Numbers Game
Ahhhh, the binomial distribution.
Let’s take the following values:
Bush: 2,794,346
Kerry: 2,658,125
Provisional Ballots: ~175,000
Now, if we make this a two-person race—hey, we’re approximating provisional ballots, so we can approximate the race as a two-person race—we can figure out Kerry’s odds of winning with enough provisional ballots as a binomial distribution.
Bush has a delta of 136,221 votes, meaning that Kerry would need 136,222 votes more than Bush amongst the ~175,000 provisional votes. This means that Kerry would need 155,612 votes of 175,000 remaining to be counted—if we again assume that every provisional will be counted. [The nature of provisionals is that some are going to be tossed out. If ~20,000 are tossed out, it's game over. That may be a reasonable assumption alone, but I've been thinking about this entry all night, and I'm not stopping now.]
So, the P(155,612) in this case has the following conditions:
N = 175,000
r = 155,612
pi = … uhhh …
There are two ways you could look at pi. One is that pi should be approximated from the present totals, which assumes that the millions of votes we have now reflect the population as a whole, and what we have is a random sampling from that pool. The other approximation of pi could be 0.5, since one over an exact tie is what Sen. Kerry needs to be Pres. Kerry. Hell, let’s do both.
P(155,612) where pi = 0.49 [Kerry's current percentage of the vote]: a number neither my calculator nor Excel will process.
Aha! Vassar to the rescue! Their calculator says: <0.000001, or in other words, less than 0.0001%.
Wow, I think my chances of being President are better.
[No point in running the other pi, I don't guess.]
Uhhhhh… Geof is realie smurt.
November 3rd, 2004 at 10:43Awww, Ryan, you didn’t have to take stats? I thought they made everyone in college take stats.
November 3rd, 2004 at 10:44i think it’s now clear that geof is skynet, the supercomputer that destroyed the world in the terminator. glad arnold is still around! lol.
November 3rd, 2004 at 10:48I was thinking about this during this morning, but I’m glad someone who’s far better at math than me actually figured it out.
November 3rd, 2004 at 10:50The thing is most people don’t remember the stats they took!
November 3rd, 2004 at 10:51Hell, I had to look it up to be sure, but that might be because I got about two hours’ sleep.
November 3rd, 2004 at 10:57NERD! Or would that be Presidential Hopeful Nerd, since your chances are better?
November 3rd, 2004 at 10:59Well Geof, Kerry must be reading your website. Kerry has conceded.
November 3rd, 2004 at 11:01[...] I would be much remiss if I didn’t at least mention a nice statistical analysis that a guy I’m familiar with (he runs the Caedmon’s Call fan website) posted on his blog last night in the middle of the Ohio discussion… way to go, Geof! [...]
December 9th, 2005 at 12:49