Outcomes Rely On Circumstances

Some time ago I wrote about statistical tricks that can influence your thinking.  In my vehicle’s owner manual I found one that I had mentioned earlier. Three out of four accidents occur within 25 miles of home.  The idea in the manual  being that you should use your seat-belts for short journeys.

Is this persuasive or even useful information?  Given that seat-belt use is a habit, every time is best.  Even backing out of the garage, then getting out to close the door, which used to fascinate my wife.  Do not try to pick and choose.  Seat-belts matter whenever you are in a crash.  The airbags are relying on their working, for example.  An airbag that hits you when you are not restrained by a seat-belt can be dangerous.

Back to the point.  Should you be surprised that 3 out 4 accidents happen within 25 miles of home?  Similarly should you be surprised that a majority of home accidents happen in the kitchen? Or, that if you are bitten by a dog, the most probable offender is a Labrador Retriever?  Or if you are analyzing expense accounts, 30% of the amounts claimed should begin with the digit “1”?

For the first three above, this distribution occurs because most of the miles driven are within 25 miles of home, most of the time is spent in the kitchen, (could be an implement and distraction component) and the most common dog by far is the Labrador Retriever.  When analyzing expectation, it is always smart to assume that the most common things will influence occurrences most often.

For example, I doubt my car is 25 miles from home more than five times a month, but it moves at least three times a day.  In my case, the expectation of an accident within 25 miles of home is more like 95%.  (the first 25 miles of a longer trip are still within 25 miles of home and so are the last 25 miles of that trip.)

The fourth condition, 30% of the expense reports begin with the digit 1 is less obvious.  It is known as Benford’s Law.  There is an excellent discussion at Wikipedia.  Suffice it to say that all accountants distrust expense reports or invoices that begin with a number bigger than 3.  According to Benford’s Law, 60% start with 1, 2 or 3.  Most accountants are suspicious of expense reports ending in 4 zeroes.  Your expectation of an unchallenged expense report that claims \$900.00 is approximately the same as the probability of Richard Nixon being elected president in 2016.

We find statistics everywhere.  It pays to have a little insight before trusting them.  Here is my favourite example of how statistically accurate information is misleading.

The probability of someone being struck by lightening on a golf course is about one in six million.  If you know and believe that fact, the odds of being struck by lightening can become about one in ten. The difference here is that the one in six million assumes that the one strike is unexpected.  If you play during a storm, the circumstances are much different and therefore so are the probabilities.

Events happen or they do not.  You cannot be 90% alive after exposing yourself to a 1 in 10 risk of death.  You are alive or you are not.  Better to avoid the exposure than to rely on the odds to keep you safe.  Just like the stock market, gold, or bonds.  Prices move randomly in the short run, but the long run is based upon complex inter-relationships.  You do better when you understand what circumstances create the event not just understand the summarized odds.

Don Shaughnessy is a retired partner in an international accounting firm and is presently with The Protectors Group, a large personal insurance, employee benefits and investment agency in Peterborough Ontario.