How accurate is the Riegel race predictor?
Peter Riegel's endurance formula predicts a race time at one distance from a known time at another using a single fatigue exponent. It is remarkably good inside its intended range and systematically optimistic outside it. Here is exactly what the formula does, how accurate it is, and when to trust a second opinion.
Open the Race Time PredictorThe Race time predictor runs the Riegel formula on any pair of distances and lets you slide the exponent, so you can watch the uncertainty band described on this page open up for yourself.
The short answer, in numbers
Between neighbouring distances — 5K to 10K, 10K to a half — Riegel is genuinely good, usually within about 1–2% for a runner whose training fits the target. The accuracy does not fall off gently, though; it falls off in proportion to how far you extrapolate. Predict a marathon from a 10K and a plausible shift in the fatigue exponent (1.06 vs 1.10) moves the answer by more than 13 minutes; the same shift moves a half-marathon prediction by barely 3. The formula is not equally accurate at every distance, and the rest of this page quantifies exactly where and why it drifts.
The formula and its one exponent
In his 1981 article Athletic Records and Human Endurance, Riegel fitted a power curve to world-record and race data across many endurance sports and found that time scales with distance by a near-constant exponent:
- T1
- your known time at the reference distance
- D1
- the reference distance
- D2
- the target distance you want to predict
- 1.06
- Riegel's fatigue exponent — adjustable, roughly 1.05–1.08 for most runners
Everything rides on that exponent. At 1.0 there would be no slowdown — double the distance, double the time. Real runners fade, so the exponent sits just above 1.0; 1.06 means each doubling of distance costs a little more than double the time. A deep aerobic base pulls a runner toward 1.05; someone who fades over distance behaves like 1.08 or higher. Because that exponent is an exponent and not a multiplier, small differences in it are magnified as the distance ratio grows — the single most important fact about the formula's accuracy, and the one covered next.
What it predicts from one race
Take a 50:00 10K as the reference and run it through the formula at the default 1.06. The arithmetic
for the half is 3000 s × (21.0975 / 10)^1.06 = 3000 × 2.206 = 6619 s ≈ 1:50:19;
every other row works the same way:
| Target from a 50:00 10K | Riegel (1.06) | Distance ratio |
|---|---|---|
| 5K | 23:59 | 0.5× |
| 10 mile | 1:22:48 | 1.6× |
| Half marathon | 1:50:19 | 2.1× |
| 30K | 2:40:13 | 3.0× |
| Marathon | 3:50:01 | 4.2× |
These look authoritative to the second, and that false precision is the trap. The 5K prediction sits close to reality; the marathon prediction is a hopeful extrapolation four times the reference distance. The next section shows how much confidence you should actually attach to each row.
Why the error grows with distance
The honest way to read a Riegel prediction is as a range, and the width of that range is not the same for every distance. Hold the reference at 50:00 and ask what happens if your true fatigue exponent is 1.10 rather than the default 1.06 — a realistic amount of individual variation. The prediction shifts by this much:
| Target | At exponent 1.06 | At exponent 1.10 | Swing |
|---|---|---|---|
| 5K | 23:59 | 23:19 | ~40 s |
| Half marathon | 1:50:19 | 1:53:37 | ~3.3 min |
| 30K | 2:40:13 | 2:47:24 | ~7.2 min |
| Marathon | 3:50:01 | 4:03:39 | ~13.6 min |
Same reference race, same 0.04 change in one number — but the marathon prediction moves twenty
times as much as the 5K one. That is the distance ratio doing its work: the exponent is applied to
(D2/D1), so the further you extrapolate, the more a small error in the exponent is
amplified. This is why Riegel is trusted for a 10K-to-half jump and quietly distrusted for a
10K-to-marathon jump. The formula is not less correct at the marathon — it is far less
certain, and it never tells you that itself.
The marathon problem
Riegel fitted a single exponent to elite record data, and analyses of large amateur race datasets since have found the same runners behave like a higher exponent as the distance climbs — often 1.07–1.10 for the marathon rather than 1.06. In plain terms: the marathon punishes an incomplete endurance base far more than the formula's default assumes. For our 50:00 10K runner that is the difference between a predicted 3:50 (at 1.06) and 4:04 (at 1.10) — and the runner who trained mostly at 10K speed will finish nearer the slower number, or behind it.
The fix is not to distrust the formula but to feed it the right exponent and the right reference. Predict the marathon from your longest recent race, not your sharpest short one, and lean the exponent up toward 1.08–1.10 if your weekly mileage and long runs are modest. Riegel himself flagged the boundaries: the model holds best for efforts of roughly 3.5 minutes to about 4 hours, so both the sprints and the ultras sit outside the data it was built on.
Second opinions: VDOT and Yasso 800s
A single prediction is a point estimate with no error bar. The way to recover the error bar is to get two more estimates from methods that fail differently, and see how far apart they land.
VDOT equivalence. Popularised in Daniels' Running Formula and built on the Daniels & Gilbert oxygen-cost model, this reads equivalent race times off a fitted estimate of the oxygen consumption a performance implies, rather than a single power law. Because it is calibrated to trained runners it usually disagrees with Riegel by tens of seconds to a couple of minutes — and that disagreement is the point. It is a performance comparison, not a training prescription; the equivalent time still assumes you have trained for the distance.
Yasso 800s. A training-based marathon benchmark rather than a formula: run ten 800 m repeats and average them, and the average in minutes:seconds is taken as your marathon time in hours:minutes. Average 3:50 per 800 and the benchmark suggests a 3:50 marathon. It is a rough check — it tends optimistic without a strong long-run base — but as a third, physiologically different data point it is genuinely useful. When Riegel, VDOT and Yasso cluster within a few minutes, back yourself; when they spread across a quarter of an hour, that spread is your uncertainty.
Picking the right exponent for you
| If your profile is… | Use an exponent near… | Because |
|---|---|---|
| High mileage, strong long runs, negative-split racer | 1.05 | You hold pace as distance grows |
| Balanced training, typical club runner | 1.06 (default) | The value Riegel fitted broadly |
| Speed-biased, low mileage, fade late in long races | 1.07–1.08 | You slow more than average with distance |
| Stepping up to your first marathon off modest mileage | 1.08–1.10 | The endurance penalty is largest here |
The honest workflow: predict from your most recent, longest race; pick the exponent row that describes your training, not your ambition; and read the answer as the middle of a range whose width you now know grows with distance.
Frequently asked questions
What does the 1.06 exponent mean?
It is Riegel's fatigue factor. An exponent of 1.0 would mean no slowdown as distance grows; 1.06 means time rises slightly faster than distance. Lower values suit strong endurance runners, higher values suit those who fade over distance.
Why does it over-predict my marathon?
Because it was fitted to race data and assumes your target-distance training matches your reference race. If you predict a marathon from a fast 10K without the endurance base, the model gives a time you are not yet trained to run.
Should I use Riegel or VDOT?
Use both. Riegel is a simple, transparent power law; a VDOT-style equivalence adds a physiology-based second opinion. When they agree you can be confident; when they diverge, the gap tells you how uncertain the estimate is.
What is the most accurate race predictor?
Between neighbouring distances (5K to 10K, 10K to half) Riegel is accurate to about 1–2% for a trained runner. No predictor is reliable for a big jump in distance without matching training — the marathon most of all. The most accurate approach is to cross-check Riegel against a VDOT equivalence and a benchmark like Yasso 800s and treat the spread between them as your real uncertainty.
Are Yasso 800s accurate?
They are a rough marathon benchmark, not a formula: ten 800 m repeats averaged at X:YY suggest a marathon of X hours:YY minutes. They run optimistic for anyone without a strong endurance base, so use them as one data point alongside a Riegel or VDOT estimate rather than on their own.
Related tools and reading
Race time predictor
Predict a time at any distance from a known result, with an adjustable Riegel exponent.
ReadHow to calculate running pace
Turn a predicted finish time into the pace you need to hold, in min/km and min/mile.
Sources
- Peter Riegel — Athletic Records and Human Endurance (American Scientist, 1981, vol. 69, no. 3), origin of the power-law endurance model and the 1.06 exponent. Checked 24 Aug 2026.
- VDOT running calculator — the Daniels & Gilbert VDOT equivalence model from Daniels' Running Formula. Checked 24 Aug 2026.
- Runner's World — Yasso 800s — the 800 m-repeat marathon benchmark. Checked 24 Aug 2026.
- Prediction and exponent-sensitivity tables were computed by ScoreIndexer by applying the Riegel formula to a 50:00 10K reference. Times are rounded to the second.