This might be my favorite graph that we’ve done so far: a comparison of Barack Obama’s popular and electoral vote totals across the first 1,000 simulations that we ran last night:

Several interesting things to point out:

1. The relationship between the popular vote and the electoral vote is approximately linear, except at the endpoints. As a rule of thumb, a gain of one percentage point in a Obama’s popular vote share results in a gain of 25 electoral votes. This is also, you will note, a pretty steep slope. If Obama wins the election by 4 percentage points, he projects to win by approximately 100 electoral votes (319-219).

2. The regression line crosses the y-intercept at 269.3 electoral votes, which is almost exactly half of 538. That means that there does not appear to be any systematic advantage in the electoral vote math to one candidate or another, at least based on our present rendering of these numbers.

3. Where you do see a little bit of skew are those scenarios where one candidate wins by about 5-15 percentage points. In those cases, the winning candidate tends to win by more electoral votes than is predicted by the regression line. This is because an especially high number of states are within reach for one or another candidate. In contrast to 2004, when 16 states and the District of Columbia were decided by 20 or more points, very few are polling that way this year.

4. The range of possible outcomes given any specific value of the popular vote is about 80-100 electoral votes wide. For example, an Obama win by 5 percentage points could easily be associated with any number from about 290 electoral votes up to as many as 390, depending on how the individual states shake out. Likewise, for any given value of the electoral vote, the range of the popular vote margin is about 6 or 7 percentage points wide. What this means, among other things, is that it’s virtually impossible for a candidate to win the electoral college while losing the popular vote by more than about 3 or 3.5 percentage points.

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