Your eyes aren't playing tricks.                                                                                                                                   
Your eyes aren't playing tricks.                                                                                                                                   

Last week, we discussed the problems with having poor reading comprehension and the impact that has on consuming news. This week, I want to look at the lack of math skills.

America seems to becoming a dangerously innumerate society. Innumeracy is incompetence with numbers rather than words. This is a worrisome issue for the future competitiveness of the U.S.

I first encountered the word in the 1988 book, "Innumeracy: Mathematical Illiteracy and Its Consequences," by Temple University math professor John Allen Paulos.

This has been an issue for quite a while, but it blossomed into view again earlier this summer in a New York Times magazine article, "Why Do Americans Stink at Math?" The deficiencies outlined are striking:

A 2012 study comparing 16-to-65-year-olds in 20 countries found that Americans rank in the bottom five in numeracy. On a scale of 1 to 5, 29 percent of them scored at Level 1 or below, meaning they could do basic arithmetic but not computations requiring two or more steps. One study that examined medical prescriptions gone awry found that 17 percent of errors were caused by math mistakes on the part of doctors or pharmacists. A survey found that three-quarters of doctors inaccurately estimated the rates of death and major complications associated with common medical procedures, even in their own specialty areas.

It is more than anecdotal: Fewer and fewer people are familiar with even the most rudimentary mathematics. People are too easily confused by simple figures. My favorite example is how many people believe that a 100 billion is more than 10 trillion (because, you know, 100 is bigger than 10).

Every now and again, events occur that cause me to shake my head in dismay at people’s math skills. When the weather forecast is a 90 percent chance of a sunshine, and it rains, that doesn’t mean the forecast was wrong; rather, it was one of those cases where the low probability event occurred. Some people seem to believe that 90 percent and 100 percent are the same. Obviously, they are not.

People fall into this trap with events that have a nonzero probability of occurring. Nonzero means there is the possibility of occurrence, however unlikely.

I ride to work on a commuter train most days. In an average year, I am on the train 50 weeks, five days a week, two times a day. That’s 500 trips a year, and if the Long Island Railroad runs very efficiently -- let’s say its on-time record is 99 percent (which it most certainly is not) -- that means at about five times a year, I am either going to be late for work or late getting home.

If you understand this, it should at least give your blood pressure a break. Same for air travel. Plan and adapt accordingly.

As for the photo above: You might think it illustrates incompetence. It actually does nothing of the sort. How many bus stops do the workers paint a year? How many are done incorrectly? If they paint four a day, five days a week (with a few days off for holidays), 52 weeks a year, that's about 1,000 bus stops a year. If the painters mess up four stops a year, it means they have a 99.6 percent accuracy rate. You should be so lucky in your own job to have that sort of success rate.

When it comes to stock picking and portfolio construction, understanding probabilities goes a long way. You must assume that some of your picks aren't going to work out. Once you recognize that simple reality, you then can have an exit strategy for when those eventualities occur.

Same with portfolio construction. As we showed last week in the annual asset-class performance chart, recognizing what you don't and can't possibly know is a key to long-term planning.

Some have suggested starting statistics education in kindergarten. That might be a little radical, but beginning early is crucial. Having an educated population that understands probability and statistics is the key to an informed citizenry and a better economy.

Corrects year of book's publication in third paragraph.

To contact the author on this story:
Barry L Ritholtz at

To contact the editor on this story:
James Greiff at