## Adventures in probability, market forecasting edition

Carl Richards has a cute graph:

The basic idea here is right. And in fact Richards understates, in his graph, just how bad things are when it comes to market forecasts: his graph curves the wrong way.

Let’s say there’s a 10% chance of any given forecast being right, and let’s say (for the sake of argument) that all forecasts are independent of each other. Then what’s the chance of at least one forecast being right? Here’s the actual graph:

By the time you get to 20 forecasters, there’s an 88% chance that at least one of them will be right. At 40 forecasters, there’s a 99% chance.

In the real world, forecasters aren’t all independent of each other — but at the same time, there’s a hell of a lot more than 40 of them. (And given the squishiness involved in what counts as “being right”, the chances of being able to say that you were right are probably closer to 50% than 10%.)

If you add together the fund managers and the economists and the TV pundits and everybody else telling you where the economy and the markets are going, you’ll get a number somewhere in the tens of thousands. The question isn’t whether one of them will turn out to be right, it’s just *how many* of them will turn out to have been right.

In fact, given the thousands of people in the market, it’s a statistical certainty that many of them won’t just be right once, but will be right time and time again. Such people are generally lauded as being fabulously smart and prescient, and lots of money gets thrown at them. As a general rule, it’s a good idea to make sure that money isn’t yours.