Waiting for runners
29 September 2026
Most trail-running events publish live results during a race, with predictions of when a runner will reach the next checkpoint. These predictions are usually linear extrapolations: they take the runner's average speed and extend it to the next stop.
This isn't predictive analytics and the results can be annoying. The website might tell supporters to wait 20 minutes but the runner turns up an hour later. They might miss their runner entirely because the prediction misjudged the runner's pace.
These race trackers should be much better because it's so easy to make more accurate predictions.
As a case study, consider Ultra-Trail Australia's 102 km event in the Blue Mountains. I examined the 2025 race data then predicted every 2026 finisher's arrival at each checkpoint as they left the one before. The chart below shows a runner's actual position, alongside four methods of predicting their speed.
The dot nearest the ground is a real runner from the 2026 race, moving at their real pace. The orange dot is the linear extrapolation often used by events, the blue dot uses multipliers for each leg (discussed below), the green dot is a linear regression model and the yellow dot is a regression fitted separately for each leg. The predictions tend to diverge sharply during steep climbs. The linear extrapolation reaches the finish about 40 minutes before the runner does.
Leg multipliers
I used the 2025 results to calculate leg multipliers: ratios of a leg's speed to the speed on the previous leg. The prediction is that leg's multiplier times the runner's speed on the last leg.
| Leg | Multiplier |
|---|---|
| Foggy Knob to the Six Foot Track | 0.97 |
| Six Foot Track to the Aquatic Centre | 0.87 |
| Aquatic Centre to Echo Point | 1.13 |
| Echo Point to Gordon Falls | 0.65 |
| Gordon Falls to the Fairmont | 1.29 |
| Fairmont to Queen Victoria Hospital | 0.87 |
| Queen Victoria Hospital to the emergency aid station | 1.21 |
| Emergency aid station to the finish | 0.62 |
Multiple linear regression
The multipliers use one thing about the runner: their speed on the previous leg. A multiple linear regression can use more information. It predicts a leg's speed as a constant, plus each predictor times a weight. The weights are calculated to minimise the regression's prediction errors (using the 2025 data).
I gave this model five predictors: the leg's climb and descent per kilometre, the runner's average speed so far, their speed on the previous leg and the hours they have already run. Fitted, it reads
where:
- \(\hat{y}\) is predicted speed this leg (km/h)
- \(x_1\) is average speed (km/h) so far
- \(x_2\) is speed (km/h) in previous leg
- \(x_3\) is hours between race start and this leg's start
- \(x_4\) is ascent (m/km) this leg
- \(x_5\) is descent (m/km) this leg
Average speed so far is the most influential predictor, though all predictors are statistically significant – that is, they help to improve the prediction.
None of these methods predicts the first leg, because nothing is known about the runner until the first timing mat.
Per-leg regression
The regression model described above uses the same equation for every leg. A second regression model fits a separate equation for each leg, with four predictors: average speed so far, speed in the previous leg, hours since the start and minutes spent at aid stations so far. Climb and descent drop out, because within one leg they are the same for every runner.
Comparing predictions
Each dot shows the error of one 2026 finisher's predicted arrival at one of the eight checkpoints after Foggy Knob. The bar marks the median.
Linear extrapolation is 37 minutes early at the Aquatic Centre, 25 minutes early at Queen Victoria Hospital and 43 minutes early at the finish, for the median runner. The multipliers are 5, 10 and 5 minutes late at the same checkpoints.
| Method | Average miss | Within 30 minutes |
|---|---|---|
| Linear extrapolation | 21.5 minutes | 72% |
| Leg multipliers | 11.2 minutes | 94% |
| Regression model | 15.0 minutes | 86% |
| Per-leg regression | 10.3 minutes | 94% |
The multipliers halve the extrapolation's average miss and put 94% of arrivals within half an hour. The per-leg regression is better again by under a minute.
Interestingly, the single-equation regression is worse than the multipliers. This lesson recurs often in predictive analytics: a simple model built on the right variable (such as the leg multipliers) is usually about as good as an elaborate one, and far easier to explain. Finding the right variable is the trick.
Let me fix this problem
Linear extrapolation can be applied without any preparation, which is why it's used on race websites everywhere.
The multipliers need previous years' splits for the course. From these the multipliers are derived, which are enough for simple but reliable predictions. A regression model needs the same splits. There are more accurate models I didn't describe in this article, which need a little more data.
Fixing these predictions is very little work. The result is supporters standing at the checkpoint when their runner comes through. If a timing business wants to use a more accurate approach, I'll build it for free.