"Short Summary: Lists all-time NFL passers through 1994 by the NFL passing efficiency rating. Associated passing statistics from which this rating is computed are included. More Details: 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. 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. Note: By using unofficial 1995 season statistics which appeared in the Thursday, December 28 and the Wednesday, December 27 issues of the newspaper _USA Today_ one can update the passers below through the 1995 regular season. (There could be, however, a new entry to the top 25 at the end of the 1995 season because of the 1,500 minimum passing attempt cutoff.) While the dataset provided gives all-time best career ratings of players, rankings of passers are often cited for a current NFL season in newspapers (e.g. _USA Today_). Different methods of ranking passers by a single numeric rating is also done by the NCAA (see Johnson (1994)) and the Canadian Football League (just the NFL method + 100/6? - this fits the data on p. 242 of Meserole (1995)). As an interesting note on the use of the rating formula by NFL teams the following appeared in the _Star-Tribune_ (Minneapolis newspaper) December 30, 1993 just before the last week of the 1993-1994 regular season: \"New York Jets coach Bruce Coslet dismissed suggestions he might not play Boomer Esiason on Sunday night at Houston if the game is meaningless. Terms of the trade last winter that brought the quarterback from Cincinnati called for the Bengals to receive a 1994 second-round draft pick if Esiason's passing rating is 89 or higher. Right now, his rating is 87.1.\" Esiason played the game against Houston, Houston eliminating the Jets from post-season play, and finished the season with a 84.5 rating (_USA Today_, January 5, 1994, 4C). 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. Submitted by (and contact for questions): Roger W. Johnson Math/CS Department Carleton College Northfield, MN 55057-4001 rjohnson@carleton.edu Distribution of the Dataset: The data from Meserole (1995) listed below may be freely distributed and used for nonprofit educational purposes such as teaching (including multiple copies for classroom use), scholarship, and research under fair use according to the copyright law encoded at 17 U.S.C. Section 107 et seq. (1982). Variables (from left to right) in Dataset: 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. Information about the dataset CLASSTYPE: numeric CLASSINDEX: 6 " "0" "nflpass" "Steve_Young" "Joe_Montana" "Dan_Marino" "Jim_Kelly" "Roger_Staubach" "Dave_Krieg" "Neil_Lomax" "Sonny_Jurgensen" "Len_Dawson" "Brett_Favre" "Ken_Anderson" "Bernie_Kosar" "Jeff_Hostetler" "Danny_White" "Boomer_Esiason" "Troy_Aikman" "Bart_Starr" "Ken_OBrien" "Fran_Tarkenton" "Warren_Moon" "Dan_Fouts" "Tony_Eason" "Randall_Cunningham" "Mark_Rypien" "Jim_Everett" "Otto_Graham" 96.8 92.3 88.2 85.8 83.4 83 82.7 82.63 82.56 82.2 81.9 81.82 81.78 81.7 81.64 81.62 80.5 80.44 80.35 80.3 80.2 79.7 79.4 79.3 79 86.6 2429 5391 6049 3942 2958 4390 3153 4262 3741 1580 4475 3225 1505 2950 4291 2281 3149 3602 6467 5147 5604 1564 3241 2335 3817 2626 1546 3409 3604 2397 1685 2562 1817 2433 2136 983 2654 1896 864 1761 2440 1424 1808 2110 3686 3003 3297 911 1805 1303 2193 1464 19869 40551 45173 29527 22700 32114 22771 32224 28711 10412 32838 22394 10985 21959 31874 16303 24718 25094 47003 37949 43040 11142 22272 16622 27613 23584 140 273 328 201 153 231 136 255 239 70 197 120 54 155 207 82 152 128 342 214 254 61 147 105 164 174 68 139 185 143 109 166 90 189 183 53 160 82 38 132 153 78 138 98 266 185 242 51 100 78 141 135 "Passing_Attempts" "Passing_Completions" "Passing_Yards" "Touchdowns_by_Passing" "Interceptions" "NFL_Rating" "Name_of_NFL_Player" "int0" "double1" "Name_of_NFL_Player" "numeric" "numeric" "numeric" "numeric" "numeric" "numeric" "nominal:Bart_Starr,Bernie_Kosar,Boomer_Esiason,Brett_Favre,Dan_Fouts,Dan_Marino,Danny_White,Dave_Krieg,Fran_Tarkenton,Jeff_Hostetler,Jim_Everett,Jim_Kelly,Joe_Montana,Ken_Anderson,Ken_OBrien,Len_Dawson,Mark_Rypien,Neil_Lomax,Otto_Graham,Randall_Cunningham,Roger_Staubach,Sonny_Jurgensen,Steve_Young,Tony_Eason,Troy_Aikman,Warren_Moon"