What do you really mean when you say you are 90% sure about something? Are you really sure about what it means to be 90% sure? Probably not, according to several studies which show people are consistently overconfident about their beliefs, pretty much like the cat in the picture below:
Let’s say you are 90% sure that the stock market will close higher in 2010 than it did in 2009. If that is really the case i.e. if you are really 90% sure about your prediction, then you should be willing to win $1 in a bet but accept a loss of $9 if you lose. Why?
We already know that either you are right or you are wrong about your prediction. In fact, you are going to be right 90% of the time according to you. Thats what being 90% sure means. If that turns out to be the case, then the expected value of your winning is 90% of $1. That comes to +$0.90
You are going to be wrong 10% of the time according to you. That’s what being 90% sure means – that you will have an error rate of only 10%. If that turns out to be the case, then the expected value of your loss is 10% of $9. That comes to -$0.90.
Therefore, if you are 90% confident that the market will close higher in 2010 than in 2009, then this is a fair bet because it involves an equal exchange.
Put in those words, you may balk at the prospect of losing $9 versus winning only $1. But that is exactly what 90% confidence level means.
When your beliefs are framed in the form of money bets instead of confidence levels, you have a better chance of understanding the odds implied by your beliefs. Keep that in mind when you express confidence in your predictive abilities.
Watch your language!