CityLab’s article about our updated map of RunKeeper’s public routes highlighted the visible difference on the map between the shorter, more urban routes that tend to be associated with running and the longer, more suburban or rural routes that are more typical of road biking. Because each route is tagged with its type – not just running and cycling, but also walking, mountain biking, hiking, cross-country skiing, skating, swimming, and rowing, among other categories – we can look more closely at what is a typical route for each of these activity and how much other routes vary from that standard and why.

## The gravity model of travel

Studies of travel behavior tend to assume what is called a “gravity model.” The analogy is that, just as two atoms will only attract each other a quarter as strongly if they are twice as far apart, people are exponentially more likely to travel to places that are close to them as they are to places that are farther away. The idea seems intuitively obvious now, but it came as a surprise to 19th century railroad managers who expected that most of their riders would travel the full length between the major cities at the ends of the lines and instead found that most of their business came from short, local trips in between.

The trouble with gravity models is that, while they are good at predicting how many trips will be made at most longer distances, they give meaningless results at very short distances, predicting infinitely many infinitely short trips as the distance approaches zero. No matter how convenient a destination is, there are limits to how many times you can reasonably visit it in a day.

## Trip lengths in RunKeeper

The RunKeeper routes allow us to look at the distribution of trip lengths across a sample of more than a million trips, shedding some light on how common trips of all lengths are, not just the longer trips that get reported in more traditional travel surveys. The number of RunKeeper routes of different lengths can be approximated with a gravity model, but as the figure below shows, the model fails to predict that the number of very short routes is low rather than high.

*Gravity model approximation of RunKeeper walking trip lengths*

It turns out that for each travel mode, the trip lengths actually tend to fall into a log-normal bell curve, and the gravity model’s power law is just an approximation of the right hand side of the bell. Each travel mode has its own median trip length that is particularly common, and the number of longer or shorter trips falls off to zero in a predictable, symmetric way.

In particular, the runs that are RunKeeper’s primary focus are typically about 4.3 miles long, and 68% of them (one standard deviation below or above the median) are between 2 and 8.5 miles. (Note that because it is the log of the distance that is normally distributed, the variance from the median is multiplicative, not additive. When a long run is about twice as long as a median run, a short run is about half as long as a median run, not 4.2 miles less long.)

Recorded walks, in contrast, are typically only 3 miles, and 68% of them are between 1.3 and 5.6 miles. Cyclists travel much further—typically 15 miles, with a short trip being 5.5 miles and a long one 38 miles. In all these cases, people are probably actually going for an hour rather than for the particular distance that it corresponds to.

In the wilderness, people walk a little further but don’t bike quite as far: Hikes have a median of 4.8 miles, with 68% of them between 2.3 and 9.5 miles, and 14 miles is typical for mountain biking trips, with 68% being between 6.5 and 26 miles. And swims are very short in comparison, with a median of only 1200 meters (0.7 miles), and a short swim of 500 meters and a long swim of 2600.

*Distributions of log of trip length by activity*

## Trip lengths in other large data sets

Other GPS sources verify that log-normal distribution of trip lengths is common, not only a RunKeeper phenomenon. For example, a sample of New York taxi trips forms two bell curves, one for in-city trips (typically only about a mile) and another for airport trips (typically about 10 miles).

It is interesting to compare the RunKeeper routes to other records of travel by the same mode. For example, data extracted from BART’s report on how riders get to its stations reveals that people only tend to walk about a quarter mile (times or divided by 2.3) to a station, compared to the 3 miles people walk with RunKeeper. Similarly, they bike about 1.6 miles to the station (times or divided by 2), compared to the 15 miles that RunKeeper bicyclists ride. In both cases, the discrepancy must be because of comparing complete (and recreational) trips in RunKeeper with partial (and practical) trips that will be completed on transit in the BART report.

## Effects of elevation gain

Running uphill is a lot more work than running on a level surface, so you might expect that runs with more elevation gain per distance would tend to be shorter. However, elevation profiles for each route generated using SRTM elevation data do not show this to be the case. Short routes are no more likely to be steep than long routes are.

What the elevation profiles do reveal is that different travel modes have different tolerances for slope. Running is the least tolerant, with a median elevation gain of only 1.2% of the length of the route. Cycling and walking have an only slightly higher median of 1.3%. Mountain biking routes have almost twice as much elevation gain, though, with a median of 2.4%. And not surprisingly, hiking routes are the steepest, with a median 7% elevation gain and a skewed distribution that puts the peak even further to the right.

*Percentage elevation gain by activity*

## Other factors

The most visually obvious thing about the RunKeeper map is the strong preference that people show for running on shorelines. But are there more total routes along the water, or are the routes longer, or both? While I’m trying to figure that out, please enjoy exploring the map yourself.