Date: Dec 28, 2012 5:32 AM
Author: Scott Hemphill
Subject: Re: Modeling of NFL game results

Ray Koopman <koopman@sfu.ca> writes:

[snip]

> 2. If win[x,m,n] is supposed to give the log of the probability
> that m beats n then low ratings are better than high ratings,
> which is fine if that's what you want.


Right. Here are the ratings through week 16.

29 Texans -0.28
14 Falcons -0.16
4 Broncos -0.12
19 Packers -0.10
21 Patriots -0.02
0 49ers 0.00
27 Seahawks 0.16
1 Bears 0.23
31 Vikings 0.31
24 Ravens 0.42
10 Colts 0.44
25 Redskins 0.55
23 Rams 0.57
15 Giants 0.61
11 Cowboys 0.69
2 Bengals 0.81
26 Saints 0.89
12 Dolphins 0.91
7 Cardinals 0.97
17 Jets 1.00
28 Steelers 1.06
20 Panthers 1.09
6 Buccaneers 1.17
18 Lions 1.18
30 Titans 1.18
3 Bills 1.30
8 Chargers 1.32
5 Browns 1.42
13 Eagles 1.45
22 Raiders 1.81
16 Jaguars 1.87
9 Chiefs 2.20

> 3. The solution is finite only if every team has won at least
> one game and lost at least one game. That doesn't happen until
> after week 10. After that the problem is well conditioned and
> you shouldn't need to mess with the precision.


Yes, I was aware of this. However, "FindMaximum" doesn't step to
infinity, and "prob[x,m,n]" returns sensible, if inaccurate, results.
(It will always find that a team with a perfect record has an estimated
100% chance of beating a team with an imperfect record.) The
predictions earlier in the season weren't really very good, but lately
they've been outperforming those of Elliot Harrison on his nfl.com blog.

Scott
--
Scott Hemphill hemphill@alumni.caltech.edu
"This isn't flying. This is falling, with style." -- Buzz Lightyear