From treadmill to trails: predicting performance of runners

Abstract

Previous laboratory studies have measured the energetic costs to humans of running at uphill and downhill slopes on a treadmill. This work investigates the extension of those results to the prediction of relative performance of athletes running on flat, hilly, or very mountainous outdoor courses. Publicly available race results in the Los Angeles area provided a set of 109,000 times, with 2200 runners participating in more than one race, so that their times could be compared under different conditions. I compare with the results of a traditional model in which the only parameters considered are total distance and elevation gain. Both the treadmill-based model and the gain-based model have some shortcomings, leading to the creation of a hybrid model that combines the best features of each. Author summaryRunning a race on a road allows absolute measures of performance. Trail running, however, has traditionally been thought of as a sport in which the only valid comparison is between different runners competing on the same course on the same day. Even the exact measurement of distance is considered to be unimportant, since courses and conditions vary so much. An extreme example is the relatively new genre of "vertical" races, in which runners race up a mountain. In a typical example, the competitors cover a horizontal distance of 5 km, while climbing about 1000 m. The winner in one such race had a time almost triple that expected for a state-champion high school runner in a 5k road race. Clearly no comparison can be made here without taking into account the amount of climbing. In noncompetitive contexts, many runners venture onto mountain trails, lightly dressed and with little equipment, so that it becomes important to be able to anticipate whether they will have the endurance needed to be able to safely complete a planned route. Again, this is impossible without some model of the effect of hill climbing.