Interactive by Chris Kirk. Ruler by Joe Harrison from The Noun Project. Stopwatch by Scott Lewis from The Noun Project. Running by Leandro R. from The Noun Project.
If you’ve ever used a running calculator to pace yourself for a marathon, there’s a good chance you set yourself up for failure. As I explained in a piece earlier this year, most finish-time calculators—like this one from Runner’s World—rely on an algorithm developed by engineer and runner Peter Riegel in the 1980s. The Riegel formula is based on the idea that you slow down by a certain amount as a race gets longer, what he called the “fatigue factor.” According to Riegel, you can’t predict how fast you’ll run a marathon by doubling your time over 13.1 miles. Rather, you can get a better estimate by multiplying your half-marathon time by 2.085.
Andrew Vickers, a competitive runner and statistician at Memorial Sloan Kettering Cancer Center, was convinced that we could come up with a better formula. Back in April, we asked for your help to find out if he was right.
Nearly 2,500 Slate readers answered the call, providing real-world race data to help Vickers and his colleagues build a better calculator. We ended up with results from 929 marathons, 1,446 half-marathons, 888 10K races, and 1,293 5Ks. The average woman who submitted data to the survey (39 percent of our respondents were female) was around 34.5 years old and ran about 29 miles a week. The average man was about 37.5 years old and ran around 35 miles a week. Runners completing the survey ranged from 16-year-olds to those in their mid-70s.
To devise the calculator, Vickers randomly divided the data into three groups. He developed a new marathon prediction formula using the first of those groups and tested it using data from another. He is reserving the final group to present when we publish the study in a scientific journal.
When Vickers’ group crunched the numbers, they found that the Riegel formula works well when you’re using one short race to predict your time for another short race. Your 10K time is pretty close to your 5K time multiplied by 2.085.
But the Riegel formula falls apart when you move up to the marathon. A typical runner in our study with a 1:45 half-marathon time (8 minutes per mile) had a marathon time of 3:53:10 (that’s 8:54 per mile). Yet the Runner's World calculator predicts that this runner will finish in 3:38:55—15 minutes faster than the actual result. That’s an “absolutely massive” error, says Vickers. If this runner paced himself according to the Riegel prediction, he would start the race at a pace that was more than 30 seconds per mile too fast. “No wonder so many runners blow up and limp to the finish,” Vickers says.
According to the numbers in our study, a more accurate formula for predicting a marathon time is your half-marathon time multiplied by 2.19. With that formula as a starting point, Vickers and his colleagues made tweaks to reflect the other lessons they pulled from the study. As you’d expect, training volume—miles run per week in preparation of a race—had a measurable influence on marathon times. “You might run a quick 5K, but if you don’t put in the miles, your marathon is going to be on the slow side,” Vickers says. Adjusting the formula to reflect training miles improved its accuracy. Our study also found that the extent to which you slow down between two shorter races, such as a 10K and a half-marathon, also reveals how much you’re likely to slow down between a short race and a marathon. Contrary to Vickers’ expectation, though, we found that age and gender had no influence on how a runner’s pace slowed from a short to a long race.
The Slate marathon calculator uses a formula adjusted to reflect your training miles. The tool performs best when you can give us your times for two previous races of different distances, though it can also be used if you input only one previous race time.
Our formula predicts that a 1:45 half-marathoner who trains 30 to 40 miles per week will finish a marathon in 3:54:50. That’s still a little bit off from the real-world results we saw in our survey—a minute and 40 seconds slower than the actual time. But if you’re using a calculator to pace yourself, Vickers says, you’re better off leaving a little in the tank for the end, when you can make up some time, rather than going out too fast and setting yourself up for a miserable finish.
Before you try the calculator, a few words of caution. Though we found that a runner’s age didn’t affect her predicted marathon time, we also didn't have many older runners in our sample, so it’s possible our predictor doesn't work as well for runners over age 60. Predictions will also be less accurate in absolute terms for slower runners, Vickers says. That makes sense, because while few runners expecting to run a 2:45 marathon end up finishing in 2:30, it’s not uncommon for a 5-hour marathoner to run 15 minutes faster or slower than expected. “In percentage terms we do just fine with slower runners; in terms of absolute time, we do slightly worse,” Vickers says.
Finally, a race that is either very difficult (because of an especially tough course or terrible weather) or very fast (because of special conditions such as a tailwind or downhill slope) makes a bad basis for predicting your marathon time, unless that marathon will be similarly hard or fast.
So, with those caveats out of the way, scroll back to the top of the page and give our new calculator a try.