Posted by: Ian | January 2, 2011

Difficulty is my friend

I’ve been working on my new exercise spreadsheet for 2011 and have decided to make the process of importing rides from my Garmin as easy as possible. Garmin offer no convenient export format for Excel but by copying and pasting from the Activities page on the Garmin Connect site it’s relatively straightforward, as I’ll show below.

A few months ago I wrote about different formulae that have been proposed for quantifying the difficulty of a ride and I’ve incorporated the formula used by ClimByBike into my sheet. A nice feature of this particular definition of difficulty is that it doesn’t have any weird fudge factors. Applying it to my rides last year, and screening out those that had a Difficulty score of less than 100 gives the following:

These are the rides as I rode them, taking the relevant measures from my Garmin 500. My corresponding blogs detail which distances I signed up for in the case of the sportives, and any unusual occurrences (notably coming off my bike on The Puncheur and taking an entirely different route back to the start/finish line).

As you can see, I include for comparison the ascent of the Tourmalet from Luz Saint Saveur, as evaluated by ClimbByBike. If I were to fly into Pau to do this, as I’d like to one day, I’d be quite likely to cycle some of the way to the start, just like the pro’s and etapers do. There are one or two lumps before the actual 19 km climb up the Tourmalet itself and adding these might well boost its Difficulty score. But this is not certain. A characteristic you might want from a difficulty index is that if you split a ride into sections and add up the Difficulty of each you get to the same as the Difficulty for the whole. This measure does not have that quality. This is well illustrated by the climb up Haleakala. On the chart above I reflect the difficulty rating calculated from my round trip up and down. This gives a Difficulty score of 228. However, if I run the same calculation for just the ride up the Difficulty score is significantly increased to 265. The descent itself scores hardly anything (29 or 49 depending upon whether you include the mountain term) but it doesn’t seem right that adding in the quick scoot down reduces the difficulty of the climb up. You could, though, argue the case, I guess, that the ride up is a much more intense one than the ride both ways.

A natural way to evaluate whether the Difficulty measure is doing what it ought to is to compare it to the calories expended. After all, both are really measures of the work that you have to put in. Last year I didn’t capture the ascent of my rides around London (and the distances were sometimes estimates) because the Garmin 500 did such a patchy job of retaining a satellite connection in the capital. Also, there aren’t any real hills in London. Nonetheless, I have 49 rides from the start of last year where I did record ascent and distance and using those I can compare difficulty and calories burned. The result is ostensibly astonishing: there’s a 96.5% correlation! A moment’s reflection makes this less spectacular than it at first appears. The “calories burned” is really the Garmin estimate of calories burned. Since the Garmin doesn’t have extensive biometric data, it’s doing its own version of the difficulty calculation and the correlation suggests that the algorithms are pretty similar. However, the Garmin (whether the 500 or my newer, superior 800) both do use a heart rate monitor in their calorie calculation. The estimates that the Garmin makes when you don’t wear a heart rate strap are much greater and, it seems to me, meaningless. Thus the Difficulty score is achieving an estimate of work done that corresponds well with the Garmin reading, which includes highly relevant data (heart rate) that is only available post facto.

In rough terms, for me, one difficulty point is equivalent to about 20 calories. This enables us to translate the Difficulty score, which is essentially meaningless in anything other than comparative terms, into a quantity (energy, measured in calories) that is well understood.

Being a touch more sophisticated and using a linear regression on the 49 rides gives this match:

The rides are in order of increasing Difficulty and the green line shows the estimated cals burned for each ride. By construction, this increases monotonically with Difficulty. The red line shows the “actual” calories burned, meaning the calories that the Garmin says I burned, taking into account my heart rate during each ride. As you can see (and the stats confirm), it’s a very decent fit.

At a mechanical level, I’ve added this to the Rides tab of my spreadsheet for 2011 (as well as backfitting it to my 2010 sheet):

Here each column is one ride – I’ve done two so far this year. The data whose names are shown with a green background come straight out of the Garmin Activities page after a copy/paste. The data whose names have a rose background I add myself. The cadence figures are in the Garmin but don’t copy over conveniently. The “Mountain” row is just there for if/whenever I’m again riding at heights over 1,000 m (see the Difficulty calc). The yellow-backed figures are derived: the Date is simply a usable version of the Start date from the Garmin.

Parenthetically, you can see that on my ride today the Garmin threw me a rogue max heart rate of 207 bpm. I periodically have had this in the past with the 500 but today was the first time I’ve seen it on the 800. It sometimes happens, as it did today, when I’m bombing downhill near the start of a ride. Who knows why?

The real benefit of the Difficulty number is that it doesn’t depend upon any factors that are only known a priori. This means that I can use it to estimate how difficult (either as a comparative Difficulty score or in calories) a ride will be in advance. This is useful for planning and training. For example, Paula and I are thinking of signing up for the 100 km route of the Lionheart sportive at Longleat in March. Now I can see that it has a Difficulty score of 108, placing it between the 44 mile Cornwall Tor (104) and the 100 km Blenheim (120), which we both did last year. The next ride that I’m actually signed up for is the Glastonbury 100 Miler – this has a score of 169, making it a shade harder than the ascent of the Tourmalet but far easier than a day on the Tour of Wessex.

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Responses

  1. […] earned our supper. For the record, the Olympic ride, ex getting to and from the start, scores 139 difficulty points. Although it’s not my preferred kind of ride, keeping to main roads with few hills made for a […]

  2. […] cadence (63 rpm) and heart rate (154 bpm) are bang in line with my norms for this sort of ride. On the climbbybike Difficulty score the route rates 175 – below each day of the Tour of Wessex, the 2010 Tour Ride and, of […]


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