Friday, September 12, 2008

How Obama Wins

I've gone through this math so many times in my head that I think I can write this without looking anything up (not sure if I'm proud of that or not). Obama has an electoral college base of 252, what Kerry won in 2004. I'll subtract New Hampshire from this (-4), because Granite Staters seems to like McCain, but I'll add Iowa (+7), because poll after poll shows Obama winning that state, so now Obama is at 255, with 269 needed to win (270 is needed to win outright, but a tie would almost certainly result in an Obama victory).

Okay, so where to get the other 14. Three general ways:

1) Several states would do it outright: North Carolina (15), Ohio (20), or Florida (27).

2) So would a combination of New Hampshire (4), New Mexico (5) and Nevada (5).

3) Or take out any two of those and add in Colorado (9) or Virginia (13).

Notice how there are a lot of 'or' statements in here, meaning additive events from a probability standpoint. From the McCain perspective, however, they are 'and' statements.

1) McCain needs to win North Carolina AND Ohio AND Florida. Lets's say he has a 90%, 60%, and 70% chance, respectively, in each of those states. This results in a 38% chance of him winning all three (.9 x .6 x .7). And that has only fended off possibility 1 for Obama.

2) Let's say that McCain has a 50%, 50%, and 60% chance for the states in scenario 2; here, he only needs to win one of the three, so that's a 90% chance (1 - .5 x .5 x .4). But, there is an 85% chance Obama wins one of them (1 - .5 x .5 x .6), and this number is important for scenario three:

3) Scenario three is a bit more complicated, because there are multiple combinations. Let's say that McCain has a 50% chance in Colorado and a 60% chance in Virginia. He must win at least one of them, which he has an 80% chance of doing (1 - .5 x .4). However, Obama has a 70% chance of winning at least one of them (1 - .5 x .6). And, don't forget that Obama also wins at least one of the scenario 2 states 85% of the time. So, back of the envelope calculation, Obama either wins both CO and VA, or one of them and at least one of the smaller states, about 60% of the time, meaning McCain prevents this Obama route to victory about 40% of the time.

Okay, so admittedly these are estimates, don't take into account all possibilities, etc. etc. But all I'm looking for is a ballpark. McCain has to triumph in all three scenarios, which is .38 x .90 x .40 = John McCain wins this election ~14% of the time. That's why I'm confident Obama will win.