- number of previous marathons
- number of training days per week
- the mean distance run for each workout
- the longest run each week
- the mean workout distance per week
- the mean training pace

The training data he considered included 11 week, 10 week and 8 week average data leading up to one week before the race. Using the 8 week data he found the best correlations between performance time (marathon finishing time) came from mean training pace and mean distance per week (see Figure 1).

Figure 1. Data taken from Tanda (2011) showing the relationship between performance time for the 46 flat paced marathons and weekly distance in the preceding 8 weeks. |

The relationship between training pace and marathon performance was also rather scattered, but can be fitted with a straight line (see Figure 2).

Figure 2. Data take from Tanda (2011) showing the relationship between performance time for the 46 flat paced marathons and average training pace in the preceding 8 weeks. |

Figure 3. Data from Tanda (2011) showing the training space that the runners occupied over the 8 week period leading up to the marathon. |

This scatter in training space can be used to produce a predicted marathon performance by combining both pace and distance into one equation with the relevant relationships. For his dataset Tanda suggested the following equation (rearranged for race time and average speed):

Race time (min) = 12 + 98.5 * e

^{(-km per week/189)}+1390/average speed in km per hour

Figure 4 shows the predicted marathon time plotted against the actual marathon performance.

Figure 4. Data taken from Tanda (2011) showing the predicted marathon time plotted against the actual marathon performance time. |

As I showed in the last post the equation is remarkably well behaved at the extremes. It predicts sensible values for someone who does no running and for an elite runner. But, to demonstrate I have plotted the data for a range of other runners (see next post).

Finally, it is possible to plot the marathon prediction times, as contour lines, on the training parameter space plot (Figure 5).

The thick lines are the Tanda prediction contour lines for four different marathon finishing times. The thin lines show 90% age-graded effort for daily training for each of the marathon prediction times. Thus, the 2:45 runners are training below 90% effort - whilst the 3:00 runners are putting in over 90% effort each day. The 3:30 runners are also mostly training below 90% age-graded effort. The Tanda equation can be extrapolated out of the fitted parameter space. That is shown to the right of the thick straight line. No one in Tanda's dataset runs these types of averages. The big question is; "Why?". Is it that the equation fails in this space (i.e. is it impossible to complete a marathon in 2:45 by training at an average of 5 mins per km and 26 km per day for 8 weeks) or is it that no-one does that form of training? This question has some critical consequences. Tanda's dataset shows that marathon runners attempt to get faster by increasing their speed up to a 90% daily age-grade. At this point training is very hard. The 3:00 marathon runners are almost certainly unable to progress further using speed as a training tool.

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