Not too long ago, Christie Aschwanden of FiveThirtyEight contacted Andrew Vickers, a statistician over at the Memorial Sloan Kettering Cancer Center, and talked about running. More specifically, they talked about interactive race time predictors.
Most of the online race time calculators available currently use engineer Peter Riegel’s algorithm published back in 1981. The concept is that as the distance of the race increases, there’s a decrease in the maximum pace a runner can endure. The Riegel formula, as it has come to be known as, factors in fatigue (the variable k) to give a more accurate race time.
The Riegel Equation:
During their talk, Vickers talked about how he thought the Riegel formula actually underestimated marathon times, and in order to prove his point, he had decided to run a marathon. Vickers told Aschwanden that he had run a 2:59 marathon even though the calculators predicted that he would actually have a finish time of 2:48. Vickers made the argument that if he had actually used the calculator’s predictions to pace his race, he would’ve run out of steam.
That’s why Vickers and Aschwanden decided to collaborate to come up with a more accurate formula. Aschwanden reached out to readers to fill out a survey developed by Vickers that included questions about recent race times and other pertinent information. The initial story was published in Slate back in April 2014, which included a link to the survey, and through that, they were able to compile information from 2,497 responses.
With all the surveys collected, Vickers and one of his colleagues, Emily Vertosick, came up with a better formula for determining finishing times and recently published their results in the BMC Sports Science, Medicine and Rehabilitation journal. Even though the data set wasn’t exactly perfect, since the information collected might not have been accurate, the end results proved that the Riegel formula only worked well for races with distances up to a half-marathon but miscalculated marathon times.
Based on the information they collected, Vickers and Vertosick found some correlations between various factors and faster race times. “People who ran more miles have faster times, and people who ran intervals and tempo runs had faster times,” said Vickers. “We found that intervals helped about the same amount, no matter what the length of the race, and the same was true for mileage.” Their final conclusion was that average weekly training mileage and past race times are the best predictors of final race time. Using that information, the final formula uses these two inputs to calculate a more accurate time prediction.
Check out the formula here.