From: karl steinhoff 
Date: Thu, 28 Nov 1996 08:59:48 -0800
Subject: t-and-f: Projecting/predicting times

Mime-Version: 1.0
Date: Wed, 13 Nov 1996 15:56:42 -0800
To: karl steinhoff 
From: Karl Steinhoff 

A couple weeks ago (I think, as I'm always behind on my digests) there
appeared another brief thread on predicting 800 times from 400 times and
vice versa. As usual, it led to the conclusion that if it were possible to
do these kinds of predictions, one guy ought to be the best at every event,
which is clearly not the case.

However, Track & Field News has for years carried in their "Little
Rainbow-Colored Book" series on how to predict times at other distances
given times at *two* other distances. Now *this* begins to sound a little
more plausible. Whether it's really accurate or not is another question.

Their model, which has changed somewhat with the color of the cover, gives
us the model

P = a + b * log(D)

where P is the pace (per 400m, per kilo, per parsec, whatever you want) and
D is the distance run (again, in the unit of your choice). Given times at
two distances, one can fit a line to determine a & b, then plug in other
values of D to "predict" a time. Roughly speaking, a is a measure of speed
and b is a measure of strength.

This model has its pitfalls, of course. For one, the two performances used
to fit the data need to be of comparable "worth", and the distances should
be spread as far apart as possible (i.e., don't try to predict a 10k time
given PRs at 1500 and a mile). Secondly, the model only fits in the aerobic
range - I'm somewhat dubious about its validity at 800. And from some of
its projections, it seems to break down by the time we get to the marathon.

Anyway, with all these caveats, I decided to apply the model to a few of
today's superstars to see what fantasies I could come up with. Some
interesting stuff, I think. (These are best viewed with a fixed-width font.)

        Komen      Hissou      Tergat Gebreselasie    Morceli
 800  1:44.83     1:49.55     1:49.22     1:46.48     1:43.96
1000  2:13.71     2:18.96     2:18.73     2:15.51     2:12.90
1500  3:27.86     3:33.95*    3:34.10     3:29.82     3:27.37*
1609  3:44.37     3:50.57     3:50.77     3:46.29     3:43.98
2000  4:44.05     4:50.48     4:51.14     4:45.97     4:44.09
3000  7:20.67*    7:26.73     7:28.70*    7:22.09     7:22.18*
5000 12:45.09*   12:47.66    12:53.02    12:44.39*   12:50.67
 10k 26:53.33    26:38.08*   26:54.41*   26:43.60*   27:12.81
 20k    56:33       55:22       56:06       55:57       57:29
 Mar  2:05:36     2:01:33     2:03:31     2:03:42     2:08:11

Some notes:

1 - Times used to calculate the fit are asterisked. I may not have all the
hundredths exactly correct.

2 - I chose to compute the fit using those times which did not result in
predictions which were slower than actual PRs at other distances. Tergat's
20k could be an exception here.

3 - Not wanting to ignore Morceli, I chose to make up a 3k time for him,
since none of his other times are close to the same level as his 1500/mile
times. If I plug in his actual time (7:25.61), we get

Maybe these aren't all that bad after all. But I think, for example, that
his 5k potential is closer to 12:50 than to 13:00.

4 - I went back and looked at the actual coefficents a and b for each fit.
Ranking them in order from lowest to highest for the "speed" coefficient,
we get:

Gebreselasie (sp?)

Here "Morceli*" is the Morceli with the 7:22 at 3k.

Interestingly enough, the rankings are exactly the opposite for the other
("strength") coefficient. (These coefficients were computing using 400m
pace and meters as the units for P and D. Different units would produce the
same projected times, but could shift the rankings of the actual

Realizing, of course, that none of this is anything beyond fun speculation
and food for thought. But it beats reading the figure skating list, I

If anyone can supply actual PRs for Mike Fox, we can add him into the mix
as well.

K Steinhoff