Data analysis of 2013–2017 Lausanne races

You want to run a marathon. You will train for it, sure! But… what pace should you aim for? For most people, race day is the first time they actually go that distance. How are you supposed to know which pace is adequate for you?

The classical calculation

You can go to some online calculator tool. The most simple ones (e.g. hillrunner.com) will estimate your marathon pace asking only for a recent time in another distance. These are based on “Peter Riegel’s formula”:

Riegel’s Formula. T2= predicted time in the distance D2 (e.g. Marathon), T1 = time you did recently in another distance, D1 (e.g. Half Marathon).

…and it will give an unrealistic number. E.g. if you run a Half Marathon in 1h45 (roughly 5:00 min/km), it will tell you your estimated marathon time is 3h38 (roughly 5:10 min/km). This is just NOT the way it goes for most of the people.

The statistical calculation

To see how it goes for most people, I took the data from two races in Lausanne: the Marathon in October and the 20km in April, and compared the times (and pace) of people running both on the same year.

** Note: there’s also the a Half Marathon in Lausanne, but this one takes place at the same time as the Marathon, so runners cannot run both in the same year. I therefore preferred to use the 20km data. If you know these races and think that the 20km of Lausanne is harder because of the uphill, check my previous post, where I showed that the pace for a given person in the 20km and in the Half Marathon is comparable.

The figure below shows the pace of the people that run the 20km and the Marathon in the same year. Linear fit of the data is shown as a dashed black line, and it is clearly not what most online calculators predict (dark blue line, Riegel’s formula). Interestingly, if we do just one little change to the formula (changing the exponent from 1.06 to 1.2), it fits then pretty well the actual performance of runners (light blue line).

Pace at 20km vs. pace at Marathon for people that run both races in the same year (between 2013 and 2017, total = 958 runners).

This change, when applied to our specific case, means:

Realistic estimation of your Marathon pace based on your 20km or Half Marathon pace.

If you run a Half Marathon in 1h45 (roughly 5:00 min/km), your marathon time would be 4h03 (5:45 min/km). To me this sounds much more reasonable.

Can you do better than that?

The above calculation is an average based on real data from people. But an average real person is not perfect. In particular, average real people (including me) seem to suck at choosing their marathon pace. In our defense, not even Riegel seemed to get it right.

The reason I am saying this is that most people choose to start with a pace that they cannot keep up until the end. In the Lausanne Marathon, the median time for the first half is 1h50, while the median time for the second half increases to 2h05. 15-min difference between Happiness and Agony.

Comparison of the times ran in the first and second halves of the Lausanne Marathon. Vertical lines indicate median times. All marathon finishers between 2013 and 2017 were considered (6295 runners).

Only 1 in 3 marathon runners is able to keep the same pace along the whole distance. And I considered “same pace” = being up to 10% slower (i.e. from 5:00 to 5:30 min/km), so I am being very generous here. Since most people don’t choose the optimal pace, perhaps you could do better than an average person by choosing a pace you can keep until the end.

What could you realistically achieve by keeping a constant pace?

In principle, one makes better times by keeping a constant pace (the maximum constant pace that one can hold for the length of the race). Is this true? Well, at least the top 5 runners of each year (both men and women, green dots in figure below) are mostly within this 10% range (yellow shade). So it seems reasonable to think that in order to make your best possible time, you should probably aim to be maximum 10% slower in the second half.

Times for the first and second halves in the Lausanne Marathon (all finishers between 2013 and 2017 = 6295 runners). Green dots are the top 5 runners (men and women) each year. Little red dot in the center is me!

If we go back, the “realistic” formula:

Pace Marathon = 1.15 x Pace 20km (or Pace Half Marathon)

is an average derived from real people’s times. But we saw that an average real person is not performing at his/her best because they start way too fast. Could you aim at doing better than average by choosing the right pace from the beginning? How much better could you be? Could you meet Riegel’s standards?

Ok, let’s focus on “good pacers”, people that kept their pace throughout the Marathon (or up to 10% slower in the second half), what’s the “formula” for those runners?

Ratio between Marathon pace and 20km pace (1.00 = same speed at both races). “All runners”: participants that run both races on the same year between 2013 and 2017 (958 runners). “Good pacers”: from all runners, the ones that kept a constant pace (up to 10% slower in the second half, 356 runners). Boxplots limits = interquartile range, whiskers = 5th-95th percentiles.

In fact, most of them seemed to do better than the average-person formula above, but still didn’t meet Riegel’s standards. The formula for good marathon pacers is:

Marathon Pace = 1.11 x 20km (or Half Marathon) Pace

To sum up:

If you want to run the Lausanne Marathon in October, and you are wondering what should your pace be, run the 20km in April, train (a lot!), then:

- Realistic expectation (average from all runners):

Marathon pace = 1.15 x 20km pace

e.g. 5:00 min/km in 20km → 5:45 min/km in Marathon

- Optimistic expectation (if you think you can do better than average because you will choose the right pace and keep it until the end):

Marathon pace = 1.11 x 20km pace

e.g. 5:00 min/km in 20km → 5:33 min/km in Marathon

You can probably apply the above calculation to any Marathon based on any Half Marathon or 20km pace. And keep in mind that numbers above are averages, you might end up doing whatever!

Good luck!