9813

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.
  • Contributed by: Kevin O'Bryant
  • City University of New York, College of Staten Island and The Graduate Center

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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 [1].
Reference
[1] A. N. Langville and C. D. Meyer, Who's #1?, Princeton, NJ: Princeton University Press, 2012.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+