Wednesday, November 28, 2012

Converting Run Times to Cycling Times for Low-Key Hillclimbs: Part 1

In the Low-Key Hillclimbs this year, cyclists were scored using a factor to adjust for how spread out they were in time. On steeper climbs, riders tend to be proportionately more spread out, but on more gradual climbs, they tend to be more closely bunched together. Rather than apply a correction explicitly based on any particular characteristic of the road, a "slope factor" was derived from the rider data to yield a similar statistical distribution for any pair of weeks for riders doing both weeks.

This worked well for cyclists, but we also allow runners in the Low-Key Hillclimbs. We don't want it to turn into a running race, with teams recruiting runners to boost their scores, so instead of scoring runners on their own scale we score runners the same as their time would have been riding. Since only on extreme grades is running faster than cycling, this results in runners scoring relatively less. It's fun when running to do as well as one can against the riders, but it's recognized in advance it's overall a losing battle.

This was okay until this year, when we intriduced a "running division" in the overall score. This was a side-effect of introducing a tandem-specific division: it forced me to extend my scoring code to accomodate riders switching divisions one week to the next, and once I'd done that for tandems, it was absolutely trivial to extend it to runners. Since I was training for the California International Marathon this Low-Key season, it additionally gave me a competitive outlet without compromising my running focus.

The problem is that runners do not behave simply like slower cyclists. At some grade, for example 15.7% in an analysis I did previously, runners and cyclists may be similar: cycling is more efficient but the rider must carry the extra weight of the bicycle. On the other hand, on flat ground a cyclist can cruise along at close along at 1.5 minutes / km or 40 kph, while for a runner will be around 2.5 times slower (3.75 minutes per km). So the steeper the grade, the better things are for runners.

This was made evident in this year's series. In week 7, Bill Bushnell did a brisk hike up Kennedy Fire trail, shooting photos. Five days later Matt Allie ran 29.6 km in 2:23:10 up Mount Hamilton. That's a 1:42 half-marathin pace for a longer distance. Yet Bill scored more points for his walk. That is what it is; the scoring is designed for cyclists, with runners a relative side-show. But if runners merit a separate division, I owe it to them to equalize the scores week-to-week somewhat.

The approach I'll take is based on the measured metabolic cost of running. I already described this when I looked at data from Minetti. Here's that plot. I'll go more into it next time.


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