Some might say that I'm full of heuristics — rules of thumb — especially for distance running, since it's a subject that has so many endearingly quantitative parameters to play with. Recently while sitting at the back of a large room during a long, boring meeting I filled a sheet of paper with calculations and came up with a new formula. It's a corollary to the old rule:

Every minute too fast that you go during the first half of a race costs you two minutes in the second half. |

The new guideline is more general:

Your optimal pace is one-third of a standard deviation less than your actual pace. |

These two formulæ are mathematically equivalent in some simple cases. Both say that it's best to go at a steady speed. *(The "standard deviation" is a measure of the plus-or-minus fluctuation in one's pace; it is zero for an absolutely constant velocity.)*

How do these rules compare when applied to actual race data? Take the latest Marine Corps Marathon (29 Oct 2006). I didn't participate in the race, but I went downtown to photograph friends there. Here's a tabulation based on their outcomes. The "half" columns are first and second halves of the marathon, "sigma" (σ) is a rough estimate of the standard deviation of the pace *(in seconds/mile, based on crude split data from miles 5, 10, 15, and 20)*, and the "actual" finishing time is compared with theoretical "best" possible result using the old rule and the new one above.

runner | half | half | σ | actual | best (old) | best (new) | ||

WC | 2:42 | 2:59 | 35 | 5:41 | 5:35 | 5:36 | ||

CJ | 2:26 | 2:42 | 45 | 5:08 | 5:03 | 5:01 | ||

KS | 2:21 | 2:37 | 20 | 4:58 | 4:53 | 4:55 | ||

GA | 1:52 | 1:59 | 15 | 3:51 | 3:49 | 3:49 | ||

TW | 1:45 | 2:05 | 40 | 3:50 | 3:43 | 3:44 | ||

MA | 1:40 | 2:02 | 35 | 3:42 | 3:35 | 3:37 |

The agreement between the "old" and "new" rules is amazingly close. I'll run some more detailed tests using my mile-by-mile splits later to see if the correlation persists, or if it's coincidental.

Of course, the **fundamental** question remains: on a given day, could a peson* really *have finished several minutes faster by using an even pacing strategy?

*(cf. TwoGreatSecrets (9 Nov 2001), NeedForSpeed (10 Aug 2002), LogbookTyrannicide (17 Oct 2002), HandicapJogging (8 Oct 2003), DecelerationParameter (28 Dec 2003), RootMeanSquareDance (24 Apr 2004), ... )*

TopicRunning - TopicScience - 2006-11-02

*(correlates: BigSecret, PrimeDirective, At My Pace, ...)*