The book "Thinking, Fast and Slow" has a great chapter on human predictions versus those made by forumlas. The superiority of simple forumlas was being demonstrated way back in the 50s (see "Clinical Versus Statistical Prediction: A Theoretical Analysis And A Review Of The Evidence"). Since then the evidence for statistical rather than intuitive prediction has only become stronger.

From "Thinking, Fast and Slow":

"The number of studies reporting comparisons of clinical and statistical predictions has increased to roughly two hundred, but the score in the contest between algorithms and humans has not changed. About 60% of the studies have shown significantly better accuracy for the algorithms. The other comparisons scored a draw in accuracy, but a tie is tantamount to a win for the statistical rules, which are normally much less expensive to use than expert judgment. No exception has been convincingly documented."

Also interesting:

"Several studies have shown that human decision makers are inferior to a prediction formula even when they are given the score suggested by the formula! They feel that they can overrule the formula because they have additional information about the case, but they are wrong more often than not."