Unveiling New NFL Rating Systems

How biased is the NFL passer rating formula? Enough for Zach Fein to modify it and come up with more rating systems for the running back, wide receiver, and tight-end positions.

by Zach Fein (Analyst)

13

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Stats

August 25, 2008

NFL, Fantasy Football, Stats

Unbalanced

The NFL’s passer-rating formula is unbalanced. Taking the stats of all 33 qualifiers* last year, totaling them, and inserting them into each component of the formula (but not adding those four components up) shows that, instead of an equal 25 percent share for each of the four portions, the completion percentage and interception percentage parts each represent approximately 31 percent of the formula, while the other two components—touchdown percentage and yards per attempt—account for a total of only 37 percent (see table below).

Completion% YPA% TD% INT%
1.612 1.014 0.888 1.616

 

The new formula

Completion % = (Completions ÷ Attempts x 100 - 30) ÷ 25

Changed: Divisor from 20 to 25

Yards/Attempt = (Yards ÷ Attempts - 1.9) ÷ 4

Changed: Subtrahend from 3 to 1.9

Touchdown % = Touchdowns ÷ Attempts x 29

Changed: Multiplier from 20 to 29

Interception % = 2.375 - (Interceptions ÷ Attempts x 36)

Changed: Multiplier from 25 to 36

By tweaking the formula, each of the four components changed from 1.62, 1.61, 1.01, and 0.89, to 1.29, 1.29, 1.29, and 1.28, which in turn produced equal value for each of the four parts. After each component is found, the normal steps (as shown in the link above) are then employed to find the final rating.

New Quarterback Ratings
Name Team New Rating % Old Rating Comp Attempts Yards TDs INTS COMP% YDS% TD% INT%
Tom Brady NE 123.5 117.2 398 578 4806 50 8 1.554 1.604 2.509 1.877
Ben Roethlisberger PIT 109.7 104.1 264 404 3154 32 11 1.414 1.477 2.297 1.395
David Garrard JAC 107.7 102.2 208 325 2509 18 3 1.360 1.455 1.606 2.043
Peyton Manning IND 100.8 98 337 515 4040 31 14 1.417 1.486 1.746 1.396
Tony Romo DAL 99.9 97.4 335 520 4211 36 19 1.377 1.550 2.008 1.060
Jeff Garcia TB 97.2 94.6 209 327 2440 13 4 1.357 1.390 1.153 1.935
Brett Favre GB 96.9 95.7 356 535 4155 28 15 1.462 1.467 1.518 1.366
Matt Hasselbeck SEA 94.1 91.4 352 562 3966 28 12 1.305 1.289 1.445 1.606
Donovan McNabb PHI 92.5 89.9 291 473 3324 19 7 1.261 1.282 1.165 1.842
Kurt Warner ARI 91.1 89.8 281 451 3417 27 17 1.292 1.419 1.736 1.018
Drew Brees NO 89.1 89.4 440 652 4423 28 18 1.499 1.221 1.245 1.381
Jay Cutler DEN 88.0 88.1 297 467 3497 20 14 1.344 1.397 1.242 1.296
Carson Palmer CIN 85.8 86.7 373 575 4131 26 20 1.395 1.321 1.311 1.123
Matt Schaub HOU 84.6 87.2 192 289 2241 9 9 1.457 1.464 0.903 1.254
Derek Anderson CLE 84.3 82.5 298 527 3787 29 19 1.062 1.321 1.596 1.077
Sage Rosenfels HOU 83.9 84.8 154 240 1684 15 12 1.367 1.279 1.813 0.575
Chad Pennington NYJ 83.7 86.1 179 260 1765 10 9 1.554 1.222 1.115 1.129
Philip Rivers SD 82.9 82.4 277 460 3152 21 15 1.209 1.238 1.324 1.201
Jon Kitna DET 78.2 80.9 355 561 4068 18 20 1.331 1.338 0.930 1.092
Jason Campbell WAS 76.7 77.6 250 417 2700 12 11 1.198 1.144 0.835 1.425
Joey Harrington ATL 75.3 77.2 215 348 2215 7 8 1.271 1.116 0.583 1.547
Damon Huard KC 73.9 76.8 206 332 2257 11 13 1.282 1.225 0.961 0.965
Eli Manning NYG 73.7 73.9 297 529 3336 23 20 1.046 1.102 1.261 1.014
Kyle Boller BAL 72.8 75.2 168 275 1743 9 10 1.244 1.110 0.949 1.066
Brian Griese CHI 72.3 75.6 161 262 1803 10 12 1.258 1.245 1.107 0.726
Cleo Lemon MIA 70.6 71 173 309 1773 6 6 1.039 0.959 0.563 1.676
Brodie Croyle KC 69.2 69.9 127 224 1227 6 6 1.068 0.894 0.777 1.411
Trent Edwards BUF 69.1 70.4 151 269 1630 7 8 1.045 1.040 0.755 1.304
Tarvaris Jackson MIN 67.8 70.8 171 294 1911 9 12 1.127 1.150 0.888 0.906
Marc Bulger STL 67.3 70.3 221 378 2392 11 15 1.139 1.107 0.844 0.946
Vince Young TEN 65.7 71.1 238 382 2546 9 17 1.292 1.191 0.683 0.773
Rex Grossman CHI 63.9 66.4 122 225 1411 4 7 0.969 1.093 0.516 1.255
Kellen Clemens NYJ 57.5 60.9 130 250 1529 5 10 0.880 1.054 0.580 0.935
Totals   85.8 85.5 8226 13215 93243 587 401 1.290 1.289 1.288 1.283

*To qualify, a player must have at least 14 attempts per team’s game played

 

Running-Back Rating

Each of the following formulas were modeled after the passer-rating formula, though most of the components for each formula don’t have approximately the same value; the components that I felt were more important for that position garnered the most value.

(For example, the Yards/Attempt element in the running-back formula had 7 percent more worth than reception percentage, as a running back with a high YPA is more valuable than one with a high reception percentage, in my opinion.)

Yards/Attempt = (Yards ÷ Attempts x 1.68) ÷ 5.25

Touchdown % = (Touchdowns ÷ Attempts x 164) ÷ 3.5

First down % = (Rushing first downs ÷ attempts x 255 - 25) ÷ 20

Reception % = (Receptions ÷ Targets x 100 - 42) ÷ 25

The same equation that was used to find the final passer rating was employed to find the total rating in all of the following ratings.

Because the formula is based on averages per attempt, LaDainian Tomlinson (315 attempts) finished behind players who had less attempts but better averages. Had Maurice Jones-Drew carried the ball 315 times, he would have finished with 25 less yards, two more touchdowns, and 12 more first downs than Tomlinson.

Only players with 140 or more attempts were included.

  • B/R Ticket Guide
Running Back Ratings
Name Team Rating % Attempts Rush Yds TDs First downs Rec. Targets YPA% TD% 1ST% REC%
 
Maurice Jones-Drew JAC 122.3 167 768 9 46 40 55 1.472 2.525 2.262 1.229
Adrian Peterson MIN 121.2 238 1341 12 62 19 28 1.803 2.363 2.071 1.034
Marion Barber DAL 119.3 204 975 10 48 44 54 1.529 2.297 1.750 1.579
Joseph Addai IND 117.7 261 1072 12 65 41 49 1.314 2.154 1.925 1.667
LaDainian Tomlinson SD 110.4 315 1474 15 75 60 86 1.497 2.231 1.786 1.111
Kevin Jones DET 108.5 153 581 8 35 33 45 1.215 2.450 1.667 1.253
Chester Taylor MIN 107.0 157 844 7 35 29 43 1.720 2.089 1.592 1.018
Ryan Grant GB 106.3 188 956 8 36 30 37 1.627 1.994 1.191 1.563
Kenny Watson CIN 104.2 178 763 7 40 52 67 1.372 1.843 1.615 1.424
Brian Westbrook PHI 102.2 278 1333 7 73 90 120 1.534 1.180 2.098 1.320
Earnest Graham TB 98.6 222 898 10 46 49 70 1.294 2.111 1.392 1.120
Maurice Morris SEA 93.9 140 628 4 32 23 32 1.435 1.339 1.664 1.195
Jamal Lewis CLE 90.7 298 1304 9 58 30 39 1.400 1.415 1.232 1.397
Willis McGahee BAL 90.6 294 1207 7 56 43 49 1.314 1.116 1.179 1.830
Clinton Portis WAS 90.4 325 1262 11 61 47 60 1.243 1.586 1.143 1.453
Laurence Maroney NE 90.2 185 835 6 49 4 8 1.444 1.520 2.127 0.320
Ron Dayne HOU 87.3 194 773 6 43 17 26 1.275 1.449 1.576 0.935
Justin Fargas OAK 87.2 222 1009 4 52 23 32 1.454 0.844 1.736 1.195
Brandon Jacobs NYG 85.2 202 1009 4 49 23 38 1.598 0.928 1.843 0.741
Reggie Bush NO 83.8 157 581 4 32 73 98 1.184 1.194 1.349 1.300
Fred Taylor JAC 83.2 223 1202 5 45 9 14 1.725 1.051 1.323 0.891
DeAngelo Williams CAR 79.6 144 717 4 27 23 38 1.593 1.302 1.141 0.741
LaMont Jordan OAK 78.1 144 549 3 24 28 34 1.220 0.976 0.875 1.614
Marshawn Lynch BUF 76.8 280 1115 7 51 18 26 1.274 1.171 1.072 1.089
Frank Gore SF 74.3 260 1102 5 42 53 69 1.356 0.901 0.810 1.392
Adrian Peterson CHI 73.6 151 510 3 26 51 65 1.081 0.931 0.945 1.458
Selvin Young DEN 72.2 140 729 1 22 35 43 1.666 0.335 0.754 1.576
LenDale White TEN 71.7 303 1110 7 57 20 31 1.172 1.083 1.149 0.901
Steven Jackson STL 71.2 237 1002 5 36 38 52 1.353 0.989 0.687 1.243
Travis Henry DEN 71.1 167 691 4 36 7 14 1.324 1.122 1.499 0.320
Julius Jones DAL 69.9 164 588 2 24 23 26 1.147 0.571 0.616 1.858
Rudi Johnson CIN 67.2 170 497 3 26 13 16 0.936 0.827 0.700 1.570
Thomas Jones NYJ 65.5 310 1119 1 55 28 34 1.155 0.151 1.012 1.614
Larry Johnson KC 64.8 158 559 3 24 30 42 1.132 0.890 0.687 1.177
DeShaun Foster CAR 63.3 247 876 3 42 25 35 1.135 0.569 0.918 1.177
Edgerrin James ARI 63.3 324 1222 7 52 24 39 1.207 1.012 0.796 0.782
Cedric Benson CHI 63.2 196 674 4 33 17 27 1.100 0.956 0.897 0.839
Shaun Alexander SEA 60.0 207 716 4 37 14 25 1.107 0.905 1.029 0.560
Willie Parker PIT 59.8 321 1316 2 49 23 31 1.312 0.292 0.696 1.288
Warrick Dunn ATL 55.5 227 720 4 34 37 59 1.015 0.826 0.660 0.828
 
Totals   85.6 8751 36627 237 1735 1286 1756 1.339 1.269 1.278 1.249

 

Wide Receiver and Tight-End Rating

The touchdown-percentage factor of the formula had the lowest value of all four, due to the fact that too many of the top wide receivers reached the maximum amount (2.375).

Reception % = (Receptions ÷ Targets x 100 - 35.5) ÷ 20

Yards/Catch = (Yards ÷ Receptions) ÷ 6.28 - 0.75

Touchdown % = (Touchdowns ÷ Receptions x 23) ÷ 1.7

First down % = (Catches for first down ÷ Receptions x 85.5 - 30) ÷ 20

Plaxico Burress is ahead of Randy Moss because, even though Moss outscored Plaxico in the touchdown component by more than eight-tenths, Burress scored a 2.32 in that category—so Moss’s extra points went to waste because he scored so much more than the maximum that those eight tenths did not count.

Moss actually outscored Burress in all but one of the categories—reception percentage—but Burress outscored Moss by a total of 0.65, while Moss only outscored Burress by a combined total of approximately 0.39.

Wide Receiver/Tight End Ratings
Name Team Rating % Catches Yards Targets TDs 1sts REC% YPC% TD% 1ST%
 
Plaxico Burress NYG 129.5 70 1025 81 12 49 2.546 1.582 2.319 1.493
Randy Moss NE 125.1 98 1493 140 23 74 1.725 1.676 3.175 1.728
Terrell Owens DAL 117.5 81 1355 169 15 69 0.621 1.914 2.505 2.142
Reggie Wayne IND 111.6 104 1510 111 10 72 2.910 1.562 1.301 1.460
Larry Fitzgerald ARI 111.2 100 1409 106 10 69 2.942 1.494 1.353 1.450
Santonio Holmes PIT 110.9 52 942 115 8 42 0.486 2.135 2.081 1.953
Braylon Edwards CLE 109.6 80 1289 153 16 57 0.839 1.816 2.706 1.546
Joey Galloway TB 108.8 57 1014 81 6 37 1.744 2.083 1.424 1.275
Nate Burleson SEA 108.4 50 694 90 9 37 1.003 1.460 2.435 1.664
Marques Colston NO 106.5 98 1202 113 11 64 2.561 1.203 1.519 1.292
Greg Jennings GB 106.1 53 920 117 12 37 0.490 2.014 3.063 1.484
Andre Johnson HOU 105.1 60 851 86 8 39 1.713 1.508 1.804 1.279
Kevin Curtis PHI 103.3 77 1110 85 6 49 2.754 1.545 1.054 1.220
Antonio Gates SD 99.5 75 984 117 9 54 1.430 1.339 1.624 1.578
Donald Lee GB 99.4 48 575 63 6 29 2.035 1.158 1.691 1.083
Hines Ward PIT 98.8 71 732 84 7 47 2.451 0.892 1.334 1.330
Chad Johnson CIN 98.5 93 1440 160 8 74 1.131 1.716 1.164 1.902
Anquan Boldin ARI 96.3 71 853 99 9 43 1.811 1.163 1.715 1.089
Lee Evans BUF 95.1 55 849 89 5 38 1.315 1.708 1.230 1.454
Dallas Clark IND 94.0 58 616 101 11 37 1.096 0.941 2.566 1.227
Shaun McDonald DET 92.4 79 943 85 6 46 2.872 1.151 1.028 0.989
Patrick Crayton DAL 92.4 50 697 95 7 33 0.857 1.470 1.894 1.322
Calvin Johnson DET 92.0 48 756 95 4 38 0.751 1.758 1.127 1.884
T.J. Houshmandzadeh CIN 91.8 112 1143 148 12 70 2.009 0.875 1.450 1.172
Chris Cooley WAS 91.5 66 786 110 8 46 1.225 1.146 1.640 1.480
Tony Scheffler DEN 90.6 49 549 65 5 29 1.994 1.034 1.381 1.030
Justin Gage TEN 88.3 55 750 87 2 45 1.386 1.421 0.492 1.998
Torry Holt STL 87.1 93 1189 141 7 63 1.523 1.286 1.018 1.396
Jerricho Cotchery NYJ 87.0 82 1130 101 2 51 2.284 1.444 0.330 1.159
Dwayne Bowe KC 86.5 70 995 122 5 51 1.094 1.513 0.966 1.615
Bobby Engram SEA 85.9 94 1147 134 6 63 1.732 1.193 0.864 1.365
Isaac Bruce STL 84.0 55 733 87 4 36 1.386 1.372 0.984 1.298
Antwaan Randle El WAS 83.5 51 728 77 1 38 1.537 1.523 0.265 1.685
Santana Moss WAS 83.5 61 808 94 3 43 1.470 1.359 0.665 1.514
Derrick Mason BAL 82.5 103 1087 88 5 60 4.077 0.930 0.657 0.990
Brandon Marshall DEN 81.8 102 1325 170 7 70 1.225 1.319 0.928 1.434
Owen Daniels HOU 81.6 63 768 94 3 44 1.576 1.191 0.644 1.486
Wes Welker NE 80.9 112 1175 149 8 65 1.983 0.921 0.966 0.981
Jason Witten DAL 79.3 96 1145 141 7 56 1.629 1.149 0.987 0.994
Deion Branch SEA 78.8 49 661 85 4 30 1.107 1.398 1.104 1.117
Roy Williams DET 78.1 64 838 97 5 34 1.524 1.335 1.057 0.771
Bernard Berrian CHI 78.1 71 951 127 5 47 1.020 1.383 0.953 1.330
Roydell Williams TEN 77.3 55 719 104 4 38 0.869 1.332 0.984 1.454
Kellen Winslow CLE 77.3 82 1106 148 5 56 0.995 1.398 0.825 1.420
Roddy White ATL 76.6 83 1202 156 6 52 0.885 1.556 0.978 1.178
Amani Toomer NYG 76.6 59 760 104 3 42 1.062 1.301 0.688 1.543
Bobby Wade MIN 75.0 54 647 83 3 33 1.478 1.158 0.752 1.113
Steve Smith CAR 73.9 87 1002 127 7 43 1.650 1.084 1.089 0.613
Tony Gonzalez KC 71.8 99 1172 154 5 59 1.439 1.135 0.683 1.048
Mike Furrey DET 68.5 61 664 85 1 37 1.813 0.983 0.222 1.093
Vernon Davis SF 68.3 52 509 85 4 30 1.284 0.809 1.041 0.966
David Patten NO 68.1 54 792 129 3 37 0.318 1.585 0.752 1.429
Kevin Walter HOU 66.7 65 800 135 4 43 0.632 1.210 0.833 1.328
Jeremy Shockey NYG 65.9 57 619 93 3 33 1.290 0.979 0.712 0.975
Arnaz Battle SF 65.9 50 600 104 5 27 0.629 1.161 1.353 0.809
Laveranues Coles NYJ 63.6 55 646 167 6 35 -0.128 1.120 1.476 1.220
Ronald Curry OAK 62.7 55 717 137 4 35 0.232 1.326 0.984 1.220
Michael Jenkins ATL 60.3 53 532 105 4 31 0.749 0.848 1.021 1.000
Joe Jurevicius CLE 60.3 50 614 127 3 34 0.194 1.205 0.812 1.407
Reggie Brown PHI 58.0 61 780 159 4 38 0.143 1.286