# Does it make sense to bike without a helmet?

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.

## 11 thoughts on “Does it make sense to bike without a helmet?”

1. PJS Inc. says:

Well…. You seem to have completely skipped the part where the author suggests that people using helmets are also more likely to get involved into the serious accidents than those without. He cites e.g. that cars tend to drive closer to bicyclists wearing helmets and posits that there are some injuries that are directly caused by bulky helmets hitting something when without helmet that obstacle could have been avoided. Also he says that some neck injuries are more likely with helmet on than without.

However, the most interesting part for me was the question “why only cyclists?”. There was this one french study from 2006 which said that pedestrians were 1.4 times more likely to have head injuries than cyclists and car drivers (and passengers) are even more likely to have head injuries during an accident than cyclists. I’m not criticizing the use of bicycle helmets, I’m just asking why not force others use them as well?

And then again, where do the diminishing returns kick in? Nobody wants to have brain damage during an accident, but there are other accidents we could prepare us for and still do not. I’m not carrying oxygen bottles in my car just in case I drive into a lake or river and I’m unable to get out immediately. I’m not carrying parachute (and oxygen bottles) while flying just in case I have to jump out from disintegrating plane. Most people would agree that it would not be reasonable to prepare for those, but where do we draw the line? Why are they worried about head injuries during cycling but are in a car without seatbelt (and helmet) or do dozens of other things that are riskier that cycling without helmet?

1. Very valid questions indeed.

1. I would say those effects go into the rebound effect. Certainly they will affect the result. I just didn’t have time to think it completely through… But here too, the real question is about the impact times probability. A helmet might increase the probability of a crash, but it decreases its impact.

2. A good question indeed. I’m actually not sure, but I would say there’s a political aspect to it at least. Forcing everyone to wear helmets all the time would be a, well, Swedish approach. It just doesn’t work in a normal country.

3. This one has a simple answer: people are extremely bad at estimating risk. But authorities and especially insurance companies have huge datasets for determining what are high-risk things that can be solved with simple and cheap solutions. Driving without a seatbelt has such a dramatic and measurable effect on crash survivability that quite simply it’s a no-brainer for society to require it, at least when emergency services and disability are provided by society. Other cases are fuzzier.

In a libertarian society it would of course not be rational to require a helmet or seatbelt (or anything else for that matter), but that would require that crash victims are left to die if they don’t have insurance. No freeloading.

1. 1 – Could you clarify the terminology here: does the rebound effect also count increased risk-taking by other parties? I.e., if the helmet use of a cyclist causes drivers to overtake him/her with smaller clearance, does that still count as rebound?

Regarding point 3 – I would not be all that sure that authorities both had huge datasets AND the inclination to use them objectively. One facet of the “helmet question” is whether the effort to convince bicycle riders (I would be very careful with the word “biker”, that usually means a dude/dudette wearing black leather and riding a Harley-Davidson…) would actually be better spent on campaigning for safer road infrastructure and traffic rules and on educating drivers, cyclists and pedestrians about the current rules.

Especially in Finnish context this is problematic given that in the principal traffic safety agency Liikenneturva the road users are represented exclusively by organizations associated with motorized traffic. This may or may not be the cause of the fact that campaigns run by Liikenneturva considering cyclists’ safety concentrate on a) helmet use; b) underlining that cyclists coming to the carriageway from a bicycle path “as a rule” must yield to vehicles using the carriageway. While technically correct, the latter gives a very skewed picture of the reality faced by drivers and cyclists, and one that is liable to cause accidents.

It would be very interesting to see an in-depth analysis concerning how effective different ways of enhancing road safety actually are. Of course, here there is a choice to be made concerning the measure of safety – for example, should cycling safety be measured in deaths or injuries per year, accidents per year, or deaths & injuries / accidents per cycled km? The former seems to be more favored (obviously, it is a lot easier to determine), but then again it would be easiest to achieve it by directing all resources towards discouraging cycling. Which actually seems, judging by recent projects, the real aim of traffic planners.

Helmet use discussion, especially one concerning risk, should also take into account that cyclists are by no means a homogeneous group. Accident causes (probably also accident rates and risks) are vastly different in, say, commuting in the city (or in suburbs), cycling in a peloton on the highway, or pedaling along a forest track.

1. I pretty much agree with everything you are saying here. (I believe that the rebound effect would indeed include the effects you mention — it’s not really an exactly defined scientific term in any case).

And indeed: a key problem is that there really is no bicycle culture in Finland — all traffic design is done around cars, the rest is given over to worrying over pedestrians. If someone remembers to put in cycleways they do so, but often not (at least in Turku). I’m not quite sure if the concept of cycleway design really even exists here — they’re just put where they fit.

Even so, I’d say it’s important to remember that risk is probability times impact. Changing the cycling culture can certainly decrease the probability of accidents, and it can probably affect what types of accidents occur, but in the end once an accident happens, a person is going to get hurt. At a personal level, it always makes sense to wear a helmet.

However, whether society should enforce that… it’s a more nuanced question. The reductio ad absurdum way to improve safety is to ban all cycling. So it’s important to define a metric, and accidents/km/person is probably what should be measured. Right now it’s not, and it really confuses the issues.

2. I would like to get back to the number crunching part later… okay, I’m lying ;) I just wanted to say that using a helmet is a question people tend to overanalyse or not think at all. That’s my impression. Leave the thinking and just wear the helmet. I don’t even have to draw in the death of my relative (not wearing a bicycle helmet and hitting a moped coming illegally in the way) to say USE THE HELMET! It’s logical, the cost is minimal. I’ve observed that in my town the usage is low, and that all the real bikers use helmet (with just one witnessed exception). Many commuters regardless of their speed, and many kids (!) don’t, especially the ones doing stunts (!). So, thinking on: helmet can be considered a kind of status symbol: I’m a biker! Reversed: if the bicyclist (in traffic law terms) doesn’t have a deeper feeling for bicycling, he/she has no need for status symbols. “I’m just riding to work.” IT DOESN’T MATTER WHY ARE YOU RIDING! There is no logic you can apply here. It’s all just safety considerations, for the best of yourself. I’ve hit my head a few times, the last time was on a solid rock. No bruises, no nothing, just get up and keep going :)

1. Oh, I agree 100%. It’s lunacy not to wear a helmet, whatever the numbers might say. A brain is a horrible thing to waste. But I couldn’t restrain my fetish for trying to calculate things which really can’t or shouldn’t be calculated… :-)

1. And I did my best to not comment on exact the topic nor personally to you. I know from the first chapters that the headline is not enough (I did read something!), or personally. I was just preaching generally. Or should I say “messaging” :) My alias is “somess”, and it’s up to the result.

2. JP says:

Still, fatal and serious brain injuries while cycling are quite rare. My impression from the helmet discussions have been (I don’t have numbers, I admit) that wearing helmet when driving a car or walking would have same magnitude health effect than wearing it when cycling. Maybe you want to crunch the numbers, and tell if walking/driving without a helmet is lunacy too. :)

1. JP says:

Sorry, I did not notice that you already partly answered the question below… I’ll tell that personally I often don’t wear a helmet when cycling, just because I find it somewhat inconvenient. It’s a trade-off between safety and convenience, like many things. I did myself crunch the numbers at one point, and at least convinced myself that cycling instead of taking motorised transport, even in Helsinki center, has a much bigger (positive) health effect than using or not using a helmet.

2. All life is lunacy! :-) The stats are indeed a bit complex. You have to take into account that the populations have very different sizes and characteristics. For example, the very old and fragile don’t cycle but do tend to walk, so they are overrepresented in the walkers that go splat. The numbers are not so much the problem as the interpretation.