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

Estimating ESPN’s QBR for Historical Seasons

Posted by Neil Paine on August 7, 2011

ESPN came out with a new quarterback rating ("Total QBR") on Friday, and if you haven't read Chase or Jason's takes, do so immediately. The early consensus seems to be this:

Pros:

  • It can't help but be better than the NFL's official passer rating
  • Based in large part on the strong analytical framework found in The Hidden Game of Football and the work of Aaron Schatz, Brian Burke, etc.
  • Takes into account all of a QB's actions (sacks, rushing carries, etc.)
  • Doesn't penalize QBs for dropped passes
  • Tries to parse credit between QB and receiver by breaking down Air Yards vs. YAC

Cons:

  • No adjustment for strength of schedule
  • A 'black box' -- we don't know the specifics about how it works
  • WPA-style clutch adjustments might be retrodictive, but aren't predictive
  • Splitting of credit between teammates appears to rely on subjective assessments

As soon as ESPN released the first batch of ratings from the 2008-10 seasons, I ran some correlations between existing stats and QBR:

                    r         R^2
    voa         0.9295      0.8639
    dvoa        0.9200      0.8464
    anypa_idx   0.8988      0.8079
    anypa       0.8960      0.8029
    rate_idx    0.8766      0.7684
    rate        0.8745      0.7647
    uAYA*       0.8647      0.7478
    aypa_idx    0.8478      0.7188
    nypa_idx    0.8445      0.7132
    aypa        0.8411      0.7075
    cmppct      0.7690      0.5913
    cmp_idx     0.7680      0.5898
    ypa_idx     0.7384      0.5453
    ypa         0.7340      0.5388
    tdpct_idx   0.7173      0.5146
    ypg         0.7146      0.5107
    tdpct       0.7027      0.4937
    intpct_idx  0.6013      0.3616
    intpct     -0.5989      0.3586
    skrate     -0.5546      0.3076
    skrate_idx  0.5516      0.3042
    (* = 2010 data only)

Basically, 86% of the variation in QBR is explained by Football Outsiders' VOA metric, and 81% is explained by our Adjusted Net YPA stat. Oddly enough, even though QBR factors in rushing plays, Ultimate Adjusted YPA correlates worse with QBR than Adjusted Net YPA -- in essence, uAYA tracks more closely with QBR if you remove its rushing components.

You can also explain 85% of the variation in QBR using the following formula composed of nothing but our Advanced Passing Indices:

QBR ~ -60.5 + 1.2 * Cmp%_Idx - 2.1 * YPA_Idx + 0.5 * TD%_Idx - 3.5 * Rate_Idx + 4 * AY/A_Idx + 0.9 * NY/A_Idx

This produces the following list of the best estimated post-merger "QBR" seasons (min 225 att):

Rk Player Year Age Tm G Cmp Att Yds TD Int Sk SkYds Cmp%+ Y/A+ TD%+ Rate+ AY/A+ NY/A+ predQBR
1 Dan Marino 1984 23 MIA 16 362 564 5084 48 17 13 120 127 140 148 141 141 153 95.8
2 Peyton Manning 2004 28 IND 16 336 497 4557 49 10 13 101 127 141 168 151 149 147 95.8
3 Kurt Warner 2000 29 STL 11 235 347 3429 21 18 20 115 138 158 125 128 136 158 90.0
4 Joe Montana 1984 28 SFO 16 279 432 3630 28 10 22 138 128 127 125 134 133 135 87.6
5 Dan Fouts 1982 31 SDG 9 204 330 2883 17 11 12 94 119 133 111 124 130 143 87.1
6 John Brodie 1970 35 SFO 14 223 378 2941 24 10 8 67 123 118 119 129 126 133 84.6
7 Steve Young 1991 30 SFO 11 180 279 2517 17 8 13 79 127 145 126 135 140 145 83.4
8 Mark Rypien 1991 29 WAS 16 249 421 3564 28 11 7 59 108 133 132 130 135 142 82.8
9 R. Cunningham 1998 35 MIN 15 259 425 3704 34 10 20 132 117 135 141 134 136 140 82.6
10 Ken Stabler 1976 31 OAK 12 194 291 2737 27 17 19 203 142 145 148 140 137 143 82.2
11 Steve Young 1992 31 SFO 16 268 402 3465 25 7 29 152 129 134 130 142 142 132 82.2
12 Steve Young 1994 33 SFO 16 324 461 3969 35 10 31 163 138 139 147 147 143 136 82.1
13 C. Pennington 2002 26 NYJ 15 275 399 3120 22 6 22 135 135 125 123 138 134 127 81.9
14 Joe Montana 1989 33 SFO 13 271 386 3521 26 8 33 198 152 145 132 149 145 138 81.8
15 Tom Brady 2007 30 NWE 16 398 578 4806 50 8 21 128 129 130 153 148 142 132 81.7
16 Erik Kramer 1995 31 CHI 16 315 522 3838 29 10 15 95 108 115 121 122 124 124 81.5
17 Brian Griese 2000 25 DEN 10 216 336 2688 19 4 17 139 125 123 121 135 134 125 81.3
18 Drew Brees 2009 30 NOR 15 363 514 4388 34 11 20 135 133 129 131 132 129 132 81.0
19 Dan Fouts 1983 32 SDG 10 215 340 2975 20 15 14 107 121 132 118 121 124 142 81.0
20 Dan Marino 1983 22 MIA 11 173 296 2210 20 6 10 80 106 107 127 125 123 120 80.6
Rk Player Year Age Tm G Cmp Att Yds TD Int Sk SkYds Cmp%+ Y/A+ TD%+ Rate+ AY/A+ NY/A+ predQBR
21 Bert Jones 1976 25 BAL 14 207 343 3104 24 9 29 284 124 139 127 139 143 134 80.4
22 Dan Fouts 1981 30 SDG 16 360 609 4802 33 17 19 134 111 118 115 125 126 131 79.9
23 Kurt Warner 1999 28 STL 16 325 499 4353 41 13 29 201 130 132 143 136 133 132 79.5
24 Brett Favre 1995 26 GNB 16 359 570 4413 38 13 33 217 117 125 135 130 131 124 79.3
25 Dan Marino 1986 25 MIA 16 378 623 4746 44 23 17 119 121 114 132 124 118 129 79.2
26 Jeff Garcia 2000 30 SFO 16 355 561 4278 31 10 24 155 121 116 119 127 125 122 79.0
27 V. Testaverde 1998 35 NYJ 14 259 421 3256 29 7 19 140 120 117 129 129 126 123 79.0
28 Bernie Kosar 1987 24 CLE 12 241 389 3033 22 9 22 129 123 117 116 127 125 123 78.8
29 Troy Aikman 1995 29 DAL 16 280 432 3304 16 7 14 89 123 122 97 122 124 130 78.4
30 Peyton Manning 2006 30 IND 16 362 557 4397 31 9 14 86 116 121 118 126 127 127 78.1
31 Joe Theismann 1983 34 WAS 16 276 459 3714 29 11 34 242 111 119 123 126 128 122 78.1
32 Norm Snead 1972 33 NYG 14 196 325 2307 17 12 8 66 126 107 109 121 115 120 77.7
33 Peyton Manning 2000 24 IND 16 357 571 4413 33 15 20 131 118 118 122 123 122 125 77.6
34 Peyton Manning 2005 29 IND 16 305 453 3747 28 10 17 81 125 124 124 129 127 129 77.6
35 Kurt Warner 2001 30 STL 16 375 546 4830 36 22 38 233 133 140 136 132 132 137 77.5
36 Steve DeBerg 1990 36 KAN 16 258 444 3444 23 4 22 191 106 117 114 128 132 119 77.5
37 Ken Anderson 1981 32 CIN 16 300 479 3754 29 10 25 140 123 117 123 137 132 125 77.4
38 Scott Mitchell 1995 27 DET 16 346 583 4338 32 12 31 145 105 117 120 120 124 121 77.3
39 Trent Green 2002 32 KAN 16 287 470 3690 26 13 26 141 107 126 123 120 126 128 77.3
40 Peyton Manning 2009 33 IND 16 393 571 4500 33 16 10 74 127 117 120 120 116 126 77.1

Finally, here are the predicted 2010 QBR leaders alongside the actual QBR leaders (min 225 att):

Player Year Age Tm G Att predQBR Rk Action Plays Actual QBR Rk
Tom Brady 2010 33 NWE 16 492 75.7 1 607 76.0 1
Aaron Rodgers 2010 27 GNB 15 475 71.5 2 627 67.9 4
Philip Rivers 2010 29 SDG 16 541 68.2 3 667 63.2 9
Peyton Manning 2010 34 IND 16 679 66.3 4 779 69.5 2
Josh Freeman 2010 22 TAM 16 474 64.0 5 626 63.5 8
Drew Brees 2010 31 NOR 16 658 62.3 6 760 65.9 6
Michael Vick 2010 30 PHI 12 372 61.9 7 547 66.6 5
Matt Schaub 2010 29 HOU 16 574 61.8 8 678 57.8 12
Ben Roethlisberger 2010 28 PIT 12 389 59.9 9 500 59.8 10
Matt Ryan 2010 25 ATL 16 571 59.8 10 709 68.6 3
Eli Manning 2010 29 NYG 16 539 58.1 11 654 64.3 7
Jon Kitna 2010 38 DAL 10 318 57.7 12 409 46.1 20
Matt Cassel 2010 28 KAN 15 450 57.6 13 566 51.2 15
Joe Flacco 2010 25 BAL 16 489 56.0 14 647 58.1 11
Shaun Hill 2010 30 DET 11 416 55.0 15 499 44.8 21
Kyle Orton 2010 28 DEN 13 498 53.5 16 612 46.6 19
Carson Palmer 2010 31 CIN 16 586 51.1 17 720 46.7 18
Ryan Fitzpatrick 2010 28 BUF 13 441 50.4 18 551 48.7 16
David Garrard 2010 32 JAX 14 366 50.3 19 510 57.3 13
Kerry Collins 2010 38 TEN 9 278 49.6 20 342 56.0 14
Alex Smith 2010 26 SFO 11 342 47.7 21 426 40.0 28
Mark Sanchez 2010 24 NYJ 16 507 45.2 22 619 47.4 17
Jason Campbell 2010 29 OAK 13 329 44.9 23 479 43.8 22
Matt Hasselbeck 2010 35 SEA 14 444 44.8 24 547 42.4 24
Chad Henne 2010 25 MIA 15 490 44.7 25 604 41.4 25
Sam Bradford 2010 23 STL 16 590 43.9 26 732 41.0 26
Jay Cutler 2010 27 CHI 15 432 41.9 27 596 42.6 23
Donovan McNabb 2010 34 WAS 13 472 40.9 28 596 41.0 26
Brett Favre 2010 41 MIN 13 358 39.4 29 459 25.8 30
Derek Anderson 2010 27 ARI 12 327 34.3 30 387 35.9 29
Jimmy Clausen 2010 23 CAR 13 299 19.2 31 397 11.7 31

This entry was posted on Sunday, August 7th, 2011 at 6:09 am and is filed under History, Quarterbacks, Statgeekery. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.