Warning: This is a long, detailed post with unsurprising results. If that's not your kind of thing, I believe there's a thread about predicted 5K times for doping course-cutters elsewhere.
Summary: When you run uphill during a marathon, slow down. When you run downhill, speed up. But not too much (+/- 10-15 seconds compared to average race pace).
Abstract: Scott Fauble, the fastest American at the 2019 Boston marathon, is the fastest Boston finisher whose data is available on Strava. The data provided by Strava make it possible to determine Fauble’s pace not just per 5K or mile segment, but more precisely for segments matching the start and end of each hill. Analyzing the Strava data—altitude, heart rate, stride length, time, distance, and average pace—suggests what may be a more optimal pacing strategy for the Boston Marathon. Fauble’s heart rate (and thus effort) and stride rate did not change on uphills or downhills compared to level segments. Instead, he changed speed by changing his stride length. Fauble’s speed varies linearly with the hill grade.
Caveats: Distances are given here are as they appear in the Strava activity, which is slightly longer than 26.2 miles. The data is ultimately derived from Fauble’s wristwatch-based GPS with heart rate monitor, a Polar Vantage V that records data at 1-second increments and has average accuracy for a GPS watch. Strava provides only a sample of these data points, approximately one out of every 10 seconds. No permission was obtained from Fauble to analyze his data; through his placing the data on Strava, his consent for viewing and analysis is assumed. Don’t sue me, bro. This research was not conducted under the auspices of any responsible institution with a competent IRB, and I am not a statistician. If you think you can do a better job, knock yourself out.
Open questions: It would be interesting to compare the pacing strategies of Jared Ward, the next American finisher and someone who has studied marathon pacing as a qualified statistician. It is also unknown if Fauble’s approach to pacing is similar to that used by elite African marathoners.
The data. The overview graph for an activity on Strava provides around 800 data points regardless of the length of the activity. For a sub-2:10 marathon, this means that there is around one data point reported for each 10 seconds of the race, although the interval between data points varies. Strava does not calculate or report average paces per 10-second segment. Instead, it reproduces the punctual pace reported for one second approximately every ten seconds. Using Strava on a different computer will result in a different set of points being reported.
Watches are very good at measuring time, but measuring distance by means of GPS is less accurate. Mistakes tend to cancel out over time, but the pace reported during any particular second can be inaccurate. Consequently, the paces reported by Strava are highly volatile and not immediately usable.
Strava does not use the watch’s own altitude data. Instead, Strava calculates the altitude at any given moment from its own altitude map based on the watch’s reported geographic coordinates. The hill grade reported by Strava is not that between visible data points, but from one visible data point to the next (invisible) data point. In addition, Strava only reports grades (for this particular activity of Strauble’s) steeper than +/-3.3%. Less steep grades are all reported as 0.0%. Consequently, Strava’s reported hill grade data is not usable.
Instead, for the purposes of this study, uphills, downhills, and level segments were identified as sequences of steadily increasing, decreasing, or unchanging altitude, with leeway for minor variations in either direction. Uphills were defined as segments with at least three data points of increasing altitude (thus around 30 seconds of running or about .1 mile) and a grade of at least 1%. Downhills were calculated in the same way, while level segments were those with grades between -1% and 1%. For each hill, its starting mileage, change in altitude, and thus grade were determined. In all, 28 uphill segments, 31 downhill segments, and 26 downhill segments were determined. The sum of their distances was 23.48 miles, as some intervening distances were too short, and therefore had too few data points, for their average paces to be reliable. Deciding whether a segment was one hill, or (for example) three downhill segments separated by two level segments, is a matter of judgment and subject to revision.
Fauble’s pace on each hill was calculated by averaging the paces reported by Strava for all points from the start to the end of the hill. The reported paces—time divided by distance—give access to the underlying distance data for each data point, which is reported with a very high degree of precision, down to fractions of a meter (although with not nearly as high of accuracy). The average paces on hill segments calculated this way produced plausible results.
The other possible method for calculating average pace would divide the time spent on each hill by its distance as determined by the distance reported by Strava. Because the distance reported by Strava is only precise to .1 mile, the results obtained in this alternative way were implausible and unusable.
With an average pace for each hill, a more accurate distance for the hill than reported by Strava could be calculated by dividing the time for the hill by the average pace.
The average heart rate and cadence for each hill were also determined, and an average stride length was calculated based on the length of each hill and average cadence.
The data for each hill is available here:
Discussion
Heart rate. Fauble’s heart rate deviated very little once it rose to 150-160 bpm. His near-constant heart rate suggests that Fauble ran uphills, downhills, and level segments at nearly constant effort. The few short spikes in heart rate appear to be associated if anything with sudden shifts from uphill to downhill running, or vice versa. There is very low correlation between hill grade and heart rate (.0816). As the accompanying chart shows, after mile 3, Fauble’s heart rate varies little and only briefly from the average rate of 161 bpm.
https://pasteboard.co/Ih2DXRA.jpg
Stride rate. Fauble’s stride rate is even steadier than his heart rate. It varies minimally from the overall average of 182 spm, again with very low correlation with the steepness of a hill (.0965). The minimum calculated average stride rate on any segment was 179.5, while the maximum was 185.6.
Therefore nearly all variation in Fauble’s speed is due to his stride length, which increases on downhills (average 188 cm) and decreases on uphills (174 cm) compared to level segments (182 cm). Fauble’s uphill, downhill, and level stride length increase only slightly over the course of the marathon and to the same extent that his speed did as well.
Pace. There is very high linear correlation between the grade of a hill and Fauble’s pace, as the graph of hill grade against average pace shows. The correlation of hill grade with pace is very high (.7505).
https://pasteboard.co/Ih2JT07.jpg
It’s important to recognize, however, that Fauble rarely sped up or slowed down more than 15 seconds per mile compared to his average pace for level segments (4:52/mile). Of the hills longer than .2 miles, where the extra data points provide greater confidence in the average pace, nearly all were run within a few seconds of the average uphill pace (5:06/mile). Of the downhills longer than .2 miles, nearly all were run within a few seconds of the average downhill pace (4:42).
Downhill pace distribution:
https://pasteboard.co/Ih2DplTX.jpg
Uphill pace distribution:
https://pasteboard.co/Ih2KduT.jpg
Some have suggested using equivalent energy expenditures based on a treadmill calculator to suggest appropriate uphill and downhill paces. For the Boston marathon, the treadmill calculator method would suggest paces far faster for downhills and far slower for uphills than what Fauble actually ran. Given Fauble’s near-constant heart rate and small range of variation in pace for hills, it appears that using treadmill inclines is not an accurate method for predicting paces for constant effort.
(Cf.
https://42.195km.net/e/treadsim/
)
Distance and location-specific factors
Fauble’s data was under race conditions where tactical factors may play a role on any given segment. In addition, there is the question of how aggregate fatigue may have affected his pace over the course of the marathon. Some final observations will address these factors.
The Boston course as a whole consists of approximately 30% uphill sections, 44% downhill sections, and only 26% level sections. One of the challenges of the course is that runners must spend significant time running (downhill) at faster than marathon pace and relatively little time at their accustomed marathon pace.
The steepest downhill is the first 0.5 miles of the course (-4.9% grade). This was also one of Fauble’s faster segments (4:29/mile), probably due both to the grade of the downhill and tactical considerations. The final segment (0.3 miles at 4:30/mile, -0.2% grade) was the fastest of the level segments.
From a linear projection of uphill pace based on uphill steepness, we would assume that each 1% rise in grade would be associated with a 4.1 second slowing of pace per mile. Fauble ran the first two Newton hills very close to this projected pace (around 3 seconds slower than projected), while the pace on the third Newton hill was significantly faster (by 12 seconds, 4:56 compared to 5:08 on a hill with 3.0% grade). The pace on the fourth Newton hill, “Heartbreak Hill,” was significantly slower (by 15 seconds, 5:25 compared to 5:10 expected on a hill with a 3.7% grade).
Fauble’s overall pacing strategy can be characterized as even pacing. The trend line of observed paces from start to finish is almost perfectly level.
https://pasteboard.co/Ih2JsaY.jpg
If we look at the trend line of deviation from expected pace based on hill grade, it is very shallowly negative: Fauble’s pace deviated from the expectation based on hill grade, running about 1 second slower at the beginning and slowly decreasing to 1 second faster at the end of the race. This is a very minor effect, however, with most deviations lying in a range of +/-13 seconds from the expected.
https://pasteboard.co/Ih2GViC.jpg
Conclusion
If you want to run the Boston Marathon like Scott Fauble, slow down a bit on uphills (up to 15 seconds/mile slower) and speed up a bit on downhills (up to 10 seconds/mile faster). Run somewhat faster at the start and the end of the race. Slow your pace by 35 seconds/mile on Heartbreak Hill if you need to.
