Probabilistic vs. Binary Forecasting: The 53%–65% Rule

When a forecaster converts a probability estimate into a binary prediction, information about conviction is discarded even though the underlying belief has not changed. This paper measures the economic value of that discarded information. Using stock market data, we find that at equal accuracy, probabilistic forecasts are more profitable than binary ones, and forecasts of outperformance magnitude more profitable than directional forecasts alone. Both advantages concentrate in a specific accuracy range — roughly 53% to 65% — that appears independently in research on human forecasting well outside financial markets, suggesting a general property of human judgment. How a forecast is expressed can matter more than how accurate it is.