The Math of Self-Driving Cars

Take a look at this video, of Google’s Self-Driving Car :

When I first saw it, I thought “Wow!”

Later, I thought “Wait a second….”

The speaker paints a dream picture – cities full of self-driving cars, saving fuel, saving the environment, and – most importantly – saving millions of lives. The video quotes the statistic that over a million lives are lost each year due to road accidents worldwide. The speaker expects that self-driving cars could eliminate road accidents.

But are computers better drivers than people? Google’s car has driven for 140000 miles so far, without incident. No accidents, certainly no fatalities. It sounds impressive, but is it?

Let’s do the math!

Looking up Wikipedia, we find that in the United States, there are 8.5 fatalities per billion kilometers driven. That’s only 13.7 – just over a baker’s dozen – deaths per billion miles. Now Google’s car has driven 140,000 miles. In that distance, the probability of a normal human driver being involved in a fatal accident is less than 1 in 500.

So, oops! The math says – Google has a lot more testing to do before they can claim their car will save lives. They seem to know that – they have said they have no plans to even try to commercialize the technology. If they are very sure it works, but want to prove it, they’ll have to do one of the following :

  • Try to make their case based on non-fatal accident rates
  • Build more cars so they can add up the miles faster
  • Keep on driving for a looooooong time
  • Take the car to a country with really high accident rates, and test it there.

Most countries don’t publish statistics on deaths versus distance driven. Of those that do, the United Arab Emirates seems to have the worst safety record, with 310 deaths per billion kilometers (500 per billion miles). At that rate, a normal driver travelling for 140000 miles has a 1 in 14 chance of being in a fatal accident. A small fleet of self-driving taxis doing the rounds in Abu Dhabi should prove their point in a relatively short time.