This article was first posted on LinkedIn in October 2019.
Improbable things happen a lot! This notion is not always intuitive, but it is true nevertheless. Jordan Ellenberg, in his book How Not To Be Wrong: Power Mathematical Thinking, tells the Baltimore Stockbroker Parable to help us understand this concept.
Improbable things happen a lot more than we expect!
Suppose you received a letter from a financial advisor stating that a certain stock would rise over the next several weeks. You watched the stock, and sure enough, it went up. A few weeks later, the same financial advisor sent another letter stating that another stock would decline over the following few weeks. Sure enough, as you watched, the stock did go down. Then that same financial advisor sent a third letter to tell you to watch another stock that was going to go up. Sure enough, it did. With the next letter, the financial advisor told you to watch another stock that was going to go up. And sure enough, it did. That same financial advisor sent another six letters, each time predicting correctly the direction of every stock he told you to watch – a perfect prediction ten out of ten times. In the eleventh letter, he asked for a big investment. What would you say? He had been right ten out of ten times.
What you (the investor) do not see is the total picture, the whole story. That financial advisor began sending letters to 10,240 prospects. In 5,120 cases, he predicted the stock would go up; in the other 5,120 cases, he predicted the stock would go down. The 5,120 to whom he sent the letter saying the stock would go down never heard from our financial advisor. Of the 5,120 to whom he said the stock would go up, 2,560 got a second letter predicting that the second stock would go up, and the other 2,560 got a second letter saying the second stock would go down. The 2,560 who received the letter predicting the stock’s wrong direction never heard from our financial advisor again. Of those who got the correct prediction, 1,280 received the third letter predicting that the third stock would go up, and 1,280 received a letter saying the third stock would go down. Only 10 prospects would get letters with 10 perfect predictions. The other 10,230 people never heard from the advisor ever again.
