In our last “Ask the Experts” article, we corresponded with Danish Engineer, Soren Jensen, to help clarify the findings from his study titled, “Road safety and perceived risk of cycle facilities in Copenhagen”. Local Vehicular Cyclists had attempted to cite the study as reason for not developing bicycle infrastructure. At the conclusion of the article, Soren summarized that if Dallas in fact added Cycle Tracks to its roadways, it would actually see “much higher ridership”, and “greater safety to bicyclists”.

In our dialog, Mr. Jensen referenced an important study from Public Health Consultant, Paul L. Jacobsen, titled, “Safety in Numbers”. This study has been the basis many US and European city planners have cited to increase bicycle infrastructure within their communities. The summary of the study states: “The risk of an individual pedestrian or bicyclist being hit by a motor vehicle decreases as the number of pedestrians or bicyclists increases, respectively.” When combined with the Soren study, which notes that implementation of Cycle Tracks increases bicycle ridership, a correlation can be inferred.

Within our comment section, commenter Steve-A, dismissed the Jacoben study, and linked to a Cycle*Dallas article he’d written citing “random numbers” could be used to achieve the same results. He drew his conclusions using a method noted in an article written by Vehicular Cycling advocate, John Forester, who questioned the study’s findings.

BFOC communicated with Paul L. Jacobsen in California, to explain his study and counter the claims made by Cycle*Dallas and Forester, and followed up once again with Author/Engineer Dr. Lon D. Roberts, to also shine some light onto the dispute.

First will start with Mr. Jacobsen:

Hi Jason,

This question comes up every 6 months or so. There’s a website out there with this argument.

First off, this is not the way I did the analysis. The folks saying the data is manipulated need to read the Methods section of my paper. (http://safetyinnumbers.notlong.com)

Secondly, having a variable on both sides changes the exponent by one, and that’s the issue that matters. The other variables change slightly. The key point is that injury rate is non-linear with the amount of walking and biking. Take a look at Table 1 in this recent paper. Lots of researchers have found the injury rate to be non-linear.

Soren Jensen provided the data used in Figure 2 of my SIN paper.

Best wishes,

Peter

Next up, we asked Dr. Roberts to also review Forester’s argument:

The argument that some have posed that Jacobsen’s “Safety In Numbers” plots can be replicated by calculations involving random number is interesting but perhaps flawed — both mathematically and logically. For instance, the assertion that a plot created by paired data where the X-axis values are represented by the quotient of two uniformly distributed random variables, N divided by C, and the Y-axis values are represented by the quotient of two uniformly distributed random variables, C divided by P, results in a quasi-hyperbolic curve, “similar in shape” to Jacobsen’s, places undue emphasis on extreme outliers on both axes to dictate the shape of the curve. For instance, if N and C are randomly chosen values between 0 and 1, on average, half of the values for N will be 0.5 or less and half of the values for C will be 0.5 or less, if N and C are randomly chosen numerous times. Using Monte Carlo simulation to plot the value of N divided by C for 1000 samples in a run that I did, 75 percent of the values were less than 2, on the other hand the single most extreme value was 973. Since the theoretical values for N divided by C can range from zero to infinity, a computer generated plot of the “best fit” curve may vaguely resemble a hyperbolic function, if you choose to ignore the distribution of the data points, but it isn’t. (For any who are interested in how trend lines and correlation coefficients can be artificially manipulated, I would refer them to Anscombe’s Quartet.)

I think BFOC readers aren’t interested into forays into the statistical stratosphere in the comments, and I would not want to poke at what appears to be a sensitive subject. I noted that the validity of the research really didn’t depend on whether Jacobsen was right or not. What I think we CAN all agree on is my comment on that Cycle*Dallas post, namely:

“We’re thinking of cyclists as analogs to zebras. If there’s a herd of 100 zebras, the lions will get the slowest one. If the herd is 1000 zebras, they’ll still get the slowest one.

“The lesson is, given a choice, you’re better off to be with a biggger herd. If you’re with a given herd, the only useful advice is – ‘don’t be a slow zebra!'”

Adding to that comment here – every day, I do everything in my power to avoid being a slow zebra in the cycling herd, regardless of how many others there are, and what the route choices are. Should anyone strive for less? And yes, my Cycle*Dallas comment DOES suggest there MIGHT be something to the Jacobsen hypothesis, just as with zebra herds.

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[…] noted Soren Jensen’s study of cycle track installation increasing ridership by 18-20%, and Peter Jacobsen’s study of safety increasing with the number of riders. What’s more telling is the fatality rates […]

Hi all,

I will be asking the researchers involved to respond to Roberts and Jacobsen.

Steve A,

With all due respect, I think your “lions and zebras” metaphor, however colorful, is misleading.

Automobiles, even Hummers, are piloted by human beings, not Lions.

I’ve been studying crash causes in extremely granular detail since 1973. I do not find that “lions and zebras” is a useful way to describe the interactions between bicyclists and motorists. Yes, a small fraction of motorists are criminally negligent. Many are clueless. Almost all can be manipulated into avoiding a collision.

By thinking of ourselves as prey animals, we lose the ability to even think about how we can modify the behavior of the clueless to avoid a collision. Therefore, I find this metaphor quite damaging to serious discussion.

I don’t even like the numbers in your metaphor. You mention one in a thousand. Those odds suck. If I had a one-in-a-thousand chance of getting struck by a motor vehicle each day, I would not cycle. The actual odds are much lower than that, so I do cycle.

I typically cycle alone. And probably always will.

You “expand the mode share” advocates won’t ever get anywhere unless you embrace the ways of helping people cycle alone safely. I’ve been spending a lot of time in New York City this year, and most of the time I see cyclists, they are not within 50 yards of the nearest other cyclist.

So what’s this ‘numbers’ nonsense?

Yes, I know… zebras are safer in herds. Fighter pilots are safer in formation. I’m neither a zebra nor a fighter pilot. These metaphors simply don’t begin to describe the roadway environment.

I ride where I’m seen. The human being driving the Hummer sees me, whether I’m alone or not, on Fifth Avenue or Podunk Street. He doesn’t want a collision, so he avoids the collision. What could be simpler?

John Schubert

Limeport.org

schubley@aol.com

610/282-3085

Non-fatal accidents are important too. They cause immense human suffering. My 29 years in accident reconstruction have brought me in touch with entire families blown apart by this fact.

Next: fatal and non-fatal accidents have VASTLY different distributions of causes. If you JUST look at fatal accidents, you will not be paying attention to some very important causes of immense pain and suffering.

Moreover, for you mode share advocates, some relatively minor injuries, combined with close calls, are a major reason to not cycle for many people.

So… you can’t just look at the ‘fatals’ and think that’s good accident prevention.

This is directed at Jacobsen’s statement:

First will start with Mr. Jacobsen:

Hi Jason,

This question comes up every 6 months or so. There’s a website out there with this argument.

First off, this is not the way I did the analysis. The folks saying the data is manipulated need to read the Methods section of my paper. (http://safetyinnumbers.notlong.com) \=============

\Page 207 of Jacobsen’s original paper presents four graphs, all of the type I described. Jacobsen says that he did not do what I described as plotting A/B against B/C. The four plots are of:

1: Relative risk index vs journey to work share

This is Accidents/cyclist vs cyclists/population, as I stated.

2: Injuries/Distance vs Distance/population

I/D vs D/P, again precisely as I described

3: Fatalities/Distance vs Distance/population

F/D vs D/P, again precisely as I described

4: Fatalities/Trips vs Trips/population

F/T vs T/p, again precisely as I described

I do not consider myself responsible for the fact that Jacobsen apparently does not understand what he did.

[…] reduce the accident rate? And a similar consideration of Smeed’s Law. JohnForester.com. [4] Ask the Experts: Paul L. Jacobsen, and Dr. Lon D. Roberts, PhD. Bike Friendly Oak Cliff. [5] Gaffney, D. September 3, 2008. A virtuous cycle: safety in numbers […]

[…] reduce the accident rate? And a similar consideration of Smeed’s Law. JohnForester.com. [4] Ask the Experts: Paul L. Jacobsen, and Dr. Lon D. Roberts, PhD. Bike Friendly Oak Cliff. [5] Gaffney, D. September 3, 2008. A virtuous cycle: safety in numbers […]