## 3 Results
### Speed Analysis between and within Genders  
The overall mean speeds of the 13 VM editions obtained by age category (AD13 and TOP13) showed a downward trend with increasing age in both genders (Figure 3a,b). The age categories of males included runners up to 80 years old, while those of females included runners up to 75 years old. In all age categories, females showed lower values than males. The mean speeds of AD13 men ranged from 11.16 to 7.62 km/h, while those of AD13 women ranged from 10.13 to 7.06 km/h. The mean speeds of men in TOP13 ranged from 18.51 km/h to 7.94 km/h, while those of women ranged from 16.01 km/h to 7.06 km/h.  
The curve patterns were not significantly different between males and females in both groups (AD13 and TOP13; \(t\)-test \(p\) = 0.266 and \(p\) = 0.404, respectively) (Figure 3a,b), although in TOP13 there were greater differences between males and females.  
The mean speed differences calculated within genders (Figure 3c,d) showed that in AD13 the difference between nearby age categories tended to increase, albeit not significantly, in both males and females (\(p\) > 0.05).  
Analyzing these differences within all trained athletes (TOP13) of both sexes, a sharp decline in performance was detected between the individuals younger than 34 years and the upper category (i.e., the 30- and 35-year age categories, respectively), with a lower peak for 40-year-old males (\(p\) < 0.001) and 45-year-old females (\(p\) < 0.001). Later, the differences tended to increase, with an interruption at 55 years old in males (\(p\) < 0.001) and 70 years old in females (\(p\) = 0.115).  
Considering the cumulative differences represented by the lines in Figure 3c,d, the gender trends appeared similar. By applying a \(t\)-test between the cumulative trends, the \(p\)-values were found to be statistically non-significant (\(p\) = 0.950 and \(p\) = 0.959 for  
Figure 2: Analysis of the running speed of participants in the 2007–2019 VM editions: (**a-d**) Regression lines for athletes’ mean speeds by year in each age category. (**a,c**) Regression lines for AD and TOP male athletes, respectively. (**b,d**) Regression lines for AD and TOP female athletes, respectively. (**e**) Slope coefficients and \(p\)-values computed by linear regression on speeds by age category and gender in the 2007–2019 VM editions. CAT = age category, M = male, F = female, 30–80 = age category. The \(p\)-values \(<\) 0.05 are considered statistically significant, and \(p\) values \(<\) 0.001 are considered highly significant.  
AD13 and TOP13, respectively). This result could be considered a \"regression to the mean\" phenomenon, in which performances between men and women tend to uniformly decrease.  
The piecewise linear regression analysis highlighted the age categories that suffered the greatest decline. Considering AD13, men showed a breakpoint at 50 years old, while women had a sharp decline at 55 years old (Figure 3e). The same analyses performed on TOP13 showed a shift in the breakpoint to 55 years old in males, while in women it occurred earlier, at 45 years old (Figure 3f).  
Figure 3: General analysis of speeds among participants in all 13 VM editions: Mean speed distributions grouping the 13 editions of the VM by age category among (**a**) AD13 and (**b**) TOP13. Differential (histograms) and cumulative (lines) differences in mean speeds by category among (**c**) AD13 and (**d**) TOP13. Piecewise regression lines for median speeds of (**e**) AD13 and (**f**) TOP13 athletes; the category 30 (24–34 years) in (**e**,**f**) has been removed. Males are represented by blue histograms or dotted lines, and females by pink histograms or continuous lines.