Runners often worry that they are wasting their time and effort doing slower additional miles  distance that is referred to as junk miles. But, how do we know when we are heading towards junk miles and the quantity no longer makes up for a lack of quality? What follows is a simple logical extension of a marathon performance prediction equation and how it can be used to calculate when it is not worth running an additional mile  just how slow does it need to be before it is junk? 

The Tanda (2011) (
link to the paper,
my viewpoint) marathon performance prediction equation is based on average training distance and pace over an eight week period. Since any additional distance run in training alters those averages, it is relatively easy to calculate when any additional mile fails to produce a better prediction of marathon performance. Actually, the calculation took me a while, but I blame that on my glass of wine and the late hour this Saturday evening  I do these things on a Saturday night so that you don't have to!
The idea here is to attempt to define what pace might represent the cutoff for a
junk mile. As you might expect the pace is dependent on both the average distance and pace that you are currently training at over an eight week period. But, to make it easier to work with I have plotted the function based on average daily distance. The shape of the junk mile function (in metric!) is shown in Figure 1. This figure requires a little bit of explanation. It is simply a rearrangement of the Tanda equation where I have solved the pace/distance which moves a runner along the same performance line. I will give some specific examples on how to use it.

Figure 1. The junk mile pace offset curve. The red line shows the additional mm:ss per km at which additional distance does not produce a predicted improvement in marathon performance. To work out your current junk mile pace threshold you need to calculate your current average daily distance and pace. If, for instance, you are currently doing an average of 5km per day then running additional kms slower than your current average pace plus 47s would constitute a junk mile. If you are averaging 25 km per day then you can afford to run 1min 37s slower per km than your average pace before you hit junk mile territory. 
One interesting feature of the maths is that the junk mile pace is an offset from your average pace. So, whether you are averaging 4 mins per km or 6 mins per km the offset that defines a junk mile is the same. However, the offset pace changes dramatically with distance. At short distances only a moderate slowing takes you into junk mile territory. But, if you are running long then you can afford to run quite a bit slower and it will still produce a better prediction of marathon performance. There are two easy numbers to remember. If you are averaging 5km per day then 45s slower than your average pace and you begin to enter junk miles. But, if you are running above 17 km per day on average then you can afford to run 1 min 30s slower than your average pace before the extra distance becomes worthless according to the Tanda equation. There is a calculator
here that shows the junk pace threshold for a given weekly distance and pace.
Anyway, that is what Tanda says is a junk mile. Of course, if you are injured and doing damage to yourself then even a faster km can be counterproductive. This calculation only works if you are fatigued but healthy......
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ReplyDeleteI love maths, I love running, Your site is great !
ReplyDeleteThanks !