Functional Threshold Power estimation for cyclists in HRV4Training Pro

Blog post by Marco Altini

We have released a new feature in HRV4Training Pro, Functional Threshold Power (FTP) estimation for cyclists. In this post, we go over the background, cover how you can use this feature to plan and track your training and progress and also provide additional details about the underlying algorithms that we developed to estimate FTP and their accuracy, as well as some of the current limitations.

In case you want to jump right in, and check out our latest feature, simply login at HRV4T.com with your HRV4Training credentials.

What's Functional Threshold Power (FTP)?

FTP is defined as the average power you can sustain for an all out effort of about an hour. 

Why is FTP useful?

By knowing your FTP, you can plan your training so that you can cover different intensities and provide the most appropriate training stimulus depending on the performance gains you are looking for (for example VO2max intervals to improve anaerobic endurance or short repeats at very high power to improve muscular force).

​The motivations behind the use of a power meter go beyond the scope of this post, and I’d recommend reading Joe Friel’s books if interested in learning more.

What’s the motivation behind our estimate and how does it differ from others out there?

Most FTP estimates out there rely on the relationship between power during shorter efforts (the most common one being the 20 minutes FTP test) and FTP itself, which is normally something like 5% less than your 20-30 minutes power. 

As we’ve discussed in the past, we believe data can be used in a bit of a smarter way, and while the 20 minutes test is certainly a very good way to estimate your FTP, we are more interested in trying to provide an estimate that works reasonably well when no test at all is performed. Why is that? We find that at least two categories of athletes would benefit, one is individuals just starting with cycling or with a power meter, and therefore having no idea what their FTP is. Similarly, doing a test of 20-30 minutes outdoor, all out, without breaks, might be simply not possible in many areas of the world, and not everyone has an indoor trainer to do the same. Additionally, for athletes training for long distances, century rides or triathletes training for half or full ironman distances, efforts similar to FTP tests might just not be very frequent, if done at all, as training specificity dictates different kinds of workouts to be preferable (long lower intensity rides as well as high intensity intervals for example). 

In any case, even if you are a cyclist training for shorter distances, an FTP test is by definition a very hard effort, and it does not make much sense in my opinion to sacrifice a workout in which we could be trying to train aspects that are more relevant in a given training phase, depending on the adaptations we are looking for, and to instead waste a good day just to get to understand what’s our FTP and how we should be planning the following workouts. This is of course an oversimplification but I hope you understand the point I am trying to make, if we can estimate FTP from your workouts data, you could track your progress and plan training accordingly with minimal effort.

How does our estimate work: the short read

We talked elsewhere (see this article for example) about how we strongly believe in the ability to further improve our understanding of complex relations between physiology and performance through large-scale research carried out in real-life. 

Our journey started by developing a validated and practical tool like HRV4Training, and releasing it in the hands of thousands of individuals, so that research can be carried out at a scale that is not possible in regular laboratory studies. 

By relying on this approach, we were able to feed our findings back to the community. We have been developing new features (for example VO2max estimation for cyclists or the current FTP estimation) that hopefully will help you better track and plan your training, and eventually lead to improved performance.

As we are a data driven company, we used data collected from thousand of individuals over two years (2016-2017) and analysed the relationship between their FTP as derived from these data (defined as the highest power normalised by distance for an individual over such time period), and the following sets of parameters, so that we could find the parameters that are able to provide the best FTP estimate:

• Anthropometrics: age, weight, BMI, gender
• Resting measurements of cardiac activity: heart rate and heart rate variability
• Physiological data during training: for example the relationship between heart rate and power
• Training power, elevation gain and training volume: distribution of power during your workouts, typical elevation gain of your rides, amount of training you do
• Training patterns: for example training polarization, or time spent at low or high intensities vs time spent at moderate intensities, for both heart rate and power
• Highest normalised power on previous rides: basically your best effort in the past few weeks, automatically derived from hard workouts, no matter the duration

What data do I need to be able to get an FTP estimate?

​You need to be a cyclist with at least 15 workouts, including heart rate and power data, in the past 45 days. Power data estimated by Strava will also work fine.

Additionally, our FTP estimation benefits from at least one hard effort of no specific duration, including very long races as well as interval sessions, no need to go out for a classic FTP test. We also recommend splitting your workouts so that the hard part is a separate activity with respect to warmup and cool down, this way the estimate will be more accurate

Estimate details: the long read

As mentioned above, we used data from thousand of individuals and analysed the relationship between their FTP as derived from two years of data, and the following sets of parameters, so that we could find the parameters that are able to provide the best FTP estimate:

• Anthropometrics: age, weight, BMI, gender
  Resting measurements of cardiac activity: heart rate and heart rate variability
• Physiological data during training: for example the relationship between heart rate and power
• Training power, elevation gain and training volume: distribution of power during your workouts, typical elevation gain of your rides, amount of training you do
• Training patterns: for example training polarization, or time spent at low or high intensities vs time spent at moderate intensities, for both heart rate and power
• Highest normalised FTP on previous rides: basically your best effort in the past few weeks, automatically derived from hard workouts, no matter the duration

In the remaining of this post, we go over the dataset and estimate accuracy for different subsets of parameters, so that we can better understand what is the relative impact of such parameters.

Let’s have a look at the data first. Here is our reference FTP, the distribution in our dataset:

Below I’ve plotted the relationship between reference FTP and two other parameters we estimate in HRV4Training, simply to show that there is an obvious relation between FTP and estimated VO2max, as individuals with an higher VO2max tend to have an higher FTP.

​Secondly, I’ve also looked only at triathletes data, so that we have data for both running and cycling, and plotted the relationship between estimated lactate threshold in running and FTP in cycling, and again we have an expected inverse relationship showing up (inverse because as lactate threshold we use 10 km running time, hence a lower time is associated with higher fitness, similarly to a higher FTP). Note that these relationships are weak, with a lot of spread in the data, hence it would be nonsense to estimate FTP just based on these parameters (as it is nonsense to estimate running racing time just from VO2max,  but I seem to recall another company selling millions of watches exactly with a feature build this way).

Alright, back to our estimate. One of the simplest methods to estimate your FTP if you have never used a power meter, is based on anthropometrics only. This is obviously extremely inaccurate, nobody claims otherwise, but it is a starting point that I’d like to show so that we can see later on in relative terms how much better we can get the estimate when adding more interesting parameters related to your physiology and training patterns. 

In particular, when using anthropometrics only we estimate FTP with a mean percentage error of 17% (explained variance R2=0.18, root mean square error RMSE=49 Watts), which is quite bad. All numbers are the results of a 10 fold cross-validation, hence these are proper estimates representative of what you’d get for individuals that were of course not part of the training set, this is how validations should be done as the idea is that the estimate will be used by new users as well, and we need to make sure it always works well, not only for the data we have used as training set. What is obvious when we look at the data, is that the model clusters men and women, and there is very little variance within a group, meaning that we can’t properly capture differences in FTP once gender (and possibly weight) have been accounted for, which is what we expect as these parameters are the most important of this set. ​

Let’s enrich a little our feature set and add features related to resting physiology (heart rate and heart rate variability in the morning). As speculated in the past especially following our analysis of VO2max and lactate threshold estimation, resting physiology tells us little about fitness, and should really be used differently, as continuous feedback to optimise performance in the long term. Results show a mean percentage error of 16% (R2=0.21), with a RMSE of 48 Watts. ​

Next, we add also training variables, for example how much you train, what’s the typical elevation gain, how much time is spent in different power zones, etc. We can see this time a pretty significant jump in estimate accuracy, percentage error goes down to 10%, R2=0.66 and RMSE=32 Watts. From the figure below we can see that this model seems to improve quite a bit the accuracy for low FTP values, but not so much for higher values, it seems incapable of discriminating correctly individuals with higher FTP, which is quite normal considering that training volume is just part of the picture:

When working on estimating lactate threshold for runners, we’ve seen how training polarisation played an important role. As expected, faster runners had more structured workouts, with a variety of intensities being present, typically a good volume of low intensity workouts next to a few quality sessions. Individuals always training at similar intensities, stuck in the so called moderate training, would tend to progress less towards better performance.

​We can see the same here for cyclists in the context of FTP estimation, where again time spent at different heart rate and power intensities, in particular more time spent at low as well as high intensities and less time spent at moderate intensities are associated with higher FTP, and provide a more accurate estimate. Note that this is again an oversimplification and of course no intensity has to be avoided, moderate training can be particularly beneficial depending on your target race and phase of the season, as you get for example into more specific workouts for your long distance racing. Let’s look at the results, we get now to a mean error of 6.8%, R2=0.85, RMSE=21 Watts, not bad considering that we do not take into account your ‘best efforts’ yet. Here is the data:

Finally, we can include in the models your best effort, or highest normalised power in previous rides, and obtain an error as small as 4%, R2=95%, RMSE = 12 Watts. Data below:

Our final estimate includes some more tweaks, for example to correct for periods in which you might not be doing any hard rides over 45 days (the window used to compute your FTP), we analyze your heart rate data with respect to your historical maximal heart rate to determine if indeed your rides were all relatively low intensity, as otherwise FTP would be most likely underestimated. We also correct your hard efforts based on duration.

By using this approach, we were able to capture up to 95% of the variability in FTP on a dataset of 3000 individuals. As all these parameters are used daily to estimate FTP, you will see small changes pretty much any time you go for a ride, and not only when you do an FTP test or hard effort, even though obviously such efforts carry more weight. ​

​Enjoy!