# Why Probability is So Difficult For Our Brains

My new book is nearing completion. INVESTMENT ILLUSIONS: 12 Common Illusions That Can Sabotage Your Financial Success should be available on Amazon in paperback and e-book in early December. In this post, I share the section about probability that comes from the chapter, The Illusion of Reason. Hope you enjoy!

### Probability & Our Brain

When it comes to investing, perhaps the biggest and most pervasive challenge we have to deal with is probability. Whenever there is uncertainty, probability abounds. An event that is certain to occur has a probability of 1.0, or 100%. An event that is certain to not happen has a probability of 0.0. Between 0 – 1 lies an incredible amount of frustration, anxiety and fear.

Most of us have a hard time calculating and interpreting probability. Interpreting probability oftentimes doesn’t seem right; it doesn’t line up with what our intuition says. Give your best guess to the following four probability examples:

1. Which is more likely: winning the lottery with your favorite six numbers or winning the lottery with the numbers 1, 2, 3, 4, 5, 6?
2. There are 50 people in a room. What are the odds that two attendees share the same birthday?
3. You flip a coin 20 times in a row. What is the chance you will flip a run of four heads or tails in a row?
4. An investment security (i.e., mutual fund) has an expected annual return of 15% and a standard deviation of 10%. Such security has a 93% chance of producing a positive outcome in any given year. What is the probability of a positive outcome on a given day?

Answers are: (1) The lottery numbers have the same likelihood of being drawn. (2) 97% chance they share a birthday. (3) 77% chance you flip four heads or tails in a row – give it a try and see what happens! (4) 54% probability that the security will be positive on a given day – are you sure you want to watch the market daily?

### Probability & Certainty

For instance, if there is only a 10% chance of rain, the brain will simply tell us that it won’t rain. If it does, we conclude that the weather forecaster got it wrong; we were misled. A high probability event equals “sure thing” and a low probability event equals “it won’t happen.”

In the election of 2016, many people criticized the polls for getting it wrong. They had Hillary Clinton as the favorite and she lost. But did the pollsters really get it wrong? Not a single poll had Donald Trump at 0% odds. Nate Silver, famous statistician for FiveThirtyEight, had Hillary Clinton with a 71% chance of winning as of election morning. There was always a chance Trump would win, but the brain took the higher odds and defaulted it to a certain outcome. Trump’s win was heralded as a shocking upset with blame pointed at the pollsters.

### Probability and Black Swans

One of the greatest fears among investors is the occurrence of a Black Swan: a highly improbable but devastating event. Extreme events, especially negative ones, get our attention and can influence our decisions. The more extreme the event, the less likely it is to occur, but that won’t stop our brains from overestimating its likelihood.

This is because improbable events often produce a strong emotional stimulus. Think of the financial crisis of 2008/2009 and current COVID-19 pandemic. Because we remember them so vividly, we tend to overestimate their likelihood of recurring. After the financial crisis, many investors remained cautious as they awaited the next crisis to happen, so they missed out on significant stock market gains. As COVID-19 gradually moves to the endemic phase, concerns may grow about the next pandemic, which may be perceived as inevitable.

Black swans occur. They always have and they always will. Even very unlikely scenarios will occur given enough time. This is one reason why a measured approach to investing is often preferred. No matter how much information we have, no matter how certain we are, we still really don’t know what will happen. Investors don’t miss their financial goals by missing out on a “hot stock”; they miss their goals when they make confident bets that don’t come to fruition.

### Final Thought

Whenever we are dealing with probabilistic scenarios, such as investing, the process we employ always trumps outcomes, especially in the short term. We don’t have to worry about correctly calculating and acting on each probability. Developing a robust plan and investment process is the best response to the probabilistic outcomes of various market and economic events.