# Tesla Fires Are Not Less Common Than Gasoline Fires

November 19, 2013

Three recent fires in Tesla Model S vehicles have prompted national news coverage, as well as indignant responses from Tesla's CEO. On the official Tesla blog, Elon Musk argued that the media coverage has been unfair. Teslas, he points out, have experienced fewer fires per miles driven (and fewer fires per vehicle) than gasoline vehicles. Furthermore, Tesla accidents have resulted in zero injuries or fatalities on account of fires, compared to hundreds of fatalities that occur every year on account of gasoline fires.

Elon may be a brilliant engineer, but he's a shoddy statistician. If you analyze the available data properly, you'll find that Teslas are statistically indistinguishable from gasoline cars. Let's take a look at the numbers.

## Claim #1: Teslas Experience Fewer Fires Per Mile Driven Than Gasoline Cars

First, we can do what Elon did in his October 4 post, which is to calculate the raw ratio of miles driven to vehicle fires for gasoline cars and Teslas.

Gasoline
Avg. gasoline-fueled miles driven per year, 2006-20102,989,054,000,000
Avg. gasoline car fires per year, 2006-2010152,300
Ratio of miles to gasoline fires19,630,000
Tesla
Number of Tesla-powered miles driven to date~100,000,000
Number of Tesla car fires3
Ratio of miles to Tesla fires~30,000,000

Note that there had been only one fire as of Elon's October 4 posting. As of this writing, there have been three, so we use figure that instead. Still, based on the data — with a 50% higher miles-to-fires ratio, Teslas are safer, right?

Wrong. The problem is that three fires aren't a whole lot of data to go on. At this rate, there could be three more fires next month! So let's calculate a 99% confidence interval using my old pal, the Wilson score interval.

Plugging in numbers...

Confidence intervals
Ratio of miles to gasoline fires19,500,000 – 19,760,000
Ratio of miles to Tesla fires~8,400,000 – ~130,000,000

Oops! Looks like the figures for gasoline are well within the 99% confidence interval for the Tesla. For good measure we can do a chi-squared test. This gives a p-value of 0.35not statistically significant.

Verdict: The claim is false. On a per-mile basis, the number of Tesla fires per mile is statistically indistinguishable from the number of gasoline fires per mile.

## Claim #2: Tesla Drivers And Passengers Are Less Likely To Be Injured In A Fire Than Their Gas-Guzzling Counterparts

We'll do the exact same kind of analysis here, but instead of fires per mile we'll look at injuries per mile, as Elon did in his November 18 post. The gasoline data is from 2012 rather than the 2006-2010 period examined in Claim #1.

Gasoline
Gasoline-fueled miles driven in 20122,938,535,000,000
Number of fire injuries in 2012800
Ratio of miles to gasoline injuries3,670,000,000
Tesla
Number of Tesla-powered miles driven to date~100,000,000
Number of Tesla car fire injuries0
Ratio of miles to Tesla injuries

Well, "infinity" is not a very useful number for purposes of comparison. But we can calculate a confidence interval for the rate of injury, even when no injuries have been observed.

Confidence intervals
Ratio of miles to gasoline-fire injuries3,350,000,000 – 4,020,000,000
Ratio of miles to Tesla-fire injuries15,100,000 – ∞

Uh-oh. Looks the gasoline figures are well within Tesla's confidence interval. A chi-squared test gives a p-value of 0.87not statistically significant.

Verdict: The claim is false. On a per-mile basis, the rate of fire-related serious injuries in Teslas is statistically indistinguishable from the rate of fire-related serious injuries in gasoline cars.

## Claim #3: Tesla Drivers And Passengers Are Less Likely To Die A Fiery Death Than Their Gas-Guzzling Counterparts

Now we look at the number of deaths instead of number of injuries. Same deal as Claim #2. We know the answer in advance because there were fewer deaths than injuries. But let's work out the math anyway.

Gasoline
Gasoline-fueled miles driven in 20122,938,535,000,000
Number of fire deaths in 2012300
Ratio of miles to gasoline deaths9,795,116,667
Tesla
Number of Tesla-powered miles driven to date~100,000,000
Number of Tesla car fire deaths0
Ratio of miles to gasoline fires
Confidence intervals
Ratio of miles to gasoline-fire injuries8,440,000,000 – 11,400,000,000
Ratio of miles to Tesla-fire injuries15,100,000 – ∞

Again, the gasoline figures are well within Tesla's confidence interval, and a chi-squared test gives a p-value of 0.92not statistically significant.

Verdict: False. On a per-mile basis, the rate of fire-related deaths in Teslas is statistically indistinguishable from the rate of fire-related deaths in gasoline cars.

## Claim #4: Teslas Experience Fewer Fires Per Vehicle Than Gasoline Cars

This is a stupid claim and not worth evaluating. It only makes sense to analyze vehicle fires per mile driven or per unit time.

Verdict: Stupid and not worth evaluating.

## Conclusion

I'm a big fan of Elon Musk's vision of an all-electric future, but I'm afraid his analysis of Tesla fire data is just plain wrong. His "fires per car" metric is downright facetious. When it comes to the number of fires per mile driven and number of fire-related fatalities per mile driven, Tesla vehicles and gasoline vehicles are statistically indistinguishable.

Perhaps in a few years, when Teslas have more miles under their timing belts, we might be able to say whether or not they are statistically less fire-prone than gasoline cars. But for now, there is no discernible difference.

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