This was a toolbar which allows athletes to upload their Garmin Forerunner data directly to the web - now the best way to do this is :-)

Saturday, April 24, 2010

Prediction and Race Estimation Tools

RunSaturday's added lots more new toys :)

During the last few weeks we've added quite a few "predicted times" to the site.
For example, you can now:
  • see some predicted times for all your sports in your blog view -
  • use our running race time predictor to estimate race performances across different distances, given inputs like your age, your gender and a previous race performance
  • use out triathlon race time predictor to estimate triathlon race performance from input statistics likes some swim, bike, and run times, and some guesses about the hilliness of the courses.
  • see a vdot estimate (an esimate ot V02) for your runs in your blog view -
To achieve this new functionality we've used 5 prediction techniques:
  • - Riegel
  • - Age-Grading
  • - V02 Max
  • - Cameron
  • - Purdy
You can see all these side by side on our race prediction tool -

Further, we've taken some of these techniques and adapted them beyond running to other sports such as swimming and cycling, taking into account some observations of the different physical properties of those sports - e.g. see

For the rest of this post, I'll try to offer an explanation of how we've worked out some of those predictions. For further information I highly recommend who've assisted us with information and content for this part of our site. Indeed, I'll even be relying on some of their explanatory content for parts of this blog post.

If you want even further information, then runningforfitness is also available as a book -

Predictions? Estimates?

Our race time predictions are estimates of what a runner or triathlete might achieve, if they train appropriately for the distance.

We are not suggesting, for example, that if you train for a 5km and achieve a good time, then you will automatically achieve the corresponding time at the marathon distance.Simarly, if you are marathon fit, then it doesn't automatically follow that you are in prime 5km race form.

Instead our predictions show what you could achieve at that distance, if you train properly, given what you have achieved at another distance.

How accurate are the predictions?

From practical experience several of the estimation techniques do seem to be "fairly good". They are, however, based on average reduction of speed as the race distance increases, and this relationship will vary from person to person (as well as on the type of training they do). There is therefore a significant margin of error around the estimates.

The margin of error is bigger if the gap between the distances is large. In other words, a half marathon will typically be a better predictor of marathon performance than a 1 mile race.
Because they work on averages, the predictions also generally don't take into account that different people perform differently - i.e. that some people are built to be sprinters, while others are more naturally built for going long. The predictions also take no account of personal mental skills such as concentration and determination, of experience, of injuries - or on race day luck!

Please be careful and sensible in your training. Don't just blindly target some mathematical prediction - if in any doubt, always seek advice - why not try your local running club?

What are the different prediction techniques used?

We've used 5 different prediction techniques across the site:
  • - Riegel
  • - Age-Grading
  • - V02 Max
  • - Cameron
  • - Purdy
You can see all these side by side on our race prediction tool -

What is the Riegel formula prediction?
Peter Riegel's formula is: t2 = t1 * (d2 / d1)^1.06

This formula was devised by Pete Riegel and published (in a slightly different form) in Runner's World. Riegel later refined the formula for other sports. This formula has stood up well over time, and has the merit of simplicity. It says, roughly speaking, that a person's speed declines by around 6% when the distance doubles.

This is the technique we most often use across the site, although we have extended and adapted the basic technique beyond running to some first attempts at estimating swimming, cycling and skating too.

If you want to change the Riegel constant used for your Blog View and Activity Notes view then you can do so on your account settings -

For swimming and cycling within the triathlon race predictor, we've used variations of the Riegel rule based on my own practical observation of swim and cycling times over different distances.

Further, for triathlon running, I've again used a slight variation - based on some estimates about how much the previous swim and bike might affect speed on the run. These triathlon models are still in there infancy - and I will continue to refine them.

What is the age-grading prediction?
Age-grading is a way to adjust an athlete's performance according to age and gender. The age-grading tables were developed by the World Association of Veteran Athletes (WAVA), the world governing body for track and field, long distance running and race walking for veteran athletes.

The tables were first published in 1989.
The tables work by recording the world record performance for each age at each distance, for men and women. Where necessary, the world record performances are estimated.
For example, the world record for a 53 year old woman running a 10km is 35:01. So if a 53 year old woman finishes a 10km in 45:18, she has an age-graded performance of 77.3% (which is 35:01 divided by 45:18). The wide availability of age-grading tables has allowed older runners to compete on even terms with younger generations - and women to compete on even terms with men. In many running clubs today, the age-graded champion earns as much, if not more, recognition as the outright (non-age adjusted) winner of the event.

You can see more some of our age-grading tools on:
  • - - which shows you all equivalent age-grade results for a given gender, age group and percentage.
  • - - which shows you some key percentile age grade times for a given gender, age and race distance.
The age-grading prediction, shown on, assumes that that the runner will run the same age-graded performance at every distance. So, for example, if the runner has run a 10km at 62% of the world record speed for his or her age and sex, the calculation assumes that the runner would run 62% of the world record speed at each distance, and calculates what time that implies for each distance.

What is the VO2 max prediction?
VO2 max is a measure of the maximum volume of oxygen that an athlete can use. It is measured in millilitres per kilogramme of body weight per minute (ml/kg/min).

There are scientific tests you can use to calculate your V02 max (see However, for the purposes of runsaturday's calculations, a numerical estimate is instead used.

The VO2 max prediction works by estimating your VO2 max, given the performance you have entered, using the Daniels and Gilbert VO2 max formula.
VO2 Max=(-4.60 + 0.182258 * velocity + 0.000104 * velocity^2)/(0.8 + 0.1894393 * e^(-0.012778 * time) + 0.2989558 * e^(-0.1932605 * time))
(from J. Daniels and J.R. Gilbert , Oxygen Power: Performance Tables for Distance Runners”, Oxygen Power, 1979)

For our prediction, this formula is reversed, using a numerical estimation technique, in order to estimate your likely speed at the other distances.

What is the Cameron formula prediction?
Dave Cameron found that doing a regression comparing times and distance was futile; but that a model to predict speed produced a good formula which worked well for world records, US national records and collegiate records. He found that the model does well for post-1945 records at the 800m through the 10000m; and that from 1964 it also worked well for the marathon.

The Cameron model is
a = 13.49681 - 0.048865*olddist + 2.438936/(olddist**0.7905)
b = 13.49681 - 0.048865*newdist + 2.438936/(newdist**0.7905)
newtime = (oldtime/olddist) * (a/b) * newdist
Within we simply apply that rule quite directly.

What is the Purdy formula prediction?
The Purdy point system is calculated from a table of running performances compiled in 1936 called the "Portuguese Scoring Tables." These velocity measures were intended to be maximum possible velocity in a straight line. Each of these performances was arbitrarily given a Purdy score of 950. (World record times in 1970 have about 1035 Purdy points.)
Purdy subsequently estimated an equation for the men's world record performances (as of 1970). This enabled Purdy points to be estimated using the equation rather than the Portuguese tables.

How is the triathlon race prediction done?
Our triathlon race prediction uses combinations of:
  • - A basic Riegel model
  • - some modified Riegel constants for swimming and cycling
  • - some modified Riegel constants for the effects of doing all 3 sports in a row
  • - some guesses (rules of thumb) for swimming speed when using a wetsuit
  • - some TBP techniques to take into account the hilliness of the courses (see
I'm not documenting this fully at present - mainly because the calculator is still under development and testing - so anything I post now might be out of date in the next few weeks.

Which prediction technique is best?

This is all subject to personal opinion. In general, all of these techniques seem to give similar results - within a few minutes at each distance. Of all 5 techniques, perhaps Purdy disagrees most significantly with the others.

In my personal opinion, if you are looking at these prediction techniques and their results, then you should not be looking at them and asking "which is best?". Instead:
  • - you should be looking at them only as a guide.
  • - you should choose your own racing targets based on your own experience and your own goals.
  • - you should always remember that your training is more important than these predictions.
  • - you should never push yourself too hard based on such averaged, numeric formulae.
Thanks - credits and a disclaimer

I hope this explanation has helped.

I'd once again like to thank Owen at for his invaluable help in collating much of this material. If you don't want to know more then please consider buying the book.

Finally... one last piece of material reused from - but which applies equally for runsaturday:

The material in this website has been provided for general information purposes only. None of the information on this site is intended to constitute specific medical, phyiscal or training advice; and none of this information necessarily reflects the opinions of the authors or of any of the sources listed. This information is not intended to create any relationship between the managers of the website and the recipient. The information is not guaranteed to be correct, complete, or current.

No warranty, express or implied, is made about the accuracy or reliability of the information at this website or at any other website to which this site is linked.

If you use the information on this website, or on any website to which this website is linked, you do so at your own risk.

Thanks - and happy running, swimming and biking!


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