# 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.