Low-Key Hillclimbs 2013: weekly score parameters

In the Low-Key Hillclimbs scoring, I calculate two parameters for each week's climb: a "rider quality" parameter which describes the average strength of riders in the climb, and a "score slope" parameter which describes how spread out the riders are. These parameters are determined from rider identification and score alone. Only riders who do more than one climb contribute to these calculations, because these riders provide a basis for comparing one climb to the next. After a single climb, if riders finish close together, than it could be due to the fact the riders are similar in ability. But if the same riders do two climbs, then assuming the riders don't naturally spread or converge in ability, then if they score closer together in one of the climbs then it might be assumed this is due to the nature of the climb, for example that the climb where they finished closer together had shallower grades where wind resistance was more important, or maybe even descents where descending speed is only partially correlated with climbing speed.

Here's the results for the 2013 climbs. First I show "quality", where I've mapped the actual variable used in the code to something close to average rider score:

week	slope
1	95.5997
2	95.6284
3	99.6606
4	97.8925
5	97.4627
6	97.268
7	101.167
7x	105.022
8	100.491
9	97.5895

The week with the riders with the lowest score here is Montebello. This is historically typical. The first week tends to draw a broader variety of riders. More dedicated riders tend to be stronger, or if they weren't strong to start with, they get stronger than those who chose to ride only the early climbs.

The quality score increases through the first three weeks, the third week being the intimidating Bohlman climb. The score again peaks with Lomas Cantadas week 7, with an even more select group moving on to accept the 7x challenge and climb Marin Ave. Interestingly Montara's score wasn't much above 100. Then Mount Hamilton, week 9, was another popularist favorite, attracting a broader range of riders.

Here's the slope score:

week	slope
1	1.0114
2	0.9930
3	0.9304
4	0.7744
5	1.1854
6	1.1860
7	1.0050
7x	0.7519
8	0.9205
9	1.0598

A slope score of less than one means the scores were spread out and need to be compressed. A slope score of more than one means the scores were compressed and need to be spread out. The conjecture that this is related to steepness of the climb is fairly well borne out. The 7X challenge had an extreme slope score: not only was there an issue with rider speed but also motivation, since for many it was challenge enough just to make it to the top of Marin Ave. Curiously Portola Valley, week 4, was next. It seems on the series of short, steep climbs, which challenged recovery as well as anaerobic power, the difference between the fastest and slowest was amplified substantially. Week 8, Montara, was next. This was the steepest point-scoring climb in the series. Next was Bohlman, week 3, which was next on the steepness scale. Lomas Cantadas, which has some very steep sections, ends up with a slope score more than one due to the dilution effect of the descent.

On the other end, weeks 5 (Black Road) and 6 (Patterson Pass) had slope scores well above one. These climbs both had some steepness, but also had extended sections of relatively gradual grade. Mount Hamilton was next, where the descents dilute the time cost of the climbing, and where drafting can be a considerable factor on the first climb.

It's encouraging when the numbers resulting from the analysis correlate with identifiable features of the climb in a way which was anticipated when the algorithm was first developed in 2011.