## Saturday, October 20, 2012

### College Football Rankings - Week 8 Update

As I mentioned in the comments of my week 8 college football rankings post, the rankings looked a bit out of whack.  I've tinkered with things a bit more and I now think that I've got an approach that I can stick with week to week.  Here is a rundown of the methodology (or you can skip to the bottom for the rankings):

### Weights

My goal is to figure out what the market thinks today, so I weight recent games more heavily.  Here is the weight formula (optimized to best predict the coming week's point spreads):

weight = 1 / (0.2 + weeks ago)

So, the current week gets a weight of 5, last week gets a weight of 0.83, the week prior a weight of 0.45 and so on...

To the extent that a game deviates from the market's expectations, one would figure that the market would factor that in to future estimates.  For example, when Georgia played South Carolina two weeks ago, South Carolina was a 1.5 point favorite.  South Carolina ended up winning the game by 28 points, meaning that the Gamecocks outperformed market expectations by 26.5 points.  If these two teams played again, I assumed the market would recalibrate itself according to the following equation:

I determine the credibility coefficient by finding the value that best predicted future week point spreads. That value was 20%.  Meaning that the college football betting market appears to treat game outcomes with 20% credibility.  So, the revised spread of the Georgia / South Carolina game is 6.8 points (= 1.5 + 0.2 x (28 - 1.5) ).  This is what ultimately gets fed into my ranking methodology.

Home field advantage is assumed to be worth 3.5 points (derived from the past four years of college football point spreads).  Using my South Carolina / Georgia example from above, since South Carolina was at home, my rankings assume the neutral field point spread would be 3.3 points in favor of South Carolina.

### Offense and Defense Rankings

In the ranking table, there are three numbers: GPF (Generic Points Favored), oGPF (Offensive Generic Points Favored), and dGPF (Defensive Generic Points Favored). oGPF and dGPF are just the offensive and defensive components of total team strength, which is represented by GPF.  To decompose team strength into its offensive and defensive components, I use the betting over/under in conjunction with the point spread.  For example, the Georgia / South Carolina game had a point spread of 1.5 points and an over/under of 54 points.  Using some simple algebra, the implied score is 27.75 for South Carolina and 26.25 for Georgia.  So, the regression equations looks something like this:

South Carolina Offense + Georgia Defense = 27.75
South Carolina Defense + Georgia Offense = 26.25

Where each team is now represented by two independent variables, one for offense and one for defense.  Looking at the table below, the number one ranked offense is Oregon and the number one ranked defense is Alabama, neither of which should be a surprise.

### The Rankings

Continuing with my unhealthy sparkline obsession, next to each team's GPF is a sparkline showing how the team's GPF rank has progressed from week 4 to week 8. The scale is identical for all teams, with the top of the scale representing #1 and the bottom #50 (if there is a gap, that's when the team dropped out of the top 50).