Tim Harford writes about a psychology experiment in which undergrads were recruited to make bets on coin flips:
The students were given tokens to gamble with and invited to bet on each coin-flip, with the stake to double or to disappear. The students were also invited to pay a fixed price to look inside each envelope ahead of time. After each coin-flip, the students could open the prediction for free and see whether it was correct or not.
You can appreciate that the forecasts here are transparently useless. With almost 400 students, some were bound to witness a string of correct forecasts by chance. The question is, would the students who randomly received correct predictions through sheer fluke actually start to pay for future predictions? And how long would it take for them to start buying?
The researchers answer these questions pithily: “Yes, and not long.” After witnessing a single correct forecast, students were more likely to pay to see a second forecast; this effect becomes large and statistically very significant after a second correct forecast. After witnessing four correct coin-toss forecasts, more than 40 per cent of students were willing to pay to see the fifth, although the chance of four correct predictions is a not-exactly-stunning one in 16.
The underlying message is: next time you see an investment manager touting impressive returns on a couple of funds, ask yourself how many other funds the company manages (because some funds are bound to do well simply by chance alone).