Fitness
Race predictions
Predicted race times from your fitness and how long you can hold a fraction of your VO2 max.
Built on Daniels' VDOT (empirical) and his sustainable-fraction curve. Predictions assume you are trained for the distance, even pacing, and normal conditions.
Once we know your Aerobic index (your VDOT), we can predict how fast you would race common distances: the 5K, 10K, half marathon, and marathon. The catch is that fitness alone does not set a race time. You cannot hold 100% of your VO2 max for a whole race, and the longer the race, the smaller the fraction you can sustain.
The idea in one line
A short race is run close to your ceiling. A long one is run well below it. So a prediction is really two questions at once: how fast can you run, and for how long can you keep the effort up. The second question is answered by a curve.
The drop-dead curve
Daniels fit the sustainable fraction of VO2 max as a function of race duration t in minutes. It is a dual-exponential that starts above 1.0 for the very shortest efforts (a short race is run above your VO2 max velocity, topped up by anaerobic energy) and decays toward a floor of 0.8 for long races:
fraction(t) = 0.8 + 0.1894393·e−0.012778t + 0.2989558·e−0.1932605tTurning the curve into a time
To predict a race, we look for the fastest velocity whose oxygen cost, once discounted by the sustainable fraction for that race's finishing time, still matches your VO2 max. There is a chicken-and-egg problem: the finishing time depends on the pace, and the sustainable fraction (so the pace) depends on the finishing time. We solve it by iterating to a fixed point, feeding each estimate back in until the time and the pace agree.
Worked example
Take a runner with a VDOT of 50. A 5K takes this runner roughly 20 minutes, so read the drop-dead curve at t = 20:
- e−0.012778·20 = e−0.25556 ≈ 0.7745
- e−0.1932605·20 = e−3.86521 ≈ 0.0210
- fraction(20) = 0.8 + 0.1894393 · 0.7745 + 0.2989558 · 0.0210
- = 0.8 + 0.1467 + 0.0063 = about 0.953
So this runner sustains about 95% of VO2 max for a 5K, and the predicted 5K time comes out at about 20 minutes. A marathon for this runner is near t = 175 minutes (about 2:54), far out on the curve close to the 0.80 floor, which is why it is run so much further below the ceiling.
What the predictions assume
A prediction is an honest estimate, not a promise. It assumes you are actually trained and fit for the distance: a marathon predicted from only short runs will read optimistic, because the curve knows nothing about whether you have the endurance to spend two-plus hours near that fraction. It also assumes even pacing and normal conditions (a flat course, fair weather, no heat, no altitude).
And it inherits the character of the number it starts from. VDOT is itself an empirical estimator, so these are well-calibrated estimates built on top of another estimate, useful as targets and reality checks rather than guarantees. Treat a prediction as the time a well-executed race would land near, then let your own racing sharpen it.