Improbable Things Happen a Lot: the Baltimore Stockbroker Parable

This article was first posted on LinkedIn on October 14, 2019.

Improbable things happen a lot! This notion is not always intuitive but 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!

Franco Folini
Money
Just money

Suppose you received a letter from a financial advisor who told you a certain stock was going up over the next several weeks. You watched the stock, and sure enough it went up. A few weeks later that same financial advisor sent another letter to say another stock was going to go down 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) does not see is the total picture, the whole story. That financial advisor began sending letters to 10,240 prospects. In 5,120 he predicted the stock would go up; in the other 5,120 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 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 got the letter predicting the wrong direction of the stock those people never heard from our financial advisor again. Of those who got the correct prediction, 1,280 got the third letter predicting a third stock would go up and 1,280 got 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.


Franco Folini lives and works in the eCommerce territory, a wild area between the Kingdom of Technology and the Kingdom of Marketing. He speaks fluently the language of both realms. For many years, Franco has been helping people bridge the divide and successfully collaborate.

If you want to find out more about Franco, visit his LinkedIn profile or send him an email folini[at]gmail.com