"We favor the visible, the embedded, the personal, the narrated, and the tangible; we scorn the abstract. Everything good (aesthetics, ethics) and wrong (Fooled by Randomness) seems to flow from it."
Nassim Nicholas Taleb, Wall Street Trader and innovation catalyst, challenges conventional logic with his discussion of probability from a more philosophical than mathematical perspective in Fooled by Randomness. The quote above is his axiom. His convincing argument is that we mistakenly attribute hard work and skill to success or failure we experience and observe instead of correctly identifying it as an instance of chance. When we maximize our probability of success, it does not maximize our gains unless our strategy includes protecting ourselves from a small chance of a large loss and betting on a large chance of small wins. We oversimplify creating generalizations and overlook anything we have not experienced. Some information we consider important is just a distraction and distorts our perception. Also, knowing where we get probability and how we can change our beliefs is more important than having a sophisticated model.
Of the many concepts worth practicing, I decided to touch on interpreting statistics and the significance of probability. The The Big Idea illustrates the common confusion between mean and median. This is one example of how we often misinterpret statistics.
The Big Idea
Understand Data Analysis
"Consider that you have a very small number of poor people and the rest clustering around the middle class. The mean will be lower than the median. Take a population of 10 people, 9 having a net worth of $30,000 and 1 having a net worth of $1,000. The average net worth is $27,100 and 9 out of 10 people will have above average wealth."
The reverse is true too, 1 millionaire would raise the average and make 9 out of 10 below average wealth. We may think by definition not more than 50% can be above or below average. We sometimes use average to refer to mean or median, but they are not the same. The key is that if the samples are not statistically symmetrical the mean or average value will not describe the median or probable distribution of the samples. We can see there may not be a single sample that fits the description of the average. Notice one rare occurrence changes statistics significantly.
When we confuse mean and median, we draw conclusions that are wrong but seem logical. For instance, 90% of drivers consider themselves above average. We may think they must be wrong, only 50% can be above average. Not so. If 10% are very bad drivers who create a high percentage of accidents and violations, 90% may be above average. However, Taleb points out we tend to overvalue our skill, and I suspect most drivers do. Perhaps we assume we have a 50% chance of a successful marriage because half of all marriages end in divorce. Not true. People who divorce once will often divorce again which creates a statistical bias. It appears divorce is as common as a successful marriage. In fact, most marriages are successful.
It is important to check facts and conclusions when we analyze data as there are many ways to get it wrong. How do we become more aware of relevant probability? Read on to the Insights.
Evaluate Risk by its Potential Impact
"Accordingly, it is not how likely an event is to happen that matters, it is how much is made when it happens that should be the consideration. How frequent the profit is irrelevant; it is the magnitude of the outcome that counts."
Avoid risk when you cannot afford the loss. Taleb uses Russian Roulette as an example. A single bullet is loaded randomly in a six chamber revolver and when the player pulls the trigger they have a 1 in 6 chance of death. The probability of loss is small but if it occurs, it is catastrophic. Taleb mentions he lost a friend who played the game. I had an acquaintance that lost his left eye playing the game. The bullet lodged in his skull, but he survived. He realized he nearly took his life for a simple thrill. The reality is some risks are not worth taking.
I am an Insurance Broker. In the insurance industry, we call this adverse selection. We have to charge more overall than it costs to cover the average client because a few will cost much more than the average. We employ actuaries, mathematicians who use the law of large numbers to ensure we have a large enough pool of low-risk clients to offset the high-risk clients and enough reserves to cover the unexpected but statistically probable losses. We balance lots of small gains, and a few big losses to keep the business profitable and the clients protected. We have the assets to protect clients from a chance occurrence that we can cover but would be an overwhelming personal loss.
In life, we often make the mistake of using small numbers to calculate risk. We take a risk, hedge our bets with the odds that if we do something a few times it’s not likely to occur. We do it, it becomes comfortable, and then we forget the risk. As the number of repetitions increases so does the probability of the unlikely event. Eventually, odds are it will happen. Reality wins, always.
Ignore the Noise
"Some so-called wise and rational persons often blame me for ‘ignoring’ possible valuable information in the daily newspaper and refusing to discount the details of the noise as ‘short-term events.’ Some of my employers have blamed me for living on a different planet."
Information is often just noise and irrelevant to good decisions and sound ideas. Oversimplifying is dangerous we may overlook significant rare events but if we look for every possibility, there are too many to comprehend. Taleb talks about incurring emotional torture or burnout focusing on too much information. He says he is aware he needs to ruminate on information, but he can only do so if he is somewhat deprived.
I have an internet connection but not television. I read the newspaper selectively. I could not tell you about the latest drama in Washington or Hollywood. Most of that information passes through a brief period of relevance and fades away. If it is significant, it will keep showing up, and I will discover the trend. I am filtering out the noise and concentrating on the significant. I feel more connected in meaningful ways but to casual observers I seem disconnected.
The curious reader will appreciate this fresh perspective and exploration of provocative ideas that Taleb illuminates with a great amount of knowledge and understanding. Most importantly he stresses keeping an open mind and balancing logic and emotion. As he points out, “Researchers found that purely rational behavior on the part of humans can come from a defect in the amygdala that blocks the emotions of attachment, meaning that the subject is, literally, a psychopath.” We build loyalty to our ideas because they seem rational but strict adherence to beliefs looks like insanity, and we play the fool.
How will you challenge your beliefs?