### Eight Key States, By The Numbers

by KTinOhio, Thu Sep 11, 2008 at 01:30:21 PM EDT

By most reasonable estimates, Obama has 238 electoral votes firmly in his column, and McCain has 200. The remaining 100 electoral votes are still in play. These votes are found in the following eight states, all of which are within 3% according to 538.com's latest estimates:

Florida, 27 EV

Ohio, 20 EV

Michigan, 17 EV

Virginia, 13 EV

Colorado, 9 EV

New Mexico, 5 EV

Nevada, 5 EV

New Hampshire, 4 EV

Obama needs 32 of these 100 votes to win; 31 will result in a 269-269 electoral tie.

According to 538.com's latest estimates, Obama's probability of winning each of these states is as follows:

Florida, 28% (McCain leads by 3.0%)

Ohio, 33% (McCain leads by 2.2%)

Michigan, 64% (Obama leads by 1.8%)

Virginia, 30% (McCain leads by 2.8%)

Colorado, 45% (McCain leads by 0.6%)

New Mexico, 64% (Obama leads by 1.9%)

Nevada, 33% (McCain leads by 2.6%)

New Hampshire, 71% (Obama leads by 3.0%)

Obama is favored in three of these states, worth 26 electoral votes. So, we're probably looking at a 264-274 loss, right?

Well, probably not. Given eight states, there are 256 (2 to the eighth power) possible combinations of states carried by either candidate. If we assume the states behave independently, we can calculate the joint probability of each of these combinations, and the sum of all combinations that give Obama at least 32 EVs can be taken as the likelihood of victory.

[Strictly speaking, the states probably don't behave independently. If there are large shifts in the national numbers, the states will more more-or-less in unison. But if the national numbers are relatively stable, independent behavior is a more reasonable assumption.]

Without further ado...

Obama wins 63.4% of the time. He wins 203 of the 256 conbimations, but his total probability is lowered because his probabilities of winning individual states tend to be lower than McCain's.

McCain wins 31.9% of the time, 47 of 256 combinations.

The remaining 6 combinations, which collectively occur 4.7% of the time, result in a tie.

Obama's mean electoral vote count is 278.68 (238 + 40.68 of the 100 in play); his median is 277 (238 + 39 of the 100 in play).

**Tags:**
electoral votes, probability
(all tags)

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