Do More Training Miles Mean a Faster Marathon? A Regression Test

With the Chicago Marathon this weekend, thousands of runners are asking the same question: did all those long weeks pay off? Training logs are a gift to statisticians, because they pair an input (weekly distance) with an outcome (finish time). They are also easy to over-read.

A straight line through eight runners

Take eight hypothetical runners averaging 30 to 100 km a week, with finish times from 270 down to 211 minutes. The simple linear regression calculator gives a slope of about −0.82, so each extra weekly kilometer goes with roughly 0.8 minutes off the finish time. The R² is 0.93, meaning the line captures about 93% of the variation, and the Pearson correlation calculator reports r ≈ −0.96.

Where the line breaks

Now use the line to predict. At 60 km a week it suggests about 236 minutes, which looks sensible. Push it to 150 km and it predicts roughly 162 minutes, and at 200 km about 121, a time near the world record for a recreational runner. The model has run far outside its data, and the straight line has no way to bend.

Real training effects level off. In a study of 126 recreational male runners, finish time followed an exponential decline in weekly distance rather than a line, and the best equation combined distance, pace and body fat (Tanda and Knechtle, 2013). An earlier study of 22 runners likewise found weekly distance and training pace were the main predictors (Tanda, 2011). A curve fitted to our eight runners levels off near 200 minutes.

Predictors beyond mileage

Distance is only one input. The multivariate regression calculator lets you add training pace, age or experience and see how much each contributes once the others are held constant. Even then, correlation is not causation: runners who log more miles may also sleep better, recover better and start with more talent, as our article on correlation versus causation explains. Rest weeks and pacing strategy matter too, and neither appears in a log of weekly distance alone. A model can explain only what it measures.

Remember too that a good R² describes the sample you collected. A model built on eight keen runners will not forecast a beginner's first marathon.

Reading the fit honestly

R² can flatter. With only eight points, a high value says little about how well the model would predict a ninth runner, and adding more predictors always pushes R² upward, even useless ones. A better question is how large the typical prediction error is. The earlier equation from Tanda's 22 runners estimated finish time with a standard error of about 4 minutes, which is a figure a runner can actually use.

Finally, remember who is missing. Finish times exist only for people who finish, and training logs come from runners disciplined enough to keep them. Such selection means the relationship in the data may look cleaner than it would in the whole field.

The sensible reading is modest: more training generally goes with faster times, with diminishing returns, inside the range where data exist. Use regression to describe your own training, but respect its limits when setting a goal time. Even two runners with identical mileage can finish far apart.

Beyond that range, a regression line is just a ruler laid over empty space.