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# Pro Football Reference Blog

## PI Finds: The Rivers Index

Posted by Neil Paine on November 11, 2010

Last week, I showed you how to set up an "expected W-L" method for a quarterback using the Play Index Team Game Finder, the QB's gamelogs, and a logistic regression formula. I found that our test case, Philip Rivers, should have been expected to win 27.7 games over the last 3 seasons (prior to the Chargers' win over Houston) based on his passing performance, but in actuality only won 24 games, a difference of -3.7 wins. Without context, though, that number doesn't really mean anything -- is that a lot, or a little? Today, I'm going to answer that question by comparing every QB's actual and expected W-L records, something I like to call "The Rivers Index" (in an homage to Doug's Manning and Dungy Indices).

First, we have to find every QB's gamelogs from the past 3 seasons, and that requires the Player Game Finder. Unfortunately, we don't have the ability to search for games started, but we can do the next-best thing -- we can find every instance where the QB was his team's leader in passing attempts in a given game, which should be a good proxy for starting.

Gather your data, run it through the same adjusted YPA/win probability formula as last week, and you come up with these results:

Peyton Manning 39 30.0 0.769 22.7 0.582 7.3 0.187
Matt Ryan 35 24.0 0.686 18.6 0.532 5.4 0.154
Kerry Collins 24 15.0 0.625 10.7 0.446 4.3 0.179
Joe Flacco 38 24.0 0.632 19.9 0.524 4.1 0.108
Eli Manning 35 23.0 0.657 19.1 0.545 3.9 0.112
Ben Roethlisberger 35 24.0 0.686 20.3 0.580 3.7 0.105
Mark Sanchez 21 13.0 0.619 9.7 0.461 3.3 0.158
Brett Favre 39 24.0 0.615 20.7 0.531 3.3 0.085
Jake Delhomme 27 15.0 0.556 12.3 0.454 2.7 0.101
Donovan McNabb 35 21.5 0.614 19.1 0.547 2.4 0.067
Drew Brees 39 26.0 0.667 23.7 0.608 2.3 0.058
Gus Frerotte 10 7.0 0.700 4.7 0.473 2.3 0.227
Vince Young 16 11.0 0.688 8.9 0.555 2.1 0.132
Tom Brady 22 15.0 0.682 13.1 0.596 1.9 0.086
Chad Henne 22 11.0 0.500 9.2 0.420 1.8 0.080
Brian Griese 5 3.0 0.600 1.6 0.330 1.4 0.270
Kurt Warner 28 18.0 0.643 16.7 0.597 1.3 0.045
Charlie Batch 2 2.0 1.000 0.9 0.446 1.1 0.554
Todd Collins 1 1.0 1.000 0.0 0.001 1.0 0.999
Kellen Clemens 1 1.0 1.000 0.3 0.329 0.7 0.671
Sam Bradford 8 4.0 0.500 3.4 0.422 0.6 0.078
Rex Grossman 2 1.0 0.500 0.4 0.192 0.6 0.308
Carson Palmer 27 12.0 0.444 11.4 0.423 0.6 0.021
Jim Sorgi 1 1.0 1.000 0.4 0.436 0.6 0.564
Billy Volek 1 1.0 1.000 0.5 0.481 0.5 0.519
David Carr 1 1.0 1.000 0.5 0.487 0.5 0.513
Brad Johnson 2 1.0 0.500 0.5 0.252 0.5 0.248
Colt McCoy 3 2.0 0.667 1.5 0.513 0.5 0.153
Matt Cassel 38 19.0 0.500 18.6 0.489 0.4 0.011
Josh Freeman 17 8.0 0.471 7.6 0.450 0.4 0.021
Chad Pennington 18 11.0 0.611 10.7 0.593 0.3 0.018
Matt Moore 9 5.0 0.556 4.7 0.522 0.3 0.033
Max Hall 2 1.0 0.500 0.7 0.367 0.3 0.133
Troy Smith 1 1.0 1.000 0.9 0.880 0.1 0.120
Dennis Dixon 2 1.0 0.500 0.9 0.446 0.1 0.054
Matt Hasselbeck 26 10.0 0.385 9.9 0.382 0.1 0.003
Michael Vick 4 3.0 0.750 3.0 0.743 0.0 0.007
Damon Huard 3 1.0 0.333 1.0 0.329 0.0 0.004
Jay Cutler 39 19.0 0.487 19.1 0.489 -0.1 -0.002
Charlie Whitehurst 1 0.0 0.000 0.1 0.126 -0.1 -0.126
Brian Brohm 1 0.0 0.000 0.1 0.129 -0.1 -0.129
Charlie Frye 4 1.0 0.250 1.1 0.287 -0.1 -0.037
Brooks Bollinger 1 0.0 0.000 0.2 0.151 -0.2 -0.151
Andrew Walter 2 0.0 0.000 0.2 0.103 -0.2 -0.103
Ken Dorsey 3 0.0 0.000 0.3 0.106 -0.3 -0.106
Todd Bouman 1 0.0 0.000 0.4 0.350 -0.4 -0.350
Chris Redman 3 1.0 0.333 1.4 0.479 -0.4 -0.146
Derek Anderson 20 7.0 0.350 7.5 0.373 -0.5 -0.023
Jeff Garcia 11 6.0 0.545 6.5 0.588 -0.5 -0.042
Kevin Kolb 7 3.0 0.429 3.5 0.499 -0.5 -0.070
Josh Johnson 3 0.0 0.000 0.5 0.176 -0.5 -0.176
Trent Green 2 0.0 0.000 0.5 0.271 -0.5 -0.271
Drew Stanton 3 0.0 0.000 0.6 0.196 -0.6 -0.196
Matt Leinart 2 0.0 0.000 0.6 0.313 -0.6 -0.313
Matt Schaub 31 18.0 0.581 18.7 0.604 -0.7 -0.023
Brady Quinn 11 3.0 0.273 3.7 0.341 -0.7 -0.068
Keith Null 4 0.0 0.000 0.8 0.192 -0.8 -0.192
J.T. O'Sullivan 6 2.0 0.333 2.9 0.480 -0.9 -0.146
Byron Leftwich 3 0.0 0.000 1.0 0.326 -1.0 -0.326
Jimmy Clausen 3 0.0 0.000 1.0 0.335 -1.0 -0.335
J.P. Losman 3 0.0 0.000 1.0 0.341 -1.0 -0.341
Shaun Hill 18 8.0 0.444 9.0 0.502 -1.0 -0.057
Brodie Croyle 2 0.0 0.000 1.0 0.524 -1.0 -0.524
Ryan Fitzpatrick 26 9.5 0.365 10.6 0.407 -1.1 -0.041
Tarvaris Jackson 5 2.0 0.400 3.2 0.632 -1.2 -0.232
Matthew Stafford 12 3.0 0.250 4.2 0.350 -1.2 -0.100
Bruce Gradkowski 9 3.0 0.333 4.2 0.468 -1.2 -0.135
Kyle Boller 5 0.0 0.000 1.3 0.269 -1.3 -0.269
Trent Edwards 22 8.0 0.364 9.5 0.431 -1.5 -0.067
Sage Rosenfels 5 1.0 0.200 2.5 0.497 -1.5 -0.297
Tony Romo 32 18.0 0.563 19.8 0.617 -1.8 -0.055
Alex Smith 17 6.0 0.353 7.8 0.461 -1.8 -0.108
Kyle Orton 38 18.0 0.474 20.1 0.530 -2.1 -0.056
Jon Kitna 6 0.0 0.000 2.2 0.375 -2.2 -0.375
Jason Campbell 35 15.0 0.429 17.5 0.501 -2.5 -0.073
Seneca Wallace 11 3.0 0.273 5.7 0.514 -2.7 -0.241
Dan Orlovsky 6 0.0 0.000 2.9 0.478 -2.9 -0.478
JaMarcus Russell 19 6.0 0.316 8.9 0.470 -2.9 -0.154
Daunte Culpepper 9 0.0 0.000 3.2 0.360 -3.2 -0.360
Aaron Rodgers 39 21.0 0.538 24.3 0.622 -3.3 -0.084
David Garrard 37 15.0 0.405 18.4 0.498 -3.4 -0.092
Tyler Thigpen 11 1.0 0.091 5.0 0.458 -4.0 -0.368
Philip Rivers 40 24.0 0.600 28.0 0.701 -4.0 -0.101
Marc Bulger 21 3.0 0.143 8.1 0.384 -5.1 -0.242

(Click the red text to sort by that header)

Peyton Manning has traditionally owned adjusted YPA, but over the past 3 seasons, he won more games that he "shouldn't have" (based on AY/A) than any other QB. Here are the seven games in which Manning had a win probability of less than 50% but won anyway:

11/30/2008 IND @ CLE W 10-6 12 13 Sun 15 21 125 0 2 1.67 0.117
12/13/2009 IND DEN W 28-16 13 14 Sun 20 42 220 4 3 3.93 0.253
10/10/2010 IND KAN W 19-9 5 5 Sun 26 44 244 0 1 4.52 0.302
11/23/2008 IND @ SDG W 23-20 11 12 Sun 32 44 255 2 1 5.68 0.411
9/14/2008 IND @ MIN W 18-15 2 2 Sun 26 42 311 1 2 5.74 0.417
11/8/2009 IND HOU W 20-17 8 9 Sun 34 50 318 1 1 5.86 0.429
11/29/2009 IND @ HOU W 35-27 11 12 Sun 27 35 244 3 2 6.11 0.455

Compare that to the 3 games where he played well enough to have a win probability over 50% and still lost:

12/27/2009 IND NYJ L 15-29 15 16 Sun 14 21 192 0 0 9.14 0.744
9/12/2010 IND @ HOU L 24-34 1 1 Sun 40 57 433 3 0 8.65 0.704
10/3/2010 IND @ JAX L 28-31 4 4 Sun 33 46 352 2 1 7.54 0.601

So much for the idea that Peyton's stats always outpace his wins!

Meanwhile, it turns out that poor Philip Rivers is indeed at the opposite end of the spectrum, finishing 2nd-to-last in terms of the difference between actual wins and expected wins. Rivers has lost eleven games with a win probability of 50% of greater:

9/14/2008 SDG @ DEN L 38-39 2 2 Sun 21 33 377 3 1 11.88 0.900
10/10/2010 SDG @ OAK L 27-35 5 5 Sun 27 42 431 2 0 11.21 0.873
11/23/2008 SDG IND L 20-23 11 12 Sun 24 31 288 2 0 10.58 0.841
9/7/2008 SDG CAR L 24-26 1 1 Sun 17 27 217 3 0 10.26 0.822
10/19/2009 SDG DEN L 23-34 5 6 Mon 20 33 274 1 0 8.91 0.726
10/26/2008 SDG @ NOR L 32-37 8 8 Sun 25 40 341 3 1 8.90 0.725
10/4/2009 SDG @ PIT L 28-38 4 4 Sun 21 36 254 3 0 8.72 0.710
9/13/2010 SDG @ KAN L 14-21 1 1 Mon 22 39 298 2 0 8.67 0.705
9/20/2009 SDG BAL L 26-31 2 2 Sun 25 45 436 2 2 8.58 0.698
9/26/2010 SDG @ SEA L 20-27 3 3 Sun 29 53 455 2 2 7.64 0.610
10/19/2008 SDG @ BUF L 14-23 7 7 Sun 22 29 208 2 1 7.00 0.546

He has only won 3 times in games where his win probability was less than 50%:

9/28/2008 SDG @ OAK W 28-18 4 4 Sun 14 25 180 1 2 4.40 0.291
11/8/2009 SDG @ NYG W 21-20 8 9 Sun 24 36 209 3 2 4.97 0.342
9/14/2009 SDG @ OAK W 24-20 1 1 Mon 24 36 252 1 1 6.31 0.474

Marc Bulger is the undisputed king of unlucky QBs, though, racking up the biggest negative differential between actual and expected wins while playing half as many games as Rivers:

9/7/2008 STL @ PHI L 3-38 1 1 Sun 14 26 158 0 0 6.08 0.451
9/14/2008 STL NYG L 13-41 2 2 Sun 20 32 177 1 1 4.75 0.322
9/21/2008 STL @ SEA L 13-37 3 3 Sun 18 31 184 1 1 5.13 0.357
10/12/2008 STL @ WAS W 19-17 5 6 Sun 15 26 136 0 0 5.23 0.367
10/19/2008 STL DAL W 34-14 6 7 Sun 13 18 163 1 0 10.17 0.816
10/26/2008 STL @ NWE L 16-23 7 8 Sun 18 34 304 1 1 8.21 0.664
11/2/2008 STL ARI L 13-34 8 9 Sun 16 33 186 2 2 4.12 0.268
11/9/2008 STL @ NYJ L 3-47 9 10 Sun 6 13 65 0 1 1.54 0.112
11/16/2008 STL @ SFO L 16-35 10 11 Sun 34 53 295 1 2 4.25 0.278
11/30/2008 STL MIA L 12-16 12 13 Sun 16 35 149 0 3 0.40 0.073
12/7/2008 STL @ ARI L 10-34 13 14 Sun 22 37 228 1 1 5.49 0.392
12/14/2008 STL SEA L 20-23 14 15 Sun 19 32 207 1 0 7.09 0.556
12/21/2008 STL SFO L 16-17 15 16 Sun 19 36 227 1 1 5.61 0.404
12/28/2008 STL @ ATL L 27-31 16 17 Sun 19 32 230 1 0 7.81 0.627
9/13/2009 STL @ SEA L 0-28 1 1 Sun 17 36 191 0 0 5.31 0.374
9/20/2009 STL @ WAS L 7-9 2 2 Sun 15 28 125 1 0 5.18 0.362
10/18/2009 STL @ JAX L 20-23 6 6 Sun 22 34 213 1 1 5.53 0.396
10/25/2009 STL IND L 6-42 7 7 Sun 14 26 140 0 2 1.92 0.129
11/1/2009 STL @ DET W 17-10 8 8 Sun 17 35 176 0 1 3.74 0.239
11/15/2009 STL NOR L 23-28 9 10 Sun 26 40 298 2 1 7.33 0.579
11/22/2009 STL ARI L 13-21 10 11 Sun 19 37 215 0 1 4.59 0.308

I always thought Bulger was a quality QB; it's a shame his last few viable seasons as a starter were spent surrounded by some of the worst supporting casts of any passer in the league.

This entry was posted on Thursday, November 11th, 2010 at 2:16 pm and is filed under PI Finds, Play Index, Quarterbacks, Statgeekery. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.