The question of which swing state is the most important is difficult to answer. I considered at least 4 approaches:
- How well does a candidate do when they win a given state (President Obama wins 92% of the time he wins Ohio)?
- How likely is a candidate to, when he wins, win while simultaneously losing a given state? (When President Obama does win, 2% of those wins include winning Ohio)?
- Which state is the closest to a toss-up? (Iowa at the moment)
- Which state is most likely to put each candidate over 270 electoral votes (Wisconsin at the moment)
Options 3 and 4 are too simple, and don't allow for ranking states. They are too blunt a hammer with which to approach this problem.
Options 1 and 2 do (sort of) allow for ranking of states, and allow for a more complex view of the problem in general. Option 1 is more sensitive to national outcome probabilities (saying Romney wins 10% of the time when he wins State A is different than saying Obama wins 10% of the time when he wins state A since Romney only wins 15% of the time).
For this reason I prefer option 2, which allows a more direct comparison on how important each swing state is to each campaign. I've excluded non-swing states. Obama wins 0% of elections where he loses Vermont, but it's obviously to everyone that if he's losing Vermont he's in big trouble. The same goes for Romney and, say, Georgia.
Below are all 12 states not currently categorized as safe Obama or safe Romney, ordered by how likely Obama was to win in the most current simulation. For each combination of state and candidate the numbers presented are: If the candidate wins the presidency, how likely are they to have done it without winning the given state.
In 12% of the simulations where Obama won, he won despite having lost Florida. In 10% of them he won despite having lost Nevada.
There is more subtlety to this data. The numbers shown, how likely is [candidate] to win the presidency without the help of [state] are inversely correlated with a candidate’s odds of winning that state (0% of Mitt Romney wins include a victory in New York where he can’t win, 100% of them include a victory in Utah where he will win).
States who deviate down from that general trend stand out. They are states where a candidate's paths to victory without that state are fewer than his overall chance to win the state would indicate. Under this principle Ohio and Florida stand out as important for both candidates while Michigan appears important to Mitt Romney. Lastly, Iowa looks unimportant.
This data seem to tag Florida as the most important swing state. Just 12% of Obama victories come without Florida, and just 4% of Romney victories are Florida free.