Pictured here is a generic graph that relates finish time to age and depicts the various performance elements that will be examined in upcoming figures. The points on the graph are the mean finish times at the mid-point age of each of the age groups (excluding age groups from 80 on ).

First, a broad-brush summary can be obtained by dividing the performance curve into a younger period (21-52) and an older period (57-77) and calculating the average change in finish time/year for each period. The dividing point between the periods is somewhat arbitrary, but it works for most of the figures that follow. As will be seen, there really is a relatively long period of sustained performance that is then followed by a more marked decline starting somewhere within the ages from 50 to 60 .

The broad-brush approach, however, does not capture all the information that is retrievable from these data. The performance trends are much better depicted by modeling the data with polynomial equations. The reason for this is that fitted polynomials highlight the critical age periods when skiers are slowing down or speeding up. For example, the third-degree polynomial model used in this schematic detected two changes in direction. There was a short initial period where skiers were slowing down with age (finish times were increasing) that ended at point A (~age 25). From point A to point B (~age 45) skiers were actually skiing faster as they aged. Then, from point B on, skiers slowed down forevermore with every new birthday. Points A and B are referred to as local maxima and local minima, and they can be determined using differential calculus (more).

Skiers can hold out for a long time. It appears that good performance can be maintained throughout much of middle age and even longer, at least for endurance events like the Birkie.

For the freestyle event, men have remarkable staying power through their middle years. There is an inflection point at 25 years, indicating that thereafter speeds are slowing down, but men add on average only 38 sec/year to their finish times during their younger period. In their older period, each birthday adds about 2 1/2 min.

For the classic race there is a pretty significant slow down until age 40 and then times level out. The local minimum at 47.3 years is the point when speeds start slowing again. The initial slow down may be, in part, an artifact stemming from the fact that many of the younger classic skiers have only skied the Birkie since the separate classic trail was established in 2008 (more). This issue will come up again in later figures.

Ignoring the initial blip in finish times, during their younger period, classic skiers add an average 44 sec to their time each year. In their older period, the increase is around 2 3/4 min/year.

**Note: Finish times are standardized to a 55k classical race or a 51k freestyle race.**

Women show the same general pattern as men. For the freestyle event there is an initial slowing until the inflection point at age 33.6 after which times remain fairly steady until the late 40s. For the classic event, speeds slow down until the age of 36, then speeds actually increase until age 50.3.

Ignoring the initial blips, the increase in finish time during the younger period averages 29 sec/year for freestyle and 44 sec/year for classic. The slow down during women's older period is more pronounced than seen in men - a little over 6 min/year for freestyle and 7 min/year for classic.

**Note: Finish times are standardized to a 55k classical race or a 51k freestyle race.**

So far, all we’ve looked at is the performance of an average skier. What about the best skiers in each age group? Are they better at maintaining performance as they age than the average skier?

The following graphs show the same data as in the previous two graphs but for the mean of the top three finishers in each age group (ignoring the top overall finishers who have been removed from this analysis). Looking at only the top three skiers in each age group also eliminates the artifact of shifting age demographics encountered in the previous graphs.

These "elite-skier" graphs show remarkable staying power for top cross country skiers, especially classic skiers. For males in their younger period, the increase in finish time for freestyle averages about 39 sec/year. The inflection point at 37.3 is the age at which finish times begin their inexorable increase.

Classic male skiers in their younger period actually speed up as they age by by an average of -25 sec/year! While there is a slight slowing until the local maximum at age 26.8, there is a long period of faster and faster finish times until age 48.2.

On average over their older period, males in the freestyle event add a little under 6 1/2 min/year to their finish times, while classic skiers add a little under 7 1/2 min/year.

Even though the possible effect of shifting age demographics is removed by considering only the top 3 finishers in each group, the curve for classic skiers remains distinct from that of freestyle skiers because of the initial slowdown to the mid-20s. As will be seen in the next figure this distinction will remain for elite females as well.

**Note: Finish times are standardized to a 55k classical race or a 51k freestyle race.**

For women in their younger period, the increase in finish time for the freestyle event averages 36 sec/year. The inflection point at age 34 represents the age at which finish times will increase forevermore.

As for men in the classic event, women in their younger period actually speed up as they age, and do so at nearly twice the average rate for men, -43 sec/year. There is an initial slow down until the age 25.4, but then speeds ramp up again until age 45.5.

For elite women, it seems that the performance decline that comes with advancing age starts at an earlier age than for men and proceeds more rapidly. Women in their older period add a little under 10 1/2 min to their finish times each year for both the freestyle and classic events.

**Note: Finish times are standardized to a 55k classical race or a 51k freestyle race.**

## Age effect for main pack skiers

If you are a "main pack" Birkie skier and wonder what effect age is having on your results, you can use this table to estimate your Birkie finish time based on your previous year's time. For example, if you are male, were of age 32 in last year's Birkie, and you ski the freestyle event, you can expect the aging effect will add 28 seconds to your finish time from the previous year.

The numbers in this table are derived from the polynomial models used in the previous graphs.

## Age effect for age-group contenders

If you are an age-group contender for the Birkie and wonder what effect age is having on your results, you can use this table to estimate your Birkie finish time based on your previous year's time. For example, if you are female, were of age 41 in last year's Birkie, and you ski the classic event, you can expect to ski the Birkie 45 seconds faster than the previous year.

The numbers in this table are derived from the polynomial models used in the previous graphs.

Another way to look a longevity is to examine how performance declines with age after the point of inflection or local minimum (depending on the shape of the fitted polynomial), which represents that age after which speeds invariably slow down at an ever increasing rate. From the previous graphs, these points for the classic event range from ages 45.5 to 50.3, and for the freestyle event, the range is 25.0 to 37.3. So it seems reasonable to examine the decline in performance relative to a base level of performance set by the mean finish times of the 45-49 age group for the classic event and a base level set by the 35-39 age group for the freestyle event. Each point on this figure is merely the mean base level finish time divided by the mean finish time for each age group (represented by its mid-point age). The points were modeled with a second-order polynomial (more).

For the classic event, female performance falls to a little under 70% by the time skiers reach their late 70s, while that of males falls to around 83%. It is apparent in this figure that female performance degrades more rapidly than male performance for the classic event. This is a common observation in studies of aging master athletes across a variety of athletic endeavors (see Baker et al., 2010).

The performance decline curves for the freestyle event are similar to those for the classic event in that, again, female performance declines faster than male performance, although this conclusion seems particularly reliant on the polynomial model. The last point on the graph for males at age 77 pulls the model away from the curve for females and may exert undue influence.

It is not possible to compare rates of decline for classic versus freestyle events since the baseline levels are different.

Performance decline analysis can also be applied solely to the top 3 finishers in each age group (ignoring the top overall finishers). For the classic event, the first notable observation is that performance decline extends to nearly 50% for both males and females by age 77 (i.e., finish times are nearly double those of the base level at age 45-49). This is likely due to the fact that these elite skiers are near their optimum level of performance and close to their prime age at the base level of 45-49, while the average skier depicted in the two previous figures operates at somewhat less than maximum potential at this age. Therefore, average performance of all skiers, as a percentage of the baseline, declines at a slower rate than for elite skiers.

The performance of females seems to drop off more steeply than males, although both end up near the same level by age 77.

This figure is similar to the previous figure for elite classic skiers with the exception that performance decline dips even further, to below 40% for females and below 50% for males, by the late 70s. Female performance again seems to decline more rapidly than male performance with age.

Here is an example of how you might use this and the previous three figures. Say you are a 62 year-old male who has entered the freestyle event. You've been competitive in your age group in the past and occasionally make it to the top 3. What finish time should be your goal to show that you are doing better than your physical condition, skill level, and chronological age would predict?

From this figure, you note that if you are at the the fractional level of 0.8 or higher, your are doing well for your age and ability. Since the base level finish time for elite freestyle male skiers is 2:19:06, you should be happy to finish at 2:54 or better.

Repeating the same exercise, but for a recreational (not top 3) male freestyle skier of age 62, would suggest that a finish time of 4:48 would be an appropriate age-adjusted goal.

This table uses the polynomial models that were fitted to performance degradation rates to predict how old skiers are when they decline by 25%, 50%, 75%, and 100% from their peak performance years (as defined by the base levels used in the previous figures). Recall that a 50% reduction corresponds to a doubling of finish time relative to the base level. A 100% reduction means that a skier is incapable of finishing the Birkie anymore.

The predictions are probably within reason for the 25% and 50% levels of decline, and perhaps the 75% level for the top 3 skiers. But the 100% level is way outside the range of the data and is provided merely as a conversation piece. In fact, the 75% level doesn't make much sense for the non-elite skiers since the predicted finish times may be beyond the cut-off times for completing the Birkie.

Still, the models do show that cross country skiers have the potential to ski Birkie length events-well into their 80s and beyond.