Thursday, June 23, 2016

Published June 23, 2016 by with 0 comment

How Safe Is Driving In The US?

I noticed an interesting trend in the data...

Note that the analysis below is solely based on traffic fatalities and does not factor in the problems caused by pollution (both particulate and noise) from automobiles. 

Basic Numbers

If we check wikipedia, we find that there were 1.08 traffic fatalities per 100,000,000 miles driven in 2014 along with that value per year for roughly the entire previous century. Converting those to a plot, we get the following:

To get a yearly trend, we can offset by the starting year and get the following:

The trendline there is an exponential fit and actually looks really good. Sometimes it's easier to see a linear fit, so we can convert the vertical axis to a logarithmic one and the exponential fit becomes a linear fit:

Again...this looks quite good. Looking at it, I'd be confident using this as a model. Thus, we can say that driving in the US has been getting exponentially safer each year since we've recorded numbers and it follows this equation:

Using that, we can say that it gets twice as safe according to the following:

That gives us ~21 years. For 10 times as safe, just use 0.1 instead of 0.5 and you get ~70 years. For a yearly amount, just plug in 1 for x and get a bit better than 3% lower risk each year.

This is actually much better than I would have guessed and is pretty impressive to me.

How Does This Affect Life Expectancy?

I don't know of a great way to get an exact value, but we can get a rough estimate. Assume that half of your travel in a car happens before the age of 40 and half happens after 40. Extending that assumption, that would mean that a typical traffic fatality takes away 40 years of life. Given that there's 1.08 fatalities per 100,000,000 miles driven, there's (40*1.08) effective years lost per 100,000,000 miles driven. Thus, you expect to lose 1 effective year for every 2,300,000 miles driven.

Converting that into more manageable numbers, we can say that there are roughly 31,500,000 seconds in a year. Using the result from above, we get that there are 31,500,000 effective seconds of life expectancy lost per 2,300,000 miles driven, or ~14 seconds per mile.

You can use this as a fun way to determine how risky you really think something is. For example...the risk of death from skydiving is ~1 out of each 100,000 attempts. To have a 1 in 100,000 chance of dying in a car crash on a trip, you'd have to drive roughly 1,000 miles (1 death per 100,000,000 miles means you have a 1 in 100,000 chance of dying from driving [100,000,000]/[100,000] miles).

Another quick approximation would be to say that you travel 10,000 miles per year in a car on average. An 80 year lifespan would mean you travel 800,000 miles in a car throughout your life. At ~14 seconds of life expectancy lost per mile, your traffic fatality risk drops your life expectancy by 14*800,000 or 11,200,000 seconds which is about 4 months.

Where Does This Fall Apart?

These are all very gross assumptions and do not factor in a huge number of things...probably most importantly, it doesn't factor in:
  • how drunk are you?
  • what time of day is it?
  • how fast are you going?
  • are you in a safe car wearing a seatbelt?
You could surely improve your odds by not drinking, driving when it's not dark or raining, wearing a seatbelt, etc. Still fun to go through the numbers though.


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