Have you ever been solicited by a fellow who wants to give you access to his incredibly insightful and prescient sports-betting strategies? Have you ever received a newsletter from an investment company showing how it has regularly beat the market? Have you ever seen a testimonial from someone who has been healed from homeopathy? And so on?
I am sure of it. I have. Indeed, there have been times when the siren call of success has made me anxious about not taking advantage of such wisdom. Now, you might reasonably ask, “if this fellow’s strategy is such a good idea, then why is he sharing it with me?” It’s a good question, and a little probability theory will help you understand how. Imagine I am trying to convince you that I have a surefire way of picking the winners of 3 football games per weekend. Assume for the time being that I have a 50% chance of being right on any one game. What is the chance that I pick the winners of all 3 games? It is 50% x 50% x 50% = 12.5%.
So, how can I convince people that I am a game picking genius? First, recognize that there are 8 possible combinations of winning picks. If the three games are Game 1 sets Team A against Team B, and Game 2 sets Team C against Team D and game 3 sets Team E against Team F, then the following outcomes of winners are possible:
Each of these outcomes has a 1 in 8 chance of happening. What I can do is solicit a large number of potential gamblers with information about my picking prowess. I might talk about how my unique research methods and data analysis allows me to see trends in team performance that others miss. And I might send 80,000 solicitations to potential customers. These 80,000 solicitations will be comprised of 8 sets of 10,000 letters, each set reporting on the “can’t miss” winning strategy. After the week is over, 70,000 of these picks would have been wrong, but 10,000 would have been right. So what I will do is send out the very next week 8 batches of letters only to the winners from week one. I would therefore be sending out 1,250 letters each with a different gambling strategy. One of course would be the winning strategy, or 1250 correct letters sent, and 8750 incorrect letters would have been sent. For the winners, they would have seen me pick all 3 teams correctly for 2 straight weeks! Now, I can repeat the process, sending 8 different sets of letters to each of 156 different customers – each of whom has enjoyed watching me pick winners for the previous 2 weeks. Again, one of these groups will have been lucky, and see that I picked all 3 weeks correctly. So now I have 156 people who have seen me pick 3 teams correctly for 3 straight weeks – pretty incredible odds (less than 1/5 of a percent). All that I need to do now is send these lucky 156 people a letter telling them that if they really want to see my picks for week 4, that they should subscribe to my website now for a modest fee of $100. If they all do this, then I am going to “earn” $15,600. Not bad for some fraudulent work!
Keep this strategy in mind the next time you are solicited to believe in someone’s incredible expertise in predicting the future. You might also keep in mind that it is fairly easy to play this game in reverse – I have in mind the many lectures and articles I have been exposed to pointing to this or that environmental travesty and then hearing the author exclaim, “in every one of these cases, collapse happened because of INSERT PET FEAR HERE.” Indeed, their comment may be true. But it is true in exactly the same sense that our football game soothsayer was able to identify a common thread for every one of the successful series of picks he made. In every game played that he successfully predicted, there was an opening kickoff! You see, having an opening kickoff is a marker for something VERY important! Sure, it is a marker for the fact that a game was being played, and that’s about it.