What is interesting is that the 'average' person can be modelled reasonably well with a very simple equation. There are multiple forms of the equation but the most popular in running is the one Peter Riegel introduced back in the late 1970s/early 1980s. The equation is a simple scaling of one performance to another using an exponent, Whilst the value of that exponent has been discussed and argued about at length, most agree that the equation provides one of the better 'ball-park' values[1,2]. I don't intend to add to that discussion, but I do want to start from the premise that the formula does 'sort-of-work' and that it also represents a way of estimating what a 'maximum' effort might look like at a range of distances.

I have plotted Riegel's formula in the graph below (Figure 1) as the dotted lines for five different marathon preformances.

First, this graph is complicated for a number of reasons. But, the graph is worth a bit of effort since it encapsulates much of why people hit performance limits. Let me start by taking the example of the yellow dotted lines which is the Riegel line for a 3 hour marathon runner. The dotted yellow line shows the speed the 3 hour marathon runner might hope to maintain for a range of race distances. In a 5km race the runner should manage around 16 km h

^{-1}and in a 15km race about 15 km h

^{-1}. The dotted line is simply plotting how a maximum 'race' effort scales with distance. What is noticeable about the dotted lines (which are for faster and slower runners - see figure legend for details) is that the maximum speed that can be maintained drops dramatically at short distances and then changes relatively little at longer distances.

Also plotted on this graph are the race predictions (solid lines) from the Tanda equation. Now here I have taken the liberty of playing with the 'meaning' of the axis labels. Whilst the x-axis is still distance and the y-axis is speed, they are the distance covered in training on an average day and the speed at which it was done. Again the colours match the Riegel prediction times. So, let's go back to the yellow lines. The solid yellow line shows you the average distance and speed you need to run each day to become a 3 hour marathon runner. You could run 10 km each day at 14 km h

^{-1}or 5 km each day at 16 km h

^{-1}or a mixture of the two. As long as you stay on that line (on average) for eight weeks, you should get the 3 hour marathon (actually it is a bit more complicated than that, but to a first approximation it will do). Now, the interesting observation is how the dotted line and the solid line relate to each other. If you train above the dotted line then you are doing an effort, each day, that is HARDER than a race effort. You must be doing the effort as interval training, by definition since you could not have kept up a faster run than your Riegel prediction. If you train below the line then you are below a race effort - each day.

Now, look at the thick purple line. That shows the trajectory for training by doing a race effort every day! If you want to become a 3 hour marathon runner you will need to race a 5km every day. If you want to be a 2:45 marathon runner (red line) you need to race 9km every day. Notice that for a 3:15 marathon runner and slower any race effort every day is more training than necessary to get that time.

So, the faster you are the closer you need to be to sustaining a race effort every day and the longer that race effort has to be. The benefit of running more miles is that you are training much slower than race speed. The damage is far less and the training is 'possible'.

*So, you definitely want to train below and to the right of the purple line.*Now the take-home message from this is that both the Riegel formula and the Tanda predictor are both race predictors using similar data - they are just different equations. For Riegel you put in any race and time but for Tanda you put in an 8 week average. As I have said before (but, it has not got traction) the Tanda 8 week period is just another race. It is the training race - a race with no defined distance or time but a race nevertheless.

The difference between Riegel and Tanda is that Riegel is the output of a short race effort whereas Tanda is the output of a long race effort - they work from opposite ends of the spectrum. The great thing about the Tanda equation is that you don't need to RACE before the marathon - you just use the training data you have (that is the training race). The second great thing about the Tanda equation is that it predicts from the very stimulus that makes you a marathon runner in the first place, namely the training. It is the bees-knees.

OK, there are other things you need to be aware of - and some of you will out-perform it by some margin - but the formula captures what it takes to train for a marathon. It is just running (and heat adaptation and growing large adrenals etc....but those are either previous posts or posts to come).

Hi Christof, some great analysis. I very much enjoy reading this. Perhaps a bug in the discussion? A 3 hour marathon requires an average speed of 14.1kph. Hence the Tanda graph seems to suggest than the race pace training would require about 10km/day at 14.1kph? The intersection of the purple and yellow at 16kph is well above race pace is it not? Am I reading the graph wrong? ( This seems to agree with the Tanda calculator)

ReplyDeleteDear Klute, You are right that running a 3 hour marathon requires that you run at about 14.1 kph for 3 hours. But, the solid yellow lines shows the daily training load you would need to do and the dotted line is a race effort. Where they intersect is 'race-pace' training - i.e. doing a race EVERY day as training. For someone aiming to do a 3 hour marathon they would need to do 5km everyday at 16kph - which is the 5km race-pace of a 3 hour marathon runner. You could do this for a few days, maybe even a week, by doing the 5km as intervals of 200m. But, it would do more damage than good. So, I don't think there is a bug in my discussion - I took it off-line for a few minutes whilst I checked the numbers. It is conceptually hard to understand these sorts of graphs - and most people never bother to even try. But, this sort of analysis shows why running 'long' is the best way of getting faster.

DeleteGreetings,

Christof