Let’s talk about the odds of something happening


Several times a day, I receive a response to something I’ve written that goes something like this:

You and your polls! You said Hillary Clinton had a 90 percent chance of winning/that Clinton would win in a landslide! Polls are wrong and you don’t know what you’re talking about!

Usually those comments include other phrases meant to denigrate me on a more personal level.

It’s not the case that polling was generally wrong in 2016. Clinton had a wide advantage in the polls multiple times over the course of the campaign, but those leads consistently narrowed again. To President Trump’s benefit, one of those narrow points coincided with the Nov. 8 election. Clinton still won the popular vote by a few points — which is what national polling predicted — but because polls missed Trump leads in several key states, his electoral college victory was generally unexpected.

Take the election forecast at FiveThirtyEight. The site distinguished itself in 2012 by accurately predicting Barack Obama’s reelection. Coming into Election Day in 2016, it had Clinton with 71 percent odds of winning the White House. Trump had a better than 1-in-4 chance of winning, and did.

This forecast wasn’t simply a reflection of national polling and it wasn’t simply a function of state polling. It was an estimate based on running thousands of simulations of the election, resulting in a number of possible outcomes in each state. Clinton won the presidency in 71 percent of those cases. Have you seen the “Black Mirror” episode “Hang the DJ” where the two people are dating in a weird, walled-off universe? What FiveThirtyEight did was sort of like that.

Other forecasts, using different methodologies, gave Clinton much better odds, which often inform the sort of critique shown above. There’s also a big difference between having a 71 percent chance of winning and winning with 71 percent of the vote, a difference that also gets blurred in those complaints.

But it’s hard not to see “71 percent” and think “Oh, this is going to happen.” We’re seeing that pattern again: The Democrats have a 78 percent chance of retaking the House this November, according to FiveThirtyEight — which means that in 1-of-5 scenarios, the Republicans hold it! That’s not generally the way this is presented.

So let’s say that someone you know, perhaps your friend who sent me the response above, seems convinced that 71 percent odds mean that a Democratic takeover of the House is basically a sure thing. Have those people see how much money they can make playing this game.

You have $1,000. How much would you bet on a red square being randomly picked out of the box below?


Sometimes it looks like easy money. So many red boxes. At other times, it seems trickier. Without knowing the odds in the first place, the chances that you’re going to win seem a lot harder to ascertain.

Here’s the game above preset with 78 percent odds of victory — what FiveThirtyEight gives House Democrats as of writing.

You have $1,000. How much would you bet on a red square being randomly picked out of the box below?


Are you still making money? Is it easier or harder?

Statistical odds are one of many numerical blind spots that humans have. (Another is the vast expanse between the number “one million” and the number “one trillion.”) We see pretty good odds as suggesting that something is more of a certainty than it actually is.

It was never the case that Clinton was a sure thing. There was always a chance that she would lose — obviously. But that line got blurry and led to the common, incorrect line of thinking at the top of this post.

And there is a 92 percent chance that this article won’t disabuse many stalwart adherents of that line of thinking.

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