Race Time Predictor

How this works

Your race times are predicted from a real recent run using a science-backed endurance model. Here is exactly how, and where it can mislead.

The Riegel formula

Pete Riegel fitted a single power law to endurance performances across distances. To predict a time T2 at a new distance D2 from a known time T1 at distance D1:

T2 = T1 × (D2 / D1)1.06

• T1 your known race time
• D1 the distance of that race
• T2 the predicted time
• D2 the target distance
• k = 1.06 the fatigue exponent, below

The fatigue factor

If you could hold your pace forever, doubling the distance would exactly double your time, an exponent of 1.0. In reality pace fades with distance through glycogen depletion, muscular fatigue and heat. The exponent 1.06 captures that fade: doubling the distance multiplies your time by 2^1.06, about 2.08, not 2. The bigger the number, the more you slow down over distance.

Why the marathon runs optimistic

Riegel's 1.06 was fitted to world-record data, so it flatters recreational runners at the longest distances. In a study of 2,303 runners, the marathon predicted from a half came out more than 10 minutes too fast for about half of them. The missing ingredient is endurance: predicting a marathon from a short race assumes your long-run training can carry the pace. If you have not built the mileage, treat the marathon estimate as a best case.

Your personal fatigue factor

With two race efforts at different distances we can solve for your own exponent instead of assuming 1.06. It is just the slope of your times on a log-log plot:

k = ln(T2 / T1) / ln(D2 / D1)

A lower k, around 1.04 to 1.05, means you hold pace well over distance, typical of high-mileage runners. Above about 1.08 means longer races cost you proportionally more. We clamp the fit to between 1.00 and 1.15 to reject noisy inputs.

The confidence range

The range beside each prediction widens the further we extrapolate, and leans slower for long races to reflect the optimism above. It is an honest band, not a guarantee. Weather, terrain, fuelling and pacing all move the real result.

References

• Riegel, P.S. (1981). Athletic Records and Human Endurance. American Scientist, 69(3), 285 to 290. Background on Peter Riegel
• Vickers, A.J. & Vertosick, E.A. (2016). An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation, 8:26. Read the study

Valid for roughly 1.5 km up to the marathon. We do not predict ultra distances.