In the last 6 months, I have gotten into Zwift racing. Compared to running, (in the real world), the world of indoor (virtual) cycling offers a controlled environment with excellent metrics for performance. There is no wind, no surface variation, and relatively little temperature variation. The control of these variables gives us a chance to extract a deeper understanding from the data.

This post is an investigation into the correlation between heart rate and power data. Interesting questions include:

• Can long-term fitness be identified in Power / HR data?
• Can form for a particular day be identified in Power / HR data?
• Can Power / HR data be used, live, to control an effort during a cycling race?
• Can we identify rider type based on Power / HR data?

The value of the above depends on who you are - if you’re team Ineos and you’re interested … get in touch.

My hypothesis is that on a longer time basis power and HR will be correlated and that this will be close to linear. A few more obvious things:

• Heart rate will lag power (it takes the body time to respond to a change in output)
• Heart rate will be much smoother than power (again, it takes the body time to respond to a change in output)
• The intercept of 0W will not be 0BPM. I’m not dead.

Taking a particular activity we can look at fitting our power and HR data. We can measure the quality of the fit of this data using statistical measures like R^2. For a stream of power and HR data, this can be calculated. We can then adjust these data streams. For example, varying the smoothing of the power data (moving average), and the lag between the power and HR data. We can look on this surface for a maxima in the correlation and this can be plotted.

There is a maxima. Luckily. We’re looking at that yellow circle signifying the peak of the hill. This tells us we see the greatest correlation (in terms of linear best fit) when power is smoothed over the previous 120 seconds and there is relatively little lag between HR and power.

If we then plot the optimally smoothed power and lagged HR against time, and against each other, we get the below.

There are some interesting points here:

• It is quite linear. But then we are choosing the ‘most linear’ way to view this data so maybe this isn’t a surprise.
• There’s a fair bit of variation about the line. It would be interesting to know how much hysteresis there is.

So the next step is to look at whether a trend can be seen tracking ‘fitness’ and comparing results from a few different people to understand individual variation.