How to predict your performance in a race, knowing your actual pace per minute? This info would be useful as we don’t often cover the full distance, while preparing an event. Many plans suggest to run up to a 70-75% of the target distance, before the tapering phase. So, besides experience and gut feelings, is there a scientific answer to this question?

Actually it is a tricky question, and for more than one reason. Let’s see some:

Everyone is different

The most obvious reason why there is no universal formula is that we are all different! Our body structure, sex, age, Body Mass Index, but also personal predisposition, play an important role. Someone could find ideal to run one mile, others the ultra marathons for example.

Another important parameter is the pace: is the change in performance the same for who runs a 10K in 40 minutes, than who covers the distance in one hour? Everything that is related to me, or you, cannot be taken into account into a general formula.

We also change, day by day!

The fact we can calculate with a certain accuracy what can be anticipated, is not a performance guarantee! We all know that, when we score a personal best in an unexpected moment, or when we have no gasoline… and we do not know why.

Our level of performance can vary for many reasons (ambient temperature, weight, level of training, stress or sleep quality, etc.) that cannot be part of a formula.

Where are we running today?

We cannot compare a trail in the snow with a flat city run. And even a flat city run can have lots of bends, people forcing us to zig-zag, altitude gain. We should take into account what is the baseline we are comparing our performance to.

All these points show how important is the compromise between accuracy and need to keep a formula simple. The american engineer Alan Riegel developed a very simple formula in 1977, cross referencing performances: given D1 and D2 two distances, if T1 is the time spent to cover D1, then the time T2 to run D2 is given by this formula:

T2 = T1*(D2/D1)^1,06

I checked and this rule matches with the predictors of my Garmin Fenix 5. This means that if you run an Half Marathon in exactly 2 hours, your expectation for the full one, in the same conditions, is 2*2^1,06 = 4h 10min according to Riegel’s formula.

Easy? Probably. But I found an article on the Guardian challenging the original formula. A study on a sample of 1071 runners who had ran at least 5 full and 5 half marathons, showed that the statistic distribution of the change in pace between the two distances was not matching the 1.06 exponent.

Only 5% of runners were at, or below the 1,06 exponent. The median distribution was instead at an exponent of 1,15. This means that – at least for the sample with over 1000 runners – Riegel expectations were optimistic, with data matching more a 1,15 power factor.

For your convenience I created an user friendly tool below, where you can use the original formula as well as the one with an exponent 1.15, to predict anticipated paces and times.

It is easy to use: type a distance D1 (in km) you ran, and the time T1 (one field for minutes, one for seconds). Add the distance D2 you want to estimate your performance. The tool will do it using the original Riegel’s formula, and the exponent 1.15. You may let me know how this formula works with you 🙂 .

What if it doesn’t work well with you? Well, we said it before.. it doesn’t have to. But it could give you food for thoughts: it could mean that you may dare and push more in certain distances, or that you simply give your best in particular distances. Try the formulas and comment down with your impressions!

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