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
Next, the simple rating I described in an earlier post:
rating = net climbing × ( 1 + [ 10 × net climbing / distance ]² )
And next, my newest rating, which uses full profile data, with g0 = 10% (my initial guess at what it should be):
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:
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.
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.
Comments