Three Times and You're Out!

So…something that came up at dinner after Schwartz’s talk was things that it’s difficult or impossible to make your students believe (when they’re true). Schwartz’s glaring example was the extent of randomness, especially as it affects our understanding of sports. He’s had the darndest time convincing Swarthmore undergraduates that what they call a “hot” or “cold” streak is really no such thing. He’s not saying that such a thing may not exist, mind you, but that what we often term evidence that a player is on a hot or cold streak is not really evidence. It’s very hard for us to believe that chance could generate long streaks. Schwartz mentioned that many iPod shuffle users complained to Apple that the shuffle wasn't really playing music at random. Their evidence? That sometimes the same song would play twice in a row. But that is, indeed, something that can happen at random. Our difficulty in believing in chance is easy to test: statistics professors will give the assignment of flipping a coin 100 times to their students. They can tell who ACTUALLY flipped the coin vs. those who made up their flips by the ‘runs’ (of just heads or tails) their students report. Most students will not make up long runs--and a long run tends to be (only) 3 or more in a row. Mere chance (per the coin flip) will generate long runs of heads or tails—but hardly anyone believes that. So when a player has a streak of hits or misses, we say he’s hot or cold. But really, it’s just him (or her) being himself—a player’s performance is surprisingly consistent over time. But who will believe it?