Estimating the impact of climbs and descents on running pace

Running Speed on Hilly Courses

When running on paths with elevation changes, average speed can be significantly impacted compared to flat courses. It is known, in fact, that the decrease in running pace on uphill sections is only partially compensated by the faster pace on downhill sections. As a result, a route with equal amounts of uphill and downhill is generally completed in longer times than a flat route of the same distance.

But how can we calculate this difference and what factors influence it?

The Challenge of Estimating Speed on Hilly Courses

Calculating running speed on a hilly course versus a flat one is a complex problem, because it depends on various factors, including:
- runner's fitness level: higher fitness levels may lead to better adaptation to elevation changes;
- slope of the route: steeper inclines or declines have a more pronounced effect on pace;
- distribution of ascents and descents: the order and frequency of hills can alter the overall pace;
- running surface: uneven, wet, or slippery terrain can slow a runner down even further.

To estimate the variation in speed caused by elevation changes, algorithms and models are used to calculate the so-called Grade Adjusted Pace (GAP).

Grade Adjusted Pace (GAP) - Known Calculation Methods

One of the best-known models is the formula proposed by Professor Minetti in 2002. This algorithm explores the relationship between energy expenditure and ground slope, providing a method to calculate the optimal speed for inclined terrains. However, Minetti’s model is complex and requires detailed data on ground conditions.

A simpler and more commonly used estimation method involves these steps:
1) Uphill adjustments: Add 15–20 seconds per 10 meters (approximately 33 feet) of positive elevation gain for every kilometer (0.62 miles) of running.
2) Downhill adjustments: Subtract 5–10 seconds per 10 meters of negative elevation gain for every kilometer of running.
For example, consider a 10 km course with 100 meters of total positive elevation gain and 100 meters of negative elevation loss. If the flat-ground running time is 60 minutes (6 minutes/km or 9'39"/mile):
- For the 100 meters uphill, add 150–200 seconds.
- For the 100 meters downhill, subtract 50–100 seconds.
This results in an adjusted total time of 60:50 (best-case scenario) to 62:30 (worst-case scenario). The corresponding pace ranges between 6:05/km (9'47"/mile) and 6:15/km (10'03"/mile), representing a speed loss of 5–15 seconds per kilometer (8–24 seconds per mile).

A variation of this method, suggested by Jack Daniels in Daniels’ Running Formula, adds 18–24 seconds for every 10 meters of ascent and subtracts 8–12 seconds for every 10 meters of descent.

The main limitation of these approaches is that they do not account for the steepness of the slope. Estimates become highly inaccurate for steep inclines or declines, where running is either extremely inefficient or not feasible.
To address this issue, the Go&Race algorithm, which we will now explain, offers a more refined solution.

The Go&Race Algorithm Based on Elevation Profiles (Version 1.0, 2024)

Our experimental method relies on analyzing the elevation profile of a course: by reading data from a .gpx file, we extract slope information and apply the Go&Race algorithm, developed through extensive analysis of training sessions and races. Essentially, the algorithm recalculates running speed along the route, taking slope into account.

The following zones are identified:
- Downhill gradients between -8% and -12%: These provide the maximum possible advantage, with an approximate 13% increase in speed.
- Downhill gradients steeper than -12%: The downhill advantage decreases rapidly, disappearing entirely around a -17% gradient. Beyond this point, running speed becomes slower than on flat terrain.
- Uphill gradients: The reduction in speed is more pronounced. At a 10% uphill gradient, running speed decreases by approximately 45%.
- Due to the uncertainty in the elevation and slope data, no correction is applied for slopes ranging between -1% and +1%.

This model provides a more accurate representation of performance variations due to slope, enabling runners and race organizers to better predict and plan for elevation-related challenges.

GNR-GAP index

The Go&Race algorithm calculates the GNR-GAP index, an index that represents the percentage change in an athlete's speed on a hilly course compared to a flat course.
A GNR-GAP of 25 indicates a 25% slower pace. Negative values indicate a faster pace and occur in the case of downhill paths.

EXAMPLE 1 - Elba Marathon, Italy

Let's start with this first example using the elevation profile of the Elba Marathon, a 42.2 km race held in May in Tuscany on a stunning panoramic course overlooking the sea. Based on the 2024 course data, the race is characterized by numerous rolling hills, with a minimum elevation of 0 meters above sea level and a maximum of 90 meters, totaling approximately 530 meters of both ascent and descent.

The following graphs display the elevation profile and slope gradient of the course.

Using our algorithm, we estimate a pace that is 4.5% slower than on a flat course.
For instance, if a runner is capable of completing a flat marathon at a pace of 5'00"/km (8'03"/mi), equivalent to a finish time of 3h30'58", the adjusted estimated finish time would be 3h40'27". The recalculated average pace (GAP) rises to 5'13"/km (8'25"/mi), meaning the pace slows by 0'13"/km (+0'22"/mi).

A table below provides estimates for various other paces.