How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

It’s the very same effect that makes political polls less reliable when fewer voters are polled. And it’s the same, too, for brain cancer. Small states have small sample sizes—they are thin reeds whipped around by the winds of chance, while the big states are grand old oaks that barely bend. Measuring the absolute number of brain cancer deaths is biased toward the big states; but measuring the highest rates—or the lowest ones!—puts the smallest states in the lead. That’s how South Dakota can have one of the highest rates of brain cancer death while North Dakota claims one of the lowest. It’s not because Mount Rushmore or Wall Drug is somehow toxic to the brain; it’s because smaller populations are inherently more variable. That’s a mathematical fact you already know, even if you don’t know you already know it. Who’s the most accurate shooter in the NBA? A month into the 2011−12 season, five players were locked in a tie for the highest shooting percentage in the league: Armon Johnson, DeAndre Liggins, Ryan Reid, Hasheem Thabeet, and Ronny Turiaf. Who? That’s the point. These were not the five best shooters in the NBA. These were people who barely ever played. Armon Johnson, for instance, appeared in one game for the Portland Trail Blazers. He took one shot. He made it.