Sports Pace Strategy Planner

Pace is simply elapsed time divided by distance, but distributing that average across a race is a physiological allocation problem. Endurance performance is bounded by aerobic capacity, by the lactate threshold above which blood lactate accumulates faster than it clears, and by stored carbohydrate. Trained runners hold only about 1,500 to 2,000 kilocalories of muscle and liver glycogen while a marathon costs roughly 2,500 to 3,000, which is the physiological basis of the wall that commonly appears around 30 kilometers or 20 miles. Running the early kilometers above threshold drains glycogen faster and raises lactate at a point in the race where there is no time to recover, so the cost of a fast start is paid back with interest. Marathon effort for most runners corresponds to about 75 to 85 percent of maximum heart rate, and the conversions are exact: a mile is 1.609344 kilometers, and a 5:00 per kilometer pace equals 12.0 kilometers per hour, or 8:03 per mile. The splits produced here scale the average pace by a strategy factor across five equal segments: negative splits run the opening segment roughly 6 percent slow and the last roughly 6 percent fast, positive splits invert that, even splits hold pace constant, and the variable option applies a sinusoidal surge through the middle. Those percentages are a reasonable planning convention rather than a measured optimum, and a few limits should be kept in mind. The model divides by distance rather than by terrain, so on a hilly course you should hold effort constant and let pace vary, adding roughly 12 to 15 seconds per mile for each one percent of uphill grade and taking back about half that downhill. Heat matters more than most runners expect above about 13 degrees C, and the calorie figure assumes a 70 kilogram runner at about 1 kilocalorie per kilogram per kilometer, which ignores running economy, grade and wind.

The distances being paced are historical accidents before they are physiological categories. The marathon had no fixed length in the early modern Olympics; the 1908 London course, run from Windsor Castle to the White City Stadium, measured 26 miles 385 yards, and the International Amateur Athletic Federation adopted that figure as the standard 42.195 kilometres in 1921. Systematic thinking about how to distribute effort over such a distance grew from the exercise physiology of the 1920s, when A. V. Hill and his colleagues described maximal oxygen intake and the relationship between sustainable speed and duration, work for which Hill had already shared the 1922 Nobel Prize in Physiology or Medicine. Practical pacing tools followed. Coaches such as Arthur Lydiard in New Zealand built training systems around sustained aerobic effort in the 1950s and 1960s, and in 1981 the engineer and race measurer Peter Riegel published in American Scientist the endurance formula that predicts a time at one distance from a time at another using an exponent of about 1.06, still the basis of most equivalent-performance tables. Jack Daniels, working from oxygen cost data with Jimmy Gilbert in the 1979 book Oxygen Power, turned the same relationship into the VDOT tables popularized by Daniels Running Formula in 1998. Analysis of record performances subsequently made the case for even and negative pacing concrete, and the engineered sub-two-hour marathon attempts, Nike's Breaking2 in Monza in 2017 and the INEOS 1:59 Challenge in Vienna in October 2019 where Eliud Kipchoge ran 1:59:40, were built around rotating pacemakers holding almost metronomically constant splits.