Thursday, 28 January 2016

Filling the training parameter space

The marathon prediction equation produced by Tanda (2011) did not look at the performance of any sub-elite runners, his fastest was 2:47. In this post I have added in some data from a few faster runners - the results are surprising.

In the last post I talked a bit about Tanda (2011) and how his group of 22 runners trained in terms of average distance and pace over an 8 week period. I ended-up showing this graph (Figure 1) which demonstrates that most marathon runners tend to train in rather similar ways - at least in terms of the average speed and distance - there are no runners to the right of the thick black line.

Figure 1 Tanda (2011) dataset shown plotted in training parameter space. There were no runners to the right of the thick black line. Why is this? Is running 20 km per day at 5 mins per km not a viable training strategy for a marathon? Is it necessary to have a training diary average to the left of the thick black line to be successful at a marathon?

I thought it might be useful to see whether this is generally the case - or whether there is something odd about Tanda's dataset. I thought the first person I could look at is me! I have a lot of marathon performances from BEFORE I knew about the Tanda prediction equation from when I was training in a normal fashion with Cambridge and Coleridge Athletics Club. It might also be a good test of the general applicability of the Tanda equation. Whilst Tanda's paper was subject to peer review, that is it was read and vetted by experts in the field, it is possible that it only applies to Italian marathon runners training in an Italian fashion on an Italian diet etc. etc.......
In Figure 2 I have plotted my distribution of training averages for 10 marathons over a two year period from 2011 together with Tanda's dataset.
Figure 2. The Tanda dataset (black circles) and mine for 10 marathons from 2011 to 2013. My training looks very similar to the Tanda runners in terms of distance and pace.

It is clear that during this period I was training in a very similar space - but, did my training produce the performance the Tanda prediction equation suggests it should have. In Figure 3 I have plotted my Tanda prediction from the pace and distance against my actual performance time.
Figure 3. My Tanda prediction time for 10 marathons plotted against my actual performance time all from before I knew about the equation. The correlation coefficient is surprisingly high.
It appears that the Tanda prediction equation rather closely matches my actual performances. Indeed, it is rather surprising since not all of the marathons went 'to plan'. If I remove the marathons with 'odd' (toilet-related) events (which we do not need to discuss here) then the fit is considerably better (r2=0.91).

I have found some runners who lie to the right of the thick black line in Figure 1 - and they are fast runners. In Figure 4. I show data for 4 fast marathon runners - Nathan Kilcourse, Frank Berersford &
Jonathan Walton all at the Yorkshire Marathon (2015) and Aly Dixon at Berlin. Interestingly they suggest that runners tend to train with their average distance and pace around a curve (indicated in Figure 4).
Figure 4. Tanda data (black circles) and four faster runners (yellow diamonds) plotted in training space. The red line shows the general (vague) region around which runners tend to cluster. To the right of the thick black line, now repositioned for the fast runners, there is still no-one. There must be something terrible there - perhaps dragons?

Now it is worth wondering whether Tanda's formula predicts these faster runners' times. In Figure 5. I have plotted their predictions against their performances.
Figure 5. Tanda predictions (y-axis) against actual marathon performances for the Tanda dataset (black circles) and the faster runners (yellow diamonds). The black line is the Tanda prediction projected to the faster times (it is the equality line). The green line is the best fit to the faster runners.
Given that the Tanda equation was generated from runners slower than 2:46 the equation does a remarkably good job of predicting the performance of these four runners. The fit to their data suggests that the Tanda equation might need some refinement - however, the basic idea of combining speed and distance in this form works for fast runners too.

So, my conclusion is that there are areas of training space that could be occupied by runners - but is not generally used. The prediction equation seems to be able to extrapolate to faster runners that operate within the normal training curve (red line in Figure 4). This led me to wonder whether it might also work in the area of training space which might be occupied by dragons. The benefit of training in that region becomes clear when the Tanda prediction contours are plotted (Figure 6).
Figure 6. Training space with the pink (magenta) line revealing an opportunity. Could a 3 hour marathon runner training in the normal way (i.e. average of 10 km per day at 4:25 per km) turn themselves into a 2:45 marathon runner by slowing down and just running more?
The contours show that in the space to the right hand side of the thick black line lies a performance within the grasp of an averagely capable runner. If I could increase my mileage and slow down (follow the pink arrow) could I get to a 2:45 marathon performance. The Tanda extrapolation reveals that possibility - but, I would be training slower - and to make that distance each day I would not be able to do any fast running at all. Indeed, most of my running would have to be at the same speed as a 3:15 marathon runner training with a normal program but I would be running over twice the distance each day.

Next: What makes you faster, pace or distance?.

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