Monday, November 19, 2012

Bicycle helmets III

Last post about bicycle helmets, I mentioned that their defenders talked about risk reduction, but never brought out any actual risk numbers.  So let me do that now.

Before I start, let me ask you: how low would the risk have to be for you to withdraw your recommendation that I wear a helmet?  You can't insist on zero, because then you'd have to wear a helmet as a driver and pedestrian.  So you must have some minimum risk level in mind.  Maybe not a real number, but an intuitive idea.

So, let me ask you: suppose a helmet saved 100 lives, per million people, per year.  Is that low enough that you'd realize it's not worth it?  What about 50 lives? 10 lives? 1 life?  Half a life?  One-tenth of a life?

Think about it, before you read on and I look at some actual data.


During a Google search, I found this Coroner's Report from the Province of Ontario, that looked at all bicycling deaths over a five year period, 2006 to 2010.  I'm sure there are other sources of data, and I expect the numbers to be roughly the same.  (In any case, I haven't analyzed many multiples of sources and picked the one most favorable to my argument.  And, indeed, even if the numbers were off by double, or half, I don't think it would make that much difference.)

In that five year period, there were 129 cycling deaths in Ontario.  The report breaks them down in a number of ways, including by helmet use.  It says:

"In this Review, only 34 of 129 cyclists (26%) sustaining a fatal injury were wearing a helmet. Of particular concern was that observation that, despite existing legislation, only 1 of 16 cyclists (6.25%) under the age of 18 who died were wearing a helmet.

"In 71 of the 129 cases (55%), the cyclist sustained a head injury which caused or contributed to their death. In 43 of those 71 (60%), a head injury alone (with no other significant injuries) caused the death. Those whose cause of death included a head injury were three times less likely to be wearing a helmet as those who died of other types of injuries."

As an aside, I find the presentation a bit biased ... it seems more an attempt to promote helmets than to give us the actual data.  I'd expect that in an op-ed or an internet comment, but not in a coroner's report.  (And, what's with "three times less likely"?  Taken literally, that means that some people were brought back from the dead.  I'm going to assume they mean "one-third as likely.")

Anyway, I had to solve a couple of equations to get what must be the real numbers:

-- of those who died (at least partially) of head injuries, 10 of 71 (14%) were wearing helmets.

-- of those who died of other causes, 24 of 58 (41%) were wearing helmets. 

That makes the numbers work out: 41% is around three times 14%.

So, how many lives would helmets have saved? 

Well, if helmets had nothing to do with head injuries, we'd find 41% of riders who died from head injuries had been wearing helmets.  We'd still have 10 deaths from the helmet wearers, but now we'd have only 14 non-helmet wearers (that is, we'd have 10 of 24, rather han 10 of 71).  So, the extra 47 deaths would have been averted by helmets.

(This is consistent with other reports that helmets cut deaths by 30 percent: 47 deaths out of 129 works out to 36 percent, which is close.)

Those 47 deaths were over five years, so around 10 deaths per year.

The population of Ontario is about 13 million.  So, the annual death risk from not wearing a helmet is around 1 in a million.  Not everyone is a bike rider, though, so let's maybe call it 1 in 250,000.


To put that in perspective: for driving, the death rate in Canada is 9.2 people per 100,000, which is around 1 in 11,000.  You're around 20 times more likely in a car crash than you are to die a non-helmet-related death in a bike crash.

Therefore, the increase in safety from wearing a bicycle helmet is the equivalent of improving your driving safety by 5%. 

A more intuitive way to equate the risk is by driving distance.  There are 8.2 fatalities per billion miles driven.  To get the equivalent risk of riding helmetless for a year -- 1 in 250,000 -- you only need to drive 487 kilometers -- once.  That's 300 miles.  One five hour drive.

I drive from Ottawa to Toronto around once a month, for about 500 miles.  To those of you who are scared for my helmetless head: why aren't you scared about my monthly trip?  Why aren't you also demanding that I take a plane, or a train?

For those of you who worry about my helmetless head costing tax money in medical care ... if I eliminate one trip to Toronto, will you now be happy, since I'm actually saving you more money than if I wore a helmet all year?


Now, you might say, a 5 percent increase in driving safety is a lot!  Well, you want to know an easy way to increase driving safety by 5%?  Don't drink.

The legal breathalyzer limit, most places, is .08%.  In Ontario, they take your license for a day if you blow over .05%. 

But, .03% is perfectly fine.  Aside from the most rabid MADD activists, nobody's going to demand you take a cab at .03%, which is just a couple of drinks.  They'll just say, "be careful".

Well, those two drinks increase your risk by more than 5 percent.  You can see why, if you criticize me for not wearing a helmet, when you happily drive home at .03%, I'm going to be irritated at your double standard.

Oh, and when I say "more than 5%", I mean, according to this study (.pdf), 190%.  In that light, I'm sure even ONE beer will increase your risk more than 5%.  If you assume a constant risk increase (like compound interest), a level of .01% raises the risk 43%.  That's not even a whole beer ... well, maybe a whole beer in Oklahoma supermarkets


The Ontario report also notes that in 21 of the 129 deaths, the cyclist was encumbered by unwieldy cargo, like shopping bags hanging from the handlebars.  That's 16 percent of deaths.

My own observation is that far, far fewer than 16 percent of cyclists are doing that.  Let's suppose it's 8 percent, which is probably still too high.  That would suggest that shopping bags increase the risk by around 100%.  Actually, it's probably much more than that: if you're wobbling about with groceries, you probably aren't out for a 25 mile ride.  I bet the risk is at least triple.

Helmetlessness, on the other hand, is only around 40%.  

Oh, and, by the way ... I don't ride encumbered.  I have panniers.  So you can reduce my risk by 16 percent right there.


Here's the breakdown by what the dead cyclist hit:

102 - Car/Streetcar
15 - Nothing
2 - Other bike
2 - Train
1 - Pedestrian
3 - Unknown

It looks like cars are the main danger, doesn't it?  Suppose you don't drive on roads much, just on bike paths (like I do).  You'd think the risk would drop by 80 percent.  That is: driving on roads is 300 percent riskier than driving off road.

I see lots of cyclists using the road, when there's a perfectly good bike path right beside them, that goes roughly the same place.  Why aren't you upset about their risk?

More important for me, you have to discount *my* risk?  Instead of 1 death in 200,000 per year, it's probably ...  well, it's probably around 1 death in a million per year.  Generally, I'm only on major roads when I'm crossing them, or using them to get from one bike path to another. 

So, even if I had been riding my bike, without a helmet, since the birth of Jesus ... I'd still only have had a 1 in 500 chance of being killed, in that time, by my bare head.


Last post, commenter Swoods made me realize that we can quantify the risk pretty well.  Economists have studied the value of a life, in terms of how much extra money people are willing to give up, or earn, for a given probability of death.  (Like, for instance, coal miners, who have a higher risk than, say, gardeners.)

A typical number is $6,000,000.  That sounds reasonable. 

(For instance: there are around 47,000 underground coal mining jobs in the US.  Thirty deaths a year is typical.  At $6 million per death, miners would have to earn an extra $4,000 or so to compensate them for the risk.  That doesn't seem out of line.

Other such calculations come up with similar, reasonable numbers.)

Suppose my helmetless risk is 1 in 500,000.  That's $12 a year.

But, to be honest, I probably value my life at more than $6MM.  So let's double it, to $24.  Let's double it again, to take injury into account, instead of just death.  Now we're at $48.

I'm willing to accept that.  It's not an unreasonable risk I'm taking, at all, $48 worth to not wear a helmet. 

In fact, I bet if someone invented an invisible "force field" helmet, that let you get all the safety of a helmet without having to wear one -- and it was $48 a year -- many of you would buy it. 


It occurs to me, as I write this, that this is perhaps a reasonable framework for deciding what risks are OK and which aren't.  Look at the cost to the risk-taker, and the benefit.  $48 a year for helmetlessness is cheap.  $4800 wouldn't be.  I'd probably be willing to consider helmet laws if the risk were 100 times as high. 

According to this story, not wearing a seat belt makes you 47 times as likely to die in a car crash.  That gives you a 1 in 100 chance of dying per year, assuming you drive 25,000 km.  That's huge, much higher than I would have expected.  It's $60,000 worth of risk, compared to only $1,230 for the rest of us.  

So, I can see why you might want to nag a loved one who won't use his seat belt, and even pass a law.  It's over a thousand times different.


The numbers show that the risk of riding without a helmet is quite low.  

In terms of added risk, it's 8 times as "riskier" to have a beer before driving.  It's more than twice as "riskier" to ride a bike at all (compared to staying home).  It's probably twice as "riskier" to speed in a car by 5 mph.  It's ten times as "riskier" to let your teenager drive you to the mall, instead of you driving yourself (same .pdf as before).  And it's more than 100 times as "riskier" to not wear a seat belt, which is the activity that it's most compared to.

Even if you never do any of these things -- and, by the way, I won't believe you if you tell me you don't -- I'm sure I can find other things in your life that are riskier than riding without a helmet.  Your diet, your sex life, your hobbies, your vacations ... you take comparable risks all the time.

So, again, why are you picking on bicycle helmets?  Why are your risks OK, but not mine?

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At Monday, November 19, 2012 12:12:00 PM, Anonymous Alex said...

Your invisible helmet comment reminded me that there is such a thing, or might be soon: . My guess is that it'll cost more than $48, but assuming it lasts multiple years it could still be worthwhile.

At Monday, November 19, 2012 12:18:00 PM, Blogger Swoods said...

Quibble: it's not just your burden and your benefit. The utilitarian analysis inclues the burden and benefit on all of society. So the "burden" could also be born by anybody who is adversely affected by your having to wear your helmet (say, somebody who has to listen to you complain about it). More realistically, the "loss" includes all of those who benefit from your existence, like the people who depend on you, the people who buy the things you output, and the people who sell you the things you consume.

A lot of times you're going to bear almost all of the burden and the loss and the rest is going to be spread thinly among a lot of people, so a lot of times we can consider those things to be de minimis (although in the case the loss to a person's family certainly seems more than negligible). Paternalistic intervention in a hermit's life is less warranted than in the average person's.

At Monday, November 19, 2012 12:19:00 PM, Blogger Phil Birnbaum said...

Alex: cool! That would be great in the winter, when you'd be wearing a scarf anyway.

At Monday, November 19, 2012 12:22:00 PM, Blogger Phil Birnbaum said...

Swoods: OK, but then you have to consider the burden on all of society for EVERY risk. My point is mostly comparing helmetlessness risk to other forms of risk, so the ratios stay the same.

BTW, do you really want to burden everyone with everyone else's expectations? Do you want to stop men from being gay because of the loss to wedding dress makers?

Do you want more restrictions on more popular people? That's what you're implying. Also, do you want to limit the risks doctors can take because their death would cost society more than the death of a construction worker?

At Monday, November 19, 2012 1:22:00 PM, Blogger Swoods said...

Exactly. This is the way you should approach policy making. It's easier to see when you're talking about a quantifiable risk like wearing or not wearing a helmet, but it also applies where we're not talking about the risk of life or death.

Many, many times you're not going to have sufficient information to actually figure out the answer, which as I said on your last post is why we presume liberty because it's the superior default position.

But a lot of times when you're doing this analysis the liberty-enhancing alternative wins anyway because of the value of that liberty.

Should we keep doctors from driving because the odds that they're going to save lives in their careers are substantial? Of course not: the burden on society of not allowing a competent person to drive are huge (most of that burden, again, is born by the doctor himself but it could also be born by, say, that person's children that he can't drive around); it's almost certainly far greater than the probability that people are going to die because the supply of doctors has shrunk by one multiplied by the value of those lives.

Should we keep gay people from getting married because, say, some religious people are offended by it (I'm going to use that because I don't think any wedding dress makers would lose business if gay people were allowed to get married)? Of course not: the cost of not allowing certain people to get married is certainly far greater than the odds that someone's going to be offended multiplied by how much they're offended.

In the case of seat belts where you have good information you can probably overcome that presumption. In most cases it's much more difficult.

At Monday, November 19, 2012 5:32:00 PM, Blogger Millsy said...

"Not everyone is a bike rider, though, so let's maybe call it 1 in 250,000"

You guys in Canada must make much more use of bikes than us in the states.


At Tuesday, November 20, 2012 6:16:00 PM, Anonymous TB said...

If you read the coroner report really fast, it almost looks like wearing a helmet increases your chances of dying from non-head related injuries.

At Wednesday, November 21, 2012 8:35:00 AM, Anonymous Anonymous said...

You lost me at the 1 in 4 people ride bikes comment.

Makes the whole article meaningless.

At Wednesday, November 21, 2012 8:41:00 AM, Blogger Phil Birnbaum said...

Anonymous, why does "1 in 4" make the whole article meaningless? If you change it to some other number, and update accordingly, what suddenly becomes "meaningless"?

At Wednesday, November 21, 2012 10:44:00 AM, Anonymous AB said...

Here are additional victim data from the Coroner's report and their implications.

55% (71 of 129) either wore helmets or died of causes other than head injuries. A public helmet policy addresses only 45% of the fatalities and doesn't address accident prevention at all.

33% (30 of 90) on whom alcohol and drugs toxicology tests were performed returned positive indicators. Other research has found an association between alcohol impairment with non-helmet use.

23% (29 of 129) did not involve a motor vehicle and thus would not be addressed by cycling specific infrastructure such as off-road bike paths. .

74% (92 of 126) of the fatal crashes either wholly (44) or partially (48) were attributed to the action of the cyclist. 64% (81 of 126) either wholly (33) or partially (48) were attributed to the action of the motorist. Most involved traffic infractions. These data clearly show that modification of driver and cyclist practices offer the greatest potential for crash prevention. Even without modification of motorist behaviour, cyclists themselves can reduce their risk significantly by abiding by the rules of the road and by acquiring and practising basic cycling skills.

For those doubtful about the "1 in 4" figure, Stats Canada's survey states that 11.4 million Canadians aged 12 and over reported bicycling during 2009: Stats Can source

Related article

At Wednesday, November 21, 2012 10:00:00 PM, Blogger Phil Birnbaum said...

AB: interesting site!

At Monday, November 26, 2012 9:54:00 AM, Anonymous Mike said...

Phil, great piece. The 1-in-4 surprised me as well, but certainly agree that it has no bearing on the overall result of the analysis. Really awesome post.

At Monday, November 26, 2012 10:42:00 AM, Blogger Phil Birnbaum said...

Thanks, Mike! Further to the 1-in-4 ... the site below says that 27.3% of the population 16+ rode a bike at least once in 2002. Assuming that nobody under 7 rides, and 90% of people ages 7-15 ride, the overall number should be around ... 34 percent, maybe?

That includes very casual riders. So 25 percent for "typical" riders seems reasonable. If I had to do it again, knowing the reaction here, I might do 20 percent instead. But it doesn't make a lot of difference to the argument.

At Monday, November 26, 2012 10:57:00 AM, Blogger Phil Birnbaum said...

Forgot the link!

At Monday, November 26, 2012 11:15:00 AM, Blogger Phil Birnbaum said...

But, now I notice I rounded 13 million people down to 10 million, so I probably *was* using around 20 percent. Again, not that it really matters.


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