## Wednesday, August 9, 2017

### An Equation for Running Stress Score (RSS)

On Stryd's website, there is a narrative about their proprietery scoring system based on power called Running Stress Score (RSS).

The key statement is how RSS is defined using a 'co-efficient' K.

Someone who would like to reverse engineer this formula would wonder if co-efficient 'K' is a constant or does it vary depending on the intensity.

One clue to help in finding K is a table of examples in which Stryd states an expected value of RSS.

Infact, from the equation of RSS, the value of K is defined as :

K = [ Natural log (RSS/min) - Natural log (100)] / Natural log (Power/CP)
where CP = critical power

One finds from this calculation that there is not a single value of K that can be fitted to the running examples in the table above. So either this is a small mystery or K is not constant.

Might there be an easier model to explain the change of RSS/min with intensity? As a first goto, a simple exponential model would reflect rapidly increasing stress scores for higher intensities.

So I took the data and tried to force fit an exponential line through. The result gave 98.7% fit based on the data fed to it.

Based on this exercise :

RSS/min = A x exp(B x Power/Cp)
where parameter A = 0.0758
and     parameter B =  3.1297

How does this equation fit with a real run and it's corresponding RSS from Stryd's powercenter? I took a recent run from the running database and threw it into the model.

I found that the modeled RSS/min is within 3% of the actual value, which says that the fit is alright but more importantly, I can produce a better match by decreasing assumed CP to around 193.5 W.