If we plot the intensity of earthquakes along one axis and their frequency along the other, the plot is surprisingly linear, provided both axes are logarithmic. That is why the Richter scale is not linear, but logarithmic. An earthquake that registers a ten on the Richter scale is not ten times more intense than an earthquake that registers a one on the scale, but a billion times more intense.
No geologist in his right mind would try to predict earthquake intensity assuming a normal distribution of the underlying data. That would be bizarre. Earthquake intensity doesn’t follow the normal distribution.
A logarithmic relationship between earthquake intensity and earthquake frequency is just what Mother Nature gave us. Statisticians call that type of distribution a power law. Power laws plot as straight lines on log-log graph paper.
The signature feature of a power law data set is the logarithmic relationship between size and frequency. Data sets with a power law distribution have lots and lots of data points with small values, a few big values, and the very rare monumental value. Other data sets that follow power law distributions include the populations of U.S. cities, the number of hits on websites, and the diameter of the craters on the moon. They each have lots and lots of little ones, a few big ones, and the very rare monumental one.
What if a geologist trying to predict earthquake intensity and frequency erroneously assumed that the underlying data set followed the normal distribution? That geologist, it turns out, would significantly underestimate both the frequency and the intensity of the very rare but monumental earthquakes. That geologist would consider the 1906 San Francisco earthquake (probably an 8.0 on the Richter scale) as impossible. Ironically, the very events that have the most meaning and affect the most people would be considered too many standard deviations from the mean to exist, until one actually happened.
Converting means and standard deviations into probabilities only has meaning when the underlying data is normally distributed. Not all data sets are normally distributed.
In Blindsided by the Impossible we showed how Wall Street Insiders are nearly always surprised by the low probability high magnitude event. Buried deep inside their models in nearly every case is the assumption that market prices follow the normal distribution. We don’t think they do.
We believe Wall Street Insiders are routinely blindsided by the impossible because they erroneously assume a normal distribution for a data set that very likely follows a power law. In doing so, they miss the very events that affect the most people in the most meaningful ways. They miss the devastating monumental low frequency event. They are blindsided by the impossible.
