Why Playing the Odds Underestimates Trump's Chances
What are the odds that Hillary Clinton will win the White House this November? The polls-plus model at FiveThirtyEight shows her with a roughly 60 percent chance, while the New York Times Upshot model has her at 69 percent.
But if you’re not a data geek who thinks about probability theory all day, it’s easy to see those numbers and overestimate Clinton’s actual chances. Specifically, in my experience people are prone to two mistakes when thinking about probability -- unconscious rounding and forgetting that presidential elections aren’t blackjack. These errors are likely causing many to underestimate Donald Trump’s chances despite the accuracy of projections at sites like FiveThirtyEight and The Upshot.
The first error, unconscious rounding, happens when someone sees a probability greater than 50 percent and rounds it up to a near certainty or looks at a probability under 50 percent and treats it as a near impossibility. For example, about a month ago I thought Trump had about a 25 percent chance of winning the general election (with the caveat that these probabilities change over time). When I told my Clinton-supporting friends this, they often reacted with sighs of relief, believing Trump was toast if he only had a one-in-four chance of winning.
But events with a 25 percent chance happen all the time. Flip two coins -- if both come up heads, you’ve seen an event with a 25 percent probability happen right in front of you. So if a model says Trump has a 40 percent chance of winning, it’s important not to round that down mentally and feel comfortable about the prospects of a Clinton win. A 40 percent chance means a Trump victory is more likely than rolling a one or a two with a six-sided die, and I doubt very many readers would feel comfortable betting something important on the prospect of rolling less than three on a six-sided die.
Second, people forget that presidential elections aren’t blackjack -- there are no repeated trials. To see why this matters, suppose you have a blackjack strategy that gives you a 51 percent chance of winning each hand. If you sit at the table all night, you’ll lose a lot of hands. But over the course of the night your winnings should slowly accumulate, and you’ll eventually be able to walk away from the table richer. In other words, over time, you should feel quite comfortable that you’ll come out ahead.
But a 51 percent chance of victory means something very different with a single test. Imagine that you have the same strategy, but that you only get one hand and you’re forced to go all in on it. Suddenly, your 51 percent strategy isn’t so helpful – you’d likely be very concerned about losing everything. In fact, a strategy that has a 55 percent or 60 percent chance of success wouldn’t be very comforting either. Even with those odds, it would be very easy to lose a single hand, and lose everything you owned.
That’s why a 55 or 60 percent chance of winning shouldn’t be too comforting to Clinton or her supporters -- this election will only happen once. Clinton and Trump only get to play one hand, and they're both all in.