Try not to be blinded by big, scary numbers

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Opinion

Today I am going to indulge in a pet peeve of mine, one that I hope you will find helpful. It's about a bias called denominator blindness and it is the scourge of anyone who has even the most rudimentary understanding of mathematics in the real world.

A quick definition: Denominator blindness is the failure to put big, scary numbers into context. I am reminded of this every time I see one of these headlines: "ABC Fund Loses $879 million"; "XYZ Corp. Cuts 3,000 Jobs"; "Stocks Drop 100 Points."

The top number in a fraction is the numerator, and it tells you the raw change that took place in any measured data; the bottom number in the fraction is the denominator, and it indicates the total size of the data set. In the examples above, you are seeing only numerators, not denominators.

So headlines that provide only a numerator are of limited use.

Consider each in full context: The fund that lost $879 million -- were total assets $1 billion or $100 billion? Asked another way, was the fund's loss almost 90 per cent -- a rout that destroyed its investors? Or was it less than a 1 per cent drop, part of the daily noise? Based on the headline, you can't tell, and without any context, all you see is a big scary number; whether $879 million is meaningful depends upon the total amount under discussion.

As for the company that fired 3,000 people, that sure sounds like a huge down-sizing. Although it is painful to those who lose their jobs, from a macro perspective, we don't know how significant it is to the company as a whole. It's a function of whether it's a smaller, regional corporation or a giant, global one. What if it's Wal-Mart, with 2.2 million employees?

The 100-point market drop is perhaps my favourite example: If that's referring to the Dow Jones Industrial Average, now trading at more than 17,000, that decline is little more than static, a move of less than 0.5 per cent. If it was the Standard & Poor's 500 Index, now at about 2,000, that's an unnerving 5 per cent decline.

We have discussed variations of this before when I accused you, dear readers, of not understanding risk. It's a very real problem for investors, who consistently fear the wrong things.

Worried about market crashes? How many market crashes have there been relative to the number of trading days during the past century? That's a subtle example of denominator blindness. Relative to total returns, investors would be better off focusing on over-trading, fees and taxes.

Let's take another example. Concerned about terrorism? Since the 9/11 attacks, only a handful of Americans have been killed each year worldwide as a result of terrorism. But that's out of more than 300 million Americans. By comparison, there are more than 30,000 automobile fatalities each year. Worry less about terrorist attacks, and instead stop texting while driving and wear a seat belt.

And none of those risks is as great as the odds that you will die of heart disease or cancer, which cause about 1.2 million deaths in the U.S. each year.

Here's another example. Few concerns about risk are more off-base than the notion that vaccines cause childhood autism -- a fear driven by a discredited paper, written by a doctor who engaged in fraud and no longer is allowed to practice medicine. These people, and their children, would be much better off if they instead considered the genuine threats from whooping cough, mumps and measles.

Dan Gardner, in his book "Risk: Why We Fear the Things We Shouldn't -- and Put Ourselves in Greater Danger," calls this practice Fear Inc. There are many industries that thrive on unfounded fears and are only too happy to sell you things you don't need to keep you safe from criminals, terrorists, germs, end-of-times, hyperinflation and other calamities.

I see examples of denominator blindness every day, as I assemble my morning reads. I sift through dozens of websites, ranging from mainstream media to more obscure finance blogs and tech sites. I skip the stories with breathless, context-less, uninformative headlines with a screaming numerator, as I know that if they don't understand the issue, they are not worth my time or yours.

This isn't merely a matter of media criticism; it has implications both for investors and for policy makers. Much of this was laid out in a 2002 paper called "The Denominator Blindness Effect: Accident Frequencies and the Misjudgment of Recklessness," which looked at the impact of this phenomenon on jury awards for punitive damages. As you might guess, the bias played a significant role.

Maybe there's an instinctual reason some people are so impressed by large numbers. We surely know that simple innumeracy is rampant, so let's leave it at that. But there is something else at work that is both intentional and insidious and we should be aware of it.

All of which brings us back to errors that we make as investors. When we fear things because they seem scary, despite being highly unlikely, we make poor decisions relating to how much risk we should assume, and how much risk we take.

Regardless of the situation, anytime someone trots out a big number, make sure you understand the context and look for the denominator.

Barry Ritholtz, a Bloomberg View columnist, is the founder of Ritholtz Wealth Management. He is a consultant at and former chief executive officer for FusionIQ, a quantitative research firm.