## Tuesday, October 5, 2010

### 2010 Low-Key Hillclimbs scoring

Well, the Low-Key Hillclimbs are in full swing for the fifth consecutive year and that means less time for blogging, at least until things settle down.

I've made a lot of changes to the Low-Key scoring this year, keeping the same general idea, but tweaking it. The last four years, I'd divided the riders into three groups: men, women, and "hybrid-electric" bicycles. This last group usually consists of one rider: Bill Bushnell, and his machine is almost as remarkable as he is. But although one could devote an entire series of blog posts to Bill's bike, let's leave it that there's different groups which are each scored separately.

In the past, each week I calculated the median time for each group (excluding tandems), then scored each rider with 100 points multiplied by the ratio of the median time for the rider's group to the rider's time. Simple! But the issue with this is that while it works great for the men, who are generally present in large numbers, the women's turnout is more variable. If four or five strong women showed up, the median time would be relatively low, and everyone would score lower than usual. Meanwhile poor Bill was typically the only hybrid-electric out there, and so he'd score 100 points, week after week, not matter how well he and his machine climbed the hill.

So this year I changed things. First, I analyzed the entire history of Low-Key Hillclimb data, dividing riders up into a number of groups: men, women, hybrid-electric, tricycles, unicycles, mixed tandems, recumbents, and runners (we allow runners to participate). The "men's" and "women's" groups consisted only of riders on standard bikes. Then I did a weighted mean of how each group's times compared with each other group's times. Most relevant was the comparison to men's times, since the men's group has always been the largest and therefore the most statistically stable.

As a result, I calculated the following conversion factors for times:

women: 82.7%
hybrid-electrics: 161.7%

Note by excluding tricycles, tandems, etc from these calculations I reduced the variability of the result, since these groups tend to all be slower than riders on single bikes. Okay, actually the runners tend to be faster, but that's because the runner has usually been Gary Gellin, and Gary is incredibly fast uphill.

Anyway, the process is thus simplified: I convert women's times to an effective men's time by multiplying by 82.7%, and the hybrid-electric times to effective men's times by multiplying by 161.7%, then I score everyone together. I find the median of this combined population then each rider's score = 100 multiplied by the median divided by the rider's adjusted time.

Mixed tandems get special treatment: I then just average together the scores for riders on a mixed tandem and each rider gets that score. So even though men and women getting the same time get different scores, if they're together on a mixed tandem, the men on the tandem will get a slightly higher score than they would on a single, while the women get a slightly lower score. This is under the assumption a 2-person mixed-tandem climbs as fast as the average of the riders on board. This seems like a decent upper bound on a tandem's speed. I did some analysis of this nature last year.

So far, with week 1 in the bag, things seem to be working well.

I'll talk more about Low-Key scoring in a future blog post. But if you're impatient, here's the reference page on the matter.