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.

  1. Calculate the rider’s speed from changes in position
  2. Calculate the gradient of the road from changes in altitude
  3. Estimate air density from historic weather reports
  4. Make assumptions about rider/bike mass, aerodynamic drag, rolling resistance
  5. 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.

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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.

Froome versus Dumoulin

Screen Shot 2017-10-27 at 19.04.21Many commentators have been licking their lips at the prospect of head-to-head combat between Chris Froome and Tom Dumoulin at next year’s Tour de France. It is hard to make a comparison based on their results in 2017, because they managed to avoid racing each other over the entire season of UCI World Tour races, meeting only in the World Championship Individual Time Trial, where the Dutchman was victorious. But it is intriguing to ask how Dumoulin might have done in the Tour de France and the Vuelta or, indeed, how Froome might have fared in the Giro.

Inspiration for addressing these hypothetical questions comes from an unexpected source. In 2009 Netflix awarded a $1million prize to a team that improved the company’s technique for making film recommendations to its users, based on the star ratings assigned by viewers. The successful algorithm exploited the fact that viewers may enjoy the films that are highly rated by other users who have generally agreed on the ratings of the films they have seen in common. Initial approaches sought to classify films into genres or those starring particular actors, in the hope of grouping together viewers into similar categories. However, it turned out to be very difficult to identify which features of a film are important. An alternative is simply to let the computer crunch the data and identify  the key features for itself. A method called Collaborative Filtering became one of the most popular employed for recommender systems.

Our cycling problem shares certain characteristics with the Netflix challenge: instead of users, films and ratings, we have riders, races and results. Riders enter a selection of races over the season, preferring those where they hope to do well. Similar riders, for example sprinters, tend to finish high in the results of races where other sprinters also do well. Collaborative filtering should be able to exploit the fact that climbers, sprinters or TTers tend to finish close to each other, across a range of races.

This year’s UCI World Tour concluded with the Tour of Guangxi, completing the data set of results for 2017. After excluding team time trials, 883 riders entered 174 races, resulting in 26,966 finishers. Most races have up to 200 participants , so if you imagine a huge table with all the racers down the rows and all the races across the columns, the resulting matrix is “sparse” in the sense that there are lots of missing values for the riders who were not in a particular race. Collaborative Filtering aims to fill in the spaces, i.e. to estimate the position of a rider who did not enter a specific race. This is exactly what we would like to do for the Grand Tours.

It took a couple of minutes to fit a matrix factorisation Collaborative Filtering model, using keras, on my MacBook Pro. Some experimenting suggested that I needed about 50 hidden factors plus a bias to come up with a reasonable fit for this data set. Taking at random the Milan San Remo one day stage race, it did a fairly good job of predicting the top ten riders for this long, hilly race with a flat finish.

 Model fit (prediction) Rider Actual result
1 Peter_Sagan 2
2 Alexander_Kristoff 4
3 Michael_Matthews 12
4 Edvald_Boasson_Hagen 19
5 Sonny_Colbrelli 13
6 Michal_Kwiatkowski 1
7 John_Degenkolb 7
8 nacer_Bouhanni 8
9 Julian_Alaphilippe 3
10 Diego_Ulissi 40

The following figure visualises the primary factors the model derived for classifying the best riders. Sprinters are in the lower part of chart, with climbers towards the top and allrounders in the middle. Those with a lot of wins are towards the left.

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Now we come to the interesting part: how would Tom Dumoulin and Chris Froome have compared in the other’s Grand Tours? Note that this model takes account of the results of all the riders in all the races, so it should be capable of detecting the benefit of being part of a strong team.

Tour de France

The model suggested that Tom Dumoulin would have beaten Chris Froome in stages 1(TT), 2, 5, 6, 10 and 21, but the yellow jersey winner would have been stronger in the mountains and won overall.

Giro d’Italia

The model suggested that Chris Froome would have been ahead in the majority of stages, leaving stages 4, 5, 6, 9,  10(TT), 14 and 21(TT) to Dumoulin. The Brit would have most likely claimed the pink jersey.

Vuelta a España

The model suggested that Tom Dumoulin would have beaten Chris Froome in stages 2, 4, 12, 18, 19 and 21. In spite of a surge by the Dutchman towards the end of the race, the red jersey would have remained with Froome.

Conclusions

Based on a Collaborative Filtering approach, the results of 2017 suggest that Chris Froome would have beaten Tom Dumoulin in any of the Grand Tours.