Charles Komanoff


Komanoff 2001 letter, "Safety in numbers? A new dimension to the bicycle helmet controversy"


EDITOR,—The recent exchange about risk compensation and bicycle helmets overlooked an important dimension of the issue.1,2 By reducing cycling and, hence, diluting the effect of "safety in numbers", compulsory helmet laws could have the perverse effect of increasing serious injury rates among those who continue to cycle.

Nearly all fatal cycling crashes involve motorists. But there is evidence that the rate of bicycle-motor vehicle crashes declines as the amount of cycling on a road or in a region increases. This "safety in numbers" effect is thought to occur because as cyclists grow more numerous and come to be an expected part of the road environment, motorists become more mindful of their presence and more respectful of their rights.

The implication is that adding cyclists to the road makes it less likely that a motorist will strike an individual cyclist and cause serious injury; and, conversely, removing cyclists from the traffic stream raises the risk to those who continue to cycle. One empirical estimation of this effect, preliminary and site-specific, pointed intriguingly toward a cyclist safety-volume "power law" of approximately 0.6.3

According to this relationship, the probability that a motorist will strike an individual cyclist on a particular road declines with the 0.6 power of the number of cyclists on that road. Say the number of cyclists doubles. Then, since two raised to the 0.6 power is 1.52, each cyclist would be able to ride an additional 50% without increasing her probability of being struck. (The same phenomenon can be expressed as a 34% reduction in per cyclist crash risk per doubling in cycling volume, since the reciprocal of 1.52 is 0.66.)

A confident estimate of the precise value of this safety-volume relationship will require further study, but two other studies report similar relationships, one for cyclists4 and the other for pedestrians.5 This suggests an important thought experiment regarding compulsory helmet legislation:

Suppose that (i) cyclists currently are split between helmet wearers (one third) and bareheaded cyclists (two thirds); (ii) there is no self selection or other confounding difference between bareheaded and helmeted cyclists as regards their risk of injury-causing accident; (iii) a helmet law provokes one third of the bareheaded cyclists to quit cycling, or slightly less attrition than occurred in Australia when cycling helmets were made compulsory6; (iv) all cycling fatalities are motor vehicle related (as is nearly the case); (v) risk compensation does not occur, that is, helmeted cyclists do not ride more adventurously than bareheaded ones; and (vi) helmets are 10% effective in preventing fatalities in the event of crashes, reflecting the modest reduction in severe injury rates found by Rivara et al for 3390 cyclist injuries reported from seven Seattle area hospital emergency departments and two county medical examiners' offices.7

With these assumptions and the foregoing safety-volume power law, it is easy to show that a compulsory helmet law, far from reducing the rate of cycling fatalities, would increase it by 8%. The culprit is the hypothesized 22% decline in cycling volume, which engenders a 16% increase in per cyclist crash risk for all cyclists (since 0.78 raised to the 0.6 power equals 0.86, the reciprocal of which is 1.16). This more than offsets the assumed 10% reduction in fatalities per crash among previously bareheaded cyclists.

To be sure, the model is simple, and the assumptions are at best first approximations. If the "safety in numbers" power law constant is in fact 0.6, then a helmet effectiveness rate over 20% in preventing fatalities (not just injuries) implies that compulsory helmet laws will reduce fatality rates for those who continue to cycle, as claimed. Of course, those who quit cycling will no longer reap the manifold and extensively documented health benefits.

This thought experiment indicates the need to add another dimension, that of "safety in numbers", to the ongoing debate over helmet promotion and policy. It also makes clear the need for further research to measure the precise value of the safety in numbers effect. It may very well prove to be the case that more cycling is better for reducing cyclist casualties than more helmets.


  1. Thompson DC, Thompson RS, Rivara FP. Risk compensation theory should be subject to systematic reviews of the scientific evidence. Inj Prev 2001;7:86–8.[Free Full Text]
  2. Adams J, Hillman M. The risk compensation theory and bicycle helmets. Inj Prev 2001;7:89–91.[Free Full Text]
  3. Leden L, Garder P, Pulkkinen U. An expert judgment model applied to estimating the safety effect of a bicycle facility. Accid Anal Prev 2000;32:589–99.[Medline]
  4. Ekman L. On the treatment of flow in traffic safety analysis: a non-parametric approach applied on vulnerable road users. Lund, Sweden: Department of Traffic Planning and Engineering, University of Lund, bulletin 136, 1996.
  5. Leden L. Pedestrian risk decrease with pedestrian flow: a case study based on data from signalized intersections in Hamilton, Ontario. Accid Anal Prev (in press).
  6. Robinson DL. Head injuries and bicycle helmet laws. Accid Anal Prev 1996;28:463–75.[Medline]
  7. Rivara FP, Thompson DC, Thompson RS. Epidemiology of bicycle injuries and risk factors for serious injury. Inj Prev 1997;3:110–4.[Abstract]