The graph above shows how cross-sectional analyses were conducted. Each point (circle) represents the average finish time for a particular age averaged over all Birkie finishers at that age from 1999 to 2025. There may be many hundreds, if not thousands of observations used to calculate the average finish time for most ages. However, towards the older ages, relatively few observations are available, and the pattern becomes more variable.
A broad-brush summary that relates age to performance (as measured by finish time) can be achieved by dividing the performance curve into distinct linear periods separated by breakpoints. Segmented regression models were used to approximate the actual performance curve with a maximum of four linear regression lines separated by three breakpoints.*
The breakpoints (junctions) of the linear lines represent estimates of the transition ages between performance periods. In the above schematic, there is a period of slowing performance from age 18 to 33, followed by an intermediate period of sustained performance up to age 60 that is then followed by a more marked slowdown. The slope of the lines estimates the effect of age on performance within the three periods. For example, the average slowdown (increase in finish time) for ages 18 to 32 is 1 minute and 50 seconds per year.
There are three distinct subsets of skiers used for cross-sectional analysis: all skiers, top 5 skiers, and Birchleggers. The subset “all skiers” speaks for itself, but it’s also interesting to see if there is a different aging pattern for elite/top 5 skiers, and those long-term stalwarts – the Birchleggers who have skied 20 or more Birkies.
*Vito M. R. Muggeo. Regression Models with Break-Points / Change-Points Estimation (with Possibly Random Effects) Version:2.1-4, 2025-02-26, R package.