I was home baking cookies Saturday afternoon and so rediscovered that MPR chooses to air its best shows while productive members of society are grocery shopping or watching young children play ball. This American Life was pretty good but I liked even more Radiolab, which took as its subject stochasticity, or randomness. You can listen to the show here, if so inclined. Here's a little teaser to help you decide whether you're interested. A statistics professor asks one group of students to flip a coin a hundred times and record the results. A second group is tasked with setting out a likely result of a hundred coin flips; that is, instead of actually flipping a coin, and recording either an H or a T, they simply set out a 100-string-long sequence of Hs and Ts that in their opinion mimics the random result that will be achieved by the actual coin flippers. The professor leaves the room while the two groups do their work and then, returning to scan the two completed H-T strings, takes around five seconds to identify the one that is based on actual flips. Always. Without fail.
I'm enough of a contrarian to be attracted to the way in which students of probability are less apt to be taken in by "miracles" and assorted other fond beliefs. Take the notion that shooters in basketball games get a "hot hand." Years ago, another statistics professor, this one also a fan of the Philadelphis 76ers, tracked the result of every shot taken by individual 76ers over the course of a season. He then began looking for evidence of streaks when a shooter was "hot." Turns out that, while fans have a powerful impression that players "get hot," the notion is refuted by data. For example, Andrew Toney, who was at the time one of the team's leading scorers, made 46 percent of his field goal attempts over the course of the season. But supposing you look only at shots taken immediately after three successive "makes." He made only 32 percent of those attempts. It seems that the players themselves are victims of the "hot hand" fallacy. A little bit of success changes their conception of what's a good shot, and so their percentage slides until they recalibrate.
People love good stories and aren't inclined to look into them too closely. Every lottery winner seems to have a unique story but really they aren't different from the losers, who of course don't get interviewed in the media. If you determine before the numbers are drawn to do a story on the winner, it's a safe bet that word of a "miracle" is going to be promulgated. The "hand of God" will be detected in an unbelievable outcome. Indeed, the discovery of theological significance in necessary facts is pervasive. Another instance: it's not really a sign of God's great beneficence that he placed human beings here on earth, where conditions are such that we can live and prosper, instead of on some eternally frozen and poisonous orb where no one will ever sit down at a word processor to compose a sermon.
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