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Rushing, passing, and sacking simplicity II

Posted by Doug on December 18, 2007

As I mentioned in yesterday's post, the plan for today is to try to determine The Greatest Statistical Accomplishment Of All Time. Of course, it is to be understood that "All Time" means "since the merger," and only a pretty small subset of statistical accomplishments are eligible for consideration. To be more specific, here is the plan:

1. Look at the following stats: points, rushing yards, passing yards, total yards, sack yards, turnovers. For each stat, we will look at offense, defense, and margin (offense minus defense). So we have 9 x 3 = 27 different statistical categories to consider.

2. For each category, we give each team (1970--2006) a rating that accounts for how well they did and how tough their schedule was. Full methodology described in yesterday's post (linked above).

3. Then, for each category for each season, we compute the standard deviation of the league's ratings in that category for that season. To jog your memory, the standard deviation measures how spread out that collection of numbers is. You may recall from your stat class that, for normally distributed things (and it's probably pretty safe to assume these ratings are), about 68% of the observations will be within one standard deviation of the mean, about 95% will be within two standard deviations, and about 99% will be within three. The mean, in this case, is necessarily going to be zero, so we can simply divide a team's rating by the league standard deviation to get a measure of "how remarkable" a team's performance was in a particular year in a particular category.

Essentially, the above process is a way to express the all the numbers from yesterday's post --- all years and all categories --- on a common scale. This allows us to compare not only 1970 point margins to 2006 point margins, but also 1983 sack margins to 1999 rushing yardage totals, and so on.

According to this methodology, the most remarkable team achievement is the 2001 Pittsburgh Steelers' rushing yardage total. They amassed 2774 rushing yards against a slightly tougher-than-average schedule of rushing defenses. The league average was 1788. The second place team had 2240. The Steelers were 3.6 standard deviations away from average.

The worst team effort was the 2005 San Francisco 49ers passing yardage margin. They ranked last in the league in both passing yards and passing yards allowed. According to these calculations, if the 49ers were to square off against an average team, they would get outpassed by 146 yards. They were 3.63 standard deviations on the wrong side of average.

Here are the top 10 best and worst lists for each category.

Points for

best

STL  2001     3.22    14-2-0
SFO  1994     2.85    13-3-0
GNB  1996     2.71    13-3-0
SFO  1993     2.67    10-6-0
SDG  1981     2.66    10-6-0
STL  2000     2.64    10-6-0
DEN  1997     2.62    12-4-0
WAS  1983     2.59    14-2-0
IND  2004     2.54    12-4-0
MIN  1998     2.52    15-1-0

worst

IND  1991    -2.48    1-15-0
OAK  2006    -2.47    2-14-0
SEA  1992    -2.46    2-14-0
TAM  1977    -2.42    2-12-0
ATL  1974    -2.37    3-11-0
BUF  1985    -2.37    2-14-0
PHI  1998    -2.34    3-13-0
BOS  1970    -2.29    2-12-0
TAM  1976    -2.29    0-14-0
DAL  1989    -2.25    1-15-0

Points against

best

TAM  2002     2.88    12-4-0
KAN  1995     2.73    13-3-0
BAL  2006     2.66    13-3-0
MIN  1970     2.48    12-2-0
CHI  1985     2.33    15-1-0
DEN  1978     2.26    10-6-0
MIN  1971     2.26    11-3-0
DEN  1977     2.25    12-2-0
MIA  1998     2.14    10-6-0
KAN  1997     2.14    13-3-0

worst

BAL  1981    -3.11    2-14-0
TAM  1986    -2.85    2-14-0
NOR  1980    -2.64    1-15-0
NWE  1972    -2.58    3-11-0
IND  2001    -2.55    6-10-0
SEA  1976    -2.55    2-12-0
HOU  1983    -2.48    2-14-0
RAM  1982    -2.37     2-7-0
STL  2000    -2.31    10-6-0
HOU  1973    -2.30    1-13-0

Points margin

best

GNB  1996     2.81    13-3-0
WAS  1983     2.59    14-2-0
CHI  1985     2.59    15-1-0
STL  2001     2.47    14-2-0
DAL  1978     2.40    12-4-0
WAS  1991     2.38    14-2-0
SFO  1994     2.35    13-3-0
MIN  1988     2.33    11-5-0
SFO  1987     2.28    13-2-0
SFO  1995     2.24    11-5-0

worst

BAL  1981    -2.99    2-14-0
TAM  1986    -2.62    2-14-0
NWE  1990    -2.48    1-15-0
IND  1991    -2.47    1-15-0
ATL  1987    -2.41    3-12-0
ARI  2000    -2.37    3-13-0
NWE  1972    -2.32    3-11-0
ARI  2003    -2.31    4-12-0
TAM  1976    -2.28    0-14-0
CLE  2000    -2.27    3-13-0

Rushing yards for

best

PIT  2001     3.60    13-3-0
ATL  2006     3.16     7-9-0
BUF  1975     2.87     8-6-0
CHI  1984     2.74    10-6-0
DET  1981     2.50     8-8-0
PIT  1976     2.49    10-4-0
RAM  1984     2.49    10-6-0
SFO  1998     2.47    12-4-0
PHI  1992     2.40    11-5-0
BAL  2003     2.39    10-6-0

worst

HOU  1971    -2.36     4-9-1
TAM  1983    -2.23    2-14-0
IND  1993    -2.19    4-12-0
SDG  1987    -2.18     8-7-0
NOR  1972    -2.12    2-11-1
MIN  1978    -2.12     8-7-1
GNB  1977    -2.10    4-10-0
IND  1992    -2.08     9-7-0
BOS  1970    -2.07    2-12-0
TAM  1977    -2.06    2-12-0

Rushing yards against

best


BAL  2000     2.60    12-4-0
MIN  1994     2.42    10-6-0
PIT  1997     2.35    11-5-0
OAK  2002     2.34    11-5-0
SFO  1995     2.34    11-5-0
DAL  1992     2.33    13-3-0
DET  1970     2.29    10-4-0
SDG  2004     2.27    12-4-0
CHI  1984     2.22    10-6-0
BAL  1971     2.19    10-4-0

worst

NOR  1980    -3.01    1-15-0
CLE  1999    -3.00    2-14-0
IND  1993    -2.77    4-12-0
SEA  1982    -2.77     4-5-0
GNB  1979    -2.65    5-11-0
NWE  1981    -2.62    2-14-0
HOU  1984    -2.61    3-13-0
WAS  1996    -2.53     9-7-0
KAN  1977    -2.51    2-12-0
SEA  1981    -2.51    6-10-0

Rushing yards margin

best

PIT  2001     3.27    13-3-0
CHI  1984     2.81    10-6-0
PIT  1997     2.61    11-5-0
KAN  1995     2.45    13-3-0
PIT  1976     2.42    10-4-0
RAM  1984     2.40    10-6-0
RAM  1973     2.38    12-2-0
DEN  2005     2.37    13-3-0
BAL  2003     2.37    10-6-0
DEN  1996     2.37    13-3-0

worst

IND  1993    -2.96    4-12-0
NOR  1980    -2.89    1-15-0
IND  1991    -2.78    1-15-0
CLE  1999    -2.62    2-14-0
SEA  1976    -2.47    2-12-0
SEA  1982    -2.46     4-5-0
BOS  1970    -2.41    2-12-0
ATL  1989    -2.38    3-13-0
NWE  1990    -2.37    1-15-0
SEA  1981    -2.30    6-10-0

Passing yards for

best

HOU  1990     3.28     9-7-0
SDG  1982     3.19     6-3-0
SDG  1985     3.13     8-8-0
SDG  1980     3.12    11-5-0
HOU  1991     2.90    11-5-0
STL  2001     2.89    14-2-0
SDG  1981     2.75    10-6-0
STL  2000     2.71    10-6-0
MIA  1984     2.71    14-2-0
MIA  1988     2.67    6-10-0

worst

PHI  1999    -2.55    5-11-0
PIT  1989    -2.49     9-7-0
CHI  1972    -2.47     4-9-1
ATL  1974    -2.42    3-11-0
CHI  1993    -2.40     7-9-0
DAL  2001    -2.39    5-11-0
KAN  1979    -2.38     7-9-0
HOU  2002    -2.31    4-12-0
SFO  2005    -2.29    4-12-0
TEN  1997    -2.25     8-8-0

Passing yards against

best

NOR  1992     2.98    12-4-0
MIA  1982     2.88     7-2-0
OAK  2006     2.62    2-14-0
PHI  1991     2.61    10-6-0
WAS  1980     2.46    6-10-0
PIT  1990     2.43     9-7-0
ATL  1971     2.37     7-6-1
KAN  1989     2.34     8-7-1
BUF  1980     2.25    11-5-0
MIN  1989     2.22    10-6-0

worst

SFO  2005    -3.19    4-12-0
NYJ  1986    -2.88    10-6-0
NYJ  1979    -2.82     8-8-0
SDG  1981    -2.80    10-6-0
NOR  1970    -2.78    2-11-1
TEN  2001    -2.74     7-9-0
DEN  1994    -2.60     7-9-0
CLE  1978    -2.60     8-8-0
BUF  1975    -2.58     8-6-0
SDG  1985    -2.50     8-8-0

Passing yards margin

best

HOU  1990     3.32     9-7-0
SDG  1980     3.27    11-5-0
STL  2001     3.25    14-2-0
WAS  1974     2.81    10-4-0
CIN  1975     2.74    11-3-0
SFO  1995     2.67    11-5-0
IND  2003     2.62    12-4-0
IND  2006     2.60    12-4-0
NOR  2006     2.54    10-6-0
GNB  1996     2.41    13-3-0

worst

SFO  2005    -3.63    4-12-0
ATL  1985    -2.81    4-12-0
IND  1994    -2.73     8-8-0
CIN  2000    -2.69    4-12-0
PHI  1999    -2.63    5-11-0
PIT  1989    -2.59     9-7-0
BAL  1983    -2.59     7-9-0
CHI  1972    -2.55     4-9-1
TEN  1997    -2.52     8-8-0
BUF  1973    -2.46     9-5-0

Total yards for

best

SDG  1980     2.96    11-5-0
SDG  1982     2.96     6-3-0
SFO  1993     2.83    10-6-0
STL  2001     2.81    14-2-0
SFO  1998     2.80    12-4-0
SDG  1981     2.71    10-6-0
MIA  1984     2.62    14-2-0
BUF  1975     2.56     8-6-0
SFO  1987     2.44    13-2-0
CIN  1986     2.43    10-6-0

worst

BOS  1970    -2.86    2-12-0
HOU  2002    -2.78    4-12-0
NYG  1996    -2.71    6-10-0
DET  1988    -2.66    4-12-0
OAK  2006    -2.62    2-14-0
IND  1991    -2.52    1-15-0
CHI  2004    -2.50    5-11-0
PIT  1989    -2.45     9-7-0
TAM  1977    -2.41    2-12-0
NYJ  1995    -2.41    3-13-0

Total yards against

best


CHI  1984     3.10    10-6-0
PHI  1991     3.00    10-6-0
BAL  2006     2.56    13-3-0
MIA  1982     2.52     7-2-0
NOR  1992     2.52    12-4-0
MIN  1970     2.42    12-2-0
MIN  1989     2.40    10-6-0
TEN  2000     2.31    13-3-0
TAM  2002     2.30    12-4-0
BAL  1971     2.29    10-4-0

worst

TAM  1986    -2.84    2-14-0
BAL  1981    -2.75    2-14-0
SFO  2005    -2.73    4-12-0
OAK  1997    -2.66    4-12-0
NOR  1970    -2.55    2-11-1
NWE  1972    -2.51    3-11-0
GNB  1983    -2.47     8-8-0
SEA  1976    -2.38    2-12-0
DEN  1994    -2.35     7-9-0
SDG  1974    -2.33     5-9-0

Total yards margin

best

DEN  2004     2.77    10-6-0
STL  2001     2.74    14-2-0
DAL  1978     2.52    12-4-0
PIT  1979     2.52    12-4-0
PIT  2001     2.50    13-3-0
SFO  1987     2.46    13-2-0
SFO  1993     2.37    10-6-0
SDG  1980     2.35    11-5-0
RAM  1973     2.34    12-2-0
SFO  1995     2.22    11-5-0

worst

SFO  2005    -2.89    4-12-0
CLE  1999    -2.72    2-14-0
BOS  1970    -2.57    2-12-0
TAM  1986    -2.56    2-14-0
CHI  2004    -2.54    5-11-0
HOU  1982    -2.47     1-8-0
BAL  1981    -2.46    2-14-0
BAL  1978    -2.39    5-11-0
IND  1991    -2.34    1-15-0
HOU  2005    -2.20    2-14-0

Sack yards for

best

NYJ  1981     2.92    10-5-1
SFO  1976     2.88     8-6-0
BAL  2006     2.81    13-3-0
MIN  1989     2.80    10-6-0
BAL  1975     2.76    10-4-0
DEN  1971     2.73     4-9-1
SFO  1972     2.69     8-5-1
IND  2004     2.66    12-4-0
NWE  1977     2.65     9-5-0
RAM  1980     2.53    11-5-0

worst

ARI  2003    -2.55    4-12-0
NWE  1992    -2.51    2-14-0
SDG  1997    -2.47    4-12-0
MIA  1970    -2.28    10-4-0
JAX  1995    -2.25    4-12-0
NWE  1972    -2.22    3-11-0
DAL  2001    -2.20    5-11-0
SDG  1974    -2.20     5-9-0
GNB  1990    -2.15    6-10-0
ARI  2000    -2.11    3-13-0

Sack yards against

best

MIA  1988     2.59    6-10-0
STL  1975     2.51    11-3-0
STL  1976     2.43    10-4-0
MIA  1984     2.41    14-2-0
SFO  1970     2.39    10-3-1
NYJ  2000     2.35     9-7-0
TAM  1979     2.30    10-6-0
MIA  1985     2.20    12-4-0
RAM  1983     2.19     9-7-0
DET  2003     2.14    5-11-0

worst

PHI  1986    -3.02    5-10-1
PIT  1993    -2.74     9-7-0
CHI  2004    -2.68    5-11-0
SEA  1992    -2.66    2-14-0
IND  1991    -2.63    1-15-0
HOU  2002    -2.57    4-12-0
BUF  2003    -2.57    6-10-0
ARI  1997    -2.52    4-12-0
OAK  2006    -2.49    2-14-0
HOU  2005    -2.42    2-14-0

Sack yards margin

best

NWE  1977     2.67     9-5-0
BAL  2006     2.58    13-3-0
PIT  1996     2.42    10-6-0
SFO  1983     2.41    10-6-0
NYJ  1981     2.41    10-5-1
RAM  1980     2.41    11-5-0
IND  2004     2.39    12-4-0
IND  2005     2.37    14-2-0
SDG  1978     2.37     9-7-0
CHI  1985     2.33    15-1-0

worst

DAL  2002    -2.77    5-11-0
NWE  1972    -2.62    3-11-0
NWE  1992    -2.59    2-14-0
ARI  2003    -2.57    4-12-0
CHI  2004    -2.55    5-11-0
JAX  1995    -2.55    4-12-0
CLE  1999    -2.44    2-14-0
IND  1991    -2.43    1-15-0
ARI  1997    -2.43    4-12-0
ATL  2000    -2.42    4-12-0

Turnovers for

best

SEA  1984     3.12    12-4-0
CIN  2005     2.76    11-5-0
PHI  1989     2.75    11-5-0
GNB  2002     2.72    12-4-0
PIT  1973     2.62    10-4-0
MIN  1988     2.61    11-5-0
CHI  2006     2.58    13-3-0
NYG  1997     2.53    10-5-1
GNB  1981     2.45     8-8-0
STL  2003     2.43    12-4-0

worst

WAS  2006    -2.59    5-11-0
RAI  1992    -2.50     7-9-0
BUF  1986    -2.50    4-12-0
DAL  1988    -2.48    3-13-0
STL  2004    -2.37     8-8-0
CLE  1973    -2.34     7-5-2
DAL  1979    -2.26    11-5-0
NYG  1975    -2.24     5-9-0
DAL  1989    -2.22    1-15-0
SFO  1982    -2.21     3-6-0

Turnovers against

best


WAS  1983     2.71    14-2-0
NYG  1990     2.49    13-3-0
GNB  1972     2.48    10-4-0
MIA  1976     2.38     6-8-0
STL  1974     2.29    10-4-0
BAL  1975     2.13    10-4-0
SFO  1981     2.11    13-3-0
NYJ  2004     2.09    10-6-0
PHI  1980     2.08    12-4-0
SDG  1993     2.05     8-8-0

worst

SFO  1978    -3.12    2-14-0
DEN  1982    -3.10     2-7-0
NOR  1997    -3.00    6-10-0
SDG  1998    -2.96    5-11-0
ATL  1974    -2.83    3-11-0
NYJ  1996    -2.64    1-15-0
BUF  1970    -2.63    3-10-1
OAK  2006    -2.63    2-14-0
SDG  1972    -2.50     4-9-1
TAM  1988    -2.48    5-11-0

Turnovers margin

best

WAS  1983     3.19    14-2-0
CHI  1985     2.73    15-1-0
MIA  1978     2.59    11-5-0
SEA  1984     2.55    12-4-0
KAN  1999     2.37     9-7-0
CIN  2005     2.34    11-5-0
DEN  1984     2.29    13-3-0
NOR  1987     2.19    12-3-0
KAN  1990     2.19    11-5-0
PIT  1972     2.19    11-3-0

worst

DEN  1982    -3.01     2-7-0
ATL  1974    -2.88    3-11-0
CIN  1994    -2.71    3-13-0
OAK  2006    -2.68    2-14-0
SDG  1998    -2.58    5-11-0
HOU  1973    -2.57    1-13-0
WAS  1988    -2.55     7-9-0
BUF  1970    -2.52    3-10-1
CLE  1990    -2.44    3-13-0
BUF  1971    -2.44    1-13-0

This entry was posted on Tuesday, December 18th, 2007 at 5:30 am and is filed under General, History, Statgeekery. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.