What marathon can I run off my half?
In 7,663 Valencia runners: marathon ≈ 2.28 × half time − 6 min (men) or − 12 min (women), off by 5.7% on average (4.1-4.8%, about 10-11 min, near 4 h); VDOT was closer under 3 h.
Main caveat: One race pair. Valencia's half and marathon are flat, fast and usually mild, six weeks apart; the authors say the equation is specific to this marathon.
Oficial-Casado, Priego-Quesada and Pérez-Soriano asked whether a simple equation from the half marathon predicts the marathon, whether half-marathon pacing adds to it, and how it compares with Daniels' VDOT.
The race organiser supplied results of the 2022 and 2023 Valencia half marathon (third weekend of October) and marathon (first weekend of December): 8,261 runners finished both in the same year (3,817 in 2022, 4,444 in 2023); after dropping those with a missing 5-km split or a half marathon run at a slower pace than the marathon, 7,663 cases remained.
Half-marathon time correlated with marathon time at r = 0.92. With 80% of the data the authors fitted three models: half time and sex (Model 1); plus half-marathon pacing range, the spread between the fastest and slowest 5-km split speed (Model 2); plus age group (Model 3).
All three explained 85% of the variance, so the simplest was kept: marathon minutes = 2.28 × half minutes − 6.21 for men, − 11.70 for women. On the remaining 20% its mean absolute error was 5.67% against 7.92% for VDOT (look-up of the half time in the fourth-edition tables).
The two methods behaved differently by level: VDOT was more accurate under 3 h (sub-2:30: 1.11% vs 4.06%), the regression more accurate from the sub-4:00 to the sub-5:30 category (for example sub-5:00: 5.56% vs 10.43%), and the regression's agreement with actual times fell from very good under 3:30 to poor beyond 4:30.
Our reading: an honest planning anchor for the mass of recreational marathoners on a flat course, consistent with REF-1282 that standard calculators flatter them; the equation implies a slow-down well beyond Riegel's (an effective exponent of about 1.15 for men from a 1:30 to 2:00 half, our arithmetic), and its average error near a 4-h finish, 4.10-4.76% or about 10-11 min (our arithmetic), is too large to set a pace to the minute.
Protocol
Design: retrospective analysis of official results; ethics approval from the University of Valencia committee (ref. H1544598666277); informed consent not required. Data: name, age category, sex, 5-km splits and finish time.
Races: Valencia half marathon (third weekend of October) and marathon (first weekend of December), six weeks apart; finishers 17,063 and 19,493 (half, 2022 and 2023) and 21,813 and 26,251 (marathon). Flat and fast (69 and 76 m elevation gain), usually mild (15-20 °C and 10-15 °C).
Sample: 8,261 runners in both races of the same year (3,817 in 2022, 4,444 in 2023); runners missing a split or whose half-marathon pace was slower than their marathon pace were discarded, leaving 7,663 cases. Grouped by sex, age group (U-20 to M-70) and marathon time category (under 2:30, 3:00, 3:30, 4:00, 4:30, 5:00, 5:30 and 6:00 h).
Pacing range: the difference between the highest and lowest relative split speed (each 5-km split speed as a percentage of the runner's mean speed) in the half.
Models: split 80/20 stratified by marathon time, sex and age group; linear regressions Model 1 (half time, sex), Model 2 (+ pacing range), Model 3 (+ age group); polynomial, exponential and power-law fits explored and not better; non-significant terms removed; best model chosen for simplicity and explained variance.
Comparison: each test-set runner's half time matched to the nearest half-marathon entry of the official VDOT table (Daniels' Running Formula, 4th edition) and that row's marathon time taken as the VDOT prediction; absolute percentage error compared by three-factor ANOVA with Bonferroni post hoc and Cohen's effect sizes; agreement by ICC(2,1).
Funding and interests: "The author(s) declared that financial support was not received for this work and/or its publication"; no commercial or financial conflicts. The results were provided by the race organiser; the data set is in a Mendeley repository (doi 10.17632/fbtbc38fhr.1).
Key Results
Mean absolute error of the marathon prediction by finish-time category (Table 2; test set):
| Category | Model 1, MAE % (95% CI) | VDOT, MAE % (95% CI) | Difference |
|---|---|---|---|
| Sub-2:30 | 4.06 (3.10-5.02) | 1.11 (0.54-1.69) | p < 0.001, ES 2.12; VDOT better |
| Sub-3:00 | 3.79 (3.46-4.12) | 2.22 (1.97-2.47) | p < 0.001, ES 0.82; VDOT better |
| Sub-3:30 | 3.85 (3.55-4.15) | 3.90 (3.56-4.24) | p = 0.83 |
| Sub-4:00 | 4.10 (3.79-4.41) | 5.96 (5.54-6.38) | p < 0.001, ES 0.49 |
| Sub-4:30 | 4.76 (4.29-5.23) | 7.61 (6.99-8.23) | p < 0.001, ES 0.61 |
| Sub-5:00 | 5.56 (4.38-6.74) | 10.43 (9.10-11.77) | p < 0.001, ES 0.81 |
| Sub-5:30 | 8.92 (5.67-12.18) | 14.38 (11.27-17.48) | p = 0.049, ES 0.60 |
| Sub-6:00 | 10.33 (2.44-18.21) | 17.73 (11.82-23.64) | p = 0.25 |
| All | 5.67 | 7.92 | ANOVA p = 0.02 |
Model 1 (Table 1, seconds): intercept −701.85 (95% CI −883.06 to −520.64); half-marathon time × 2.28 (2.25-2.3); male +329.59 (264.01-395.16); R² = 0.85. In minutes: marathon = −6.21 + 2.28 × half (men), −11.70 + 2.28 × half (women). At the same half time a man's predicted marathon is about 5.5 min slower than a woman's (our arithmetic from 329.59 s).
Adding pacing range or age group: R² stayed 0.85. Pacing range was significant (Model 2: +16.12 s per unit of pacing range, 8.19-24.06; 2% of explained variance), as were the U-20, U-23 and senior groups in Model 3; none improved prediction.
Pacing: the half-marathon pacing range correlated r = 0.39 with both half and marathon time and was larger in slower finish categories.
Agreement (ICC): 0.92 overall for Models 1 and 2 (VDOT 0.83); by category 0.70 (sub-3:00), 0.60 (sub-3:30), 0.47 and 0.46 (sub-4:00), 0.35 (sub-4:30) and 0.02-0.08 (sub-5:00 to sub-6:00).
Worked examples (our arithmetic from the equation): a 1:30 half gives about 3:19 (men) or 3:14 (women), a 1:45 half 3:53 or 3:48, a 2:00 half 4:27 or 4:22. Riegel with k = 1.06 gives 3:08, 3:39 and 4:10 for the same halves. The equation's effective exponent is about 1.15 for men and 1.10-1.13 for women across these halves.
Numbers that do not add up: the abstract's MAE of 5.9% sits in its sentence on the pace-range model and matches no number in the Results (Model 1: 5.67%, which the Discussion rounds to 5.7%); the abstract counts 8,261 runners as included after the pace filter, while the Methods apply that filter to reach 7,663; the abstract adds age before pacing range, the Methods and Table 1 the reverse; the Discussion says VDOT was more accurate in the sub-2:30 and sub-3:30 categories, but Table 2 shows sub-2:30 and sub-3:00 (sub-3:30: 3.85 vs 3.90%, no difference); the Figure 3 alt text, which Frontiers says it generated with AI support, says Model 1 had the lower error in every category, which Table 2 contradicts; and the Introduction says Riegel's equation takes age group and sex into account; the formula has no such terms, although Riegel cited different exponents for different groups (REF-1282).
Mechanisms
Measured: slower runners had more uneven half-marathon pacing and less predictable marathons; VDOT's error grew steadily from 1.11% (sub-2:30) to 17.73% (sub-6:00), while the regression's stayed between 3.79% and 4.76% up to sub-4:30 and was larger than VDOT's under 3 h. The paper gives absolute errors only, so the direction of each miss is not reported.
Authors' interpretation: VDOT is a power law derived from trained, faster runners, while the regression reflects the most crowded categories (sub-3:30 to sub-5:00, finishers from 3:00 to 5:00); accuracy falls beyond 4:30 because relative intensity and pacing vary more; half-marathon time already carries most of pacing's influence; a half run in under 2 h may not reveal durability, so tests of longer duration might improve prediction.
Inference: VDOT probably predicts slower runners too fast (its exponent comes from trained runners who slow less), and the regression probably predicts the fastest runners too slow (one slope fitted on the crowd); both directions are our reading, not shown in the tables.
Inference: the regression bakes the crowd's typical durability into one slope (2.28), so it cannot tell a durable slower runner from a fragile one; the large errors beyond 4:30 are where individual durability, fuelling and pacing decisions dominate.
Inference: women's better conversion at the same half time matches REF-1282's finding that the sex gap narrows with distance.
Practical Application
What marathon can I run off my half? In 7,663 Valencia runners: marathon ≈ 2.28 × half time − 6 min (men) or − 12 min (women), off by 5.7% on average (4.1-4.8%, about 10-11 min, near 4 h); VDOT was closer under 3 h.
Use it as a window, not a pace to the minute: a 1:45 half gives about 3:53 for a man and 3:48 for a woman (our arithmetic); the average error is 3.8-4.8% in the sub-3:00 to sub-4:30 categories and grows beyond 4:30, where agreement was poor. Flat course, mild weather, half run six weeks before.
Standard calculators flatter most recreational marathoners: from a 1:45 half, Riegel (k = 1.06) gives 3:39 against this equation's 3:53 for men (our arithmetic), in line with REF-1282. For a runner under 3 h, Daniels' VDOT was the closer tool here (MAE 1.11-2.22%).
Pacing on the day: start from the slower of the available estimates. Not from this paper; the base's own practice (SYNTH-64: first half at or slightly below goal pace).
Scope: pacing range and age did not improve the prediction; training volume, long-run history and heat were not in the data, so a runner whose preparation differs from a typical Valencia entrant's (low mileage, a hot race) should expect a wider error (inference).
Limitations
One race pair. Valencia's half and marathon are flat, fast and usually mild, six weeks apart; the authors say the equation is specific to this marathon.
Selection. Runners who ran the half slower than the marathon were dropped, which probably removes those who used the half as a training run (our reading); only finishers of both races are included, so runners who did not finish the marathon are missing.
No training data. Mileage, long runs, training history and experience were not available, though they are known to matter (REF-1282).
Model built on the crowd. The single slope fits the crowded sub-3:30 to sub-5:00 categories best and is less accurate than VDOT for the fastest runners; agreement was poor beyond 4:30.
Reporting. The abstract's 5.9% matches no Results number (5.67%, rounded to 5.7% in the Discussion); the order of models and the categories where VDOT won differ between sections; the figure description contradicts Table 2. The numbers in Table 2 are internally consistent and are the ones used here.
Interests. No funding; no conflicts declared; results supplied by the race organiser.
How this entry was checked and changed
Why this level
large observational measurement study (the rubric's B+ for 100 or more), read from the full text (open access, CC BY 4.0). Chip times are objective, but it is one city's flat, mild-weather race pair; runners who ran the marathon at a faster pace than the half were dropped; there are no training data; and the paper reports its own headline error two ways (5.9% in the abstract, 5.67% in the Results)
Full text (checked 2026-10-27)
A total of 8.261 runners, who participated in both events (Valencia Half Marathon and Marathon) in the same year, for the 2022 and 2023 editions, and ran the half marathon faster than the marathon, were included in the study (abstract; full text)
Runners missing a split or who ran the Half Marathon at a slower pace than the Marathon were discarded, leaving the selectable sample at a total of 7.663 cases (full text)
The introduction of the pace range variable did not improve the model's prediction, obtaining an explained variance of 85% and an mean absolute error of 5.9% (abstract; full text)
Model 1 obtained an average mean absolute error (MAE) of 5.67%, while that of the VDOT was 7.92% (full text)
Valencia Marathon race time men (min) = −6.21 + 2.28 × Valencia Half Marathon race time (min); women (min) = −11.70 + 2.28 × half marathon time (min) (full text)
Table 2 MAE, Model 1 vs VDOT: sub-2:30 4.06 vs 1.11; sub-3:00 3.79 vs 2.22; sub-5:00 5.56 vs 10.43; sub-5:30 8.92 vs 14.38 (full text)
ICC poor in the slower categories (sub-5:00, sub-5:30 and sub-6:00 = 0.02–0.08) (full text)
The Valencia Half Marathon was held 6 weeks before the Marathon; minimal elevation gains (69 and 76 m for half and full marathon, respectively) (full text)
The author(s) declared that financial support was not received for this work and/or its publication (full text)