# Election Probabilities Made Clear

Over the past few weeks, Donald Trump’s odds of winning the presidency have dropped significantly.

Heading into the first debate with Hillary Clinton, Trump had a 45.2 percent chance of winning the White House, according to the FiveThirtyEight model. He now has a 16.5 percent chance. In the Upshot model, his chances have dropped from 30 percent to 12 percent since the first debate. If Hillary Clinton keeps leading Trump by a large margin (which isn’t a certainty) her win probability could exceed 90 percent.

But unless you’ve spent a lot of time playing poker or studying probability, numbers like these might seem opaque. It might be hard for the layman to get a strong sense of how different an 85 percent probability is from a 95 percent probability or even a 100 percent certainty. So I’ve put together a few examples and rules of thumb to help readers get their heads around the extremely high (and low) probabilities they might see between now and Election Day.

**What Does a 5 or 10 Percent Win Probability Look Like in Real Life?**

When something has a 15, 10 or 5 percent chance of happening, it’s easy to mentally round that probability down to zero. And while that’s not correct (events with low probability do happen), the certainty that an event won’t happen increases as its probability gets closer to zero.

Here are some examples to help illustrate this: There’s a 15.4 percent chance of drawing an ace or a king off the top of a standard deck of 52 playing cards. It’s not impossible to draw one of those two types of cards, but drawing a jack, queen or any number from 2 to 10 is much more likely. There’s a 16.7 percent chance of rolling a 1 on a fair, six-sided die and a 12.5 percent chance of flipping three heads in a row using a fair coin. Low double-digit probability events like these do happen, but the smart bet is against them.

Single-digit probability events also happen, but they’re long shots. For example, there’s a 7.7 percent probability of drawing an ace from the top of a shuffled deck of cards. The probability of getting four heads in a row on fair coin flips is 6.3 percent. In academic research, the concept of “statistical significance” centers on getting results that have a 5 percent or less chance of happening if your hypothesis is incorrect (this is a major oversimplification of the p-value; it’s used here only for illustrative purposes).

In other words, events with a 15 percent or 5 percent probability can happen, but events with that likelihood are truly improbable and there’s a tangible difference between a 15 percent and a 5 percent chance. And while there’s no substitute for a 100 percent certainty, probabilities in the 90s afford a good deal of confidence.

**Putting It in Political Terms**

But the 2016 presidential race is an election, not a game with dice or cards. So it’s worth talking about what a 90 or 95 percent probability means for the final weeks of the campaign. There’s more than one way to think about this, but a simple rule is that a 90 percent or higher win probability allows Clinton to run a “some” campaign and forces Trump to run an “and” campaign. I’ll explain.

Right now, Clinton’s lead (6.2 points in the Trump vs. Clinton RealClearPolitics average and 4.8 points when third parties are included) is safe enough that she can take some hits. If Clinton were to take some damage from newly released emails, perform well in the final debate and slightly underperform her polling, she would probably still win. Or if Clinton didn’t perform well at the final debate, endured a few bad news cycles but managed to stave off most other negative news, she would probably still have a lead heading into Election Day. I think of this as a “some” campaign because she only needs to get some things right to maintain her lead. If some events break her way and some don’t, she has enough padding that she’ll likely be in good shape come Nov. 8. And if she keeps gaining over the next few weeks, a landslide victory isn’t out of the question.

Trump, on the other hand, would have to have an extremely good run of luck and/or series of great strategic moves to catch up to Clinton. For example, if news shifted back to a prolonged focus on Clinton’s emails *and* she had another health issue *and* polls underestimated Trump’s support, then he might win the election. In that way, he has to run an “and” campaign. One decent debate or a few news cycles breaking his way probably isn’t sufficient to deplete all of Clinton’s lead. He needs to see a string of helpful developments (or maybe one extended or especially impactful one) in order to catch up to Clinton. And with less than four weeks left on the clock, that’s a very tall order.