# Reading Half Marathon

The annual Reading half marathon
provides a reasonably large (4000+ runners)
dataset
of results for analysis.
In particular, we can consider the distribution of
performances (in the same way as for fell races),
which is surprisingly "Normal" when when looked at in terms of speed.

The data also includes the ages of (most) athletes, so that we can
investigate age-graded performances - the winners turn
out to have the best age-graded results, but there are some good ones at
all ages.

## Distribution of performances

Below are the distributions of results in the Reading half marathon 1999.
(a) shows the times - slightly skew, so that the slowest runners (on the
right) have quite slow times.
(b) shows the speeds (1/time), where now the winner is on the
right - this is a more symmetric distribution and is surprisingly "Normal",
so that comparing results in terms of speed is more sensible.

(c) and (d) show the distributions of 1/time for men and women separately -
women's results are more concentrated around the central value as there are
less of them, but both distributions remain symmetric.

We could for instance turn these results into %WR(speed) (as in running page). However, they are all at the same distance, so we can
compare them directly - either as %(median-speed) or as percentiles of a
Normal distribution fitted to these data.

## Age-graded performances

Since the data contains the ages of (almost) every athlete, we can compute
age-graded performances - times as a % of the WR for that age, or, since the
distributions are better, speeds as %AGE-WR speed.

Howard Grubb

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Updated: May 20, 1999