon performance of all time. Within sex, however, WRadj provides a more meaningful or perhaps useful score than the WR/WRpred ratio alone as the h:m:s units of WRadj are interpretable by virtually any runner. As stated previously, it is a statistical estimate of what the WR holder would run if he/she were of the age of the open WR holder for that sex. Such an estimate has been published elsewhere (Vanderburgh and Laubach 2007; Vanderburgh 2015a).
Use of the present iterative technique to examine elite age-adjusted performances may also inform the study of the effect of aging on physical performance in a way that controls for confounding factors such as physical activity level, body composition, effort, etc. In other words, this technique may yield important information about the inevitable loss of function with age, or the physiological limits of human performance with age.