Race Time Predictor

The model behind the numbers

Peter Riegel was an engineer and a course measurer, and in 1977 he published a relationship that has outlived most of the sports science of its era because it is simple and it holds up. His observation was that when you plot finish time against distance on logarithmic axes for a single runner, you get something very close to a straight line.

The exponent is the whole model. If k were exactly 1.0, doubling the distance would exactly double the time and pace would never decay. Riegel found 1.06 fit his data across a wide range of runners, which means each doubling of distance costs about four percent of pace. That is why a 20-minute 5K predicts roughly 41:40 for 10K rather than 40:00.

A worked example

Say you race 10K in 44:30 — 2,670 seconds. To predict the half marathon: D₂ ÷ D₁ is 21.0975 ÷ 10, or 2.10975. Raise that to the power 1.06 and you get 2.2064. Multiply by 2,670 and the prediction is 5,891 seconds, or 1:38:11.

Run the same input out to the marathon and the ratio is 4.2195, raised to 1.06 gives 4.6008, and the prediction is 3:24:43. Hold that figure lightly. It is the time your aerobic engine could support if fuelling, pacing, weather and long-run preparation were all perfect. In practice, most runners predicting a first marathon from a 10K should add somewhere between five and fifteen minutes.

Choosing your exponent honestly

The default of 1.06 describes an average runner. You are probably not average in this specific respect, and you can find out which way you lean by testing the model against two races you have already run.

This is more useful than any generic prediction, because it turns the calculator from a fortune-teller into a diagnostic. The exponent is a measurable property of your current training, and it moves when your training moves.

Half to full: two models that disagree

The half marathon is the most common launching point for a marathon prediction, and it is where the gap between models is most visible. Riegel gives a multiplier of 2.085 — two raised to the power 1.06. The coaching convention is to double the half and add ten to twenty minutes.

For a 1:45 half, Riegel says 3:38:56 and the coaching rules say 3:40 to 3:50. The spread is not noise; it is a disagreement about what limits you. Riegel is modelling aerobic decay and assumes you are trained for the distance. The coaching cushion is pricing in the things Riegel omits: glycogen depletion, the musculoskeletal cost of an extra ninety minutes on your feet, and the fact that most people preparing for a first marathon have not run one.

Use Riegel if you are running high volume with long runs beyond 30 kilometres. Use double-plus-twenty if this is your first marathon or your weekly mileage is modest. The honest answer for most amateurs sits closer to the second.

Where the model fails

Riegel’s relationship assumes the same runner, similarly trained for both distances, on comparable courses in comparable conditions. Break any of those assumptions and the prediction drifts.

• Very short inputs. Predicting from 400 metres or 1 mile overweights anaerobic capacity, which contributes almost nothing past 10 kilometres.
• Untrained distance. A runner doing 30 kilometres a week cannot execute a marathon prediction built from their 10K speed. The engine is there; the chassis is not.
• Heat and hills. The model has no environmental input at all. A 5K run in cool conditions predicting a July marathon is comparing two different sports.
• Course profile. A downhill 10K personal best inflates every prediction downstream of it.

Alternative models exist. The Cameron formula adjusts more conservatively at marathon distance, and Jack Daniels’ VDOT tables approach the problem from oxygen cost rather than pure regression. All three agree closely in the 5K to half marathon range and diverge at the extremes, which tells you something honest about how much certainty is available.

Turning a prediction into a plan

A predicted time is only useful if it changes what you do on Tuesday. Feed the result into the training pace calculator to get the specific paces your intervals, tempo runs and easy days should sit at, then use the pace calculator to build the split sheet for race day.