Paste a recent race result into any predictor and a wall of finish times appears. Nearly all of them run on one equation, published by Peter Riegel in 1981 in a note entitled fittingly for what it became: Athletic Records and Human Endurance. Understanding its one assumption tells you when to trust it and when it flatters you.
The equation
T₂ = T₁ × (D₂ / D₁)^1.06
Where T is time, D is distance. The exponent 1.06 was fitted from decades of world-record and age-group performances across distances — it encodes how human endurance performance decays as distance grows. Double the distance and required time grows by 2^1.06 ≈ 2.09×, not 2×. That 9% premium is the physiology of fuel, fatigue, and economy stretched over time.
What the exponent assumes
Riegel's world records belong to athletes trained specifically for their distances. The equation assumes you are too. For a runner with a proper endurance base — weekly volume and long runs matched to the target — 1.06 is remarkably accurate, typically within 2–4%.
The assumption bends in two directions:
- Speed-biased runners (track backgrounds, thin long-run volume) decay faster than 1.06 at long distances — their real exponent is 1.07–1.09. The 5K-to-marathon prediction that "came true as a blowout" belonged to this group.
- Endurance-biased runners (high-volume, long-history) decay slower — 1.05–1.06 or better. Their marathon predictions from halves are conservative.
| From → To | 1.06 prediction | 1.08 prediction | Trust |
|---|---|---|---|
| 50:00 10K → Half | 1:50:44 | 1:52:38 | High, if volume supports it |
| 50:00 10K → Marathon | 3:42:46 | 3:49:44 | Low — extrapolation ×4 |
| 1:50 half → Marathon | 3:51:31 | 3:56:47 | Moderate — ×1.9 |
Practical use
- Pick the most recent all-out effort within 4–6 weeks. Stale anchors predict stale fitness.
- Match exponent to your base: dedicated marathon block → 1.06; typical amateur with 25–35 miles/week → 1.07; first marathon off a speed background → 1.08.
- Read long extrapolations as ceilings. Race the first attempt at the 1.08 pace and negative-split; the finish tells you which exponent you really are.
- Update after every race. The predictor improves with each honest anchor — that is the entire feedback loop of training.
The formula's genius is its honesty about one variable. Every other input — heat, hills, fueling, sleep — remains yours to manage. Our predictor and zone calculator apply the same math; the running is the part no formula can do.