Monday, July 19, 2010

Rating Climbs: Low-Key Hillclimb rank comparison

I encoded the previously described algorithm in a Perl script, and the results were interesting. Here's a comparison of a ranking of the climbs used in the 2008 through 2010 versions of the Low-Key Hillclimbs. All ratings are normalized to Old La Honda, something of a standard unit in any climb parameter.

First the Fiets formula, sort of the prevailing standard for hill ratings (and also used by John Summerson):
rating = net climbing² / distance

rank climb                               Fiets/OLH
1    Mount Diablo (N)                    2.22693  
2    Alba Road                           2.16942  
3    Soda Springs Road                   2.11797  
4    Hicks - Mt Umunhum                  1.92388  
5    Kennedy Trail                       1.90262  
6    Bohlman-Norton-On Orbit-Bohlman     1.89235  
7    Welch Creek Road                    1.81027  
8    Quimby Road                         1.78158  
9    Sierra Road                         1.75709  
10   Mt Hamilton Road                    1.59271  
11   Montevina Road                      1.49401  
12   Montebello Road                     1.43379  
13   Jamison Creek Road                  1.39096  
14   Portola State Park - W. Alpine Rd.  1.34549  
15   Bonny Doon - Pine Flat Rd.          1.34382  
16   west Alpine Road                    1.30607  
17   E. Dunne Ave (Henry Coe)            1.25048  
18   Metcalf Road                        1.13607  
19   Kings Mountain Road                 1.11102  
20   Tunitas -Star Hill - Swett          1.06779  
21   west El Toyonal - Lomas Cantadas    1.05474  
22   Old La Honda Road                   1  
23   west Bear Gulch Road                0.292306

Next, the simple rating I described in an earlier post:
rating = net climbing × ( 1 + [ 10 × net climbing / distance ]² )

rank climb                               rating/OLH
1    Mount Diablo (N)                    2.36806  
2    Mt Hamilton Road                    2.22919  
3    Alba Road                           2.06452  
4    Soda Springs Road                   2.04599  
5    Hicks - Mt Umunhum                  1.83563  
6    Kennedy Trail                       1.81136  
7    Bohlman-Norton-On Orbit-Bohlman     1.80174  
8    Welch Creek Road                    1.72821  
9    Quimby Road                         1.69522  
10   Sierra Road                         1.67331  
11   Montebello Road                     1.45653  
12   Bonny Doon - Pine Flat Rd.          1.43248  
13   Montevina Road                      1.43017  
14   Portola State Park - W. Alpine Rd.  1.35568  
15   E. Dunne Ave (Henry Coe)            1.35277  
16   west Alpine Road                    1.33856  
17   Jamison Creek Road                  1.3301  
18   Tunitas -Star Hill - Swett          1.15097  
19   Kings Mountain Road                 1.13853  
20   Metcalf Road                        1.08961  
21   west El Toyonal - Lomas Cantadas    1.01946  
22   Old La Honda Road                   1  
23   west Bear Gulch Road                0.390641

And next, my newest rating, which uses full profile data, with g0 = 10% (my initial guess at what it should be):

rank climb                               rating/OLH
1    Mount Diablo (N)                    2.36453
2    Mt Hamilton Road                    2.19454
3    Alba Road                           2.14279
4    Bohlman-Norton-On Orbit-Bohlman     2.04943
5    Soda Springs Road                   2.03079
6    Kennedy Trail                       1.95249
7    Welch Creek Road                    1.92278
8    Hicks - Mt Umunhum                  1.90514
9    Quimby Road                         1.78918
10   Sierra Road                         1.7342
11   Montebello Road                     1.49266
12   Bonny Doon - Pine Flat Rd.          1.48414
13   E. Dunne Ave (Henry Coe)            1.45157
14   Montevina Road                      1.4318
15   Montevina Road                      1.4318
16   Jamison Creek Road                  1.37138
17   Portola State Park - W. Alpine Rd.  1.36612
18   west Alpine Road                    1.36049
19   Tunitas -Star Hill - Swett          1.16956
20   Kings Mountain Road                 1.13787
21   Metcalf Road                        1.11249
22   west El Toyonal - Lomas Cantadas    1.11174
23   Old La Honda Road                   1
24   west Bear Gulch Road                0.36675

Well, a first observation is all three of these rating systems give fairly similar results. A notable difference is Mt. Hamilton Road, which rates higher under each of my schemes than under the Fiets formula. This is because my systems, for small average grade, always rank a climb at least proportional to total climbing, while the Fiets formula maintains a grade proportionality even for very small average grades.

Another observation is Bohlman does a bit better with my full-profile formula than it does with the simple formula or, to a lesser extent, with Fiets. This is as expected, since the simple formula results in a stronger "dilution" of the super-steep portions with the final kilometers, which are more gradual. You can see Lomas Cantadas also rates a bit higher with the full-profile formula, because like Bohlman, it has some very steep segments.

They all agree, however, that Diablo ranks #1. It's hard to argue with this one.

I then compared the natural logarithms of the ratios of the different ratings of each climb. This gives how consistent the ratings are in how they relatively rate different climbs. The result is the simple formula and the Fiets formula tend to differ by around 10%, while the full-profile formula tends to differ from Fiets by 8.5%. On the other hand, my two formulas tend to differ by only 4.1%. So the conclusion is the simple formula is going to reproduce fairly well a ranking of different climbs produced by the more complex full-profile algorithm.

Anyway, rankings such as these are always going to come with a big dose of subjectivity, and as I noted no two people would agree on what the "proper" ranking is. For example, I discussed this with my girlfriend, and she suggested the formula might under-weight the importance of steepness Soda Springs, she said, clearly should not rank higher than Bohlman or Welch Creek. I tweaked g0 down to 8% to account for this perspective. This implies an extended 8.5% section now rates twice has high as an extended 3% section (before it was an extended 10% section which rated twice as high). Here's what I get:

rank climb                               rating/OLH
1    Alba Road                           2.35213
2    Mount Diablo (N)                    2.30759
3    Bohlman-Norton-On Orbit-Bohlman     2.29859
4    Kennedy Trail                       2.18769
5    Welch Creek Road                    2.1426
6    Hicks - Mt Umunhum                  2.11641
7    Soda Springs Road                   2.072
8    Mt Hamilton Road                    2.05291
9    Quimby Road                         1.98273
10   Sierra Road                         1.86041
11   Montebello Road                     1.50087
12   Jamison Creek Road                  1.48926
13   Montevina Road                      1.48908
14   Bonny Doon - Pine Flat Rd.          1.48079
15   E. Dunne Ave (Henry Coe)            1.46687
16   Portola State Park - W. Alpine Rd.  1.36471
17   west Alpine Road                    1.35593
18   Metcalf Road                        1.23638
19   west El Toyonal - Lomas Cantadas    1.19099
20   Tunitas -Star Hill - Swett          1.14852
21   Kings Mountain Road                 1.12687
22   Old La Honda Road                   1
23   west Bear Gulch Road                0.336128

The steep stuff really rose to the top. The comparison between this rating and other ratings: Fiets = 6.8%, my simple rating = 9.3%, full profile rating with 10% g0 = 5.8%. So it's coming close to the Fiets rating is placing a high importance on grade. However, by using the full profile data it's clear that a climb like Bohlman does better here than it does under Fiets, and even Hamilton does a bit better relative to Old La Honda since with this rating the short descents aren't treated quite as harshly.

I like this one. Maybe I'll stick with it.

No comments: