Fat Tail Graphs

Most people have heard of a Bell Curve. This is the graph that is formed when measuring many small, independent effects that are additively contributing to each observation. The bell curve is found when measuring a great many effects in nature such as the height of people, people’s IQ, and in many areas of astronomy.

If we measure the heights of a large number of people, we see the graph below. On the x- axis (the horizontal direction) is the height of the person. On the y-axis (the vertical direction) we plot the number of people who are that particular height. What we see is that there is a middle height value at which is the height of the greatest number of people. As we go above that height, we find less and less people and as we reduce the height we also see less people and the fall off happens at the same rate above the median height as it does going below; the graph is symmetrical about the median point.

When we make the same graph of a complex system, where the elements are not independent, but highly interdependent, we get a graph that is a bit different. The basic shape is the same, but the graph does not fall away as quickly as it does for a bell curve.

This means that there are more extreme elements in the whole distribution of effects. If we take the example of the amount of money in people’s bank accounts. The amount is determined by an enormous amount of interconnected trading between people. There will be more extremely rich people that we would expect in a bell curve and we would find more extremely poor people.

For this reason it is known as a fat tail curve. This may explain why some extreme events seem too random; too out of the ordinary. Our mind is expecting a bell curve of something more linear and straight forward, whereas it is in fact a fat tail curve. Events like the Wall Street Crash seemed like they were too extraordinary to be an event within the bounds of ordinary experience and yet it is.