Ratings of NFL Teams from 1985 to 2012
There are numerous ways to decide which teams were better than others in a given year, and this Demonstration shows four methods across 28 seasons of American professional football. Massey's method relies on points scored and points allowed, and the overall difficulty of the schedule. Colley's method also incorporates the strength of the schedule, but relies only on wins and not on points. One thing is clear: the 2007 and 2012 Giants are two of the worst teams to ever win the Super Bowl.
Let be the Laplacian of the game graph; that is, is the number of games played between team and team , and is the number of games played by team . Let be the column vector whose component is the number of wins less the number of losses of team . Let be the column vector whose component is the number of points scored less the number of points allowed by team .
The Massey ratings are the vector that solves the equation and whose components have mean 21 and standard deviation 7. The Colley ratings are given by the vector that solves the equation . The Colleyized Massey ratings are given by the vector that solves the equation . The Masseyized Colley ratings are the vector that solves the equation .
These four methods are detailed in the first chapters of .
 A. N. Langville and C. D. Meyer, Who's #1?, Princeton, NJ: Princeton University Press, 2012.