No, the paralympians would not have won the Olympic 1500 meter finals

Posted by Dave on September 13, 2016 | Comments Off

A story on the Huffington Post is making major traction these days: The winning time in the Paralympic 1500-meter run was actually faster than the winning time in the Rio Olympics.

Technically that is true: The Paralympic champion, Abdellatif Baka of Algeria, finished in 3:48.29, while Matthew Centrowitz’s winning time in the Rio games was a tad slower, 3:50.00. Baka’s pace was truly amazing and inspirational, even more so because he is legally blind. But the Post article goes on to claim that the first four finishers “would have beat out Matthew Centrowitz” for the Gold if they had been competing in the Rio games. Um, I’m sorry, but they would not have.

The 1500-meter dash at the Olympic level is a tactical race. The first two laps this year were run at an excruciatingly slow pace as runners jockeyed for position. Centrowitz held off all challengers when the race finally sped up in the final lap, running the last 400 meters in just over 50 seconds. None of the participants in the Paralympics have that kind of foot speed, which would work out to a blistering 3:09 1500 meters (or a 3:23 mile) if it was sustainable.

Centrowitz is capable of running a much faster 1500 than he did in the Olympics, but he was counting on having a better final sprint than the rest of the field, so he was happy to run at a very slow pace for the first half of the race if no one challenged him. But make no mistake, if someone had challenged him by running faster at the start, he could have easily kept up. His PR in the 1500 is 3:30.4, which would have put him nearly 150 meters ahead of the fastest paralympian at Rio.

The Paralympics are an astonishing testament to the dedication of hard-working athletes who have beaten dismal odds, but let’s not exaggerate the accomplishments of these athletes by suggesting they would win in a head-to-head matchup against the medalists in the traditional Olympic games.

That said, a 3:48 1500 and a gold medal is impressive in its own right! Congratulations to the truly amazing Abdellatif Baka and his fellow Paralympic champions!

Should Boston make it tougher for women to qualify?

Posted by Dave on October 1, 2015 | 1 Comment

The Boston Athletic Association just announced the list of people who were accepted as registrants in the 2016 Boston Marathon by virtue of their qualifying times. This year, as in the previous two, not everyone who made a qualifying time has been accepted into the race. You had to beat your official qualifying time by 2:28 this year in order to even make it into the field. Thousands of runners who thought they had a chance were denied.

This has added intensity to a debate that’s been raging for years: Many runners claim the standards are too easy for women, giving women an unfair advantage. For 45-year-old man who ran a 3:23 — 2 minutes faster than his 3:25 qualifying time — and didn’t get in, it might seem wrong that 45-year-old women needed only a 3:52:32 to make the cut.

But just because it “feels” wrong doesn’t mean it’s really unfair. There are many physiological reasons why the fastest women probably won’t ever run marathons as fast as the fastest men their age. One example is their naturally higher body fat levels, which don’t improve performance in marathons but do add to the amount of weight women must convey for 26.2 miles. A fit 150-pound man carries about 12 pounds less fat than an equally-fit woman the same size.

That said, the official Boston Qualifying (BQ) times are a full 30 minutes slower for women than men in every age group. Could this rather arbitrary-sounding number truly reflect the physiological differences between men and women? Does it make sense to keep that same difference in qualifying standards, for every age group?

One way to answer this question is by looking at age-grading. Age-grading attempts to form a consistent standard for every age runner by comparing their performance to the world record for their age. You can enter your age, gender, and time for any race in a calculator and it will give you an “age grade,” which is really just your speed for that distance as a percentage of the world-record speed for your age.

I downloaded the tables that were the basis for this table and used them to graph the age grades (AGs) for each BQ time. Here are the results:


This graph gives the age grade for every BQ time. As you can see, up to age 50, men score higher (meaning this is a more difficult time for them to achieve), but after age 50, women score much higher than men. At the very least, this means we are definitely right to question the 30-minute difference in BQ times for men and women for each and every age group. In general, young men and older women have the toughest BQ times, while older men (at least those under 80) and younger women have it relatively easy (assuming the age-grading model is sound).

So what could we do to improve the system? Let’s turn this graph around and look at what the BQ times would be for a given age grade (AG):



The thicker lines plot the current BQ times against age. The light-colored thin lines (green for women, blue for men) plot what the times would be if we kept the AG at a constant 0.62 for men and women. As you can see, this would make it easier for everyone. It’s just slightly easier than the BQ times for women age 40-45 and men age 70 and much easier for everyone else. Older women would benefit most of all. This makes sense since the current system is hardest for them. Unfortunately, this would create another problem: There would be even more qualifiers than before, and the BAA would have to set another arbitrary cutoff to limit the number of runners to the available spots.

The dark-colored thin lines correspond to an AG of 0.65 for men and women. This would make it easier for men under 30, much easier for women over 60, and harder for just about everyone else to qualify. That might be just about the right solution for the BAA to adopt. Based on these results the BAA qualifying table would look about like this:



Of course the BAA might want to tweak this to get round numbers, but something like this would probably more representative of actual ability than the current system, which seems to favor younger women and older men. This all assumes that the current age-grading system is accurate. I’m not so sure it is. It’s all based on the current world-record times for each age group, and that assumes that every age group is working equally hard to break world records. It’s also important to note that in this model, the women’s age groups that would be affected the most (between 35 and 49), the change isn’t quite as dramatic as it appears (the BQs are reduced by 7 to 8 minutes) because presumably nearly everyone who qualifies would get in to the race — there would be no 2:28 cutoff because there would be fewer qualifiers.

If I had to guess (and it would just be guessing at this point), the reason AG times increase so dramatically for women over 60 is because women that age weren’t allowed to compete in distance races when they were younger, so you don’t see as many competitive older women. The first women’s Olympic marathon was in 1984, and the winner, Joan Benoit, is now just 58. Expect to see some of the records for 60-and-older women to improve dramatically in the coming decades. Then we may have to revisit BQ times yet again (which isn’t a bad idea to do in any case).

The Basics: Running Tangents

Posted by Dave on December 4, 2014 | Comments Off

You have probably heard runners speak of “running the tangents” in a race — but what does that mean, exactly, and what’s the best way to do it? Running tangents is just a geeky way of saying “running the shortest legal distance in a race.”

Geometrically speaking, a “tangent” is a straight line that touches a curve but doesn’t cross it, like this:



The red line is a tangent of the circle. When you “run the tangents,” however, you don’t just touch a corner like the illustration above, you go around it, like this:


The tangents are actually the straight lines heading into and out of a corner. In a race with many corners, running the tangents often means crossing from one side of the road to the other:



Assuming the entire roadway is open to runners, this is entirely legal and expected. When a course is measured and certified for a particular distance — say, 5 kilometers — the certifier measures on the shortest possible route.

In some races, it’s impractical to run the tangents: Large races may simply be too crowded, and at smaller races often the road is not completely closed to traffic, so you may be asked to stay to one side of the road or another. But assuming you are running on a greenway or road that is closed to traffic, if your goal is to complete the race as quickly as possible, you should run the tangents!

But even in races where the road is closed and there is plenty of room, I’ve often seen runners stay to one side of the road, or cross the road all at once instead of on the shortest possible route. In fact, it’s rare to see any runner run perfect tangents. How much time are they losing in doing this? DC Rainmaker did a thumbnail calculation for the National Marathon (now the Rock N Roll USA) and came up with a full half mile, which might be 5 minutes or more for a typical runner! (As an aside, I think he may have gotten it wrong. If you stay to one side of the road, you only run extra distance on half the corners in the race, not every corner — but he also included a fudge factor by not accounting for the wide roads on the course). In any case, everything else being equal, running the tangents means you run the shortest possible route. There are not many occasions when running a longer distance results in a faster time!

So assuming they know to run tangents, how do people go wrong? The most common mistake I see is crossing the street all at once:


The runner following the green path thinks he is running tangents — after all, he is switching sides of the road and taking the shortest line around each corner — but he’s clearly traveling farther than the runner following the red path.

The other errors come up when only a portion of the roadway is open to runners. If a part of the roadway is coned off for runners but the other part is open to traffic, some runners seem to think that means they need to run next to the the curb. Not true! You can use the entire width of the road out to the cones, like this:


The red runner is following the shortest legal path. By staying next to the curb, the green runner is traveling farther than necessary. And tempting as it may be in some races, the blue path is not legal. Runners must stay on the marked course at all times, and the cones delineate the course boundary. Even running on the wrong side of one cone, say, to pass a crowd of runners, while it might not shorten the course, is not allowed! Notice here that the red runner runs straight lines between the cones. Each cone is like its own mini-corner, and if it is safe to do so, you can save a bit of distance by running straight between the cones, even if the road you are on has a gradual curve.

One scenario where you may want to keep to something more like the green path is when there is a lot of car traffic on the road traveling at a high speed. Though technically you are allowed to run right next to the cones, this may put you at an unsafe distance from cars traveling at 55+ mph!

Another exception: It might not pay to run a precise tangent on an extremely sharp corner or a turnaround. In these cases, especially if you are a fast runner, you may need to swing wide in order to make the turn without slowing down too much. When you do this, however, don’t let yourself drift all the way across the road. As soon as you round the corner, sight the next corner and run straight for it on the shortest diagonal.

Because so many runners fail to properly run the tangents, especially in the situations I show you above, it might feel like you are doing something “wrong” when you are actually running the correct line on a course. If you take care to understand the rules, you can save yourself valuable time, and you might just beat some of those other runners who aren’t as well-informed as you are!

Should you start out slow in a 10K?

Posted by Dave on April 10, 2014 | 1 Comment

Conventional wisdom is that you can get your best time in a race by starting off a little slower than your goal pace: “Negative splits” are the ideal — times for each mile run should decrease over the course of the race.

So, for example, if you were running a 10k and had a goal of finishing the 6.2 miles in 62 minutes, then you should not, according to conventional wisdom, start out by running your planned average pace of 10 minutes per mile. You should start a little slower, maybe 10:15 per mile, and make up for it by running faster at the end.

But why? I’ve seen several web pages make the assertion that “every world record from the 1500 meters to the marathon has been set running negative splits” or something similar. But rarely do such assertions come backed by hard evidence. So I was interested to see this paper, which seems to turn that notion on its head:


In fact, most world records at distances above 200 meters have been set with positive splits, not negative splits. The article goes on to argue that the best strategy for 400- and 800-meter races is a positive split, where the finish is slower than the start.

But typical runners are not setting out to break a world record. They just want to do the best they can, perhaps setting a personal record in a race. They visit sites like, which can predict, say, a 10K pace based on previous 5K. If I enter my personal best 5K time, 17:49, it spits out a projected time of 37:00 for a 10K. But it doesn’t offer any strategy for achieving that time other than letting me know that’s an average pace of 5:57 per mile. Supposing I feel like I have a shot at that time, should I start out a little slower, a little faster, or right on pace?

I can see that most men’s world-records at 10,000 meters were set with positive splits, suggesting I should start out a little faster. But for a recreational runner, is that realistic?

I decided to take a look at some real-world results and see what runners like me do. The Ukrops Monument Avenue 5K in Richmond, Virginia, was run a couple weeks ago and has a large field of runners. I decided to look at the second page of mens’ results (since the race leaders may have been running a strategic race rather than going for the all-out best time). Here’s what I found:


As you can see, the men ran the race in an average time of 36:31, and their pace on the first 5K was 3 seconds faster than the pace on the second 5K. 26 of the 44 runners had positive splits while only 18 had negative splits. Maybe there is something to this idea that a positive split is better for a 10K after all.

So I decided to look at the women’s results as well:


Once again, there is a similar pattern, only more pronounced. The women in this sub-elite group ran the second half 23 seconds slower than the first half of the race.

So perhaps starting out fast is the best way to finish fast. But there might be some problems with this data. What if the runners who started fast were actually capable of going even faster, but made an error and paid for it with a slow finish?

To test for this eventuality I eliminated runners who were positive or negative by more than 3 percent. When I did this, the numbers evened out a bit: 19 men had positive splits while 14 had negative splits. And 13 women had positive splits compared to 14 with negative splits. Overall, more runners had positive splits, but it was much closer.

Interestingly, though, this race has a harder first half than second half: the first half is a gradual uphill. So even if all the runners had put out precisely even splits, they were actually exerting more effort in the first half than the second half.

This suggests to me that starting out slow in a 10K is not a good idea. An even pace, or even slightly positive splits (though no more than 5 seconds or so per mile) will probably generate the best results.

Reardon J. (2013). Optimal pacing for running 400- and 800-m track races, American Journal of Physics, 81 (6) 428. DOI:

Are runners likely to be targets of violent crime?

Posted by Dave on October 23, 2013 | Comments Off

As the days get shorter, I hear more and more concerns about safety from crime during runs, both in online forums and from my running friends. Soon, for many of us, it will be impossible to go for a run outside of normal working hours without running in the dark. Runners, especially women, are concerned about the possibility of being attacked when running on dark, isolated trails and greenways.

But how significant are those concerns? When we hear of a case like the Central Park Jogger or the more recent murder of a runner in Ohio, are we terrified because it’s an example of an all-too-common occurrence, or is it only surprising because attacks like this are rare?

I decided to look into crime statistics to see if I could parse out the actual danger runners face when heading off into the darkness. Unfortunately, the U.S. Department of Justice, while it does track violent crime nationwide, doesn’t have a readily-accessible statistic for attacks on runners. If any readers have better numbers than those I’m about to present, I’d love to hear from you, but for now, what I can offer are a few thumbnail calculations that may help you understand how much risk you might face by going out for a solo run in the dark.

This report gives some good data on crime in the US, and we can use it to get a rough sense of the crime dangers runners may face. In 2012 there were 12,765 murders in the US; 9,917 of the victims were male and 2,834 were female. That means that the average American had a .0004 percent chance of getting murdered that year.

But most murders are committed by people who know their victims. The random guy jumping out from behind a bush is responsible for relatively few murders. Indeed, only 1,557 of the 12,765 murders in 2012 were committed by strangers. When you limit the murders to the categories likely to affect runners (e.g. not bar-room brawls or gang wars), the number drops below 400, or about one in 100,000. And again, runners are likely to be only a portion of these cases.

That said, people aren’t just worried about getting murdered. Rape is a serious concern as well, especially for women. The numbers of rapes are much larger, as this report shows. In 2009, there were 327,600 reported cases of sexual assault of women in the US. That means an average woman had a 0.2 percent chance of being sexually assaulted that year — over 1,000 times the likelihood of being murdered.

Again, however, the “random guy jumping out from behind a bush” sort of rape is much rarer. Seventy-eight percent of assaults were committed by someone known to the victim. Less than 14 percent of rapes were committed in open areas like parks and greenways (the numbers we have in this report combine “locations such as an apartment yard; a park, field, or playground not on school property; a location on the street other than that immediately adjacent to home of the victim, a relative, or a friend; on public transportation; in a station or depot for bus or train; on a plane; or in an airport.”).

It’s not necessarily valid to suggest that we can combine the “stranger rape” percentage with the “open space” percentage to get a percentage of rapes committed by strangers in open spaces, but that gives us a figure of 3 percent. I think it’s reasonable to guess that less than 3 percent of all rapes are this sort of “random guy jumping out from behind a bush” attack. Even so, that’s still a pretty large number: about 10,000 sexual assaults per year. It would mean that women face a 0.006 percent chance of being attacked in this way each year, or more than 35 times their chance of getting murdered in a similar sort of attack. And let’s not forget that most rapes go unreported (though I suspect more of the “random attack” rapes are reported than rapes by acquaintances), so this may be a significant source of danger for women.

But how does this compare to other dangers runners might face, such as getting hit by a car? Once again, it’s difficult to find statistics just for runners, but we can find statistics on pedestrian deaths and injuries in car crashes. In 2010, 4,279 pedestrians were killed in car crashes, and 70,000 were injured. Male pedestrians had a .0019% chance of dying in a car crash and females had a .0008% chance. That means, if our thumbnail estimates are correct, female runners could be as much as 10 times more likely to be sexually assaulted while running than dying in a car crash. They are, however, somewhere around 4 times as likely to be injured in a car crash than to be sexually assaulted.

Of course, these estimates could be off by a lot! We don’t know what portion of pedestrians are runners, and whether runners are more or less likely to get hit by cars than walkers. We don’t know what portion of “open space” rapes really affect runners. That said, these thumbnail estimates definitely demonstrate that women should be concerned about the possibility of a sexual assault while running. While the biggest danger is probably injury in a car crash, women runners are almost certainly more likely to be the victim of sexual assault than killed in a car crash.

I wish we had better data for women about the safest places to run. While it might seem that less-traveled greenways and trails would be the most dangerous places, perhaps attackers stay away from these areas because there aren’t many potential victims. Again, if any readers have access to additional data that might help shed light on this issue, I’d appreciate hearing from them.

Is stigma stopping exercise in obese people?

Posted by Dave on October 15, 2013 | 1 Comment

I’ve struggled to maintain a healthy weight my entire adult life. For me the most humiliating moment came about 13 years ago when I was visiting an allergist about a skin condition and noticed that he had written “moderately obese” on my chart. At that point, I weighed 245 pounds with a BMI 32.3, well above the standard definition of obesity.

I increased my exercise and started dieting, but my BMI remained stubbornly above the “overweight” threshold of 25. It wasn’t until two years ago that I finally lost enough weight to be considered “normal.” I am quite sure that the reason I succeeded was social support: I joined groups of people with similar goals. I hooked up with a running group locally; these people were instrumental in ensuring I got up every morning to run. And I signed up with a weight loss / fitness web site (myfitnesspal) for online support.

Despite the amazing support I received from these communities, I’ve also noticed that many people in similar circumstances are self-conscious about exercising. Locally, I’ve heard from lots of folks who don’t want to join our running group because it is “too intimidating.” On the myfitnesspal message boards, there are dozens of stories every day from overweight / obese people who won’t go outside to run, or who are uncomfortable going to the gym, because they are worried that others will mock them.

Could it be that the same powerful social forces that helped me get in shape are, paradoxically, preventing many others from participating in exercise? Surprisingly, I haven’t been able to find much research on this question. A 2012 review article entitled Overweight and obese adolescents: what turns them off physical activity? summarizes the state of research on obese adolescents and exercise, but doesn’t touch on adults.

The research shows that obese adolescents are definitely self-conscious about exercise. They avoid gym class because of the skimpy clothes they must wear, or because girls are concerned about messing up their makeup and hair and getting taunted for that. They are worried about getting teased for being overweight and unfit — even when teasing doesn’t actually occur. It isn’t so much that they don’t enjoy PE; they don’t like being “visible” in PE class. They are concerned about how others perceive them much more than their own experience engaging in PE activities.

In a 2008 study led by Margaret Schneider, researchers tried to address these issues by enrolling unfit, sedentary teenage girls in an exercise program. In one school girls recruited for the program were tested and enrolled in a special PE class designed to improve fitness. In another school the participants were tested at the beginning and end of the school year but weren’t enrolled in a special class. The special class included increased physical activity compared to regular PE classes, and also had extra instruction about the benefits of physical activity.

Unfortunately, Schneider’s team found that there was no overall improvement in self-image for the girls who had enrolled in the special class. Perhaps related to this, overall, there wasn’t a significant improvement in fitness, despite the increased activity. In fact, when the researchers broke down the girls into one group that had improved fitness and another group that had not, the improved-fitness group did have an improved self-image and body-image. In other words, once they started seeing results, their attitudes about their bodies improved.

This certainly seems to match my experiences interacting with the myfitnesspal community. New members of the community who haven’t seen improvements due to exercise are intimidated by exercising. But if and when they do improve, their attitude improves substantially. What neither my experience nor the research yet supports, however, is whether it’s possible for large numbers of people to improve their attitudes about fitness and actually permanently change their lifestyles and become healthier.

Maybe the “success stories,” the folks who sustain these communities of fit and healthy people, are simply the lucky few who are capable of staying healthy in today’s sedentary world, saturated by drive-through restaurants, monster-sized soda cups, and jumbo bags of potato chips.

What’s clear to me, however, is that one of the major hurdles a sedentary person must first overcome in order to get fitter is a social one. Maybe it’s even the most important hurdle.

Stankov I., Olds T. & Cargo M. (2012). Overweight and obese adolescents: what turns them off physical activity?, The international journal of behavioral nutrition and physical activity, PMID:

Schneider M., Dunton G.F. & Cooper D.M. (2008). Physical activity and physical self-concept among sedentary adolescent females: An intervention study, Psychology of Sport and Exercise, 9 (1) 1-14. DOI:

Why doesn’t the up/down pacing strategy work?

Posted by Dave on September 30, 2013 | 2 Comments

This past weekend I ran a 15K race and was hoping to achieve a PR — finishing the race in under 60 minutes. It’s a good goal because it’s not only a nice, round number, but it’s also right at the threshold of my abilities. I’ve finished 5Ks in under 20 minutes and 10Ks in under 40 minutes, but I’ve never been able to sustain that pace for any longer race.

To achieve a nice, round, 20-minute 5K or a 60-minute 15K requires the same, not-so-round pace: 6:26 per mile. If a course is perfectly flat and perfectly well-marked, all you need to do is run 6:26 every mile and you can reach your goal.

But of course, most races have hills, and courses are often poorly marked, so runners rely on their GPS watches to monitor pace. But what pace should you run on the hills? Typically in the past I’ve resorted to guesswork. If mile 1 has a big hill, I plan on giving myself a little extra time, and then making that up later in the event. But this event seemed evenly hilly throughout, and most of the hills were short, often a quarter-mile long or less:

I decided on a different strategy: Instead of planning for each mile, I’d just set an uphill pace and a downhill pace. Then all I’d have to do is take a split at the top and bottom of each hill and I could almost run the race on autopilot.

To account for GPS error, I set a goal pace for the entire race of 6:20 per mile. Then I just added 15 seconds for each uphill section and subtracted 15 seconds for each downhill section. Since the race starts and ends at the same elevation, I should have just as much uphill as I have downhill, right?

During the running of the race, I wasn’t quite able to maintain the paces I planned: I was running the uphills a little fast and the downhills a little slow. But I figured that should probably even out and I’d still be okay. Except for one niggling detail: As I ran, I could also track my average pace for the entire race, and that figure kept increasing for the entire event. I was shooting for 6:20 per mile, and it crept up little by little — 6:22, 6:23, 6:24. I was quickly running out of wiggle room for GPS error. As it turned out, I’d need that wiggle room. In the end, my GPS measured the course at 9.46 miles, instead of the 9.3 I was expecting. At that distance, I’d need every bit of a 6:20 pace per mile. My finishing time was 1:00:37; I missed my goal by barely 1 percent. Even though my GPS put my average pace for the race at 6:25, I still didn’t finish in under an hour because of the small GPS error.

But after I got home, I downloaded my GPS record and noticed something interesting: If I took an average of the paces I ran on the uphill and the paces I ran on the downhill, it seemed like I should have been much closer to that 6:20 pace. The average of the paces for each uphill section was 6:31 per mile, and the downhill sections averaged 6:11 per mile, for a net average of 6:21. That might just have been enough to get me my sub-60 15k — especially if I saw I was close at the finish and made a final, mad sprint. When I weighted the averages to account for the fact that there were 5.44 miles of down and only 4.02 miles of up, my theoretical pace improved even more, to 6:20 per mile.

So why didn’t I achieve that pace in reality? It took me a while to figure it out. Imagine a race that runs over a hill and back: There are two ups, and two downs. If the hills are equal lengths, then my strategy works perfectly, even if I don’t run the exact same pace on each hill:


 Here, my average pace on the downhills is 6:30 and my average pace on the uphills is 7:30. You can average those together and get 7:00 per mile for the whole race.

But now consider a course where the hills are unequal in length, like this:



Now the uphills are all each the same length and the downhills are different lengths. Suppose the uphills are 1 mile each — then I averaged 7:30 on all the uphills. But if the first downhill is 1 mile and the second downhill is 2 miles, then I didn’t average 6:30, I averaged 6:40 per mile on the downs, which means my overall average is worse than 7:00 per mile.

That’s what happened during my 15k. The slowest downhill sections were also the longest downhill sections (which makes some sense, since those hills weren’t as steep). Instead of averaging 6:11 on those hills, when I take the length of the hills into account, I actually averaged 6:21! Put that together with my 6:31 pace for my uphills, account for the fact that I ran a longer distance downhill than uphill, and you arrive at my 6:25 average pace, which wasn’t fast enough to overcome my GPS error.

I probably would have been better off just trying to run 6:20 per mile throughout, instead of relying so heavily on the up/down strategy. Of course, an alternative explanation is just that I’m not in good enough shape to run a 60-minute 15k on a hilly course! But either way, I think a straight-up mile-by-mile plan would have been easier to adhere to during the race.

Does Garmin give you credit for the vertical distance you run?

Posted by Dave on July 16, 2013 | Comments Off

If you’ve ever looked closely at a topographical map, you might notice something odd. It’s not actually odd, because there is no other way to make the map, but it does cause some interesting problems. Take a look at this close-up of the USGS map of Half Dome, in Yosemite National Park.

Half Dome’s peak is at an elevation of 8,836 feet, and to the northwest from the peak, there’s a sheer vertical drop of over 2,000 feet. It takes place in just about the width of the “H” in the word “Half Dome” on the map. If you look at the legend, you’ll see that that’s perhaps only 200 feet of horizontal distance representing a 2,000-foot drop!

When slopes get steeper on a topographical map, the contour lines get closer together — but that doesn’t necessarily mean that the physical distance a person covers is actually less. When you climb Half Dome, you’ve climbed 2,000 feet, not 200!

Obviously a runner isn’t going to tackle anything as steep as the face of Half Dome, but even on slopes that are actually runnable, the same problem exists. When you run up a steep hill, you cover more distance than what is represented on a conventional map — even if your entire run is represented as a straight line on the map. So when your GPS trainer tells you how far you ran, does it count the vertical distance you ran, or just the horizontal distance?

The thought occurred to me when I ran a race a couple weeks ago in Squaw Valley, California. The run covered 2.88 miles and climbed over 1,700 vertical feet. But did I actually run farther when you count those vertical feet? My Garmin could conceivably have been off by 1,700 feet — a third of a mile! Did I get credit for the climb?

Unfortunately, it’s not an easy question to answer on most running routes, because roads — especially roads on hills — aren’t usually perfectly straight. Even when they are straight, they don’t often have a consistent incline for their entire length. The rough dirt road I ran up at Squaw Valley was anything but straight!

Ideally, to know whether the GPS gives you credit for those vertical feet, you’d record something like an elevator ride. But I don’t have an elevator handy right now, and I’m not sure I’d get GPS reception in any of the buildings that are nearby. But I do have a GPS record of a ski trip I took a couple years ago. I recorded the whole day of skiing, including the lift rides up. Ski lifts travel in a straight line, and their runs are often at a fairly consistent incline as well. Here’s the map of my day’s skiing:

As you can see, there are several straight lines on the map — they represent my lift rides. The lifts go straight up the mountain with very little change in the grade of their ascent. So we can use our old friend Pythagoras to figure out how far I went on the lift:

The Pythagorean Theorem states that for any right triangle labeled as above, the lengths of the sides a, b, and c are related by the formula a2 + b2 = c2. I picked one lift ride (ending at the marker on the map) and looked at the data for that ride:

So the question is, does the 0.79 miles the Garmin recorded reflect only the horizontal distance covered, or does it take into account the 1,074 feet of elevation gain in the lift ride?

I measured the pixel length of the ride (using the Pythagorean Theorem to calculate the length of the diagonal) and got 314 pixels. The 350-meter scale itself measured 94 pixels (the image has been reduced in size for this post). Using simple proportions, I came up with a map length of 1,170 meters for the lift, or 3,838 feet. Remember, this represents only the horizontal distance covered!

So how does that compare to my Garmin data? Garmin gives the length of the lift ride as 0.79 miles, or 4,171 feet. That’s longer than 3,838, but it’s not 1,074 feet longer. But since the lift ascends at a fairly constant slope, its length should be less than the sum of the horizontal and vertical length.

We can use the Pythagorean Theorem to calculate the shortest possible distance between the base of the lift and the top, assuming the lift went in a perfectly straight path from the bottom to the top. We know from the map that the horizontal distance (a) is 3,838 feet. We know from my Garmin that the elevation gain (b) is 1,074 feet. The length of the lift should be the square root of a2 + b2, which works out to 3,985 feet.

At a minimum, Garmin should have given me credit for traveling 3,985 feet, and it did! It claimed my distance was 4,171 feet. But why the discrepancy? We know that the lift doesn’t travel in a perfectly straight line because the lift cable sags between poles. This sagging might account for the entire discrepancy, or there could be other sources of error.

The takeaway from this is that there’s no way that the Garmin should have measured my ride as shorter than 3,985 feet, even though I only covered 3,838 feet horizontally. It didn’t do that, which suggests it is taking vertical distance into account. If the lift cable sag or a varying rate of climbing were a significant factor, they’d only increase the difference between my Garmin-reported distance and the calculated straight-line distance, and that’s what we see in the numbers. Take a look at this image to convince yourself that in any real-world case, the lift is going to travel farther than the straight-line distance covered:

So it looks to me like the Garmin is indeed giving credit for the actual distance travelled, in three dimensions. To truly verify this, we’d probably need a Garmin plot of an elevator ride or a long rappel, which would be the ideal, straight-line, vertical case.

In the end, though, as you can see, the vertical component doesn’t add much to a typical run. It only added about 300 feet to my very steep 0.79-mile lift ride. Let’s see what kind of an impact it would have on a run.

We know my Squaw Valley race covered 2.88 miles and gained 1,719 feet. 2.88 miles is 15,206 feet. That means I climbed more than a foot for every 10 feet I ran, or better than a 10 percent grade, a very steep run! When we calculate the horizontal distance travelled using c2 – b2 = a2, the result is just 15,108 feet. All that climbing would only result in an extra distance traveled of 98 feet, assuming the pitch of the run was consistent from start to finish. In my case, I’m quite certain it wasn’t — there were even a few downhill stretches — but it’s still clear that the vertical component of the run didn’t add much to the total distance travelled at all.

In a typical road race, 200 feet per mile would be considered a very steep hill. If that hill was perfectly graded, then it would add only 4 feet to the horizontal component of the run. But rest assured that your GPS does appear to take this distance into account (though as we have discussed, there are many other sources of GPS error!).

OMG we’re all gonna die!!!!!eleventy!!

Posted by Dave on May 24, 2013 | 3 Comments

Just a quick post to note this article that appeared in the Wall Street Journal today.

Look familiar? It ought to. The same author wrote this article last year.

Both articles basically say the same thing, and quote the same authorities, citing the same research. The suggestion is that running too much is bad for your health. A moderate amount of running might be helpful, but running more than, say, 30 miles a week, is too much and is actually harmful.

What bugs me about today’s article in particular is the suggestion that “new research” is telling us these things. There is no new research. There is the same old research. And Alex Hutchinson responded quite well to that research when the same author reported on it in the Wall Street Journal last year:

But here, from the actual abstract, is the part they never mention:

Cox regression was used to quantify the association between running and mortality after adjusting for baseline age, sex, examination year, body mass index, current smoking, heavy alcohol drinking, hypertension, hypercholesterolemia, parental CVD, and levels of other physical activities.

What this means is that they used statistical methods to effectively “equalize” everyone’s weight, blood pressure, cholesterol, and so on. But this is absurd when you think about it. Why do we think running is good for health? In part because it plays a role in reducing weight, blood pressure, cholesterol, and so on (for more details on how this distorts the results, including evidence from other studies on how these statistical tricks hide real health benefits from much higher amounts of running, see my earlier blog entry). They’re effectively saying, “If we ignore the known health benefits of greater amounts of aerobic exercise, then greater amounts of aerobic exercise don’t have any health benefits.”

Unsurprisingly, the new article in today’s Wall Street Journal has generated hundreds of comments. What frustrates me is that the Journal is playing on the fact that millions of runners will be interested in this sort of research and drawn to the article thinking that something new is being reported. In fact there is no new research. Indeed, the sort of research that could actually generate authoritative results will probably never be conducted, because it would be very difficult indeed to do a long-term experimental study on this phenomenon. We’ll probably never know for sure whether running, say, 50 miles a week, is more or less harmful than running 20 miles a week. We’ll probably also never see the Wall Street Journal report on that.

Is it best to start slow in a marathon?

Posted by Dave on October 4, 2012 | 1 Comment


One of the toughest things about running a marathon is the fact that if you’re running it correctly, the first half seems almost ludicrously easy. Most runners I’ve talked to — and my own experience bears this out — say that if they feel like they are exerting themselves much at all during the first half, they inevitably crash and burn at the end. A friend of mine, the always-entertaining Allen Strickland, had this experience just this past weekend. He started a bit too fast, and although the first 20 miles felt pretty easy for him, he struggled at the finish and just missed an opportunity to qualify for the Boston Marathon.

Now, it’s probably impossible to say whether the fast start caused Allen to run slower than he wanted to at the end; there are too many other factors at play. But a new study by Andrew Renfree and Alan St. Clair Gibson seems to suggest that starting not just at your target pace per mile, but actually slower than target pace, might be the best strategy.

Renfree and St. Clair Gibson analyzed the pacing strategies of the participants in the 2009 Women’s World Marathon Championship by dividing the finishers into four groups: the top 25%, the next 25%, and so on. They compared the average speed of each group of runners to their speed when running personal-best times (PB). They found that the fastest group did better relative to their PB than the second-fastest group, and so on down the line to the slow group:


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