Probability is counterintuitive.
The idea that the chance of something happening doesn’t change is hard for us to wrap our heads around. Understandably so—if I tell you that you have a 70 percent chance of making a putt, most people expect that after ten putts, seven will have gone in the hole. This, however, is not necessarily the case. If you make six out of the first nine putts, the tenth putt isn’t guaranteed to go in the hole.
That’s what’s hard to grasp about probability, the idea that one result has no effect on what happens in the future. See, when I tell you there’s a 70 percent chance you’ll make this putt, what I’m really saying is, “If I take a group of people and have them try that putt, over and over, thousands of times, the number of times they make the putt will work out to about 70 percent. It could be that they made 70,421 putts out of 100,000. Or 7,034 putts out of 10,000.” Those results have no effect on whether the ball drops in the hole when you’re on the green.
Let’s say you make the first putt. What bearing does that have on the outcome of your second putt? Literally none. You have the exact same chance of making the putt the second time as you did the first time. The universe doesn’t remember whether you made the first putt; your odds are reset, and unchanged.
Probability is an average, a generality. It’s observation, not prescription.
Most people can realize this once it’s pointed out to them, but the tendency to equate the odds of something happening with certainty that it will is nonetheless widespread. Thus the backlash against FiveThirtyEight's Nate Silver.
Like the golf example, Silver’s model says there’s about a 70 percent chance of Obama winning reelection. Most people misinterpret what exactly this means; how Silver arrives at the 70 percent figure is lost on many of his detractors.
So here it is, in basic form: His program conducts virtual elections, over and over, thousands of times, based on the data he inputs to reflect the electorate. When he says there’s a 70 percent chance of Obama winning, what he’s really saying is, “I’ve conducted 1,000 simulated elections, and Obama won 700 times.” No more, no less.
But something gets lost in translation between Silver running the numbers and the average reader coming across the 70-percent figure. Ask someone what it means for Obama to have a 70 percent chance of reelection and they probably can’t deconstruct the thinking behind it. That’s where Silver gets into trouble when he talks about probability—most of his critics aren’t speaking the same language.
If you want to learn more about probability, this episode of WNYC’s RadioLab is excellent. (Jonah Lehrer is a guest, but still good)
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