GoldenCheetah provides three different TRIMP metrics for an activity: TRIMP points, TRIMP(100) points, and TRIMP Zonal points. In its trend view, one of these is used to show you your training stress over time through the metrics TRIMP Short Term Stress Balance, TRIMP Long Term Stress Balance, and TRIMP Stress Balance. I assumed (correctly) that it was TRIMP points, but confirming this suspicion took more effort than I expected as I found a slight difference between how GoldenCheetah calculates stress and how I have been doing it. The difference is what I wanted to document here.

## Quick Overview of Stress

I have some notes that go into more detail on measuring stress, but I figured it would be useful to provide a summary here. Tracking stress comes in two parts:

1. Assign a number to an activity. The number indicates how much stress the activity placed on the body. In the context of this post, we will consider TRIMP values. How exactly these are calculated does not necessarily matter here.
2. Summarise these numbers over time. These numbers may then indicate, for example, your Long Term Stress (LTS, form) or your Short Term Stress (STS, fatigue). This summary was slightly different than what I was used to.

## Summarising Stress

What I had documented as the more popular approach, was the following formula. In it, $Y_n$ is the stress on a given day and $S_n$ is the accumulated stress on that day.

$S_1 = Y_1$ $S_n = \alpha Y_n + (1 - \alpha) S_{n-1}$

The $\alpha$ is defined in terms of the number of days you find important: $\alpha = 1 / d$. For short term stress, you would keep the number of days low (default seems to be 7, so $\alpha = 1/7$). For long term stress, you would keep the number of days a bit higher (default seems to be 42, so $\alpha = 1/42$).

## In GoldenCheetah

So to find out which of the three TRIMP activity stresses was being used, I figured I would just throw the numbers in and see which matched. None did. There seems to be little documentation in the GUI around this, so I dug into the code. In src/Metrics/PMCData.cpp, I found the following

double lte = (double)exp(-1.0/ltsDays_);
double ste = (double)exp(-1.0/stsDays_);

// Bunch of code snipped

// LTS
if (day) lastLTS = lts_[day-1];
lts_[day] = (stress_[day] * (1.0 - lte)) + (lastLTS * lte);

// STS
if (day) lastSTS = sts_[day-1];
sts_[day] = (stress_[day] * (1.0 - ste)) + (lastSTS * ste);


Do not worry if you have trouble reading that. The conclusion here is that GoldenCheetah does not use $\alpha = 1 / d$. Instead they set

$\alpha = 1 - e^{-1/d}$

The difference in the resulting $\alpha$ is pretty small, but it is a difference nonetheless. With the recursive way stress is calculated, this also leads to the difference accumulating. I am not really sure why they use this value as $\alpha$. Likely there is some other paper I missed, I am no expert either. Of course, for all these metrics, you should tweak them in function of how you actually feel. That also counts for this $\alpha$, the recovery of an older person is not the same as for a younger person.

## TRIMP

I used that adjusted stress formula to see which activity metric matches up to the stress metrics. This was just some trial and error of throwing the numbers in. TRIMP won out. For completeness sake, I will explicitly state what this TRIMP score signifies. As mentioned in GoldenCheetah, this is the “Training impulse according to Morton/Bannister with Green et al coefficient”.

Calculating it is just a matter of throwing together some information from your activity. First grab the average heart rate and see how it stacks up to your maximum and resting heart rate.

$HR_{rel} = \frac{HR_{avg} - HR_{rest}}{HR_{max} - HR_{rest}}$

Then combine that relative heart rate with the time you spent exercising and a $k$ adjusted to your sex: $1.92$ for men, $1.67$ for women.

$TRIMP = t_{min} * HR_{rel} * 0.64 * exp\left( k_{sex} * HR_{rel} \right)$