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Calculate grade (Read 2573 times)

va


    Consider the following elevation profiles of two imaginary courses. They both ascend the same total distance, and descend the same total distance, with the same incline and decline angles. So for example, the first course may have 3 identical hills 100 ft high, and the second course may have one big hill 300 ft high, and all inclines/declines are 5 percent. Do these courses have the same level of difficulty? That is, would you finish these courses in the same amount of time?
    eric :)


      That's a good point. The second course would seem harder.
      Trent


      Good Bad & The Monkey

        That is, would you finish these courses in the same amount of time?
        I do not know. It merits testing...
          This is a great way to look at the problem, Stephen. I would have to say that, in general, the single large hill would be harder than the 3 smaller hills. I'm not saying heart rate needs to be in your equation, but it seems to me that change in heart rate is the key reason why one course would be harder than another, if you assume the same constant pace on both courses. This also means, to me anyway, that for newer, more out of shape people, like myself, with a lower LT than many of the others around here, the single hill course would seem much harder than the series of three smaller ones. And I'm guessing that a very fit runner would only think the single hill was somewhat more difficult than the three little ones.

          When it’s all said and done, will you have said more than you’ve done?

          Trent


          Good Bad & The Monkey

            Remember, there are contributors to the difficulty (i.e., variables) and there are the results of the difficulty (i.e., outcomes). Everything to the left of the '=' sign is a variable, and everything to the right is an outcome. The primary outcome we are looking at is difficulty, which is a result of an as-yet-undefined combination of the variables. Variables, of course, include number of peaks, number of drops, grade up, grade down, elevation above sea level, etc. As for outcome, we cannot easily measure difficulty (given its high subjectivity). However, we can look at surrogate outcomes. Possible surrogate outcomes include heart rate, average pace, perceived difficulty, DNF rates, etc. Eric, this is all AWESOME. But it would still be great just to get some simple grade statistics for our routes... Big grin
            va


              ...As for outcome, we cannot easily measure difficulty (given its high subjectivity). However, we can look at surrogate outcomes. Possible surrogate outcomes include heart rate, average pace, perceived difficulty, DNF rates, etc...
              I was thinking that the only surrogate outcome that should really matter is finish time. For example, if most people perceive course 1 to be more difficult than course 2, yet those same people always finish course 1 quicker than course 2, then course 2 should have a higher difficult rating. Put another way, there should be a direct correlation between difficulty and finish time.
              Trent


              Good Bad & The Monkey

                The problem with times is that they do not always capture all the reasons why somebody may run a course slow or fast. Take CMM for example. It is a tough course, but it is far easier than Monkey. Jeff and Gorilla each just ran CMM faster than they ran Monkey. But I ran CMM slower due to poor planning and a tired body. A buddy of mine, Dan, ran CMM an hour and a half slower than Monkey because he was pacing his father. Ditto a pace group leader. And if you look at the average times that Gorilla and I have run CMM (as opposed to just this season), our CMM times are slower. But Monkey is still a far tougher course. Plus, CMM is often hotter; is this inherent to course difficulty or a confounder? Just using folks' finish times may confound your difficulty evaluations.
                va


                  The problem with times is that they do not always capture all the reasons why somebody may run a course slow or fast. Take CMM for example. It is a tough course, but it is far easier than Monkey. Jeff and Gorilla each just ran CMM faster than they ran Monkey. But I ran CMM slower due to poor planning and a tired body. A buddy of mine, Dan, ran CMM an hour and a half slower than Monkey because he was pacing his father. Ditto Benn, who was leading a pace group. Just using folks' finish times may confound your difficulty evaluations.
                  Yes, these things you mention make deriving a difficulty rating from finish times challenging. I was just saying that, when all is said and done, regardless of how a difficulty rating is determined (either caluclated from a formula or derived from race results), the difficulty rating should be directly correlated to finish time. That is, all other things being equal, a higher difficult rating would result in a longer finish time. So, for example, if the same runner were to run two courses, with the same level of training and fitness, with the same knowledge of the course, an equally good race strategy, and the same intent to perform at a certain level, a difference in difficulty rating would be refelected in the finish time.
                  Trent


                  Good Bad & The Monkey

                    Here is the key: "all other things being equal". In complex multivariate systems such as this, all things are NEVER equal, but if they can be measured, they can be controlled. I agree that the primary outcome is finish time, but this must be further narrowed to those people who are racing, who run a smart race, who have adequately rested, who have adequately trained, who take in correct hydration on days with equal weather conditions. Since we cannot measure all of these things, we need to start looking for surrogates. HR, as suggested above, is an excellent surrogate for effort, and effort is probably a good surrogate for training, rest, weather and nutrition. So too would be a validated scale for perceived exertion. Also, in your graph, you had a 5% grade. What if the grade was 1%? Thinking back, I know of one race course where the single steady 1% climb followed by the single steady 1% drop is actually easier than anotehr course where that 1% up and down is broken into a bunch of rolling hills. The reason is that the 1% climb does not really reach my threshold for work, but the long steady downhill is very fast. The best way to do this, IMO, would be to mine marathonguide's database and only look at data for multiple marathoners, apply a multivariate anlaysis that takes into account all the environmental factors we can get (such as weather) and the variables we think important, and then see what the best fit equation is.
                    eric :)


                      The best way to do this, IMO, would be to mine marathonguide's database and only look at data for multiple marathoners, apply a multivariate anlaysis that takes into account all the environmental factors we can get (such as weather) and the variables we think important, and then see what the best fit equation is.
                      Mining Marathon Guide's database might be a little tricky. Regardless, I think we were all thinking of the same thing when we said use statistical analysis to derive an equation. Maybe it's easier to come up with a equation and use the data to validate it. The equation doesn't need to describe a course precisely. It only needs to be able to distinguish one course as harder than another.
                      JakeKnight


                        Do these courses have the same level of difficulty? That is, would you finish these courses in the same amount of time?
                        I'm joining your geekfest for a second. The answer - as others have suggested - is definitely not. The second course is far harder. There are diminishing returns in effort and effect from both an ascent and descent. If I climb a 100 foot hill, my muscles may be able to continue at a certain pace, but at some point I'm going to start slowing down dramatically. Thus on a 300 foot hill, I'm crawling at the top; on a series of 100 foot hills, I might have the lactate threshold and muscle strength and conditioning to make it to the top of each at a (relatively) steady pace. I'd compare it to weight lifting. If you ask me to do 300 pushups, and I do them 10 at a time, I could do them at a steady pace; ask me to do 300 at a time, and I either won't be able to do it, or will be going awful slow at the end. Then there's the downhills. On a series of hills, you can fly on the downhills - maybe even make up some (or all) of the time lost on the uphills. On your one-hill race, you can't. There's a ceiling to just how fast you can go, and your quads will give out. And most people, on a hill like that, would be actively slowing themselves down. On a series of shorter hills, you can open up. The bottom line: elevation gain/loss isn't a very accurate picture of how hard a course is. Trent's Monkey-thon is a good example. If I had to climb 1500 feet straight up, my time would be miserable. But the series of hills lets you fly on the downs, and keep the pace pretty consistent, with a few exceptions (the bastard at mile 19 being the worst). That's why I don't think his race takes more than 10-12 minutes off your time, whereas if it was one big hill, it might be more like an hour or two. ------------------------------ As for your quest to come up with a reliable ranking of course difficulty ... that's gonna be tough. I think at the very best, it might be useful only on a given day, once you enter some of the climate variables into the equation. And just as Trent noted there are a great many variables, and there are some that just aren't really quantifiable. Reading my last year's review of the CMM is a good example. It's pretty funny. I actually used the word "hilly" in the subject line. This year, I'd have described it as "flat." Same exact course. And does difficulty really correlate with finish time? I guess in general, but there might be problems there, too. Like I'd guess races like Boston, or Disneyworld, or Big Sur, would have skewed results - too many people stopping to pose for pictures or admire the scenery. Would you restrict your study sample only to the world class elites? Maybe that'd be more accurate? By the way, there does seem to be one assumption in this discussion: that elevation change = difficulty. I'm not sure that's true. I think depending on the course, varying the terrain might make it easier. A perfectly flat course stresses the same muscles. Going up and down can keep you fresher to some extent, I think, if its not extreme. I personally prefer some hills to a total pancake. Interesting discussion, gentlemen. I'll go back to lurking. May the force be with you.

                        E-mail: eric.fuller.mail@gmail.com
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                        Trent


                        Good Bad & The Monkey

                          I agree with Gorilla man about a perfectly flat course being difficult. And folks, don't forget, downhills are not free; they force eccentric contractions and burn more energy than a flat.
                            Almost-perfectly-flat courses are always faster, though. See Chicago or the Bay State marathon course here in MA where everyone goes if they are on the edge of qualifying for Boston. Difficulty definitely correlates to finish times but you'd have to control for the quality of the field. You could never take the average finish times at CMM and compare them to Boston and determine anything about the relative difficulty of the courses. The only way to really determine which of two courses is more difficult would be to compare finish times of people who had run both multiple times over several years. If you could find results of a couple hundred (maybe even a few dozen would be enough?) common runners over a few years (to control for year-to-year variations in weather) you'd be able to come up with the % difference for those two races. My strong suspicion, though, is that if you went through that exact exercise, your results would be no more accurate than going by what the average person perceives. For example, it's universally understood that Chicago is an easier course than Boston, probably by about 2-3 minutes at the elite level--so calculate the % difference. I could rank the difficulty of most of the popular road races in New England and I betcha my rankings would be very similar to the average NE runners rankings too. Which would be very similar to the best statistically generated ranking you could come up with.

                            Runners run

                            Trent


                            Good Bad & The Monkey

                              your results would be no more accurate than going by what the average person perceives
                              Agreed. Now, if we could get Meb to run the Monkey, we might have something Wink
                                my contribution: a useful variable to solve the one big hill vs. many small ones problem may be to include average uphill length in the equation. That is, divide the distance covered on uphills by the number of hills. It would also probably be useful to somehow not count small dips in big hills as actual breaks. A five foot downhill in the middle of a 200 foot climb doesn't matter much as far as difficulty goes.

                                sean

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