Week 12, In We Delve

Man, rhyming with 12 was tough.

Oh, and bear with me on this tangent.  It won't take long.  You can check for yourself, you DO have a scroll bar.

So I have a final paper for my Linear Algebra class (yes, a math paper) this semester, and it can be written about pretty much anything as long as it can be connected to the subject.  Seriously.  My friend is knitting a hat and writing about how that relates to linear algebra.  I'm not even sure what the scope of linear algebra is, if you're wondering, but as far as I know it's basically a wide-ranging application of matrices.  My friend Nathan and I are tag-teaming on this paper (because we can), and since we are both pretty big sports fans we thought that it would be a good idea to write a paper about some application of linear algebra to sports.

Lo and behold, it turns out that some of the computations involved in the Division I Football BCS system utilize linear algebra!  However, since we don't really care too much about college football (and there's WAY too many schools to get data for), I figured it would be more appropriate to use these calculations to rank something a little smaller, like the teams in the NFL!  Turns out that I've already found two ranking methods (only one of which is actually used) that I could do myself, and I thought that looking at how the rankings for these systems turned out would be a good wrap-up for Week 12 in the NFL.

First, just a few notes:

1. The Bears defense is pretty good, and when their offense is able to harness the ridiculous speed they have at receiver in Johnny Knox and Devin Hester, they're pretty tough to cover (just ask Dmitri Patterson and Joselio Hanson).  Having said that, Andy Reid's late game field-goal shenanigans and useless timeout to avoid a delay-of-game on 3rd-and-19 were bad.

2. I guess the Falcons are the best team in the NFC now?  But if they lost to the Eagles who lost to the Bears who beat the Packers too, where does that leave the Bears?  Why am I still talking about the Bears?

3. I am SO rooting for the NFC West champion to go 7-9, and for that team to be the Rams.  It would involve a first-overall-pick-to-playoffs turnaround that mirrors the Dolphins' 1-15-to-11-5 one-year improvement from 2007 to 2008.  Except that they would still be a losing team.  On a related note, I would not mind so much if the Eagles lost the division to the Giants, because a wild card berth might mean playing a sub-.500 team in the playoffs, and that's just delightful.

4. What in the world is Dwayne Bowe doing?  During the past seven games, in which he has scored a touchdown each time, he is averaging 7 receptions, 105 yards, and 1.9 touchdowns.  As a reference point, if he did that for the entire season, he would have 112 receptions, 1675 yards (7th all-time), and 30 touchdowns (all time record).  And since I have him on a fantasy team or two, that would put him on pace to be the overall leader in fantasy points for this season.  Too bad he had fewer fantasy points in the first 4 weeks of the season than he has had each of the last three weeks...

5. Andre Johnson is a man.  He has an intense deep voice (just check the Nike Vapor Trail Glove commercial), is the first player to record 60+ receptions in his first 8 years in the league, and beats down cornerbacks.  Fortunately, he was able to accumulate fantasy points before he got ejected.  Although I would have appreciated him getting suspended for one game since the Texans play the Eagles this week.


All right, so here's some power rankings based on Linear Algebra!  The two ranking systems are based off of simple data (one by wins/losses, one by points for/against), but use an iterative calculation that allows teams to be accurately compared despite the NFL not having a round-robin format.  Keep in mind that there is no human input into these models, just pure win/loss ratios or points scored/allowed for opponents.  Which looks better to you?

Points For/Against
1. Green Bay Packers (8-3)
2. Atlanta Falcons (9-2)
3. Pittsburgh Steelers (8-3)
4. San Diego Chargers (6-5)
5. New York Jets (9-2)
6. New Orleans Saints (8-3)
T7. Baltimore Ravens (8-3)
T7. Indianapolis Colts (7-4)
9. New England Patriots (9-2)
10. Tennessee Titans (5-6)
...
12. Detroit Lions (2-9)
...
T15. Chicago Bears (8-3)
T15. Miami Dolphins (6-5)
...
T25. Tampa Bay Buccaneers (7-4)
...
27. St. Louis Rams (5-6)  **The NFC-West-leading St. Louis Rams**


Wins/Losses (ranking for other system in parentheses)
1. Atlanta Falcons (2)
2. New England Patriots (9)
3. New York Jets (5)
4. Pittsburgh Steelers (3)
5. Baltimore Ravens (7)
6. New Orleans Saints (6)
7. Chicago Bears (15)
8. Philadelphia Eagles (11)
9. Green Bay Packers (1)
10. Miami Dolphins (15)
...
11. Tampa Bay Buccaneers (25)
...
15. San Diego Chargers (4)
...
24. St. Louis Rams (25)  **Still leading the NFC West**
...
31. Detroit Lions (12)


For the record, I think that an appropriate ranking would be somewhere in the middle of these two systems, and for our paper I'm sure I will find some sort of weighting for the two computations to account for this.  Someone's gotta do some justice with those Lions and Buccaneers...