Friday, August 21, 2020

Course Direction Analysis of Hardrock

Each year Hardrock 100 is run in the opposite direction as it was run the previous time.  While the same ground is covered, the uphills become the downhills creating different challenges for the runners.  One common theory is that the clockwise course is faster.  At first glance this makes sense because in 2008 Kyle Skaggs's unbelievable 23:23 finish came in the clockwise direction.  Then came Kilian Jornet's 22:41 in 2014 on the clockwise course.

The logic is that on the clockwise course, the runners go up the "walls" and down the "ramps".  While climbing the walls might require a slower pace than the ramps, the walls are shorter which means fewer miles at a slow pace.  The ramps lead to a faster downhill pace than the walls because the walls are so steep its hard to get moving fast.  This means more miles downhill at a faster pace.  When this all gets added up, it means on the clockwise course, runners will gain a little time on the uphill because the uphills are shorter and a little more time on the downhills because the downhills are faster.  I have run enough hills that I can say from personal experience, you are almost always better off going up the steep route and down the gentle grade, at least when you are looking to go fast.  So on the surface, this theory seems to hold.  The steeps ups and "easy" downs on the clockwise course have yielded that fastest times in the history of the race.

However, I've always been a little skeptical of this theory.  I have never been to Hardrock so there are certainly other people who know the course a lot better than I do, but here's my opinion.  First, looking at the elevation profiles of the clockwise and counterclockwise courses, the uphills and downhills look equally steep in both directions (images below).  Second, there's the snow.  Since 1992, Hardrock has been cancelled twice because of snow (2019 and 1995).  Snow conditions vary and there are years when runners face a lot more snow than other years.  Sometimes its good as glissading down the snow is a lot faster than picking your way through technical terrain.  But it can be bad too, as slipping and sliding up a steep snowy slope is a lot slower than a dirt trail.  Also, Diana Finkel's course record of 27:18, set on the counterclockwise course, is substantially faster than the women's clockwise record of 28:32 also set by Diana Finkel.

From the 2018 Hardrock Runners Manual

From the 2017 Hardrock Runners Manual

While speculation is a lot of fun, I thought it would be worthwhile to test the theory about which direction at Hardrock is faster.  To do this, I imported all the Hardrock finishing times into an excel spreadsheet and calculated average times for each course.

Counterclockwise: Average time: 39.66 hours, Standard Deviation: 5.78 hours

Clockwise: Average time: 40.00 hours, Standard Deviation: 5.58 hours

So, it looks like the counterclockwise course is faster, just the opposite of the walls-and-ramps theory.  And doing a quick two-tailed t-test, we can say with 80% confidence that there is a statistically significant different in the average times.  In statistics, 80% confidence is not very high, but it does show that there is some difference between the times based on course direction.  And with the average counterclockwise time being faster, it almost certainly means that the clockwise course is NOT faster.  Right?...

Well, I created a histogram (images below) of the time from each course and these start to tell a different story.  First, the histograms reveal the times are not normally distributed which is one of the assumptions when using a t-test.  This means that the t-test might not be an accurate evaluation of the data.  When looking at the histograms, the right side of the normal distribution(if it is a normal distribution) is cutoff which is likely due to the 48-hour race cutoff.  The clockwise direction sees the most finishers in the 43-48 hour range while the counter-clockwise direction sees the most in the 47-48 hour range.  Additionally, the shape of the distributions is different.  If these were normal distributions, with the right sides cutoff, then it looks like the "mean" value of the normal distribution for the clockwise course would be around 46 hours and the "mean" value of the normal distribution for the counterclockwise course would be >48 hours.  Of course, now I'm starting to speculate again which is what I was trying to avoid in the first place.  At this point, I haven't shown one direction to be faster than the other.  To show one direction is faster, I will need to acquire some more stats skills to be able to deal with these (not normal) time distributions.  In the meantime....keep speculating.

Counterclockwise Histogram

Clockwise Histogram

Combined Histogram