aging stats

Derick asked about aging stats for skiers as compared to runners, as
discussed in that NYTimes article. I did a bit of work on that for
the Ontario Masters a few years ago, and, at the risk of boring some
old-timers here, will try to summarize the thing below.

After trying to get time for a few days to dig up the article
itself by that Yale prof., I've decided to leave it and just go by what
the newspaper guy wrote. I can't quite tell if the latter is an appreciator
or a victim of the humour in confusing _regression analysis_ with
the _regressing_ of us old farts! It's a bit surprising to see this
kind of stuff turning up as refereed publications by academics, but
maybe I'm being a snobbish mathematician, especially since I've not
had a chance to read the real thing yet.

Ken gave theoretical reasons why, if it did turn out to be the case,
skiers and runners might have different rates of losing speed
with age.

It does sound from the Times article that the runners' and skiers' rate
of aging deterioration is quite comparable. I seriously doubt
that anybody can do this kind of study without a wide margin of error.
I also have serious doubts about using world best times, in something
like the marathon, because of
widely varying courses, point-to-point courses with elevation
differences, etc. You have to compare people in the same race, same
day, use more than just the age category winners because of the existence
of really exceptional individuals, but on the other hand, use only
athletes from the top of the heap in each age category.

I used quite a few years data from the Norwegian Birkebeiner (so results
might be questioned for short races). The top 5 in each age category
averaged is easy to get because of their use by the race in deciding
who gets the "pin". Remember that, at least between ages 40 and 70,
there are hundreds in each age category (5 year) for the men. (The
women's data gave comparable results, but with less confidence
because of smaller numbers.) Also, these top guys in Norway train
like demons--Don Karig, who is probably the best of the N. Americans
that do it regularly (top 20 this year as I recall), has some stories
of 65 year olds ripping up and down mountain roads on rollerskis,
through rain and hailstorms etc. for hours! So the dedication of
the people I'm using is little if any less than that of national
team athletes.

A rough, but reasonably accurate, summary of the results is that
you lose about 5% between ages 40 and 50, another 10% from 50 to 60,
and another 15% from 60 to 70, so with 'compound interest', it's
about 34% from 40 to 70. I wrote down a couple of formulas for that
percentage, for example

multiply 23 into (age - 40)divided by (90 - age)

This gives ridiculous answers as you aproach 90 years old, but it's
only intended for the range 40 to 70. I've been keeping my eye on the
N. Birk. results each year since then, so there's about 12 years
worth in there now, and no significant difference has emerged since
the original stuff was done.

Best, Peter