Jon and I were debating the following pet theory of mine during Monday Night Football: if you've just scored a touchdown to go up 7 very near the end of a football game, you should go for two and not one. Jon told me I was wrong, and after some probability calculations we decided that I probably am wrong. But I decided to check it out with slightly more rigour now.

So here's the math. I've made several simplifying assumptions, e.g. that the chance of making an simple extra pt is 1.0, that the opposing coach will play for the tie if he scores a touchdown and he's down 1, and that the probability of winning in regulation if you convert the two is 1.0. Of course, we're assuming that the other team will score a touchdown because that's the only relevant case. Without further ado:

x = 2pt conversion success rate for both teams
p = your team's chance of winning in overtime

prob. of winning going for 2 > prob. of winning going for one

(explanation: the addends on both sides of the first inequality are the probability of winning in regulation and the probability of winning in overtime, respectively)

x + (1-x)p > (1-x) + xp
x + p-xp > 1-x + xp
2x - 2xp + p -1 > 0
2x(1-p)-(1-p) > 0
2x - 1 > 0 [since p < 1, 1-p > O]
2x > 1
x > .5

So it turns out my strategy is a good one if the 2pt conversion rate is greater than .5 (which it is not) and a bad one otherwise, regardless of one's chances of winning in overtime, which is perhaps counterintuitive. Though I haven't done ol' al-jabr in quite a while, so it wouldn't surprise me if I've made a mistake.

Of course, if the 2pt conversion rate were greater than .5, my assumption that the other coach will go for the tie if down 1 would be wrongish.

Just to be clear dear friends: I don't really care about this, but the alternative would for me to blog about Rawls, feminist philosophy, introductory ethics or Anselm (i.e. my current slate of school stuff).  ¶ 11:21 PM