When I originally wrote this essay I railed against averages. Since that time we have experienced the Great Recession and I have spent more time thinking about this topic. While before I never trusted averages, I must admit that for many things in business I no longer even trust standard deviations. It is not that either is mathematically wrong, it is that they lead one to qualitative conclusions that do not sufficiently presage dramatic or outlier events. The classic example is of a man with his head in the oven and feet in the freezer. On average, he feels just fine. Not.
Though I had read Against the Gods: The Remarkable Story of Risk and When Genius Failed: The Rise and Fall of Long-Term Capital Management, I underestimated the impact of the fat probability tails. Trained as an engineer, I am facile with Gaussian or “Normal” distributions, stationary processes, correlations, linear systems, and so forth. This is knowledge is backed not just by training, but also by personal real-world experience over decades. I have lead teams that built some fantastically complex electro-opto-mechanical machines. It seemed a miracle that they worked, but they did. They wouldn’t have stood a chance if the physical world in which engineers live had fat tails.
On the other hand, I have worked a lot with people. Unless you care about their weight or height, the affairs of men and women are decidedly not Normal. I also have personal experience here. As a General Manager and later as a Group VP managing a billion dollars of annual revenue, I confronted volumes of real-world data on bookings and, frustratingly, on project delays. I tried to apply the statistics I knew to these data. They emphatically did not fit Normal distributions. There were many too many outliers. As I read Taleb’s book on The Black Swan: The Impact of the Highly Improbable, I could see his assertions in my own data. Gauss must have had great marketing to have his distribution called “Normal.”
I have recently taken to listing to investing podcasts. Barry Ritholtz often ends his podcast by asked the guest what they know now that they wish that they new decades ago. Many times the answer is, effectively, how often surprises happen and how big they can be.
And for the affairs of men and women, so do Normal statistics.