So today I prove that actuaries can ruin any joke.
Last week, Allstate tapped its mighty database to figure out which sign of the Zodiac had the best drivers. The results, according to a company press release:
Virgos, known to be critical, meticulous and reserved, are also more likely to get into a car accident, according to Allstate Insurance, which recently compared claims data against the recently “revised” zodiac calendar.
Over the past year, Virgos were nearly 700 percent more likely to be in a car accident when compared to the determined and aware Scorpio, the best drivers in the study. Perhaps a Virgo’s shy, perfectionist nature leads to overly cautious and timid driving habits. By contrast, Scorpios were only involved in 1.5 percent of all accidents in 2010.
Apparently customers took it seriously, because a few days later. . .
“We recently issued a press release on zodiac signs and accident rates, which led to some confusion around whether astrological signs are part of the underwriting process,” said the insurer, in its retraction. “Astrological signs have absolutely no role in how we base coverage and set rates.”
Allstate also said, “We deeply apologize for any confusion this may have caused.”
The data that Allstate used was real, based on the birthdays of customers actually involved in accidents. But the company’s conclusion was tongue in cheek.
“Rating by astrology would not be actuarially sound.”
Now that’s pretty funny. (H/t to reader JN.) But being an actuary, I’m going to un-funny things a bit.
Rating by astrology would be actuarially sound if there was a strong, consistent correlation between astrological sign and driving record. We wouldn’t have to know why a Scorpio had fewer accidents than, say, Capricorns or Gemini. The correlation itself would be enough, provided we didn’t already have rating variables that explained the phenomenon. (There are also exceptions if using the variable is outlawed or is otherwise morally repugnant.)
So let’s look at Allstate’s data – my chart from data in the original press release:
This chart shows the number of Allstate drivers involved in accidents by astrological sign in 2010. The center of the chart is zero accidents. And the farther a data point is from the center of the chart, the more accidents drivers under that sign were involved in.
Normally, you’d think each sign would have the same number of accidents, in which case the blue line would be a circle. (Well, a regular triskaidecagon, if you want to get particular.)
But it’s not. By golly, not many Scorpios got into accidents (26,833, according to Allstate), and a whole lot of Virgos did (211,650). That implies Scorpios should pay lower premiums.
But look a bit closer at the range of birth dates for Scorpios: Nov. 23 to Nov. 28. That’s just six days. And Virgo covers Sept. 11 to Oct. 30 – that’s 45 days. Of course Virgos are 7.5 times more likely to be in an accident. Virgos probably outnumber Scorpios 7.5-to-1!*
Here’s an adjusted chart. Now we’re looking at the number of accidents by sign, pro-rated by the number of days the sign covers:
The number of accidents per birthday for a sign falls pretty consistently between 4,500 and 5,000, with differences attributable to random variation.
So when it comes to driving, the fault lies not in the stars, but in ourselves.
* I’m assuming birthdays are uniformly distributed across the year. They’re not, but it’s close enough for this blogging actuary. Lighten up!