At the end of 1927 Alfred Cowles, an American investment adviser, began recording stock market forecasts on the day they arrived, before anyone knew how they would turn out. From January 1928 to June 1932 he tabulated more than 3,300 forecasts from 24 publications, right through the crash. In 1931, when the market fell 54 percent, there were sixteen bullish forecasts for every three bearish ones.

To tell skill from luck he built forecasters with no skill at all. Cards numbered 1 to 229 were shuffled and drawn to pick the weeks the advice changed, and nine more cards picked the advice. His best real record beat the average of chance by 72.4 percent, his luckiest shuffled one by 71.1 percent. As a group the real forecasters did about 4 percent a year worse than chance. In his words, the most successful records are "little, if any, better than what might be expected to result from pure chance."

Our version uses coins: 1,024 forecasters, one coin each per year, and a wrong call puts you out. In our run 518 were left after one year, 31 after five and one after ten. Halve 1,024 ten times and you get one. Before you trust a winning record, ask how many tried.

Cowles's figures are whole records measured against the average of all random results, not yearly returns, and the top real record ran two years on one unchanged call. In a 1944 follow-up he judged one agency's 40-year record "not entirely accidental"; the group result stood.

Genius, or luck: what did you guess?

Sources: Alfred Cowles 3rd, "Can Stock Market Forecasters Forecast?", Econometrica 1(3), 1933; Alfred Cowles, "Stock Market Forecasting", Econometrica 12(3/4), 1944.
Sounds: our own, made in code (earshot, CC0).