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Approximate value, part III

Posted by Doug on April 10, 2008

Here are the links to part I and part II.

Getting approximate values for defensive players proved to be quite a bit tougher than I had anticipated. What I've ended up with is a method that seems pretty sloppy, with lots of arbitrary "add three points for this" and "multiply this times 1.6" sort of rules. But I generally like the results it gives. And since the point of this is not to be theoretically correct, but to build an objective method that matches peoples' subjective opinions, I'm OK with it.

I'm going to do here the opposite of what I did in parts I and II. That is, I'm going to post some lists before posting the complete methodology. The basic idea is the same on the defensive side of the ball as on the offensive: while we don't know the contributions of each individual player, we do know what they should add up to, because we know how good the team was. So I've given each team defense a certain number of points, based on its points allowed per (estimated) possession compared to the league average. And then I've done my best to divvy up those points among those players according to: sacks (post-1982), interceptions, defensive touchdowns, tackles (post-1994), and all-pro status.

As I mentioned above, the exact mix of those ingredients is something I arrived at by trial and error. I've spent a lot of time asking, why does that guy rank so high? Oh, it's because of the way such-and-such a stat gets figured in. That needs fixing. OK, so now why is this other guy so low? Ah, I see, let's tweak that a little.

The main "breakthrough" here, which I've also applied to the offensive linemen, is that, instead of having a binary was-he-or-wasn't-he an all-pro system, I am now using three different degrees of all-pro-ness: first-team AP all-pro, second-team AP all-pro, and pro bowler who didn't make the first- or second-team all-pro list. This helps to separate the Kevin Williamses from the Trent Coles. Not that there's anything wrong with Trent Cole, but he's no Kevin Williams.

Enough chit-chat. I'm just going to post my approximate value estimates for a handful of famous teams and a few '07 teams. The number immediately after each player is my approximate value estimate. The second number, which is either a 1, 2, or 3, signifies the level of all-pro-ness of that player for that year. 1=first team, 2=second team, 3=pro bowler not on first or second team. But note that this information is only figured into the system at the non-skill positions, where I feel like we don't have the stats necessary to give them reasonable ratings without it. In other words, I'm comfortable (approximately) rating Derek Anderson and Franco Harris and Wesley Walker without knowing whether or not they made the pro bowl in a given year, but I'm not comfortable rating Jeff Saturday or Dave Duerson or Terrence Newman.

Peruse the lists and let me know what sticks out. Who's way off? Do you see anything that appears to you to be a systematic error?

2007 Patriots

Tom Brady               26   1
Randy Moss              21   1
Matt Light              21   1
Wes Welker              17   2
Mike Vrabel             15   1
Vince Wilfork           13   2
Logan Mankins           13   2
Asante Samuel           13   1
Dan Koppen              12   2
Laurence Maroney        10
Nick Kaczur             10
Donte Stallworth        10
Ty Warren                8
Kevin Faulk              8
Ellis Hobbs              8
Adalius Thomas           8
Tedy Bruschi             7
Ben Watson               7
James Sanders            6
Rosevelt Colvin          6
Jabar Gaffney            6
Jarvis Green             6
Russ Hochstein           5
Junior Seau              4
Rodney Harrison          4
Richard Seymour          4
Steve Neal               4
Sammy Morris             4
Kyle Brady               3
Randall Gay              3
Eugene Wilson            3
Heath Evans              3
Willie Andrews           2
Ryan O'Callaghan         2
Kyle Eckel               1
Lonie Paxton             1
Brandon Meriweather      1
Corey Mays               1
LeKevin Smith            1
Mike Wright              1
Billy Yates              1
Eric Alexander           1
Pierre Woods             1
Mel Mitchell             1
Larry Izzo               1
Wesley Britt             1

2000 Ravens

Ray Lewis               23   1
Rob Burnett             20   2
Rod Woodson             19   2
Sam Adams               17   2
Michael McCrary         12
Jamal Lewis             12
Jonathan Ogden          12   1
Jamie Sharper           11
Chris McAlister         11
Peter Boulware          10
Duane Starks            10
Kim Herring             10
Tony Siragusa            9
Shannon Sharpe           9
Qadry Ismail             7
Priest Holmes            6
Tony Banks               5
Edwin Mulitalo           5
Harry Swayne             5
Mike Flynn               5
Trent Dilfer             5
Jeff Mitchell            4
Jermaine Lewis           4
Travis Taylor            3
Spencer Folau            2
Patrick Johnson          2
O.J. Brigance            2
James Trapp              2
Cornell Brown            2
Brad Jackson             2
Lional Dalton            2
Corey Harris             2
Obafemi Ayanbadejo       2
Robert Bailey            2
Brandon Stokley          2
Ben Coates               2
Anthony Mitchell         2
Keith Washington         2
Anthony Poindexter       1
Billy Davis              1
Sam Gash                 1
Kipp Vickers             1
Larry Webster            1
Anthony Davis            1

1999 Rams

Marshall Faulk          25   1
Kurt Warner             20   1
Kevin Carter            19   1
Orlando Pace            19   1
Isaac Bruce             14   2
Todd Lyght              14   2
Mike Jones              11
Grant Wistrom           11
Fred Miller             10
D'Marco Farr             9
London Fletcher          9
Torry Holt               9
Az-Zahir Hakim           9
Ray Agnew                8
Mike Gruttadauria        8
Adam Timmerman           8
Billy Jenkins            7
Todd F. Collins          7
Tom Nutten               7
Dexter McCleon           7
Devin Bush               5
Robert Holcombe          4
Ricky Proehl             4
Keith Lyle               4
Roland Williams          4
Jeff Robinson            3
Dre' Bly                 3
Jeff Zgonina             3
Charlie Clemons          2
Jay Williams             2
James Hodgins            2
Chad Lewis               2
Lorenzo Styles           2
Tony Horne               2   2
Taje Allen               2
Andy McCollum            2
Ron Carpenter            1
Justin Watson            1
Rich Coady               1
Mike Morton              1
Nate Hobgood-Chittick     1
Joe Germaine             1
Troy Pelshak             1
Ryan Tucker              1

1978 Steelers

Terry Bradshaw          16   1
Jack Ham                15   1
Mike Webster            14   1
Joe Greene              13   3
Jack Lambert            12   3
Donnie Shell            12   3
Lynn Swann              12   1
Mel Blount              11   2
Franco Harris           11   3
John Stallworth         11
L.C. Greenwood          10   3
Jon Kolb                10
John Banaszak            9
Ron Johnson              8
Randy Grossman           8
Rocky Bleier             8
Dwight White             7
Ray Pinney               7
Sam Davis                7
Mike Wagner              7
Gerry Mullins            7
Loren Toews              6
Bennie Cunningham        5
Robin Cole               5
Steve Furness            4
Sidney Thornton          3
Larry Anderson           3
Larry Brown              3
Tony Dungy               3
Steve Courson            2
Fred Anderson            2
Tom Beasley              2
Dirt Winston             2
Gary Dunn                2
Nat Terry                1
Rick Moser               1
Theo Bell                1
Jim Smith                1
Ted Petersen             1
Wentford Gaines          1
Jim Mandich              1

1985 Bears

Walter Payton           19   1
Richard Dent            18   1
Mike Singletary         17   1
Steve McMichael         16   1
Gary Fencik             16   2
Jimbo Covert            16   1
Otis Wilson             15   2
Dan Hampton             14   2
Jim McMahon             13   3
Dave Duerson            12   3
Willie Gault            10
Leslie Frazier           9
Jay Hilgenberg           9   3
Keith Van Horne          9
Mike Richardson          9
Emery Moorehead          7
Wilber Marshall          7
Matt Suhey               7
Mark Bortz               7
Dennis McKinnon          7
Tim Wrightman            6
Tom Thayer               6
William Perry            5
Mike Hartenstine         4
Steve Fuller             4
Dennis Gentry            3
Calvin Thomas            2
Ron Rivera               2
Reggie Phillips          2
Ken Taylor               2
Andy Frederick           2
Cliff Thrift             2
Shaun Gayle              2
Ken Margerum             2
Tom Andrews              1
Jim Morrissey            1
Tyrone Keys              1
Thomas Sanders           1
Henry Waechter           1
Stefan Humphries         1
Kurt Becker              1

1990 Bills

Thurman Thomas          19   1
Bruce Smith             15   1
Jim Kelly               15   3
Andre Reed              13   2
Kent Hull               13   1
Will Wolford            11   3
Shane Conlan            11   2
Darryl Talley           10   3
Cornelius Bennett       10   3
James Lofton            10
Nate Odomes              9
Howard Ballard           9
Keith McKeller           8
Leonard Smith            8
John H. Davis            7
Jeff Wright              7
Leon Seals               7
Jim Ritcher              7
John Hagy                5
Kirby Jackson            5
Don Smith                4
Ray Bentley              4
Kenneth Davis            4
Carlton Bailey           3
Don Beebe                3
Jamie Mueller            3
James E. Williams        3
Pete Metzelaars          2
Mark Kelso               2
Frank Reich              2
Glenn Parker             2
Marvcus Patton           1
Dwight Drane             1
Gary Baldinger           1
Chris Hale               1
Mike Lodish              1
Hal Garner               1
Steve Tasker             1   3
Jeff Hunter              1
Mark Pike                1
Butch Rolle              1
David Pool               1
Carwell Gardner          1
Adam Lingner             1
Mitch Frerotte           1

2007 Giants

Osi Umenyiora           12   3
Eli Manning             11
Plaxico Burress         10
Brandon Jacobs           9
Kareem McKenzie          9
Kawika Mitchell          9
Antonio Pierce           8
Jeremy Shockey           8
Amani Toomer             8
Michael Strahan          8
Rich Seubert             7
Sam Madison              7
Chris Snee               7
David Diehl              7
Shaun O'Hara             7
Fred Robbins             7
Barry Cofield            7
Gibril Wilson            6
Derrick Ward             6
James Butler             5
Aaron Ross               5
Mathias Kiwanuka         5
Justin Tuck              4
Michael Johnson          3
Kevin Dockery            3
Corey Webster            3
Reggie Torbor            3
Kevin Boss               2
Chase Blackburn          2
Reuben Droughns          2
Michael Matthews         2
Sinorice Moss            2
Madison Hedgecock        2
R.W. McQuarters          2
Craig Dahl               1
Guy Whimper              1
Grey Ruegamer            1
Steve 2. Smith           1
Gerris Wilkinson         1
Russell Davis            1
Zak DeOssie              1
Jay Alford               1
Domenik Hixon            1
Ahmad Bradshaw           1

2007 49ers

Patrick Willis          17   1
Frank Gore              10
Marques Douglas          8
Bryant Young             8
Mark Roman               8
Nate Clements            7
Michael Lewis            7
Derek Smith              7
Aubrayo Franklin         6
Tully Banta-Cain         6
Walt Harris              6
Parys Haralson           6
Arnaz Battle             5
Vernon Davis             5
Joe Staley               5
Eric Heitmann            4
Darrell Jackson          4
Adam Snyder              4
Larry Allen              4
Isaac Sopoaga            3
Donald Strickland        2
Justin Smiley            2
Jonas Jennings           2
Jeff Ulbrich             2
David Baas               2
Brandon T. Moore         2
Keith Lewis              1
Zak Keasey               1
Moran Norris             1
Hannibal Navies          1
Manny Lawson             1
Dashon Goldson           1
Ray McDonald             1
Shaun Hill               1
Brian Jennings           1
Bryan Gilmore            1
Roderick Green           1
Ashley Lelie             1
Tarell Brown             1
Ronald Fields            1
Shawntae Spencer         1
Billy Bajema             1
Maurice Hicks            1
Michael Robinson         1
Marcus Hudson            1
Delanie Walker           1

2007 Browns

Derek Anderson          15   3
Braylon Edwards         13   2
Kellen Jr. Winslow      13   3
Jamal Lewis             12
Joe Thomas              10   3
Robaire Smith            8
Kevin Shaffer            8
Kamerion Wimbley         7
Leigh Bodden             6
Shaun Smith              6
Joe Jurevicius           6
Sean Jones               6
D'Qwell Jackson          6
Hank Fraley              6
Eric Steinbach           6
Brodney Pool             6
Willie McGinest          5
Leon Williams            5
Eric Wright              5
Andra Davis              5
Josh Cribbs              4   2
Ryan Tucker              4
Jason Wright             4
Lawrence Vickers         4
Antwan Peek              3
Daven Holly              3
Ethan Kelley             3
Seth McKinney            3
Orpheus Roye             3
Brandon McDonald         2
Simon Fraser             2
Steve Heiden             2
Mike Adams               1
Lennie Friedman          1
David McMillan           1
Chaun Thompson           1
Ted Washington           1
Ryan Pontbriand          1   3
Nick Sorensen            1
Jerome Harrison          1
Kris Griffin             1
Tim Carter               1
Kenny Wright             1
Darnell Dinkins          1

This entry was posted on Thursday, April 10th, 2008 at 9:45 am and is filed under Approximate Value, General. You can follow any responses to this entry through the RSS 2.0 feed. Both comments and pings are currently closed.