# Safety in Numbers Hypothesis for Cycling

Safety in Numbers is a well known hypothesis in cycling safety. Essentially, the argument is the number of injuries per cyclist decreases as the amount of cycling increases [1,2]. Or put another way, the risk of cycling injury increases when cycling amounts decrease.

The mathematical expression for safety in numbers can be written as

$I=I_0\left(\dfrac{C}{C_0}\right)^{0.4}$

where I and C represent number of injuries and amount of cycling respectively. The exponent 0.4 has been suggested by Robinson[2].

Is there evidence supporting this phenomena using NSW hospitalization and cycling participation surveys? The data used can be found here [3,4].

Here are plots of the expected (red dashed line) number of head and arm injuries (left panel) and head injuries only (right panel) if the Safety in Numbers hypothesis is true. The black line represents the observed number of injuries by year.

There is a clear divergence between what was observed and what was expected. Therefore, the evidence does not support Robinson’s safety in numbers hypothesis. In fact, the estimated exponent is 0.94 (95% CI: 0.59-1.30) and suggests increases in cycling is associated with a roughly equal increase in injury.

A more detailed analysis (and other cycling-related analyses) can be found in our peer-reviewed paper[5].

1. Jacobsen, P.L. (2003). Safety in numbers: more walkers and bicyclists, safer walking and bicycling. Injury Prevention, 9, 205-209.
2. Robinson, D.L. (2005). Safety in numbers in Australia: more walkers and bicyclists, safer walking and bicycling. Health Promotion Journal of Australia, 16, 47-51.
3. Olivier, J., Walter, S.R., & Grzebieta, R.H. (2013). Long-term bicycle related head injury trends for New South Wales, Australia following mandatory helmet legislation. Accident Analysis and Prevention, 50, 1128–1134.
4. Australian Bureau of Statistics, 2001. Participation in Exercise, Recreation and Sport 2001. ABS, Canberra.
5. Olivier, J., Grzebieta, R., Wang, J.J.J. & Walter, S. (2013). Statistical Errors in Anti-Helmet Arguments. Australasian College of Road Safety Conference.

## 5 thoughts on “Safety in Numbers Hypothesis for Cycling”

1. Yes, there are a number of unanswered research questions about the Jacobsen safety-in-numbers effect, including:
a) Does it apply in all situations? Is it different in sparse-traffic rural area versus suburban metropolitan settings versus high-traffic density inner-city settings?
b) Does it differ between countries and/or cities?
c) Is it a function of just cyclist numbers, or both cyclist and motor vehicle density or mode-share? In fact, is it a function of mode-share or vehicular density?
d) Is absolute cyclist numbers an effect modifier i.e. is the change in accident rates the same for a shift from 1.0% cycling mode-share to 1.5% cycling mode-share as it is for a shift from 10% cycling mode share to 15% cycling mode share?

and most important of all:

e) What is the direction of causality – do more cyclists cause a safer cycling environment, or does a safer cycling environment cause more people to cycle?

Obviously that last question cannot be answered merely by examination of cross-sectional data.

• That last sentence is incomplete – it should read:

“Obviously that last question [direction of causality] cannot be answered merely by examination of cross-sectional data, as Jacobsen did.”

2. Presumably the relationship between cycling numbers and injuries/fatalities is modified by other factors such as the nature of cycling and road infrastructure, population density, driving culture, etc. This could be why the simple 0.4 exponent doesn’t work in all settings and suggests the possibility of a study to try to separate out the safety in numbers effect (if any) from other factors, i.e. a multivariate analysis.

3. Hi Tim,

Thanks for the response. With those issues in mind, some authors argue against the use of the safety in numbers concept as a means for informing road safety policy.

Bhatia, R. & Wier, M. (2011). “Safety in Numbers” re-examined: can we make valid or practical inferences from available evidence? Accident Analysis and Prevention, 43, 235-240.