Tuesday, February 28, 2012

The math of rear car cameras

It seems as if all media outlets, not to mention most lawmakers and laypeople, lack a grasp of basic arithmetic. Perhaps that's why so many people make absurd statements like "you can't put a price on a human life". Oh really? Then why don't we prevent every preventable death? 8.8 million children die before their fifth birthday and I'm sure most of the deaths are preventable, so why don't we stop those deaths? Obviously, it's because saving their lives costs more than we are willing to pay. It's considered just too costly to save them. The same goes for every homeless person who dies in the snow, and everyone that dies because their medical treatments cost far more than they can afford.

In most preventable deaths worldwide, I'm guessing lifesaving measures would probably cost under $100,000 per person, and probably much less for children. But instead of going after the low-hanging fruit, we prefer to find the most expensive ways to save lives. The worst example of this phenomenon is no doubt the War on Terror, which, if you count Iraq*, must have cost at least a trillion dollars by now and has caused far more deaths from terrorism than it has saved (mostly in Iraq).

* (I realize Iraq was not part of the war on terror if we are to be honest, but without the War on Terror the Bush Administration would not have been able to convince the media and the public that we needed a war, so it deserves at least some of the blame... but if my reasoning is in error, simply think about the cost of the TSA instead of Iraq.)

So it's irritating every time the media reports a story about a program that would cost a lot of money to save a few lives, without giving any hint as to how much value we would be getting for our money, and it's irritating everytime lawmakers pass a law without any real cost/benefit analysis. I heard that airbags cost $1000 per car (or was that per bag?), that the number of lives they save is apparently minimal among those like me that already use seatbelts, and that airbags can actually cause injuries and deaths of young children. But that didn't stop the Canadian government from mandating them on all new cars, which of course cost me money personally when I bought a car.

So now U.S. government regulators want to mandate rear-facing cameras in all new cars to reduce injuries and deaths from cars going backwards. The article I saw about this, like virtually every article from the mainstream media, didn't translate the numbers into a form I could immediately understand.

So here are the numbers. The estimated cost of the rule change is $2.7 billion per year or $160-$200 per vehicle, a cost that will surely be passed onto the buyers. And "regulators say that 95 to 112 deaths and as many as 8,374 injuries could be avoided each year by eliminating the wide blind spot behind a vehicle".

First of all, when I read that I am immediately curious whether the text actually means what it says: is 8,374 (A) the number of injuries that would be prevented per year, or is it actually (B) the total number of injuries? Although "as many as 8,374 injuries could be avoided" sure sounds like (A), I have seen so many news articles carelessly misrepresent statistics that I'm sure the true meaning could easy be (B), because when it comes to numbers, I have developed a sense that reporters are very, very lazy people. Yes, perhaps this particular reporter is good with numbers, but I have no way to know that.

If the meaning is actually (B), the actual number of injuries prevented might just be half of 8,374, or so, since not all drivers will become much safer just because they have a camera in addition to the three mirrors and rear window they already have. Likewise I am automatically led to wonder where number $160-$200 came from: is that cost distributed among all vehicles that don't already have a rear camera? Or is it distributed among all vehicles, even ones that are already sold with a rear camera?

So what's the cost here? Well, admittedly it's hard to decide how to explain the value proposition. What is the relative worth of saving a life compared to preventing an injury? If we assume that saving a life is worth ten (10) times as much as preventing an injury, then what we are buying for $2.7 billion dollars is as follows:
  • $286,800 to prevent each injury (times 8374 injuries)
  • $2,868,000 to prevent each death (times about 104 deaths)
Or if we assume that saving a life is worth 50 times as much as preventing an injury, the results become as follows:
  • $198,900 to prevent each injury (times 8374 injuries)
  • $9,945,000 to prevent each death (times about 104 deaths)
Anybody with basic math skills and a calculator can work this out. Admittedly it's a bit more complicated when you have to decide how much of the $2.7 billion to count toward injuries and how much to count toward deaths, but even in the simplest cases the media doesn't make any effort to communicate the costs in ways that are easy to understand. Now that you can see the cost, you might think twice about supporting this proposal.

Another way to look at this is comparing the number of lives saved to the number of cars with cameras, in order to determine the individual chance that you'll kill someone while backing up. There are 254.4 million registered cars in the U.S.. Comparing this to the expected number of injuries prevented, it seems that the chance you will, during your lifetime, not personally injure or kill someone while backing up because you have a government-mandated camera that you would not have chosen to buy yourself is close to zero. I can't actually calculate the chance, however, without knowing how many additional cars must be fitted with cameras in order to prevent the 8374 injuries (it must be less than the full 254.4 million.)

Now, maybe you think $2.9 million to $10 million dollars is a reasonable price to pay to save a single life of a middle-class person, and that $200,000 to $287,000 is reasonable to prevent a single injury. Personally, I disagree, I think the price is too high in this case, although at least there's the side benefit that we'll all have these cool display screens in our cars, and a little most peace of mind. It seems to me that in cases like this where the cost/benefit ratio is poor, the government should not be forcing everyone to spend more (or buy used).

And what about alternatives? A rear camera plus a LCD screen is not the only way to reduce injuries and deaths. It might be cheaper to use infared or radar sensors plus a warning sound (or even automated braking) to tell drivers when they are about to hit something. If an automaker wants to use this approach instead, will it be allowed to? But the humble New York Times did not consider the issue.

In any case, I wish our media would put a little more effort into their coverage and take a little time to break down the numbers for us. But you know what? They won't. So we would be wise to learn how to use a calculator ourselves.


Simon said...

According to Kia (used in the article) : The rear-camera display and back-up warning system are not substitutes for proper and safe backing-up procedures.

I was taught that when you reverse the car you ensure that all is clear. If that means getting out and walking around it so be it. If you have a toddler you should be even more cautious - where are they.

These cameras are an aid not a substitute for Mark I Eyeballs. You will react faster by actually looking as opposed to using your mirrors. If you cannot actually see out the back of the vehicle and rely on your mirrors all the more reason to get out and verify.

If the suggested cost is under 200$ a car then that would appear to be a lot cheaper than if you add one currently as an extra. I would guess it is a made up figure working on the fact that once it is law they can be mass produced and competition will rise.

I am not certain I follow your thinking on the cost per life/injury. This is not a cost being born by the 'Companies' in millions. It is a cost being born by each of us in hundreds - the cost of fitting the device at manufacture.

I wonder what the insurance pay-outs are for all those deaths and injuries (money that we, as assured, would save on our premiums).

The numbers are somewhat immaterial and are probably as you suggest fairly random in anycase. I would propose that if you asked any parent who had reversed over their child if they thought that 200$ was a reasonable price to try and prevent such accidents they would say yes.

But regardless of the cost it wont benefit careless drivers.

Qwertie said...

Sigh. Well, there will always be some for whom relative costs, opportunity costs, and aggregate costs mean nothing... insurance seems like a good point though (not that it could possibly cost as much as the cameras.)

An alternative to the nanny-state "you buy a car with a rear camera or no car at all" would be to force manufacturers to offer a camera+screen at a more reasonably price than they normally do, e.g. $250 or less in models where it is optional, to eliminate the problem of overpriced dealer add-ons. (In the event that the government-mandated price is below cost, the manufacturer can still comply; they would simply be forced to raise the base price slightly.)