REF-1282 · Vickers & Vertosick, 2016 · BMC Sports Science, Medicine and Rehabilitation · Paper · PubMed · Free full text

Can I predict my marathon from my half or 10 km?

Riegel fit up to the half but put the marathon 10+ min too fast for half of 156 recreational runners; adding weekly mileage halved that share. Self-reported data.

Main caveat: Self-report. Race times, course difficulty, fitness on the day, mileage and training type are all as the runner remembered them.
moderate evidenceMeasured on recreational to trained athletes

Vickers and Vertosick asked two questions with data any recreational runner has: which runner and training characteristics go with faster races, and how well a marathon can be predicted from shorter races.

A questionnaire linked from a Slate.com article on race-time prediction (24 April to 16 June 2014) collected age, sex, height, weight, typical and maximum weekly mileage, whether the runner did intervals or tempo runs most weeks, injuries, footwear and two or three recent races of different distances with course difficulty and fitness on the day; 2,303 of 2,497 respondents had usable data.

Riegel's formula (time₂ = time₁ × (distance₂/distance₁)^k, here k = 1.07, chosen by the authors as an average of the 1.05-1.08 that Riegel cited) was well calibrated for the 10 km and the half marathon but not for the marathon: in the 156 validation runners with a marathon and two shorter races its median error was 10:09 too fast, about half were predicted 10 min or more too fast and nearly a quarter more than 20 min too fast.

Two regression models fixed most of this: Model 1 adjusts the Riegel marathon velocity from one prior race by typical weekly mileage; Model 2 predicts the marathon exponent from the exponent between two prior races and weekly mileage. Mean squared errors were 227.6 and 208.3 against 380.7 for Riegel, and the share 10 min or more too fast fell to about 25%.

In both models runners with more weekly mileage were predicted to slow less to the marathon. Across runners, 50 rather than 30 miles a week went with a marathon 25:32 faster in men and 31:41 faster in women, intervals most weeks with about 3% faster times at every distance, and women were 20.9% slower than men at 5 km but 10.6% slower over the marathon.

Our reading: the most useful single finding for an assistant is that a standard calculator flatters most recreational marathoners, and that the gap grows as weekly mileage falls; the absolute numbers rest on self-reported data from a faster-than-average sample.

Protocol

Recruitment: an online questionnaire attached to a Slate.com article ("help Slate build a better predictor"), open 24 April to 16 June 2014; 2,497 responses. Excluded: all races the same distance (171), duplicates (8), only one unique race with full data (7), a longer race run faster than a shorter one (6), obviously erroneous or falsified answers (2).Final: 2,303 runners with full data on at least two races of different distances. Race data were also dropped for missing fields or a velocity under 4 or over 20 min per mile (Additional file 1). The chair of the Memorial Sloan Kettering IRB judged that no oversight was required (anonymous, deidentified survey; completion taken as consent).
Who (Table 1): age 35 (29, 42); 1,413 men (61%), 890 women (39%); BMI 23.4 (21.7, 25.2); typical weekly training mileage 30 (20, 42); intervals most weeks 51%, tempo runs most weeks 58%. Races reported: 5 km 1,387, 5 mile 313, 10 km 946, 10 mile 357, half marathon 1,579, marathon 1,022; marathoners' typical mileage 40 (30, 50).
Representativeness (Additional file 1): median marathon about 40 min faster than the 2013 New York Marathon (men 4:11:17, women 4:38:01) and Running USA; 165 of the 890 women and 150 of the 1,413 men reported a marathon over 4 h; the supplement calls these 19% and 11% of female and male marathon runners, but they are shares of all respondents (of the 366 women and 656 men with a marathon, about 45% and 23%, our arithmetic).
Associations: separate linear regressions of race velocity (m/s) for each distance on sex, age, BMI, typical weekly mileage (cubic splines for age, BMI and mileage), intervals and tempo runs, with and without BMI; sex interactions; 5-mile and 10-mile races left out for small numbers.
Prediction: a 2:1 random split into training (n = 1443) and validation (n = 721) sets balanced for marathon runners and times. Races rated "very difficult" or "very fast" (5.6% of the data) excluded; "difficult" and "fast" races adjusted to an average course with distance-specific velocity coefficients.Riegel used k = 1.07 from the runner's longest non-marathon race, with sensitivity analyses at 1.06 and 1.08. Model 1 (one prior non-marathon race): marathon velocity = 0.16018617 + 0.83076202 × Riegel velocity + 0.06423826 × (typical weekly miles / 10), velocities in m/s.Model 2 (two prior races): marathon exponent = 1.4510756 − 0.23797948 × (exponent between the two races) − 0.01410023 × (typical weekly miles / 10). Compared by mean squared error (MSE, minutes squared) and a penalised MSE that doubles the weight of predicting too fast, on the same 156 validation runners. Formulae from Additional file 1.
Funding and interests: "supported in part by the NIH/NCI Cancer Center Support Grant to MSKCC under Grant P30-CA008748"; no conflicts of interest. Both authors list Memorial Sloan Kettering Cancer Center, New York, as their only affiliation; the survey ran on a news website; no device maker, data platform or federation is involved. The full data set is published as Additional file 2.

Key Results

Marathon prediction in the 156 validation runners (Table 4): predicted minus observed time (min:s); a negative value means the prediction was too fast.

CentileModel 1 (one race + mileage)Model 2 (two races + mileage)Riegel, k = 1.07
5th−23:53−21:38−36:17
10th−18:25−16:47−30:24
25th−9:55−7:31−19:47
50th−1:470:23−10:09
75th6:287:20−2:48
90th11:4915:012:53
95th15:2321:055:12
Mean squared error227.6208.3380.7
Penalised mean squared error646.1525.01429.8

The root mean squared errors are about 15.1, 14.4 and 19.5 min (our arithmetic from the MSEs).

Calibration of Riegel by distance: the coefficient for Riegel's marathon predictions differed from 1 (p < 0.0001); for the half marathon and 10 km there was no evidence of a difference (p = 0.3 and p = 0.9).
Other exponents: k = 1.08 improved Riegel slightly, but its MSE stayed much higher than the new models' and it still predicted the marathon too fast for about 75% of runners.
Mileage in the models: at a fixed prior race, each extra 10 miles a week raises the predicted marathon velocity by 0.064 m/s (Model 1) and lowers the predicted marathon exponent by 0.014 (Model 2).Worked example (our arithmetic from the published formulae): from a 1:40 half marathon Riegel (k = 1.07) gives 3:30; Model 1 gives about 3:44 at 30 miles a week, 3:35 at 50 and 3:31 at 60; Model 2, with an exponent of 1.06 between a 10 km and that half, gives about 3:43 at 30 miles and 3:39 at 50.
Associations across runners (Table 3, not adjusted for BMI): women slower than men by 20.9% at 5 km, 18.5% at 10 km, 14.9% in the half and 10.6% in the marathon (interaction p < 0.0001); tempo runs most weeks −6.0%, −7.2%, −4.4% and −4.2% (interaction p = 0.002); intervals most weeks −3.8%, −2.5%, −3.7% and −3.5% (no interaction, p = 0.5).
Marathon differences (adjusted): 50 vs 30 miles a week 25:32 faster in men and 31:41 in women; age 50 vs 30 16:18 slower in men and 21:37 in women; intervals 4:46 faster in men and 3:07 in women; about 40 s more per BMI unit in men. Maximum and typical weekly mileage were correlated above 0.9.
A number that does not add up: the training and validation sets (1,443 + 721 = 2,164) do not account for 139 of the 2,303 runners (our arithmetic); the paper does not say where they went.

Mechanisms

Measured: recreational runners slowed more from the half to the marathon than Riegel's exponent assumes, and runners with higher typical mileage slowed less; the sex gap narrowed with distance; the interval-training association was the same at every distance, the tempo-run association larger at shorter ones.
Authors' interpretation: Riegel's formula comes from world-record times and most earlier work studied elite runners, so they built models from data any recreational runner has; mileage stayed because other variables added nothing once mileage and prior races were in the model (they give no physiological reason for the marathon miss).They argue that the training associations are probably causal (biological plausibility, a dose-response gradient, no convincing alternative), for example that adding intervals should cut race time by about 3%.
Inference: the mileage term behaves like a marker of marathon-specific endurance (durability); it agrees with REF-1245, where recreational marathoners held a smaller share of their critical speed the longer they took, and with REF-1283, where the half-to-marathon conversion was poorer in slower runners.
Inference: Model 2 gives the exponent between the two shorter races a negative coefficient (−0.238), so a runner who slowed more from 10 km to the half is predicted to slow slightly less in the marathon; that is most likely regression to the mean from noisy self-reported times, and it means a personal exponent from two short races should not be extrapolated as it stands.
Inference: the authors' causal reading is not shown by a cross-sectional survey; runners who run more, or do intervals, differ in talent, history and age at start.

Practical Application

Can I predict my marathon from my half or 10 km? Riegel fit up to the half but put the marathon 10+ min too fast for half of 156 recreational runners; adding weekly mileage halved that share. Self-reported data.
Up to the half marathon, a Riegel-type calculator is a fair estimate for recreational runners (no evidence of miscalibration at 10 km or the half; B+, self-reported data).
For the marathon, expect slower than Riegel and say how much from mileage: from a 1:40 half, Riegel says 3:30, while the authors' Model 1 gives about 3:44 on 30 miles (about 48 km) a week and 3:35 on 50 (our arithmetic from their formula). Even the better models were about 10 min or more too fast for a quarter of runners and more than 11 min too slow for one in ten, so quote a window, not a time.
Pace from the slower estimate: the authors weighted predictions that were too fast double, because a runner who starts too fast slows dramatically. The pacing rule itself (first half at or slightly below goal pace) is SYNTH-64's practice, not this paper.
Do not promise a time from adding mileage or intervals: 50 rather than 30 miles a week went with a 25-32-min faster marathon between runners, an association in a cross-section, not a forecast for one runner (not from this paper; the base's own practice).
Scope: recreational road runners on ordinary courses; no data on trail, ultra, cycling or triathlon predictions.

Limitations

Self-report. Race times, course difficulty, fitness on the day, mileage and training type are all as the runner remembered them; the authors argue that self-report should not bias the associations, but the prediction errors include recall error.
Who answered. Readers of a news website who chose to respond; their marathons were about 40 min faster than New York finishers', and they were slightly younger. Slower and older runners are represented but fewer (21 marathoners over 60).
Validation sample. The model comparison rests on 156 runners with a marathon and two shorter races, within the same survey; no external validation. The 2:1 split leaves 139 runners unaccounted for.
Extreme courses excluded. Very difficult (very hilly, hot or windy) and very fast (downhill or tailwind) races were dropped from model building; the models say nothing about them.
Cross-sectional associations. The training, BMI, age and footwear effects compare different runners; the authors' causal reading goes beyond the design.
Units. Mileage is in miles a week; MSE is in minutes squared, and no mean absolute error is given.
Interests. NIH/NCI cancer-centre support grant; no conflicts of interest; no industry or platform involvement.
How this entry was checked and changed
Why this level

cross-sectional measurement study with more than 100 participants (the rubric's B+), read from the full text and Additional file 1 (open access, CC BY 4.0). Held at B+ and not higher: every input and outcome is self-reported, the respondents were readers of one news website and ran marathons about 40 min faster than New York finishers, and the prediction comparison rests on the 156 validation runners who reported a marathon and two shorter races

Full text (checked 2026-10-27)
The final cohort included 2,303 runners, with all runners having full data on at least two races of different distances (full text)
We first split the data 2:1 into a training (n = 1443) and validation set (n = 721) (full text)
All mean squared errors were calculated on the same sample of runners in the validation data (N = 156); mean squared errors for model 1, 2 and Riegel were 227.6, 208.3 and 380.7 (full text)
Predicted marathon times from Riegel are 10 min or more too fast for about half of all runners; for the new models, this drops to about 25 % of runners (full text)
Riegel 50th centile of residuals −10:09; nearly 25 % of runners have a predicted race time from the Riegel formula greater than 20 min too fast (full text)
Riegel cited a k of 1.08 for elite runners and 1.05 to 1.06 for male recreational runners aged 40 to 70; the authors chose 1.07 (full text)
The difference in marathon time for training 50 vs. 30 miles per week was 25:32 for men and 31:41 for women (full text)
Model 1: velocityModel1 = 0.16018617 + 0.83076202 × velocityRiegel + 0.06423826 × typical mileage/10; Model 2: predicted kmarathon = 1.4510756 − 0.23797948 × kr2r1 − 0.01410023 × typical mileage/10 (Additional file 1; full text)
This work was supported in part by the NIH/NCI Cancer Center Support Grant to MSKCC under Grant P30-CA008748; there are no conflicts of interest to disclose (full text)