Why race time predictors disagree (and which way they are wrong)

Three predictors, one input

The race time predictor on this site shows three columns side by side, and they rarely agree to the minute. All three start from one recent race and project it to a longer one:

• Riegel 1.06. Peter Riegel's endurance formula, T2 = T1 x (D2 / D1)^k, with the popular exponent k = 1.06.
• Riegel 1.08. The same formula with a larger exponent, a more cautious choice that adds time as the distance grows.
• The Daniels-Gilbert model. Jack Daniels and Jimmy Gilbert's 1979 equations: one for the oxygen cost of a running speed, one for the share of VO2 max a runner can hold for a given number of minutes. A race gives a fitness score (VDOT, Daniels' term, used here descriptively), and the model finds the time at which that score balances over the new distance.

I ran 5K times from 18:00 to 35:00 and half marathon times from 1:20 to 2:40 through all three, using the same engine as the calculators (run.js). The results below are the part that generic "race predictor" articles leave out: how far apart the answers are, and in which direction.

Marathon predictions from a 5K

Two patterns stand out. First, Riegel 1.08 is always exactly 4.36% slower than Riegel 1.06 from a 5K, because the two differ only by the factor (42.195 / 5)^0.02 = 1.0436. That fixed percentage turns into more minutes as the time grows: 7:31 for an 18:00 5K, 14:38 for a 35:00 5K.

Second, the Daniels-Gilbert column is not a fixed percentage away from either. Divide its marathon by the 5K and take the logarithm and you get the exponent it implies: 1.059 for an 18:00 runner, falling to 1.050 for a 35:00 runner. In other words, the model assumes slower runners slow down less over the marathon than faster runners do. The reason sits in its fatigue curve, which I take apart in how long you can hold a pace: the curve levels off at 80% of VO2 max, so a four- or five-hour effort is treated as only slightly harder to sustain than a three-hour one.

Marathon predictions from a half marathon

From a half, the three agree much more closely, because the jump in distance is only a factor of 2. The 1.08 column is now 1.40% above the 1.06 column (2^0.02 = 1.0140), so the spread for a 1:30 half is 2:41. The same flattening shows up, though, and more strongly: the implied exponent of the Daniels-Gilbert model falls from 1.063 at 1:20 to 1.029 at 2:40. For a 2:40 half the model predicts 5:26:35, seven minutes faster than Riegel 1.06 and nearly twelve minutes faster than Riegel 1.08.

A practical reading: if you can race a half before the marathon, use it. The models disagree by minutes from a half and by a quarter of an hour or more from a 5K, for anyone outside the fastest rows.

What a real-world study found

Andrew Vickers and Emily Vertosick (2016, BMC Sports Science, Medicine and Rehabilitation, open access under CC BY) collected race histories and training from 2,303 recreational runners through an internet survey. They tested Riegel's formula with k = 1.07, the midpoint between the two exponents above, and checked 1.06 and 1.08 as sensitivity analyses.

Their result: Riegel was well calibrated for races up to the half marathon, but it predicted marathons too fast. In their validation group, Riegel's marathon predictions were 10 minutes or more too fast for about half of runners, and the median runner finished about 10 minutes slower than predicted. Using k = 1.08 improved things only slightly; marathon speed was still overestimated for about 75% of runners. Their own two models, which add typical weekly mileage, cut the mean squared error from 381 to 228 (one prior race) and 208 (two prior races).

Put that next to the tables. If Riegel at 1.07 is already optimistic for most recreational marathoners, then the Daniels-Gilbert column, which sits below even Riegel 1.06 for every 5K in the table and for any half slower than about 1:29, is the most optimistic of the three for exactly the runners most likely to use a calculator. For a 25:00 5K, Riegel at 1.07 gives 4:04:57, the model gives 3:57:55 and 1.08 gives 4:10:14.

That is not a reason to throw the model away. It works well over short ranges: from a 25:00 5K it predicts a 1:55:04 half against Riegel's 1:55:00. The trouble is specific to the long jump into the marathon.

Your own exponent from two races

Vickers and Vertosick's second model started from the exponent between a runner's own two shorter races. The race time predictor and the half marathon time predictor let you do the simple version: enter a second race and the tool fits k = ln(T2 / T1) / ln(D2 / D1), then predicts with your k. (The paper's model also adds weekly mileage; its coefficients are in a supplementary file I have not verified, so the tool does not use them.)

Worked example. 5K in 25:00 (1,500 s) and half in 1:55:00 (6,900 s): k = ln(6,900 / 1,500) / ln(21.0975 / 5) = ln(4.6) / ln(4.2195) = 1.060. That runner matches the popular exponent, and the marathon prediction from the half is 3:59:46. The same 5K with a 2:00:00 half gives k = 1.090 and a marathon of 4:15:22: five minutes lost over the half becomes about sixteen over the marathon.

Two cautions. The fit is sensitive to small errors: 25:10 instead of 25:00 for the 5K, with the same half, moves k to 1.055 and the marathon to 3:59:00. And a personal k fitted on races up to the half still has to stretch to twice that distance, which is exactly where the study found the formula breaks.

Which number to plan with

None of these is a measurement of you. Here is how I would read the three columns, based only on the arithmetic above and the study:

• Use the spread, not one number. The gap between the fastest and slowest column is a fair picture of the uncertainty.
• For a first marathon, plan from the slower end. The study's runners missed Riegel's prediction much more often on the slow side than the fast side.
• Prefer a recent half marathon as the input, and if you have two races, look at your own exponent.
• Check the pace on the marathon pace chart and set training from a race you actually ran with the training pace calculator, rather than from a goal.

Limits

All three methods assume you have trained for the distance you are predicting. None of them knows your weekly mileage, the course, the weather or your fuelling, and the marathon punishes all of those more than a 5K does. The Vickers and Vertosick data come from a self-selected online survey of recreational runners, so they describe that group, not elites. The tables here are computed from published equations; they are not taken from any book's printed tables. For the fatigue curve that drives the Daniels-Gilbert column, see how long you can hold a pace; for a different kind of comparison across distances, see age grading with the 2025 tables. Turn a predicted time into a pace with the marathon pace calculator. Check the paces for a 5K goal on the 5K pace chart.

Sources: Vickers AJ, Vertosick EA (2016), An empirical study of race times in recreational endurance runners, BMC Sports Sci Med Rehabil 8:26 (CC BY 4.0); Riegel PS (1981), Athletic records and human endurance, American Scientist 69(3):285-290; Larry Simpson, The Daniels/Gilbert formula (equations from Daniels and Gilbert, Oxygen Power, 1979). Rules checked 7 October 2026. Found a problem? Tell us.

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