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A bookseller has two formulas for forecasting sales of new titles. The older formula uses a book’s genre and advance orders. The new formula also uses details of a book’s cover and description. Its designer chose the details and their weights after examining the recorded sales of every title released last spring, adjusting the formula to make its forecasts fit those records. An independent clerk then checked the arithmetic and confirmed that, on those same titles, the new formula had a lower average forecasting error than the old one. The designer argues: “The clerk’s independence answers the worry that I favor my own work. We have now demonstrated that, for next season’s new titles, the new formula will have a lower average forecasting error than the old one.”

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The designer’s reasoning is most vulnerable to criticism on the grounds that it

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