Power – Science4Performance

Fuelling for Cycling Performance

Some commentators were skeptical of Team Sky’s explanation for Chris Froome’s 80km tour-winning attack on stage 19 of the Giro. His success was put down to the detailed planning of nutrition throughout the ride, with staff positioned at strategic refuelling points along the entire route. If you consider how skeletal the riders look after two and a half weeks of relentless competition, along with the limits on what can be physically absorbed between stages, the nutrition story makes a lot of sense. Did Yates, Pinot and Aru dramatically fall by the wayside simply because they ran out of energy?

The best performing cyclists have excellent balancing skills. This includes the ability to match energy intake with energy demand. The pros benefit from teams of support staff monitoring every aspect of their nutrition and performance. However, many serious club-level cyclists pick up fads and snippets of information from social media or the cycling press that lead them to try out all kinds ideas, in an unscientific manner, in the hope of achieving an improvement in performance. Some of these activities have potentially harmful effects on the body.

Competitive riders can become obsessed with losing weight and sticking to extremely tough training schedules, leading to both short-term and long-term energy deficits that are detrimental to both health and performance. One of the physiological consequences can be a reduction in bone density, which is particularly significant for cyclists, who do not benefit from gravitational stress on bones, due to the non-weight-bearing nature of the sport. In a recent paper, colleagues at Durham University and I describe an approach for identifying male cyclists at risk of Relative Energy Deficit in Sport (RED-S).

You need a certain amount of energy simply to maintain normal life processes, but an athlete can force the body into a deficit in two ways: by intentionally or unintentionally restricting energy intake below the level required to meet demand or by increasing training load without a corresponding increase in fuelling.

EnergyBalance

Our bodies have a range of ways to deal with an energy deficit. For the average, slightly overweight casual cyclist, burning some fat is not a bad thing. However, most competitive cyclists are already very lean, making the physiological consequences of an energy deficit more serious. Changes arise in the endocrine system that controls the body’s hormones. Certain processes can shut down, such as female menstruation, and males can experience a reduction in testosterone. Sex steroids are important for maintaining healthy bones. In our study of 50 male competitive cyclists, the average bone density in the lumbar spine, measured by DXA scan, was significantly below normal. Some relatively young cyclists had the bones of a 70 year old man!

The key variable associated with poor bone health was low energy availability, i.e. male cyclists exhibiting RED-S. These riders were identified using a questionnaire followed by an interview with a Sports Endocrinologist. The purpose of the interview was to go through the responses in more detail, as most people have a tendency to put a positive spin on their answers. There were two important warning signs.

Long-term energy deficit: a prolonged significant weight reduction to achieve “race weight”
Short-term energy deficit: one or more fasted rides per week

Among riders with low energy availability, bone density was not so bad for those who had previously engaged in a weight-bearing sport, such as running. For cyclists with adequate energy availability, those with vey low levels of vitamin D had weaker bones. Across the 50 cyclists, most had vitamin D levels below the level of 90 nmol/L recommended for athletes, including some who were taking vitamin D supplements, but clearly not enough. Studies have shown that the advantages of athletes taking vitamin D supplements include better bone health, improved immunity and stronger muscles, so why wouldn’t you?

In terms of performance, British Cycling race category was positively related with a rider’s power to weight ratio, evaluated by 60 minute FTP per kg (FTP60/kg). Out of all the measured variables, including questionnaire responses, blood tests, bone density and body composition, the strongest association with FTP60/kg was the number of weekly training hours. There was no significant relationship between percentage body fat and FTP60/kg. So if you want to improve performance, rather than starving yourself in the hope of losing body fat, you are better off getting on your bike and training with adequate fuelling.

Cyclists using power meters have the advantage of knowing exactly how many calories they have used on every ride. In addition to taking on fuel during the ride, especially when racing, the greatest benefits accrue from having a recovery drink and some food immediately after completing rides of more than one hour.

For those wishing to know more about RED-S, the British Association of Sports and Exercise Medicine has provided a web resource.

A related blog will explore the machine learning and statistical techniques used to analyse the data for this study.

References

Low energy availability assessed by a sport-specific questionnaire and clinical interview indicative of bone health, endocrine profile and cycling performance in competitive male cyclists, BMJ Open Sport & Exercise Medicine,https://doi.org/10.1136/bmjsem-2018-000424

Relative Energy Deficiency in Sport, British Association of Sports and Exercise Medicine

Synergistic interactions of steroid hormones, British Journal of Sports Medicine

Cyclists: Make No Bones About It, British Journal of Sports Medicine

Male Cyclists: bones, body composition, nutrition, performance, British Journal of Sports Medicine

Strava Power Curve

Screen Shot 2018-05-11 at 16.34.08 — Comparing Historic Power Curves

If you use a power meter on Strava premium, your Power Curve provides an extremely useful way to analyse your rides. In the past, it was necessary to perform all-out efforts, in laboratory conditions, to obtain one or two data points and then try to estimate a curve. But now your power meter records every second of every ride. If you have sustained a number of all-out efforts over different time intervals, your Power Curve can tell you a lot about what kind of rider you are and how your strengths and weaknesses are changing over time.

Strava provides two ways to view your Power Curve: a historical comparison or an analysis of a particular ride. Using the Training drop-down menu, as shown above, you can compare two historic periods. The curves display the maximum power sustained over time intervals from 1 second to the length of your longest ride. The times are plotted on a log scale, so that you can see more detail for the steeper part of the curve. You can select desired time periods and choose between watts or watts/kg.

The example above compares this last six weeks against the year to date. It is satisfying to see that the six week curve is at, or very close to, the year to date high, indicating that I have been hitting new power PBs (personal bests) as the racing season picks up. The deficit in the 20-30 minute range indicates where I should be focussing my training, as this would be typical of a breakaway effort. The steps on the right hand side result from having relatively few very long rides in the sample.

Note how the Power Curve levels off over longer time periods: there was a relatively small drop from my best hour effort of 262 watts to 243 watts for more than two hours. This is consistent with the concept of a Critical Power that can be sustained over a long period. You can make a rough estimate of your Functional Threshold Power by taking 95% of your best 20 minute effort or by using your best 60 minute effort, though the latter is likely to be lower, because your power would tend to vary quite a bit due to hills, wind, drafting etc., unless you did a flat time trial. Your 60 minute normalised power would be better, but Strava does not provide a weighted average/normalised power curve. An accurate current FTP is essential for a correct assessment of your Fitness and Freshness.

Switching the chart to watts/kg gives a profile of what kind of rider you are, as explained in this Training Peaks article. Sprinters can sustain very high power for short intervals, whereas time trial specialists can pump out the watts for long periods. Comparing myself against the performance table, my strengths lie in the 5 minutes to one hour range, with a lousy sprint.

Screen Shot 2018-05-11 at 17.19.45.png — Single Ride Power Curve versus Historic

The other way to view your Power Curve comes under the analysis of a particular ride. This can be helpful in understanding the character of the ride or for checking that training objectives have been met. The target for the session above was to do 12 reps on a short steep hill. The flat part of the curve out to about 50 seconds represents my best efforts. Ideally, each repetition would have been close to this. Strava has the nice feature of highlighting the part of the course where the performance was achieved, as well as the power and date of the historic best. The hump on the 6-week curve at 1:20 occurred when I raced some club mates up a slightly longer steep hill.

If you want to analyse your Power Curve in more detail, you should try Golden Cheetah. See other blogs on Strava Fitness and Freshness, Strava Ride Statistics or going for a Strava KOM.

Froome’s data on Strava

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Chris Froome has been logging data on Strava since the beginning of the year. He had already completed over 4,500km, around Johannesburg, in the first four weeks of January. The weather has been hot and he has been based at an altitude of around 1350m. Some have speculated that he has been replicating the conditions of a grand tour, so that measurements can be made that may assist in his defence against the adverse analytical finding made at last year’s Vuelta.

Whatever the reasons, Froome chose to “Empty the tank” with epic ride on 28 January, completing 271km in just over six hours at an average of 44.8kph. The activity was flagged on Strava, presumably because he completed it suspiciously fast. For example, he rode the 20km Back Straight segment at 50.9kph, finishing in 24:24, nearly four minutes faster than holder of the the KOM: a certain Chris Froome. Since there was no significant wind blowing, one can only assume he was being motor-paced.

One interesting thing about rides displayed publicly on Strava is that anyone can download a GPX file of the route, which shows the latitude, longitude and altitude of the rider, typically at one second intervals. Although Froome is one of the professional riders who prefer to keep their power data private, this blog explores the possibility of estimating power from the GPX file. The plan is similar to the way Strava estimates power.

Calculate the rider’s speed from changes in position
Calculate the gradient of the road from changes in altitude
Estimate air density from historic weather reports
Make assumptions about rider/bike mass, aerodynamic drag, rolling resistance
Estimate power required to ride at estimated speed

Knowledge is power

FroomeyTT

An interesting case study is Froome’s TT Bike Squeeeeze from 6 January, which included a sustained 2 hour TT effort. Deriving speed and gradient from the GPX file is straightforward, though it is helpful to include smoothing (say, a five second average) to iron out noise in the recording. It is simple to check the average speed and charts against those displayed on Strava.

Several factors affect air density. Firstly, we can obtain the local weather conditions from sources, such as Weather Underground. Froome set off at 6:36am, when it was still relatively cool, but he Garmin shows that it warmed up from 18 degrees to 40 degrees during the ride. Taking the average of 29 for the whole ride simplifies matters. Air pressure remained constant at around 1018hPa, but this is always quoted for sea level, so the figure needs to be adjusted for altitude. Froome’s GPS recorded an altitude range from 1242m to 1581m. However we can see that his starting altitude was recorded as 1305m, when the actual altitude of this location was 1380m. We conclude that his average altitude for the ride, recorded at 1436m, needs to be corrected by 75m to 1511m and opt to use this as an elevation adjustment for the whole ride. This is important because the air is sufficiently less dense at this altitude to have a noticeable impact on aerodynamic drag.

An estimate of power requires some additional assumptions. Froome uses his road bike, TT bike and mountain bike for training, sometimes all in the same ride, and we suspect some rides are motor-paced. However, he indicates that the 6 January ride was on the TT bike. So a CdA of 0.22 for drag and a Crr of 0.005 for rolling resistance seem reasonable. Froome weighs about 70kg and fair assumptions were taken for the spec of his bike. Finally, the wind was very light, so it was ignored in the calculations.

Screen Shot 2018-01-29 at 14.32.39

Under these assumptions, Froome’s estimated average power was 205W. The red shaded area marks a 2 hour effort completed at 43.7kph, with a higher average power of 271W. His maximal average power sustained over one hour was 321W or 4.58W/kg. There is nothing adverse about these figures; they seem to be eminently within the expected capabilities of the multiple grand tour winner.

Of course, quite a few assumptions went into these calculations, so it is worth identifying the most important ones. The variation of temperature had a small effect: the whole ride at 18 degrees would have required an average of 209W or, at 40 degrees, 201W. Taking account of altitude was important: the same ride at sea level would have required 230W, but the variations in altitude during the ride were not significant. At the speeds Froome was riding, aerodynamics were important: a CdA of 0.25 would have needed 221W, whereas a super-aero CdA of 0.20 rider could have done 195W. This sensitivity analysis suggests that the approach is robust.

Running the same analysis over the “Empty the tank” ride gives an average power requirement of 373W for six hours, which is obviously suspect. However, if he was benefiting from a 50% reduction in drag by following a motor vehicle, his estimated average power for the ride would have been 244W – still pretty high, but believable.

Posting rides on Strava provides an independently verifiable adjunct to a biological passport.

Cycling Data Science – building models

Screen Shot 2017-12-24 at 21.19.31.png In the previous blog, I explored the structure of a data set of summary statistics from over 800 rides recorded on my Garmin device. The K-means algorithm was an example of unsupervised learning that identified clusters of similar observations without using any identifying labels. The Orange software, used previously, makes it extremely easy to compare a number of simple models that map a ride’s statistics to its type: race, turbo trainer or just a training ride. Here we consider Decision Trees, Random Forests and Support Vector Machines.

Decision Trees

Perhaps the most basic approach is to build a Decision Tree. The algorithm finds an efficient way to make a series of binary splits of the data set, in order to arrive at a set of criteria that separates the classes, as illustrated below.

The first split separates the majority of training rides from races and turbo trainer sessions, based on an average speed of 35.8km/h. Then Average Power Variance helped identify races, as observed in the previous blog. After this, turbo trainer sessions seemed to have a high level of TISS Aerobicity, which relates to the percentage of effort done aerobically. Pedalling balance, fastest 500m and duration separated the remaining rides. An attractive way to display these decisions is to create a Pythagorean Tree, where the sides of each triangle relate to the number of observations split by each decision.

Screen Shot 2017-12-24 at 16.32.02 — Pythagorean Tree

Random Forests

Many alternative sets of decisions could separate the data, where any particular tree can be quite sensitive to specific observations. A Random Forest addresses this issue by creating a collection of different decision trees and choosing the class by majority vote. This is the Pythagorean Forest representation of 16 trees, each with six branches.

Support Vector Machines

A Support Vector Machine (SVM) is a widely used model for solving this kind of categorisation problem. The training algorithm finds an efficient way to slice the data, that largely separates the categories, while allowing for some overlap. The points that are closest to the slices are called support vectors. It is tricky to display the results in such a high dimensional space, but the following scatter plot displays Average Power Variance versus Average Speed, where the support vectors are shown as filled circles.

SVM — Support Vectors shown as filled circles

Comparison of results

A Confusion Matrix provides a convenient way to compare the accuracy of the models. This correlates the predictions versus the actual category labels. Out of the 809 rides, only 684 were labelled. The Decision Tree incorrectly labelled 20 races and 7 turbos as training rides. The Random Forest did the best job, with only six misclassifications, while the SVM made 11 errors.

Looking at the classification errors can be very informative. It turns out that the two training rides classified as races by the SVM had been accidentally mislabelled – they were in fact races! Furthermore, looking at the five races the that SVM classified as training rides, I punctured in one, I crashed in another and in a third race, I was dropped from the lead group, but eventually rolled in a long way behind with a grupetto. The Random Forest also found an alpine race where my Garmin battery failed and classified it as a training ride. So the misclassifications were largely understandable.

After correcting the data set for mislabelled rides, the Random Forest improved to just two errors and the SVM dropped to just eight errors. The Decision Tree deteriorated to 37 errors, though it did recognise that the climbing rate tends to be zero on a turbo training session.

Prediction

Having trained three models, we can take a look at the sample of 125 unlabelled rides. The following chart shows the predictions of the Random Forest model. It correctly identified one race and suggested several turbo trainer sessions. The SVM also found another race.

asapv — Random Forest predictions of unlabelled rides

Conclusions

Several lessons can be learned from these experiments. Firstly, it is very helpful to start with a clean data set. But if this is not the case, looking at the misclassified results of a decent model can be useful in catching mislabelled data. The SVM seemed to be good for this task, as it had more flexibility to fit the data than the Decision Tree, but it was less prone to overfit the data than the Random Forest.

The Decision Tree was helpful in quickly identifying average speed and power variance (chart below) as the two key variables. The SVM and Random Forest were both pretty good, but less transparent. One might improve on the results by combining these two models.

apv — Distribution of APV (large peak at zero is where no power was recorded for ride)

The next blog will explore this topic further.

Cycling Data Science – clusters

Screen Shot 2017-12-11 at 13.38.30

Data Science is a hot topic that is impacting a range of diverse areas from business to sport. With so many cyclists collecting and uploading their data, there is plenty of raw material from which to draw interesting insights. This is the first in a series of articles exploring applications of data science in the field of cycling, beginning with the concept of clustering.

As a data set, I took all my Garmin files covering 2014-2017. Having previously uploaded them onto Golden Cheetah (GC), I took advantage of the API that allows external programmes, such as Python, to retrieve data. I also used a Python library to download the same rides from Strava, where I had recorded additional information about the rides.

After a certain amount of (rather time-consuming) tidying up, I ended up with over 800 rides. Each ride had over 200 summary statistics calculated by GC, as well as other meta-data, such as whether the ride was a race or turbo session. The metrics included all the standard items, such as time, distance, speed, heart rate, power, elevation gain, TSS, normalised power, as well as more esoteric metrics like “Time expended when Power is above CP and W’ bal is between 50% and 75% of W'”. When each ride is represented by a point in 200-dimensional space, it is easy to be overwhelmed. As a coach or an informed rider, which metrics are the most meaningful? This is precisely where data science steps in.

I decided to use some open source machine learning and data visualisation software called Orange. This makes it very straightforward to set up simple pipelines using a toolbox of standard approaches, as illustrated above.

One of the first things to do was to ask the computer to look for clusters of rides with similar characteristics. Orange has a useful feature that finds informative projections of the data that can be displayed on a scatter plot. As a first cut, the K-means algorithm categorised the data into four clusters that were largely explained by the time of day and the duration of the ride.

Screen Shot 2017-12-11 at 16.34.22 — Duration of ride (in seconds) versus Time of day (seconds since midnight)

Although this makes a pretty graph, it simply tells us that I start a lot of rides in the morning, but do quite a few in the afternoon and evening. The green cluster includes my longer rides that rather obviously have to start earlier in the day. The scale is annoyingly shown in seconds, so a duration of 1800 would be a five hour ride. The blue band runs from about 1:30pm to about 6:30pm.

Grouping rides by time of day was not very helpful, so I filtered out that variable and searched again for rides that were similar in terms of effort. This made the results much more interesting. Distance and Average Power Variance (APV) were among the most informative metrics. The following scatter plot does a very good job of separating out races (shown in green), from normal rides and turbo trainer sessions (red). The points I did not have time to label are shown in grey.

Average Power Variance measures the mean power deviation with respect to its 30 second moving average. This will be high when power output is continually changing sharply, as it does on very short town centre courses or the Crystal Palace loop, where you are repeatedly sprinting out of corners. When racing on the Hillingdon and Dunsfold circuits or longer Surrey League routes, power is still much more variable than on a club ride. The band of Saturday club riders is very obvious at 53km: four laps of Richmond Park, with varying levels of APV depending on how aggressively the group was riding. You can also see that I quite often do only one or two laps, at about 19km and 30km. Short TTs and hill climb races tend to have less power variability. This was also the case on the endlessly long climbs encountered on the Haute Route. Lastly, turbo sessions have much lower APV because, even if target power levels vary, they tend to be sustained at the same level for each segment.

It is worth noting that APV is not correlated with the Variability Index, which is the ratio of normalised power to average power. APV is affected by continual changes in power output, whereas the Variability Index is strongly affected by power peaks, even if they a relatively few. The two power files below illustrate the difference.

Screen Shot 2017-12-11 at 17.39.55 — Crit race: High APV Low VI

Screen Shot 2017-12-11 at 17.39.02 — Three sprints: Low APV High VI

Conclusions

This analysis draws attention to Average Power Variance as a useful metric that is high for circuit and road races, but lower for TTs and long hilly races. The key observation for me is that relatively little of my training has a high APV.

The next part in this series zooms in on the races, to identify metrics associated with good and bad results.

Kings and Queens of the Mountains

Screen Shot 2017-11-09 at 18.40.09.png

I guess that most male cyclists don’t pay much attention to the women’s leaderboards on Strava. And if they do it might just be to make some puerile remark about boys being better than girls. From a scientific perspective the comparison of male and female times leads to some interesting analysis.

Assuming both men and women have read my previous blogs on choosing the best time, weather conditions and wind directions for the segment that suits their particular strengths, we come back to basic physics.

KOM or QOM time = Work done / Power = (Work against gravity + Drag x Distance + Rolling resistance x Distance) / (Mass x Watt/kg)

Of the three components of work done, rolling resistance tends to be relatively insignificant. On a very steep hill, most of the work is done against gravity, whereas on a flat course, aerodynamic drag dominates.

The two key factors that vary between men and women are mass and power to weight ratio (watts per kilo). A survey published by the ONS in 2010, rather shockingly reported that the average British man weighed 83.6kg, with women coming in at 70.2kg. This gives a male/female ratio of 1.19. KOM/QOM cyclists would tend to be lighter than this, but if we take 72kg and 60kg, the ratio is still 1.20.

Males generate more watts per kilogram due to having a higher proportion of lean muscle mass. Although power depends on many factors, including lungs, heart and efficiency of circulation, we can estimate the relative power to weight ratio by comparing the typical body composition of males and females. Feeding the ONS statistics into the Boer formula gives a lean body mass of 74% for men and 65% for women, resulting in a ratio of 1.13. This can be compared against the the useful table on Training Peaks showing maximal power output in Watts/kg, for men and women, over different time periods and a range of athletic abilities. The table is based on the rows showing world record performances and average untrained efforts. For world champion five minute efforts and functional threshold powers, the ratios are consistent with the lean mass ratio. It makes sense that the ratio should be higher for shorter efforts, where the male champions are likely to be highly muscular. Apparently the relative performance is precisely 1.21 for all durations in untrained people.

Screen Shot 2017-11-08 at 10.23.33

On a steep climb, where the work done against gravity dominates, the benefit of additional male muscle mass is cancelled by the fact that this mass must be lifted, so the difference in time between the KOM and the QOM is primarily due to relative power to weight ratio. However, being smaller, women suffer from the disadvantage that the inert mass of bike represents a larger proportion of the total mass that must be raised against gravity. This effect increases with gradient. Accounting for a time difference of up to 16% on the steepest of hills.

In contrast, on a flat segment, it comes down to raw power output, so men benefit from advantages in both mass and power to weight ratio. But power relates to the cube of the velocity, so the elapsed time scales inversely with the cube root of power. Furthermore, with smaller frames, women present a lower frontal area, providing a small additional advantage. So men can be expected to have a smaller time advantage of around 9%. In theory the advantage should continue to narrow as the gradient shifts downhill.

Theory versus practice

Strava publishes the KOM and QOM leaderboards for all segments, so it was relatively straightforward to check the basic model against a random selection of 1,000 segments across the UK. All leaderboards included at least 1,666 riders, with an overall average of 637 women and 5,030 men. One of the problems with the leaderboards is that they can be contaminated by spurious data, including unrealistic speeds or times set by groups riding together. To combat this, the average was taken of the top five times set on different dates, rather than simply to top KOM or QOM time.

The average segment length was just under 2km, up a gradient of 3%. The following chart plots the ratio of the QOM time to the KOM time versus gradient compared with the model described above. The red line is based on the lean body mass/world record holders estimate of 1.13, whereas the average QOM/KOM ratio was 1.32. Although there is a perceivable upward slope in the data for positive gradients, clearly this does not fit the data.

Screen Shot 2017-11-09 at 17.54.43

Firstly, the points on the left hand side indicate that men go downhill much more fearlessly than women, suggesting a psychological explanation for the observations deviating from the model. To make the model fit better for positive gradients, there is no obvious reason to expect the weight ratio of male to female Strava riders to deviate from the general population, so this leaves only the relative power to weight ratio. According to the model the QOM/KOM ratio should level off to the power to weight ratio for steep gradients. This seems to occur for a value of around 1.40, which is much higher than the previous estimates of 1.13 or the 1.21 for untrained people. How can we explain this?

A notable feature of the data set was that sample of 1,000 Strava segments was completed by nearly eight times as many men as women. This, in turn reflects the facts that there are more male than female cyclists in the UK and that men are more likely to upload, analyse, publicise and gloat over their performances than women.

Having more men than women, inevitably means that the sample includes more high level male cyclists than equivalent female cyclists. So we are not comparing like with like. Referring back to the Training Peaks table of expected power to weight ratios, a figure of 1.40 suggests we are comparing women of a certain level against men of a higher category, for example, “very good” women against “excellent” men.

A further consequence of having far more men than women is that is much more likely that the fastest times were recorded in the ideal conditions described in my previous blogs listed earlier.

Conclusions

There is room for more women to enjoy cycling and this will push up the standard of performance of the average amateur rider. This would enhance the sport in the same way that the industry has benefited as more women have joined the workforce.