Marathon prediction: why the Riegel formula lies and what to do about it
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Every running calculator predicts the marathon with the same formula, and almost every recreational runner has watched that prediction run away at kilometre forty. This calculator shows three numbers side by side: the classic Riegel formula, the same formula after calibration on a large group of amateurs, and the simplest multiplier from the same survey. The difference between the first and the third is usually ten to fifteen minutes, and that difference is the most important information on this page.
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<p><a href="https://easytrackly.app/en/running-calculator/marathon-prediction">EasyTrackly running calculator</a></p>The three predictions and where they come from
Riegel, exponent 1.06. The time over the new distance equals the known time multiplied by the ratio of the distances raised to the power of 1.06. A formula from 1977, fitted to records and elite results, for whom a marathon is simply a longer race. The same formula predicts races in the running calculator.
Riegel, exponent 1.07. The value Vickers and Vertosick adopted in 2016 after checking the formula on the results of 2,303 recreational runners. Up to the half marathon the formula with this exponent fits well. For the marathon it is still too fast.
Half marathon times 2.19. The multiplier Vickers gave in his 2014 calculator as a simplified version of the model from the same survey, instead of the 2.085 that follows from Riegel. When you enter a 5K or 10K result, the calculator first converts it to a half marathon with the 1.07 exponent and then multiplies.
What the study showed
The authors collected results and weekly mileage from 2,303 runners online, split the data into a training and a validation set, and checked how well the Riegel formula hit real times. Up to the half marathon it was well calibrated. For the marathon it predicted a time at least 10 minutes too fast for half of the runners. The best additional predictor was weekly mileage: runners with more kilometres were closer to Riegel, runners with low mileage much further away. A model with mileage cut the share of predictions 10 minutes too fast from a half to a quarter. The full coefficients of that model are in a supplement to the paper that is not publicly available, so mileage is in the text here, not in the calculation.
Why the marathon is different
A 10K result speaks about aerobic capacity, not about whether the legs will last three hours and whether glycogen stores will reach the finish. A formula based on the ratio of distances assumes the same preparation for both distances, and for an amateur it almost never is: the long runs are shorter, the mileage lower, and fuelling on the course untested. So the less you run, the closer to the slowest of the three predictions you should plan your race.
How to use the prediction in a plan
Take the most cautious number as the race goal and work out the pace in the running calculator. Run the first half a few seconds per kilometre slower than that pace, because most amateur personal bests come with an even or faster second half. Halfway through the build-up, run a tune-up 10K or half marathon and enter it here again: a fresh result says more than one from six months ago.
Frequently asked questions
Is the 2.19 multiplier "scientific"?
It comes from the same survey the authors described in a peer-reviewed paper, but the multiplier itself was published in the press, not in a journal. The paper confirms the direction and size of the correction; the multiplier is a simplification of it.
I run 90 kilometres a week. Which prediction is mine?
At high mileage, Riegel with the 1.07 exponent was close to reality in the study. The 2.19 multiplier will be too cautious for you.
Which result should I use?
The longest recent one. A half marathon from six weeks ago says more about the marathon than a 5K from last week.
Does the prediction account for the course and the weather?
No. Convert the course profile on the hill pace page and the heat on the pace in the heat page.
Sources
- Vickers A. J., Vertosick E. A., An empirical study of race times in recreational endurance runners, BMC Sports Science, Medicine and Rehabilitation, 2016. Calibration of Riegel and the role of mileage.
- Riegel P. S., Athletic Records and Human Endurance, American Scientist, 1981. The 1.06 exponent.
- Vickers A. J., marathon calculator at Slate, 2014. The 2.19 multiplier as a simplification of the model; a press source.