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From: gknight@ut-ngp.UUCP (gknight)
Newsgroups: net.sport.football
Subject: Pats in Seven -- the REAL odds.
Message-ID: <2896@ut-ngp.UUCP>
Date: Fri, 31-Jan-86 21:13:57 EST
Article-I.D.: ut-ngp.2896
Posted: Fri Jan 31 21:13:57 1986
Date-Received: Sun, 2-Feb-86 07:28:14 EST
Distribution: na
Organization: UTexas Computation Center, Austin, Texas
Lines: 42

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.