The blog post “Why it makes sense to bike without a helmet” is giving me a headache. It is wrong, wrong, wrong, yet it’s surprisingly difficult to point out exactly why. The author argues that “if we start looking into the research, there’s a strong argument to be made that wearing a bike helmet may actually increase your risk of injury, and increase the risk of injury of all the cyclists around you.”
The author essentially argues that by sacrificing some personal safety now, he can improve the safety of everyone in the future. That is a laudable attitude. But is he actually doing that? I am becoming more and more interested in cycling safety as I am turning greener and greener. Thus, this needs to be analyzed out. A faulty argument in favor of a good cause is not acceptable.
The author cites an impressive number of statistics, but the arguments seem to be quite simply invalid. Correlation and causality have been confused, and so on. Multiple errors. It would be easy to shrug it off, but the post has been shared and discussed widely.
Also… it’s way too lazy to just sit on the sidelines and criticize. The author bravely went out on a limb and said something controversial, even though it seems he’s completely wrong. So, here’s a counterquestion that respects that bravery: are there any conditions under which he would in fact be correct?
The logical chain
Here’s my reconstruction of the main logic of the blog. These are not the exact claims of the author, but something that can be inferred from the text. The mathematical additions are mine.
1. Helmets decrease the risk of serious injury, if a cyclist has an accident. This is a Bayesian variable: p(S|A). p(S|A) is smaller if one wears a helmet. The probability of severe injury is then p(S)=p(S|A)*p(A)
2. Currently, the probability p(A) of being in an accident is relatively high when cycling. For someone who cycles a lot, it is probably in the range of 1% per year (my estimate).
3. If cities were optimized for biking, the probability of an accident p(A) would be much lower than it is now. Biking might not be any more dangerous than driving a car or walking. At that point, it would be irrelevant whether or not one wore a helmet.
4. To force cities to be optimized for biking, one must motivate the maximum number of people (N) to cycle for maximal amounts of time (T); that is, maximize the amount of cycling, C=N*T. The larger C is, the smaller p(A) will be. For future reference, note that C can be considered to be general measure of how attractive cycling is perceived to be.
We don’t really know how to model the effect. However, for lack of a better model, we could assume that it follows the exponential distribution p(A)~f(λ,C)=λ*exp(-λ*C) which has mean 1/λ. Since we can scale the constants freely, let us set λ=1. Then, the current probability of an accident is P0=exp(-C0). We want to evaluate how the probablity changes as C changes.
5. Mandatory helmet use is likely to decrease both the number of cyclists, and the time used for casual cycling. We can call this the F-factor, as in “F you”, where F<1. Then the accident probability given mandatory helmets is p(F)=exp(-C0*F) = P0^F.
Rough estimate: if the current personal probability of an accident per year is 1%, and a mandatory helmet decreases cycling by 10% so that F=0.9, then the mandatory helmet would raise the personal probability to (0.01)^(0.9) or 1.6%.
6. Therefore, mandatory helmet use will slow down the target of creating a biking-optimized city, and increase the probability of being in an accident. Up to here, the arguments may actually be valid. However, now it starts to break down.
What is missing 1: Going from big F to little f
There is a problem here. Whether an individual wears or does not wear a helmet does not have any bearing on whether the government does or does not make helmets mandatory.
The author seems to imply that using a helmet is “giving in”: it is a signal to society that cyclists can be trampled on. This sounds vague, but let’s model it in any case. We could consider such an effect to be similar to the F-factor, in that it makes cycling less attractive to everyone. We can even model it similarly, calling it small f.
Using a helmet would thus increase the probability of being involved in an accident to P0^f. Note that by our definitions, f is larger than F; a small effect means that the value of f is close to 1.
What is missing 2: going from probability to risk
Why does this sound completely unsatisfactory? Because we are missing something crucial. We really need to look at risk rather than probability alone. Risk is the product of the probability times the impact (almost literally, in this case). We can call this damage parameter D. (The units could for example be the cost of emergency brain surgery).
The amount of damage we can expect in an accident depends on helmet use. With a helmet it is D0, without a helmet it is D1. Set D0 to 1 for simplicity. We know that D1>>1. For very serious head injuries, which really are the crucial ones, D1 might be 10 or more.
We can then calculate a damage matrix. The calculation is identical for small f.
The values a-d are the damage we can expect within the given time period for that scenario. To get some grasp if the values, we can set P0=1%, F=0.9, and D1=2 (a very low value).
Clearly, wearing a helmet causes less damage in all scenarios. However, here is the most interesting question: are there any conditions in which a<d, that is, driving voluntarily without a helmet is safer that driving with a mandatory helmet? We need D1*P0<P0^F, or F < 1+ log(D1)/log(P0). For the sample values above (P0=1%, D1=2) we require that F<85%. If we assume a more realistic D=10, we require F<50%.
Thus, it is possible to envision scenarios in which driving without a helmet is safer. But are these credible scenarios? We would have to assume that mandatory helmets would decrease cycling by tens of percent (even 50%). Possible, but unlikely.
Even more problematic for the author’s case, we would have to assume that the peer pressure of voluntary wearing of helmets would have an effect that is similar to mandatory helmets. Perhaps, but it cannot be as large as the effect of mandatoriness.
There are in fact other arguments against mandatory helmet use. For example, there is a very real phenomenon called the rebound effect. In this case, if safety is improved by a passive solution such as a helmet, then people tend to engage in riskier behaviors because they feel safer doing so. The end result is that safety is not enhanced; it may even be decreased if the perceived improvement is much larger than the actual improvement.
However, this is not really considered in the blog. The core question is: by choosing to cycle without a helmet, is the author significantly increasing the future safety of others, and also by extension himself? Crunching the numbers: no.
Basically, the author is suggesting a massive and highly likely personal sacrifice, for a fairly small and fairly hypothetical improvement. Such a tradeoff is heroic, but it really does not make much sense.
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