Modulus

It's a classic debate... Are Pac-10 teams' offenses strong because they play against weak defenses? Are SEC teams' defenses so strong because they play against stodgy old-school offenses? Given the enormous differences in quality between the best and worst teams in Division 1-A, there needs to be a statistic that gives more information about offensive and defensive strength than the classic Yards and Points per game metrics. There needs to be a statistic that factors in the strength of a team's opponent. Laying half-a-hundred on Temple is a lot less impressive than doing the same to a team like LSU or Ohio State.

Enter the Modulus...

Modulus - A quantity that expresses the degree to which a substance possesses a property.

Modulus Example: Offensive Scoring Modulus or OSMod
The OSMod is intended to replace the Points/Game metric and will give us an idea of how good a team is at putting points on the board.

Here's how it's done:
In three of LSU's games from 2006 the Tigers beat Miss St 48-17, lost to Florida 23-10, and smashed Kentucky 49-0. To find the Tigers' OSMod for these three games we need to divide the number of points LSU scored in each game against the average number of points given up by the opposing defense.
Game 1: Miss St gave up an average 27.8 ppg in 2006. So we divide 48 by 27.8 and get 1.73.
Game 2: Florida gave up 14.5 ppg so 10/14.5 = 0.69
Game 3: Kentucky gave up 30.2 ppg, 49/30.2 = 1.62
To get the total OSMod for these three games we just average the three scores.
(1.73 + 0.69 + 1.62)/3 = 1.35

So what does this mean? It means that LSU typically scores 1.35 times as many points as it's opponents allow on average. A much more telling number than simply 35.7 ppg.

You can, of course, do this for any basic statistic although it might not be worth the effort to compute a team's modulus of penalization (or whatever you might call it).

On a week-to-week basis I keep track of the following moduli (moduluses?):
Offensive Modulus (Yards Per Game)
Defensive Modulus (Yards Given Up Per Game)
Offensive Scoring Modulus (Points Per Game)
Defensive Scoring Modulus (Points Given Up Per Game)
Passing Modulus (Passing Yards Per Game)
Pass Defense Modulus (Pass Yards Given Up Per Game)
Rushing Modulus (Rushing Yards Per Game)
Rush Defense Modulus (Rushing Yards Given Up Per Game)

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So, How much difference does it make?
Take a look at the average points per game vs the offensive scoring modulus for each of the 11 conferences and independents:

POINTS PER GAME (Conference Averages)
Big XII	26.593
WAC	26.556
Big East	26.363
Big Ten	24.715
SEC	24.176
Conference USA	23.747
Pac-10	23.712
Mountain West	22.841
Independents	21.551
ACC	21.438
MAC	21.027
Sun Belt	16.681

OFFENSIVE SCORING MODULUS (Conference Averages)
Big East	1.18272
SEC	1.14331
Big XII	1.08517
Big Ten	1.06165
Pac-10	1.03700
ACC	1.01066
Mountain West	0.97037
WAC	0.95246
Conference USA	0.92564
Independents	0.90664
MAC	0.85022
Sun Belt	0.66869

That's a pretty significant shake-up. It also tells us that when it comes to giving up points, the Big East is significantly stingier than the Big XII. Suprised anyone?
Also, only the six BCS conferences managed to crack the 1.0 mark which is the modulus version of breaking even. Another neat thing you can do with this table is divide the Points Per Game by Offensive Scoring Modulus and find out what the average number of points each conference's opponents gave up. For the SEC, it's a mere 21 ppg, for the WAC it's almost 28!