**If you are reading this directly instead of linking here, this relates to the section under the interactive map on the 270toWin home page called "The Probability of 270".**
However you get here, it is important to point out up front that the outcome of this exercise is statistically valid based on current polls and is not a projection of the election. The election could turn out completely differently than the displayed results but it doesn't mean that the underlying polls used were inaccurate. They could have been perfectly accurate when they were taken, but we'll never know since we only vote on Election Day. So don't read more into these numbers than is actually there.
Although it is rarely presented this way, statistical theory makes it possible to take the results of a state poll and calculate the probability that either candidate will actually win that state's popular vote, and thus collect its electoral votes. For example, let's say that a poll with a sample size of 600 for Missouri comes back 48% for Candidate A and 44% for Candidate B, with 8% other, undecided or some other response. Since a victory by 10 votes is the same as a victory by one million votes  the winner gets the full electoral college bounty for the state, the only question we are trying to answer is: "Given these results, what is the probability that Candidate A will actually get more votes than Candidate B in Missouri?" In this specific case, the answer is about 85%.
It is important to note that, for example, a 4% spread doesn't always equate to 85%. The number will vary based on the number of people sampled and will also vary based on the proportion of undecided/other is in the results. Smaller sample sizes and more undecided responses lead to greater uncertainty in the outcome, pushing the probabilities toward 5050. Of course, a smaller spread between candidate A & B will also result in a probability closer to 5050.
For those interested in even more detail, see below. An example is provided inside the < >.
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