Tuesday, December 1, 2009

Low-Key Hillclimbs: Mt Hamilton Trends

Some more on Hamilton at the Low-Key Hillclimbs: it's interesting to track the average or median times of finishers over the years. Median is basically the time of the middle finisher, or the average time of the two riders spanning the middle if there's an even number. Average is just the average over all riders. I like median, as if one particularly slow rider shows up, for example finishing in 4 hours out of a group of 75, that will have a strong influence on the average time: for example it would shift the average from 90 minutes to 92 minutes. On the other hand, the median is less strongly affected by what a single rider does, at least assuming there's a sufficient number of riders that around the median finisher riders are finishing several times per minute.

I plot these statistics versus year here:

Curious... But first, let me explain. There's two sets of curves, red for women and blue for men. Each counts only solo riders on standard bikes: no tandems, no unicycles, no hybrid-electrics. There's two curves for each: dashed line segments connecting squares for the median, and solid curves connecting circles for average. There's a shaded region bordered by a dotted boundary for the standard error associated with the estimate of each mean, assuming riders have "normally distributed" times to decent approximation. So basically if you can draw a horizontal line through a shaded region, there's not much significance to trends seen there. If you can only draw sloping up lines through a shaded region, on the other hand, the increase in times from year-to-year is probably significant. Similarly, a shaded region through which only downward lines can be drawn would indicate times are coming down.

Note there's two climbs for 1998: week 1 and week 7 (Thanksgiving). Since all of the other points are Thanksgiving climbs, the second data for 1998 are probably more significant.

So what does one see here? Well, it seems to my eyes that within the men's division in the 2000's, times generally trend longer year-to-year. This is most evident in the median times, but the average times also show this trend. On the other hand, the error bars get tighter: this is because more riders show up one year to the next, as people find out about the series via word-of-mouth.

So how to interpret this? On suggestion is that the "regulars" get older with each given year, and are slowing down. Another option is that only relatively fit riders tend to go to their first hillclimb, whereas in future years they may be more willing to ride with relatively less fitness. Or another option is that "early adopters" of the Low-Key Hillclimbs, both in 1995 and 2006, tended to be people who were particularly good climbers, while those joining later years took longer to come around, perhaps taking time to realize the series had a lot less emphasis on being fast relative to others than the vast majority of "competitive" cycling events.

Another option: it's all due to variation in the highly variable Thanksgiving Bay area weather, for example in nicer weather slower riders are more likely to show, as they will have to spend more time in poor weather and therefore they are less likely to want to do so.

Another possible trend: while within each decade the times seem to increase, comparing the 1990's to the 2000's the times seem to have decreased. Lighter bikes and the advantage of compact cranks, perhaps? Really, the Rorschach effect applies: there's a tendency to find patterns even in randomness. There may be nothing here.

In any case, a lot more analysis could be done, for example checking whether return riders do tend to get slower one year to the next, or analyzing first-time riders as a separate group. Or check other climbs, for example Montebello, to see if there's a similar trend. That one's no-brainer, and I'll get to that in the future.