gknight@ut-ngp.UUCP (gknight) (02/01/86)
Okay, folks -- here's how to mathematically resolve the question concerning the Pats chances of winning a 7-game series against the Bears. First, the line was 10 points. That's the most favorable number for the Pats since the line didn't move appreciably in two weeks and since the only other alternative would be to use the regular season game which had a larger spread. Points can be converted to odds by an empirical formula (based on the last 5 years' NFL data). Ten points = 4-1 odds, or a .20 probability of winning the game. Given that figure, we can use the geometric distribution equation to figure the Pats chances of winning 4 games in 4, 5, 6, or 7 games, respectively. That equation, for those who don't carry it around in short term memory, is: p(n;r,p) =((n-1)! / (r-1)!(n-r)!)) / p**r * q**(n-r) where n = the nth game in the series; r = the rth success (4th in our application); and p = the probability of winning a single game (.20 in our case). So the Pats chances of winning in the following ways are: 4 out of 4 = .0016 4 out of 5 = .0051 4 out of 6 = .0102 4 out of 7 = .0164 for a total chance of winning the seven game series in *any* fashion of: .0333 (i.e., just a tad over 3%) Now we know!!!!! -- Gary Knight, 3604 Pinnacle Road, Austin, TX 78746 (512/328-2480). Biopsychology Program, Univ. of Texas at Austin. "There is nothing better in life than to have a goal and be working toward it." -- Goethe.