Desert running

How to find your perfect running pace: a tool to reshape the face of pre-race analysis

Miles Weatherseed is an ex-international 1,500m runner and is currently studying towards a Masters in Mathematics at the University of Oxford. He has spent countless hours alongside Tim Beeson-Jones, a PhD student at Cambridge University, applying this experience towards developing the ultimate tool in race analysis for

Imagine if I told you that I knew what time you were going to run in your next race. What if I also claimed that I could provide you with the ideal splits for every section of that course, to maintain an even running economy? And what if, after all that, I told you that I could whack those splits onto your Garmin to give you real-time feedback throughout the race?

It sounds impossible, right? On the contrary — our new Race Pace Recommender tool can do all of this in just half the time it takes you to make a cup of tea.

Finishing Time Prediction

Predicting marathon times has long been a fiercely disputed topic in the political hotbed that is the world of endurance running. One of the earliest recognised efforts to predict times was by a man called Peter Riegel, who proposed that one might rescale another performance using the formula:

Above: Riegel’s Formula for time prediction

Here, k is a constant, usually between 1.03 and 1.10, depending on fitness level. For most people, k is around 1.07. However, this formula has been shown to fall apart when used on distances above half marathons. Riegel reckons I can run a 2:20 marathon, which — however flattering — is almost certainly not true!

“These variables will enable us to tailor predictions to every last bit of information we have about an athlete…”

This is presumably what spurred on a couple of researchers to study over 2,300 runners and use the resulting data to construct the Vickers-Vertosick formula, which combines average weekly mileage with historic race performances to produce a more accurate value of k.

Our pace recommender takes whatever information you give it and uses linear regression to calculate an estimate for your value of k in Riegel’sformula. We then apply Vickers-Vertosick to this k value to come up with your adapted (and hopefully accurate) k value. Finally, this is used to estimate your finishing time for whichever race you select.

Grade Adjustment

Every race has a Flat Equivalent Road Distance (FERD) associated with it. This FERD is discussed in more depth in a blog post by my colleague, Tim Beeson-Jones.

Above: An elevation profile for the 10 Peaks Brecon Beacons Long Race

A script parses the selected race’s GPX file and the latitude-longitude pairs of coordinates are run through the Shuttle Radar Topography Mission (SRTM) database to return as accurate an elevation profile as possible (as elevation data from GPS satellites is often inaccurate). Distance between adjacent pairs is calculated using Vincenty’s iterative formula — developed to consider the ellipsoid shape of the earth, rather than the spherical assumption made by most other formulae.

The resulting product is a sequence of tiny approximately 10 metre sections, all paired with a straight line distance and an FERD. The whole race’s FERD is then summed up and your predicted finishing time is then used to produce a target pace for each kilometre of the race.

For example, if I’d planned to take part in the Maverick Lancashire races a fortnight ago and had been in 14:30, 30:20 and 68:30 shape for 5k, 10k and HM respectively, the Race Pace Recommender would have advised me to complete the Middle race in the splits below:

Above: An example of a splits table for the Maverick Lancashire race series

Note: there is not a perfect correlation between the Elevation column and the pace. This is because a kilometre section may well start and end at the same height above sea level, but during that kilometre you could well be going up and down, again and again and again…

Garmin Compatability

This analysis would be utterly useless without a practical application, which is precisely why we have also developed an extension for Google Chrome. The automated response email has a JSON attached, which can be inserted into the Let’s Do This Race Pace Recommender extension. Your splits will then be used to create a workout on Garmin Connect. This workout can be sent straight to your watch, to keep you running with perfect running economy throughout your next race, regardless of how undulating it is.

This extension was written in JavaScript and should work well. However, Garmin Connect restricts the length of every custom workout to 50 “blocks”. This means that, if your race is above 50km, we have to give you a target pace to hit every 2km, which obviously restricts the resolution of our analysis. Hopefully, we’ll be able to get around this shortly.

The Whole Process

  1. Fill out the form at as accurately as possible
  2. Receive the automated response email. Download the JSON from this
  3. Download the Let’s Do This Race Pace Recommender extension
  4. Upload the JSON to this…
  5. Smash your next race!

Looking Ahead…

Currently, the whole tool is still in beta and bugs are inevitably going to emerge here and there. We intend to carefully review the formula used to estimate race predictions in light of more data once lots of runners have used the tool.

Certainly, further down the line the plan is to adopt more of a “machine learning” style approach to the whole thing, iteratively updating our pace predictions using an ever-growing data set. Furthermore, in light of research carried out by Dr Fokas (of Cambridge University) and Tim Beeson-Jones, we are also close to using a wider range of variables as inputs for our predictor. These will be incorporated and a PCA (Principal Component Analysis) approach will enable us to tailor predictions to every last bit of information we have about an athlete.

We would really appreciate any opinions and feedback, both on the experience of using the tool and on the theory underlying the whole thing. Please direct all such correspondence to

Miles Weatherseed, 6/9/17


1 “Pace and critical gradient for hill runners: an analysis of race records” (2012)

2 “An empirical study of race times in recreational endurance runners” (2016)

“Direct and indirect solutions of geodesics on the ellipsoid with application of nested equations” (1975)

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