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National Football League Passes
Dataset listing all-time NFL passers through 1994 by the NFL passing efficiency rating.
Associated passing statistics from which this rating is computed are included.
The dataset lists statistics for 26 players. The first 25 are the top 25 all-time career best rating leaders recognized by the NFL. The 26th player, Otto Graham, has statistics which include his performance in the All-America Football Conference (1946-1949) which is not recognized by the NFL. The statistics given are current through the 1994 regular season. Only passers with a minimum of 1,500 career passing attempts are included.
The NFL describes how to compute its rating in its 1977 document "National Football League Passer Rating System" (410 Park Avenue, New York, NY 10022-4444, (212) 758-1500) through the use of tables. No formula is explicitly stated for rating. But, examining the tables in the "National
Football League Passer Rating System" one can infer that NFL passer rating is
```
[5(Completion Percentage-30)/6] + [10(Touchdown Percentage)/3] +
[25(19-2(Interception Percentage))/12] + [25(Yards/Attempts-3)/6]
```
where it is understood that the values within each set of square brackets are
truncated to be no smaller than zero and no larger than 475/12. This implies a
minimal rating of 0 and a maximal rating of 475/3 or about 158.3. If
```
30% < Completion Percentage < 77.5%
0% < Touchdown Percentage < 11.875%
0% < Interception Percentage < 9.5%
3 < Yards per Attempt < 12.5,
```
which is true of most passers having a reasonable number of passing attempts,
then the rating formula simplifies to
[25 + 10(Completion Percentage) + 40(Touchdown Percentage)
- 50(Interception Percentage) + 50(Yards/Attempt)]/12
(see Johnson (1993, 1994). Note that the weights on interception percentage and
yards per attempt are greatest in magnitude, closely followed by touchdown
percentage. The weight on completion percentage is a distant fourth in
magnitude.
### Classroom Use of this Data
Using the NFL data from Meserole (1995), for which the above inequalities
hold, one can uncover (at least approximately) the simplified rating formula
using multiple regression. Students can be told that NFL rating is "based on
performance standards established for completion percentage, average gain,
touchdown percentage and interception percentage" (Meserole (1995)), but the
actual formula for rating is not widely publicized. Once the rating formula is
uncovered, one can see the relative weights that the NFL assigns to these four
performance standards (see Barra and Neyer (1995) for an alternative). Also, by
citing unusual passers who don't satisfy the above inequalities an instructor
can remind students of the dangers of extrapolation when building regression
models. Here are a few such unusual passers:
```
Name Attempts Completions Yards Touchdowns Interceptions Rating
Rypien 3 3 15 0 0 87.5
Marshall 1 1 81 1 0 158.3
Muster 1 0 0 0 1 0.0
```
The data for Arthur Marshall, a wide-receiver for Denver, and for Brad Muster,
a full-back for Chicago are from the 1992 season. The data for quarterback Mark
Rypien is for his performance at one point during the 1995 season (see _USA
Today_, Thursday September 28, 1995, 9C).
One might also try tracking down the passing (not receiving!) records of Jerry
Rice for the 1995 season as he apparently threw for a touchdown in the regular
season finale.
### Variables (from left to right)
Passing Attempts
Passing Completions
Passing Yards
Touchdowns by Passing
Interceptions
NFL Rating (usually to the nearest tenth, sometimes to the nearest hundredth to eliminate ties that would result when only given to the nearest tenth)
Name of NFL Player
### References
Barra, A. and Neyer, R. (1995), "When rating quarterbacks, yards per throw
matters", _The Wall Street Journal_, Friday, November 24, B5.
Johnson, R. (1994), "Rating quarterbacks: An amplification", _The College
Mathematics Journal_, vol. 25, no. 4, p. 340.
Johnson, R. (1993), "How does the NFL rate the passing ability of
quarterbacks?", _The College Mathematics Journal_, vol. 24, no. 5, pp. 451-453.
Meserole, M., editor, (1995), "The 1996 Information Please Sports Almanac",
p. 265.

NFL_Rating (target) | numeric | 26 unique values 0 missing | |

Passing_Attempts | numeric | 26 unique values 0 missing | |

Passing_Completions | numeric | 26 unique values 0 missing | |

Passing_Yards | numeric | 26 unique values 0 missing | |

Touchdowns_by_Passing | numeric | 26 unique values 0 missing | |

Interceptions | numeric | 24 unique values 0 missing | |

Name_of_NFL_Player (ignore) | nominal | 26 unique values 0 missing |

1.18

Third quartile of kurtosis among attributes of the numeric type.

Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .00001

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2

Third quartile of mutual information between the nominal attributes and the target attribute.

Error rate achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2

0.88

Third quartile of skewness among attributes of the numeric type.

Kappa coefficient achieved by the landmarker weka.classifiers.trees.DecisionStump -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 2

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.J48 -C .0001

-0.47

First quartile of kurtosis among attributes of the numeric type.

3564.87

Third quartile of standard deviation of attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 1

Error rate achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3

Average mutual information between the nominal attributes and the target attribute.

An estimate of the amount of irrelevant information in the attributes regarding the class. Equals (MeanAttributeEntropy - MeanMutualInformation) divided by MeanMutualInformation.

First quartile of mutual information between the nominal attributes and the target attribute.

Kappa coefficient achieved by the landmarker weka.classifiers.bayes.NaiveBayes -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Kappa coefficient achieved by the landmarker weka.classifiers.trees.RandomTree -depth 3

Average number of distinct values among the attributes of the nominal type.

0.35

First quartile of skewness among attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Standard deviation of the number of distinct values among attributes of the nominal type.

44.17

First quartile of standard deviation of attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 2

Error rate achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

Kappa coefficient achieved by the landmarker weka.classifiers.lazy.IBk -E "weka.attributeSelection.CfsSubsetEval -P 1 -E 1" -S "weka.attributeSelection.BestFirst -D 1 -N 5" -W

-0.36

Second quartile (Median) of kurtosis among attributes of the numeric type.

1149.48

Second quartile (Median) of means among attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.REPTree -L 3

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.DecisionStump

Second quartile (Median) of mutual information between the nominal attributes and the target attribute.

Minimal mutual information between the nominal attributes and the target attribute.

0.41

Second quartile (Median) of skewness among attributes of the numeric type.

Kappa coefficient achieved by the landmarker weka.classifiers.trees.DecisionStump

The minimal number of distinct values among attributes of the nominal type.

440.14

Second quartile (Median) of standard deviation of attributes of the numeric type.

Area Under the ROC Curve achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1

Maximum mutual information between the nominal attributes and the target attribute.

Error rate achieved by the landmarker weka.classifiers.trees.RandomTree -depth 1

Number of attributes needed to optimally describe the class (under the assumption of independence among attributes). Equals ClassEntropy divided by MeanMutualInformation.

The maximum number of distinct values among attributes of the nominal type.