Team Rating = (Power + Efficiency)/2

One of the most important parts of my ranking system is the Team Rating. Team Rating is a value based solely on performance and independent of achievement. What's the difference? In football achievement is measured in wins, losses, and championships. Performance is how a team played, how many yards did they gain, how many points did they score, etc. Very often a team's achievement is not reflected in their performance which is why both should be considered when ranking teams. This is in stark contrast to the pollsters who tend to focus on a team's W/L record above all else. This leads to situations where weak teams luck into high rankings. Case in point, UCLA 2005. The Bruins finished 10-2 with huge blowout losses to USC and craptacular Arizona (3-8). UCLA played four close conference games and needed serious 4th quarter rallies to win or get into overtime. Three of those games were against the worst teams in the Pac-10 (Stanford [5-6], Washington St [4-7], Washington [2-9]). Yet somehow they ended up ranked 13th in the coaches poll. If you look at their Pythagorean Win Percentage, it's 57.9%, which suggests they performed at a level consistent with a 7-5 record, hardly top 15 material. This is precisely why I include a performance based component to my rankings.

What is Team Rating?
As the title of this post suggests, it's the average of a team's Power and Efficiency, which begs the question, What is Power and Efficiency?

Power
A team's Power is an average of a team's normalized Offensive and Defensive moduluses (moduli?). What does Offensive Modulus tell us? It's based on the Yards per Game statistic so, OMod is how good a team is at moving the football, adjusted for the defensive performance of it's opponents. Similarly, Defensive Modulus is based on Yards Given Up per Game and tells us how good a team is at holding the opponent to as few yards as possible. Why use yards and not points? After all, it's points that win the game. Well, the range of possible values a team's score can take goes from about 0 to 70, while a team can gain anywhere from 0 to 600 yards. A lucky break (a fumble recovered for a touchdown) has a much more significant impact (10% of the maximum value) on a team's score than it's total yardage, so yards gained will have less error than points scored.

Efficiency
Efficiency is an average of a team's normalized Yards Per Point and Yards Per Point Given Up (or as I like to call them, Offensive and Defensive Efficiency). These values tell us how good a team is at scoring and keeping their opponent from scoring. Also, as I explained in a previous post they contain other information about a team, such as special teams play and the effect of turnovers.

So by combining, in equal parts, a team's Offensive Modulus, Defensive Modulus, Offensive Efficiency, and Defensive Efficiency we get a value that contains information on a team's ability to gain yards, score points, stop it's opponents from gaining yards and scoring points, and a little bit about special teams and turnovers. Team Rating is a good composite of performance-based metrics and is completely independent of a team's W/L record.

Addendum - Why Normalize?
In order to combine two opposing statistics (one where higher values are better and one where lower values are better) in a meaningful way you have to get them both on the same scale. This is especially true if there is no limit to the possible range of values the stats can take. To normalize the values in a set, you subtract the lowest value from each member and then divide each member by the highest value. The result is a range of values from 0 to 1 where the ordering and relative distance between values is preserved. So if you normalize the Offensive Modulus, the team with the highest score has a value of 1 and the worst team has a value of 0. For Defensive modulus the opposite is true. However, since they're now scaled the same (between 1 and 0), you can average the two by subtracting the normalized defensive modulus values from 1.