How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

So in 1933, when Secrist was ready to reveal the results of his analysis, people in both academia and business were inclined to listen. All the more so when he revealed the striking nature of his results in a 468-page volume, thickly marbled with tables and graphs. Secrist pulled no punches: he called his book The Triumph of Mediocrity in Business. “Mediocrity tends to prevail in the conduct of competitive business,” Secrist wrote. “This is the conclusion to which this study of the costs (expenses) and profits of thousands of firms unmistakably points. Such is the price which industrial (trade) freedom brings.” How did Secrist arrive at such a doomy conclusion? First, he stratified the businesses in each sector, carefully segregating the winners (high income, low expenses) from the inefficient duds. The 120 clothing stores Secrist studied, for instance, were first ranked by ratio of sales to expenses in 1916, then divided into six groups, or “sextiles,” of twenty shops each. Secrist expected to see the shops in the top sextile consolidate their gains over time, growing ever more superior as they honed their already top-of-market skills. What he found was precisely the opposite. By 1922, the clothing stores in the highest sextile had lost most of their advantage over the typical shop; they were still better-than-average stores, but by and large they were no longer the standouts. What’s more, the lowest sextile—the worst stores—experienced the same effect in the opposite dir...