Procedure and data analysis

All results were filtered by AG and outliers were defined as results lower than −3 SD of the mean of each AG. The athletes’ best results within each AG they competed in were labelled as their seasons’ best (SB, n = 51′894). Athletes who participated in at least three seasons (n = 8′583) were included in the longitudinal performance analysis, resulting in 41′253 season’s best results. The number of athletes who did not participate for two consecutive seasons or more and who did not return to competition for more than 1 year were defined as dropout. For the calculation of the longitudinal performance development curves the data were organized as follows. In the data matrix, each row represented an athlete’s performance, as repeated measurements were recorded horizontally. A multivariate, longitudinal analysis was conducted to assess the development of long jump performance over time. To calculate the change in long jump performance over time, the exact age at which athletes competed was calculated based on the athletes’ date of birth. To determine the relationship between age and performance, the CA (i.e., age in years and days as independent variable) and the furthest jump performance (performance in m as dependent variable) were examined using a mixed model regression analysis. This model takes the correlation of intra-individual datapoints into account—as repeated measures of the same person are correlated (Tantular and Jaya, 2018) and was recently used in similar studies (Abbott et al., 2021; Brustio et al., 2022). Then the trend line of performance development was calculated using the model. CA was entered as a fixed factor, while participants were entered as a random factor. To present one fitted graph for the whole population, the “population level prediction” random effects (here only participants ID) were set to zero. Using this approach multiple R-squared was 0.68 for both the Q1 and the Q4 within the age categories model and 0.69 within the exact age model. The second degree polynomial function was chosen, as the second and multiple degree polynomial models did not differ significantly. (Abbott et al., 2021).

The longitudinal Q1 and Q4 performance development curves were plotted against AG and CA. The differences in performance development between curves were statistically analyzed within a 83% CI, which indicated if the Q1 and Q4 curves significantly differed (Austin & Hux, 2002). The smallest worthwhile change in performance differences between Q1 and Q4 were used to detect relevant effects (Hopkins et al., 1999). These estimates of smallest worthwhile changes in performance are useful thresholds for interpreting the magnitude of performance changes in athletes (Haugen & Buchheit, 2016). In this context, smallest worthwhile changes can be described as a small Cohen effect size. This effect size is calculated as 0.2 times the between-subject standard deviation within a specific population (Hopkins, 2000).

To quantify the RAE, odds ratios (OR) between Q1 and Q4, with a 95% confidence interval (95% CI), were calculated relative to the birthdate distribution of registered births among the Swiss population from 2010 to 2020 (Federal Statistical Office). OR were interpreted as effect sizes as follows: the RAE was significant if the CI did not include 1 and 1.00 ≤ OR < 1.22, 1.22 ≤ OR < 1.86, 1.86 ≤ OR < 3.00, and OR ≥ 3.00, were interpreted as negligible, small, medium and large, respectively (Olivier & Bell, 2013). If the OR was <1 and the CI did not include 1, the finding was interpreted as a significant inverse RAE. Inverse ORs <0.33 (1/3), 0.33 ≤ OR < 0.53 (1/1.86), 0.53 ≤ OR < 0.81, 0.81 ≤ OR < 1.0 were interpreted as large, medium, small, and negligible, respectively. All statistical analyses were performed in RStudio.