Sunday, January 30, 2011

Astrology of Allstate Insurance: Statistics Fail Edition

Picard Facepalm

Very few things make me more discouraged than news stories and pronouncements that are so badly wrong. Captain Jean-Luc Picard knows how I feel.

On Thursday, Allstate Insurance released a statement that purported to analyze car accident claims using the “new” astrological calendar that I discussed last week, presumably as a PR stunt, and even tried to figure out what was going on based on the supposed traits associated with people within the sign.

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.

The "new" sign, Ophiuchus, fared well in the study as the second-safest drivers on the road. While the jury is still out on the exact characteristics of an Ophiuchus, most astrologers seem to indicate individuals born under this sign will be a bit luckier than the rest.

But, can an astrological sign really influence driving habits?

Generally, the signs with the fewest number of reported accidents were those associated with traits like "compassion," "graciousness" and "resourcefulness" where those with more accidents tended to be more "uncompromising," "arrogant" and "impatient."

Unfortunately it probably worked, as I’ve seen numerous re-postings and very few criticisms. ABC News posted a slideshow feature about it, and though MSN Money’s article does admit that the premise of the study was flawed, it is buried in the middle of the story. Despite it not being a ‘serious’ story, shouldn’t we expect better of real news outlets than to rebroadcast incorrect information straight out of the PR department of a company?

Where They Went Wrong: Mo’ People, Mo’ Problems

The Allstate release’s proclamations were based on the total number of 2010 accident claims by people born in a given sign. However, even if you assume that Allstate customers’ birthdays are uniformly distributed across the year (an okay, but not entirely accurate assumption as demonstrated by actuary Roy Murphy), in this strict sidereal form of the zodiac, each of the signs spans a different period of time, meaning that signs spanning a longer period will have more people in them than in signs spanning a shorter period.

If everyone is equally likely to have an accident, you would expect longer signs to represent a larger portion of total accidents. And to do this analysis right, you would need to normalize the total number of accident claims by those in a given sign to the total number of customers within each sign. Let’s see what happens when we account for the number of people in each sign*.

Corrected Allstate Car Accident Rates by "New" Astrological Sign
Sign Dates Days Drivers in Accidents Normalized Accidents Normalized Birth Rate Corrected Normalized Accidents
Aries Apr 17 – May 13 27 112,402 0.90 0.96 0.94
Taurus May 14 – Jun 19 37 177,503 1.04 0.99 1.05
Gemini Jun 20 – Jul 20 31 136,904 0.96 1.04 0.92
Cancer Jul 21 – Aug 9 20 101,539 1.10 1.06 1.04
Leo Aug 10 – Sept 15 37 179,657 1.05 1.07 0.98
Virgo Sept 16 – Oct 30 45 211,650 1.02 1.07 0.95
Libra Oct 31 – Nov 22 23 110,592 1.04 1.01 1.03
Scorpio Nov 23 – Nov 28 6 26,833 0.97 0.98 0.99
Ophiuchus Nov 29 – Dec 17 19 83,234 0.95 1.02 0.93
Sagittarius Dec 18 – Jan 17 31 154,477 1.08 1.00 1.08
Capricorn Jan 18 – Feb 15 29 128,005 0.95 1.00 0.95
Aquarius Feb 16 – Mar 11 24.25 106,878 0.95 1.01 0.94
Pisces Mar 12 – Apr 16 36 172,030 1.03 0.99 1.05

The calculated values show the deviation from the average: a value of “1” means no different than average; “<1” below average; “>1” above average. “Normalized Accidents” represents the accident rate with the assumption that birthdates are evenly spread among all 365.25 days in the year. As you can immediately see, the differences are far smaller than Allstate’s “analysis” represented (“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”) and the order is different: Aries has the lowest rate and Cancer has the highest.

Frequency graph of birthdays by date, showing a slight dip around May and increase in August through October.
(Credit: Ron Murphy)

This all rests on the assumption that birthdays are evenly distributed throughout the year. As shown in the data collected by Roy Murphy, this doesn’t seem to be the case, at least for 500,000 people applying to an unnamed life insurance company between 1981 and 1994. In the table above, “Normalized Birth Rate” comes from this data, and “Corrected Normalized Accidents” shows how the accident rates compare once the distribution of birthdays are taken into account. Now Gemini has the lowest accident rate while Sagittarius has the highest accident rate. This brings half of the values closer to the mean, two values unchanged, and the other five slightly further from the mean. However, none of the differences are on the order of the 700% originally cited by Allstate.

Allstate’s Correction

Late Saturday, Allstate released another statement correcting their previous one. But it wasn’t about the gross statistical error. No, they just wanted to make sure people didn’t think that they used astrological signs as an underwriting factor. Though it is good to know that an insurance company isn’t using astrology to guide its decisions, isn’t it just a bit disconcerting that a company almost entirely based on relative risk factors would release a "study" based on totals alone?

* Equations:
Normalized Accidents/Birth Rate = [ (total events in the sign) / (days in the sign) ] / (average events per day)
Corrected Normalized Accidents = (Normalized Accidents) / (Normalized Birth Rate)


  1. Astrology is the science of understanding the subtle influences that come to us from the greater universe, Indian Astrology

  2. That may well be its claim, but it is by no means a science--no observational or experimental studies beign conducted--and there is no good reason to think that such things influence us at all.