Problems with the Language of Probability

April 7, 2015



The language of probability to statisticians and most scientists is clear—they understand terms such as “correlation”, “statistically significant”, “confidence” and more. However, using probabilistic terminology to communicate the “likelihood” of an event occurring to those untrained in understanding such terms, can in some instances lead to the ruin of careers, companies and in worst cases—loss of life.

The “After Shocks” is a disturbing article on what some have called “science on trial”. In 2009, a swarm of small earthquakes hit L’Aquila, a small town in the mountains of Italy. This area in central Italy—much like those living near the San Andreas fault in California—is prone to continual earthquakes. In fact, over the centuries there have been tens of thousands of earthquakes in the area of L’Aquila with some having small effect and others killing hundreds of people.

Citizens in L’Aquila constantly live with an underlying fear of “the big one”—an earthquake so big that it shakes buildings to their foundation. So when a series of tremors hit the area in 2009, citizens were keen to get answers to questions such as; “is the big one coming soon?” and “if so, should I be leaving my home?” With most of the homes in the L’Aquila area unenforced—and thus unable to defend against a sizeable earthquake—government authorities came to the rescue by convening a scientific panel to answer citizen questions.

What happened next is a travesty. According to the above article, one of the scientists, Enzo Boschi, examined the earthquake data and concluded; “a large earthquake along the lines of 1703 event (the last one that killed 10,000) is improbable in the short term, but the possibility cannot definitively be excluded.”

Let’s dissect the use of the word “improbable”. Most statisticians would define “improbable” equating to a low probability, but definitely not zero. It appears this is what Boschi meant when he used the term “improbable”.  As further evidence, notice how Boschi qualified his statement; “but the possibility cannot definitively be excluded”. However, the article notes that to the untrained—even worse, the media—improbable means “ain’t gonna happen”.

Long story, short: the small shakes in L’Aquila eventually led to the big one six days later. On April 6, 2009, cumulative probabilities caught up with L’Aquila, with a 6.3 magnitude earthquake killing 308 people.  After spending weeks digging through the rubble, enraged citizens brought a lawsuit against the scientists, accusing them of negligence in not adequately sizing the risks of a large earthquake. In 2012, the scientists were convicted of manslaughter, however in November 2014; they won their appeal and are now free from jail–but not free from the associated costs of their legal defense.

There are challenges in the language of probability. What do terms such as “unlikely”, “serious possibility”, “likely” and others actually mean? The trained scientist might know in his or her mind how they are defined, but does your typical business associate, much less your CEO understand?

Surely, when we have data we can make calculations to estimate the probability of an event. But what happens when we do not? Subjective probability statements—where we’re trying to measure belief—can also get us in trouble if we don’t agree on definitions, especially for events that have never occurred.

We should not eliminate the language of probability. Even though we really don’t know everything that can happen, we still have to run our businesses and predict what’s coming next. However, we must also remember that what is “likely” to us, may be deemed “unlikely” to another—especially if they have a pre-conceived notion in mind. We should also remember that sometimes the use of statistics and probability gives us the illusion of control, where in fact there is none.

As we communicate to those not trained in the language of probability, it is critical to couch our language with key qualifiers of “estimate”,  “educated guess”, “margin of error”, “rare does not mean impossible” and more. We should avoid generalizations and any language that could be misinterpreted as “a sure thing” or “no chance in heck”. Barring that, the best solution is to keep our expert opinions to ourselves.