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For more from Chase and Jason, check out their work at Football Perspective and The Big Lead.

Twice the simplicity

Posted by Doug on August 21, 2007

Back when I used to write blog posts, I would frequently use this simple rating system as a quick gauge of team quality. To refresh your memory, it's a system that's been around forever and is extremely basic compared some of the other power rating systems out there. But I like it because it's easy to understand. An average team will have a rating of zero. An above average team will have a positive rating while a below average team will have a negative rating. Every team will have a rating that is the equal to their average point margin plus the average of their opponent's ratings, so the teams' ratings are all interdependent: the Colts' rating depends upon the ratings of all their opponents, which depends upon the ratings of all their opponents (some of which are the Colts), and so on. The 2006 Steelers had a rating of +3.4. They outscored their opponents by an average of 2.4 points per game, while their opponents were on average, according to the same kind of calculation, 1.0 points better than average. Hence we estimate that the Steelers must be 3.4 abstract theoretical points better than an abstract theoretical average team.

Another project I was working on --- and that either Chase or I will be writing about soon --- prompted me to do something I've been meaning to do for awhile, which is to separate the simple rating system into an offensive and a defensive component. Doing so, we find that the Steelers +3.4 rating breaks down into +3.0 on offense and +0.4 on defense. Meanwhile, their strength of schedule of +1.0 breaks down as +1.6 for offense and -0.5 for defense (ignore the rounding discrepancy). Here's what all that means:

The Steelers' offense scored 1.4 points per game more than an average team, but they faced defenses that, all things considered, were 1.6 points better than average. So morally the Steelers' offense was 3.0 points per game better than average.

The Steelers' defense allowed 0.9 points per game fewer than average, but the offenses they played were on average 0.5 points below average. So morally, the Steelers D was only 0.4 points per game better than average.

When you put these two facts together (and again ignore the rounding discrepancies), you get the same numbers as in the first paragraph. So what we've done is to break down the Steelers' rating --- and their strength of schedule --- into two pieces. Here are the offensive and defensive ratings for each team last season:

                offense          defense          total
            rating   SOS     rating   SOS     rating   SOS
==========+================+================+===============
nwe 2006  |   +4.3   +0.9  |   +5.9   +0.1  |  +10.2   +1.0
sdg 2006  |  +10.0   -0.1  |   +0.2   -1.5  |  +10.2   -1.6
bal 2006  |   +1.5   +0.1  |   +7.8   -0.3  |   +9.3   -0.2
chi 2006  |   +4.9   -1.1  |   +3.0   -1.7  |   +7.9   -2.9
jax 2006  |   +2.6   +0.1  |   +4.9   +1.3  |   +7.5   +1.4
ind 2006  |   +6.9   +0.9  |   -1.1   +0.8  |   +5.9   +1.7
cin 2006  |   +4.0   +1.4  |   +0.0   +0.1  |   +4.1   +1.5
nor 2006  |   +4.9   -0.2  |   -0.9   -1.4  |   +4.0   -1.6
dal 2006  |   +5.0   -0.9  |   -1.3   -0.1  |   +3.7   -1.0
pit 2006  |   +3.0   +1.6  |   +0.4   -0.5  |   +3.4   +1.0
phi 2006  |   +3.2   -1.0  |   +0.2   +0.0  |   +3.4   -1.0
buf 2006  |   -0.2   +1.7  |   +2.4   +1.2  |   +2.2   +2.9
nyj 2006  |   +0.4   +1.3  |   +1.7   -0.5  |   +2.0   +0.7
den 2006  |   -0.8   -0.1  |   +2.1   +0.5  |   +1.3   +0.4
kan 2006  |   +0.4   +0.4  |   +0.6   -0.4  |   +1.0   -0.0
mia 2006  |   -3.3   +1.1  |   +4.0   +1.1  |   +0.7   +2.1
nyg 2006  |   +1.2   -0.3  |   -1.1   +0.8  |   +0.1   +0.5
ten 2006  |   +1.0   +1.4  |   -2.3   +2.0  |   -1.3   +3.5
car 2006  |   -4.2   -0.4  |   +1.5   -0.1  |   -2.7   -0.5
atl 2006  |   -2.8   -0.4  |   -0.2   -0.4  |   -3.0   -0.8
sea 2006  |   -1.6   -1.9  |   -1.9   -1.3  |   -3.6   -3.2
stl 2006  |   +0.8   -1.5  |   -4.7   -1.6  |   -4.0   -3.1
was 2006  |   -2.1   -0.6  |   -2.0   +0.9  |   -4.0   +0.3
min 2006  |   -3.7   -0.6  |   -0.4   -0.7  |   -4.1   -1.3
gnb 2006  |   -2.3   -0.4  |   -2.1   +0.1  |   -4.4   -0.4
hou 2006  |   -3.2   +0.8  |   -1.3   +0.9  |   -4.5   +1.7
cle 2006  |   -4.5   +1.3  |   -1.3   +0.3  |   -5.8   +1.5
det 2006  |   -1.8   -0.2  |   -4.6   -0.4  |   -6.4   -0.5
ari 2006  |   -2.6   -1.6  |   -4.3   -0.6  |   -6.9   -2.2
tam 2006  |   -7.2   +0.3  |   -0.8   +0.7  |   -7.9   +0.9
sfo 2006  |   -3.5   -1.4  |   -5.2   -0.2  |   -8.7   -1.6
oak 2006  |  -10.3   -0.2  |   +0.7   +0.8  |   -9.6   +0.6

Some basic SRS trivia:

Best and worst offenses since 1970

                offense          defense          total
            rating   SOS     rating   SOS     rating   SOS
==========+================+================+===============
min 1998  |  +13.2   -0.2  |   +1.6   -1.1  |  +14.9   -1.4
stl 2000  |  +12.6   -0.4  |   -9.5   -0.7  |   +3.1   -1.2
was 1983  |  +11.7   -0.2  |   +2.2   +1.1  |  +13.9   +0.9
ind 2004  |  +11.7   +0.6  |   -0.3   +0.1  |  +11.4   +0.7
was 1991  |  +11.7   +0.4  |   +4.9   -0.0  |  +16.6   +0.3
sdg 1982  |  +10.5   -1.3  |   -5.4   -1.0  |   +5.1   -2.3
stl 2001  |  +10.4   -0.8  |   +2.9   -0.2  |  +13.4   -1.0
buf 1975  |  +10.4   +1.0  |   -3.4   +1.4  |   +7.1   +2.4
kan 2004  |  +10.0   +1.3  |   -4.7   +1.0  |   +5.3   +2.3
sdg 2006  |  +10.0   -0.1  |   +0.2   -1.5  |  +10.2   -1.6
sfo 1993  |   +9.9   -0.9  |   -0.3   -0.5  |   +9.7   -1.5
sfo 1994  |   +9.9   -1.4  |   +1.7   -0.0  |  +11.6   -1.4
den 1998  |   +9.5   -0.5  |   -0.6   -2.6  |   +8.9   -3.1
bal 1976  |   +9.3   -1.3  |   +0.4   -1.1  |   +9.8   -2.5
kan 2003  |   +9.2   -0.2  |   -0.9   -1.0  |   +8.3   -1.2
sdg 1981  |   +9.2   -0.0  |   -4.7   -1.0  |   +4.4   -1.1
mia 1984  |   +9.1   -1.8  |   +1.5   -1.1  |  +10.6   -2.9
sfo 1998  |   +8.8   +0.2  |   +1.8   +1.0  |  +10.6   +1.2
sfo 1987  |   +8.8   -0.2  |   +4.2   -0.5  |  +13.1   -0.7
oak 1977  |   +8.8   +0.9  |   +1.6   +0.9  |  +10.4   +1.7
stl 1999  |   +8.7   -3.4  |   +3.2   -2.5  |  +11.9   -5.9
gnb 1996  |   +8.7   +0.6  |   +6.6   -0.7  |  +15.3   -0.1
nyj 1982  |   +8.7   +1.6  |   +1.6   -0.1  |  +10.3   +1.5
dal 1983  |   +8.6   +0.5  |   -0.1   +0.6  |   +8.5   +1.1
kan 2002  |   +8.4   +0.9  |   -2.3   +1.0  |   +6.1   +1.9
sdg 1985  |   +8.3   +0.7  |   -7.2   -1.6  |   +1.1   -0.9
dal 1971  |   +8.3   -1.4  |   +1.6   -1.9  |   +9.9   -3.3
ram 1973  |   +8.2   -0.1  |   +5.2   -1.5  |  +13.4   -1.6
ind 2003  |   +8.2   +1.0  |   -1.2   -1.0  |   +7.0   +0.0

.....

cin 1993  |   -7.4   -0.4  |   -1.0   +0.2  |   -8.4   -0.2
chi 1974  |   -7.4   -0.1  |   -2.9   -1.2  |  -10.3   -1.2
sea 1982  |   -7.4   -1.4  |   +2.0   -1.8  |   -5.4   -3.2
tam 1983  |   -7.5   -0.7  |   -1.6   +0.4  |   -9.0   -0.3
nwe 1990  |   -7.5   +1.3  |   -7.1   +0.7  |  -14.6   +2.0
cle 1999  |   -7.6   -0.4  |   -6.5   +0.0  |  -14.1   -0.3
dal 1989  |   -7.6   +0.2  |   -2.8   +1.2  |  -10.4   +1.4
sdg 1998  |   -7.7   -1.4  |   -0.7   -0.6  |   -8.4   -2.1
nwe 1991  |   -7.9   -2.1  |   -0.8   -0.7  |   -8.7   -2.8
nyj 1995  |   -7.9   -1.0  |   -3.3   -0.8  |  -11.2   -1.7
atl 1987  |   -7.9   +0.0  |   -5.9   +1.5  |  -13.9   +1.5
cin 2000  |   -8.1   +1.0  |   -2.4   -0.6  |  -10.5   +0.4
dal 2002  |   -8.2   -0.1  |   -0.3   -1.4  |   -8.5   -1.5
nor 1975  |   -8.2   +0.6  |   -5.9   -0.7  |  -14.1   -0.1
hou 2002  |   -8.4   -0.0  |   -1.1   -0.5  |   -9.4   -0.5
chi 2004  |   -8.5   -1.4  |   +0.3   -0.5  |   -8.2   -2.0
cle 2000  |   -9.1   +1.5  |   -5.5   +0.0  |  -14.6   +1.5
gnb 1977  |   -9.1   -1.5  |   +0.4   -1.1  |   -8.7   -2.6
bos 1970  |   -9.1   -0.5  |   -6.8   -0.2  |  -15.9   -0.7
phi 1972  |   -9.2   +0.7  |   -5.3   -0.4  |  -14.6   +0.2
buf 1985  |   -9.5   -0.5  |   -0.2   +2.0  |   -9.8   +1.5
atl 1974  |   -9.7   +0.6  |   -2.6   -1.5  |  -12.3   -0.9
sea 1992  |   -9.8   +0.2  |   -0.2   +0.6  |  -10.0   +0.8
oak 2006  |  -10.3   -0.2  |   +0.7   +0.8  |   -9.6   +0.6
tam 1976  |  -10.8   -0.6  |   -8.8   +1.4  |  -19.7   +0.8
tam 1977  |  -11.1   -1.3  |   +0.3   -0.9  |  -10.7   -2.2
ind 1991  |  -11.5   -1.5  |   -5.7   -0.9  |  -17.3   -2.4
phi 1998  |  -12.3   -1.1  |   -0.5   -0.2  |  -12.8   -1.3

Best and worst defenses since 1970

                offense          defense          total
            rating   SOS     rating   SOS     rating   SOS
==========+================+================+===============
min 1971  |   -3.4   -1.5  |   +9.9   +0.5  |   +6.5   -1.1
tam 2002  |   -1.0   -0.9  |   +9.8   +0.4  |   +8.8   -0.6
pit 1976  |   +5.7   +0.4  |   +9.6   +0.3  |  +15.3   +0.8
chi 1985  |   +6.5   -0.5  |   +9.4   +0.3  |  +15.9   -0.2
den 1977  |   +1.9   -0.5  |   +9.4   +2.8  |  +11.3   +2.3
min 1970  |   +5.9   +1.2  |   +9.2   +0.1  |  +15.1   +1.4
pit 1975  |   +5.4   -0.7  |   +8.8   -0.2  |  +14.2   -0.9
ram 1975  |   +0.5   -1.2  |   +8.7   -2.3  |   +9.1   -3.5
bal 1971  |   +2.0   -1.0  |   +8.5   -0.9  |  +10.4   -1.9
mia 1973  |   +5.0   -0.1  |   +8.2   -0.5  |  +13.2   -0.6
bal 2000  |   +0.0   -0.1  |   +8.0   -2.3  |   +8.0   -2.5
bal 2006  |   +1.5   +0.1  |   +7.8   -0.3  |   +9.3   -0.2
chi 1986  |   -0.1   -1.6  |   +7.7   -1.1  |   +7.6   -2.7
nyg 1990  |   +0.0   -0.8  |   +7.6   +0.7  |   +7.7   -0.1
buf 1999  |   -0.2   +0.6  |   +7.4   +0.9  |   +7.1   +1.5
mia 2000  |   +0.0   +0.5  |   +7.1   +0.5  |   +7.1   +1.0
nor 1992  |   +0.7   -1.2  |   +7.1   +1.0  |   +7.8   -0.2
chi 2001  |   +0.8   -0.1  |   +7.1   -0.5  |   +7.9   -0.5
min 1973  |   +1.7   -0.0  |   +7.0   -0.5  |   +8.6   -0.5
den 1978  |   -1.9   -1.2  |   +6.9   +1.0  |   +5.0   -0.2
kan 1995  |   +0.8   -0.1  |   +6.9   +0.4  |   +7.6   +0.3
phi 1980  |   +2.9   -0.6  |   +6.8   +0.2  |   +9.7   -0.4
ten 2000  |   +1.5   +0.6  |   +6.8   -1.9  |   +8.3   -1.3
phi 2001  |   +0.9   -0.3  |   +6.8   -0.4  |   +7.7   -0.7
bal 2004  |   -0.6   +1.0  |   +6.8   +2.0  |   +6.1   +3.1
tam 1999  |   -4.1   -0.2  |   +6.7   +0.6  |   +2.6   +0.4
oak 1973  |   +0.1   -1.3  |   +6.7   -0.3  |   +6.8   -1.6
phi 1981  |   +2.0   -0.3  |   +6.7   -0.2  |   +8.7   -0.5
den 1984  |   +1.0   +0.1  |   +6.7   +0.5  |   +7.7   +0.7

.....

nwe 1990  |   -7.5   +1.3  |   -7.1   +0.7  |  -14.6   +2.0
hou 1982  |   -3.9   +1.2  |   -7.1   -0.0  |  -10.9   +1.2
nyj 1975  |   -1.2   +0.9  |   -7.1   +3.2  |   -8.3   +4.2
gnb 1983  |   +5.2   +0.3  |   -7.1   -1.5  |   -1.9   -1.2
sdg 1985  |   +8.3   +0.7  |   -7.2   -1.6  |   +1.1   -0.9
nyj 1996  |   -2.5   +0.5  |   -7.6   +0.3  |  -10.1   +0.8
phi 1973  |   +3.4   +0.7  |   -7.7   +0.9  |   -4.3   +1.6
ram 1982  |   +1.0   -1.1  |   -7.8   -0.1  |   -6.8   -1.2
cle 1990  |   -5.2   +0.7  |   -7.8   +1.0  |  -13.0   +1.7
hou 1983  |   -3.7   +0.2  |   -7.9   -0.9  |  -11.5   -0.8
ari 2000  |   -7.2   +0.4  |   -8.1   -1.1  |  -15.2   -0.7
min 1984  |   -2.7   +1.3  |   -8.2   +0.9  |  -10.9   +2.1
cin 1999  |   -3.3   -0.2  |   -8.2   -0.3  |  -11.5   -0.5
sdg 1973  |   -3.6   +2.4  |   -8.3   -0.2  |  -11.9   +2.2
sfo 2004  |   -5.1   +0.2  |   -8.6   -1.8  |  -13.6   -1.6
sea 1977  |   +4.2   +1.3  |   -8.6   +0.9  |   -4.3   +2.2
tam 1976  |  -10.8   -0.6  |   -8.8   +1.4  |  -19.7   +0.8
atl 1996  |   -0.2   +0.9  |   -8.9   -0.5  |   -9.1   +0.4
buf 1971  |   -4.5   +1.7  |   -8.9   -0.1  |  -13.4   +1.6
nor 1980  |   -1.1   +1.2  |   -9.4   +0.6  |  -10.4   +1.8
nor 1977  |   +0.3   +0.9  |   -9.4   -2.6  |   -9.2   -1.7
stl 2000  |  +12.6   -0.4  |   -9.5   -0.7  |   +3.1   -1.2
ind 2001  |   +6.1   +0.5  |   -9.8   +0.3  |   -3.8   +0.8
tam 1986  |   -4.6   +1.0  |  -10.8   -1.8  |  -15.4   -0.8
nwe 1972  |   -6.3   +0.2  |  -11.1   +0.6  |  -17.4   +0.7
bal 1981  |   -3.8   +0.7  |  -12.0   +0.6  |  -15.8   +1.3
hou 1973  |   -4.3   +0.9  |  -12.3   +0.1  |  -16.7   +1.1
sea 1976  |   -2.2   +0.6  |  -12.9   -1.4  |  -15.1   -0.8

Biggest discrepancies between offense and defense

                offense          defense          total
            rating   SOS     rating   SOS     rating   SOS
==========+================+================+===============
stl 2000  |  +12.6   -0.4  |   -9.5   -0.7  |   +3.1   -1.2
sdg 1982  |  +10.5   -1.3  |   -5.4   -1.0  |   +5.1   -2.3
ind 2001  |   +6.1   +0.5  |   -9.8   +0.3  |   -3.8   +0.8
sdg 1985  |   +8.3   +0.7  |   -7.2   -1.6  |   +1.1   -0.9
kan 2004  |  +10.0   +1.3  |   -4.7   +1.0  |   +5.3   +2.3
sdg 1981  |   +9.2   -0.0  |   -4.7   -1.0  |   +4.4   -1.1
buf 1975  |  +10.4   +1.0  |   -3.4   +1.4  |   +7.1   +2.4
cin 1985  |   +6.2   +0.2  |   -6.9   -1.1  |   -0.7   -0.9
sea 1977  |   +4.2   +1.3  |   -8.6   +0.9  |   -4.3   +2.2
gnb 1983  |   +5.2   +0.3  |   -7.1   -1.5  |   -1.9   -1.2
ind 2004  |  +11.7   +0.6  |   -0.3   +0.1  |  +11.4   +0.7
mia 1986  |   +6.2   -0.2  |   -5.7   -0.9  |   +0.5   -1.1
buf 1991  |   +7.6   -2.0  |   -4.1   -3.2  |   +3.6   -5.2
min 1998  |  +13.2   -0.2  |   +1.6   -1.1  |  +14.9   -1.4
phi 1973  |   +3.4   +0.7  |   -7.7   +0.9  |   -4.3   +1.6
sea 1976  |   -2.2   +0.6  |  -12.9   -1.4  |  -15.1   -0.8
kan 2002  |   +8.4   +0.9  |   -2.3   +1.0  |   +6.1   +1.9
was 1999  |   +6.8   -0.1  |   -3.9   -1.2  |   +2.9   -1.2
bal 1996  |   +3.9   +1.1  |   -6.8   +0.3  |   -2.9   +1.4
den 2000  |   +7.8   -1.9  |   -2.7   -0.3  |   +5.0   -2.2
sfo 1993  |   +9.9   -0.9  |   -0.3   -0.5  |   +9.7   -1.5
kan 2003  |   +9.2   -0.2  |   -0.9   -1.0  |   +8.3   -1.2
den 1998  |   +9.5   -0.5  |   -0.6   -2.6  |   +8.9   -3.1
det 1990  |   +4.2   +1.0  |   -5.9   -0.2  |   -1.6   +0.9
cin 1986  |   +5.7   +0.6  |   -4.2   -0.1  |   +1.5   +0.5
nor 1977  |   +0.3   +0.9  |   -9.4   -2.6  |   -9.2   -1.7
sdg 2006  |  +10.0   -0.1  |   +0.2   -1.5  |  +10.2   -1.6
was 1983  |  +11.7   -0.2  |   +2.2   +1.1  |  +13.9   +0.9
ind 2003  |   +8.2   +1.0  |   -1.2   -1.0  |   +7.0   +0.0

......

cle 1984  |   -6.1   -0.5  |   +2.3   -0.3  |   -3.8   -0.8
chi 2004  |   -8.5   -1.4  |   +0.3   -0.5  |   -8.2   -2.0
tam 1996  |   -5.9   +0.7  |   +2.9   +0.8  |   -3.0   +1.5
car 2002  |   -6.0   -0.5  |   +2.8   -0.0  |   -3.3   -0.5
tam 1995  |   -6.9   -0.3  |   +1.9   +1.4  |   -5.0   +1.1
ari 1994  |   -5.6   +0.0  |   +3.3   -0.3  |   -2.3   -0.3
den 1978  |   -1.9   -1.2  |   +6.9   +1.0  |   +5.0   -0.2
nwe 1988  |   -4.5   +0.1  |   +4.4   +1.9  |   -0.2   +2.0
chi 1993  |   -4.6   -0.5  |   +4.3   +0.0  |   -0.2   -0.5
nyg 1983  |   -5.5   -0.4  |   +3.4   +3.3  |   -2.1   +2.9
buf 2003  |   -5.0   +0.7  |   +4.0   +0.6  |   -1.0   +1.3
kan 1973  |   -4.1   -1.2  |   +5.1   -0.6  |   +1.0   -1.8
buf 1985  |   -9.5   -0.5  |   -0.2   +2.0  |   -9.8   +1.5
sea 1982  |   -7.4   -1.4  |   +2.0   -1.8  |   -5.4   -3.2
kan 1979  |   -4.0   +1.2  |   +5.4   +1.8  |   +1.4   +2.9
gnb 1977  |   -9.1   -1.5  |   +0.4   -1.1  |   -8.7   -2.6
sea 1992  |   -9.8   +0.2  |   -0.2   +0.6  |  -10.0   +0.8
phi 1983  |   -6.7   +0.5  |   +3.6   +1.9  |   -3.1   +2.4
tam 2002  |   -1.0   -0.9  |   +9.8   +0.4  |   +8.8   -0.6
tam 1999  |   -4.1   -0.2  |   +6.7   +0.6  |   +2.6   +0.4
oak 2006  |  -10.3   -0.2  |   +0.7   +0.8  |   -9.6   +0.6
was 2004  |   -7.4   -0.9  |   +4.0   -0.9  |   -3.4   -1.8
tam 1977  |  -11.1   -1.3  |   +0.3   -0.9  |  -10.7   -2.2
phi 1998  |  -12.3   -1.1  |   -0.5   -0.2  |  -12.8   -1.3
chi 2005  |   -5.2   -0.9  |   +6.6   -1.4  |   +1.4   -2.2
jax 2004  |   -5.7   -0.5  |   +6.4   +2.5  |   +0.8   +1.9
atl 1977  |   -6.1   -1.7  |   +6.6   -1.4  |   +0.5   -3.1
min 1971  |   -3.4   -1.5  |   +9.9   +0.5  |   +6.5   -1.1

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