12345

Calculate grade (Read 2573 times)

eric :)


    Ooh... RA Toughness Scale... RATS! I love it. I'll probably think this thing to death. There are two easy cases: a completely flat course, and a non-stop continuous uphill course. The problem are the ones in between. Take Pike's Peak. You run up 13.1 miles, then down 13.1 miles. Is it harder, easier, or the same as a continuous uphill of the same amount of climb? How should downhills be accounted? I think the best way to come up with a rating system is to see how a course affects someone's finish time. Anyone here a statistician? Are you thinking what I'm thinking?
    Trent


    Good Bad & The Monkey

      I am a part-time statistician. I'd love to see the simple grade stuff. Then we can come up with the scale...
      va


        ... I think the best way to come up with a rating system is to see how a course affects someone's finish time. Anyone here a statistician? Are you thinking what I'm thinking?
        Hmmm, this is a clever approach to solving this problem. Perhaps a comparison of the finish time distribution of all participants (e.g., use the finish time associated with the peak of the finish time distribution curve).
        va


          Besides maximum ascent/descent grade, there are some other simple measures that may be interesting to gather from a map’s elevation data: - average ascent/descent grade (e.g., 2%/2.4%) - percentage distribution of ascents, descents, and flats (e.g., 30% uphill, 33% downhill, 47% flat) - longest ascent/descent (e.g., 2.5 miles/1.8 miles) - total number of hills (i.e., number of local maximums) (e.g., 14) Note that for the maximum and longest ascent/descent, it would be good to inidcate the position that they occur in the course. For example: - maximum ascent/descent grade (e.g., 4%@12.5 miles/-6%@7.8 miles) - longest ascent/descent (e.g., 2.5 miles@3.6 miles/1.8 miles@21.4 miles)
          Trent


          Good Bad & The Monkey

            These are good metrics, although I am concerned that using finish times alone may introduce some bias. In a relatively tough course or a small marathon, you are less likely to get an international elite crowd. In that case, the results may be skewed towards slower finish times both due to the difficulty of the course and the lesser average abilities of the participants.
            eric :)


              These are good metrics, although I am concerned that using finish times alone may introduce some bias. In a relatively tough course or a small marathon, you are less likely to get an international elite crowd. In that case, the results may be skewed towards slower finish times both due to the difficulty of the course and the lesser average abilities of the participants.
              We don't need the finish times from elites to calculate this. Course difficulty compares the difficulty of two courses. If a person ran in both of these courses, and one is significantly slower than the other, we can assume that one is harder than another. If we run enough statistically analyses over all courses, we can come up with a course rating. Of course, this method is not completely objective and we can do better by combining it with other data, namely elevation: --------- I tried writing this post several times, trying to eliminate some of the geek/math talks from it but always ended up needing some general math so I'll just include it from the start. I've given this some thought and I have a rough formula in describing the difficulty of a course. It needs to be fleshed out but we need to start somewhere. Before I do that, let me describe the thinking behind it. The goal of this thread is to come up with a formula to describe the difficulty of a course. The intrinsic difficulty is dependent upon the existence of uphills and downhills along the way. Obviously, weather plays a part in the difficulty but in most cases, this metric is hard to measure unless you're running in antartica or Death Valley. Since each hill is independent of each other, we can rate them separately. Here's the formula I came up with so far: difficulty = (sum(u) + sum(d)) * w where: u: difficulty of an uphill climb d: difficulty of a downhill descent w: difficulty caused by weather conditions. We can assume w = 1 for now. The next step is to describe u, d, and w. This is where I need some help. For uphill difficulty (u), I think a parabola would describe it well, since the difficulty increases dramatically as the steepness increases: u = x * (g^m + e) where: x: distance of the climb g: grade of the climb m: grade multiplier. This is used to make steeper climbs more difficult than gradual climbs e: elevation For downhill difficulty (d), it's a modified version of the uphill, with additional constants: d = x * ((g - a)^n + b + e) where: x: distance of the descent n: grade multiplier. e: elevation a: a > 0 b: b < 0="" a="" and="" b="" are="" contants="" that="" effectively="" move="" the="" vertex="" of="" the="" parabolar="" to="" the="" lower="" left="" quadrant="" of="" the="" graph="" (where="" x="" /> 0 and y < 0) so that gradual descents are easier and steep descents are more difficult. do you agree on this formula? the unknowns in the formula are: m - uphill grade multiplier n - downhill grade multiplier a - downhill grade constant b - downhill grade constant we'll worry about how to derive them later. for now, we should discuss if this formula can accurately describe a course. did i kill this thread by including too much math? 0)="" so="" that="" gradual="" descents="" are="" easier="" and="" steep="" descents="" are="" more="" difficult.="" do="" you="" agree="" on="" this="" formula?="" the="" unknowns="" in="" the="" formula="" are:="" m="" -="" uphill="" grade="" multiplier="" n="" -="" downhill="" grade="" multiplier="" a="" -="" downhill="" grade="" constant="" b="" -="" downhill="" grade="" constant="" we'll="" worry="" about="" how="" to="" derive="" them="" later.="" for="" now,="" we="" should="" discuss="" if="" this="" formula="" can="" accurately="" describe="" a="" course.="" did="" i="" kill="" this="" thread="" by="" including="" too="" much=""></ 0) so that gradual descents are easier and steep descents are more difficult. do you agree on this formula? the unknowns in the formula are: m - uphill grade multiplier n - downhill grade multiplier a - downhill grade constant b - downhill grade constant we'll worry about how to derive them later. for now, we should discuss if this formula can accurately describe a course. did i kill this thread by including too much math?>
              Trent


              Good Bad & The Monkey

                If a person ran in both of these courses, and one is significantly slower than the other, we can assume that one is harder than another.
                My experience this past weekend disproves this assumption. Big grin Of course, taking all comers who did CMM 07 and Monkley 06, I think most ran CMM faster than Monkey. I did not, and if I was the only one who logged using RA, we would have a biased view. I will look at the rest of the math. I would suggest that you need to include road surface and absolute elevation above sea level as covariates.
                eric :)


                  My experience this past weekend disproves this assumption. Big grin
                  Didn't you say you're a part time statistician? We all know that one person doesn't really matter ;-)
                  I would suggest that you need to include road surface and absolute elevation above sea level as covariates.
                  The elevation is included in the math somewhere. As for road surface, maybe we can adjust the overall equation as such: difficulty = (sum(u) + sum(d)) * w * s where s is 1 for road, and 1 + c for other surface types.
                  Trent


                  Good Bad & The Monkey

                    Didn't you say you're a part time statistician? We all know that one person doesn't really matter ;-) The elevation is included in the math somewhere. As for road surface, maybe we can adjust the overall equation as such: difficulty = (sum(u) + sum(d)) * w * s where s is 1 for road, and 1 + c for other surface types.
                    One person does not matter if that person is an outlier among a normally distributed set. But if that one person is the only representative of the population, you got troubles. You need to have absolute elevation as its own variable. A climb of 100 feet over 1 mile is more painful if it occurs at 10 000 feet elevation as versus the same climb at sea level.
                      So what's the % grade on my run from yesterday? I was trying to do the math in my head but...you know.

                      Runners run

                      Trent


                      Good Bad & The Monkey

                        Dude, I am so there! Let's run this bad boy! Repeats on that hill in mile 11.
                          That one was super steep but the ones in miles 4-9 were way more fun...those were in the Breakheart Reservation and much more scenic.

                          Runners run

                          Trent


                          Good Bad & The Monkey

                            I'm confused. More fun than a super steep? Is that possible?
                              Yeah so there's super steep on a kinda busy street in a crappy, run down section of wakefield, mass. with cross traffic, or there's pretty steep and rolling like a roller coaster on a bike path through a beautiful wooded reservation with lakes and streams and ponds and ducks and chipmunks and not many people. You be the judge. Yesterday was an "I Love My Garmin" run.

                              Runners run

                              eric :)


                                Breakheart Reservations is REAL hilly but very scenic. It's probably quite similar to the monkey course (not that I've seen it other than pictures), just on a smaller scale. Anywho, how's this? difficulty = (sum(u) + sum(d)) * w * s + e At this rate, I'll have to dust off my calculus book...
                                12345