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## Approximate value II

Posted by Doug on January 16, 2008

If you haven't done so yet, you'd better read Approximate Value I. (I know you're thinking, "yeah, yeah, whatever." I do the same thing. But I mean it. Go read the old post.)

I left off last time with this bunch of questions:

• What metric do I use to determine offensive points at the team level?
• What fraction of points should go to the line?
• What is the pass/run split?
• On the passing side, what is the throw/catch split?
• We need to figure a way to give some of those offensive line points to fullbacks and tight ends, many of whose jobs include a lot of blocking.

Hopefully, I'll be able to answer all these today, and run through an example or two. Before I do, I'd like to make a few comments about the method and about my style of doing these sorts of things:

• I'll just state upfront that this is a case where I'm not necessarily opposed to tweaking the metric until it gives us results we're happy with, instead of picking a theoretical basis and forcing ourselves to stick with it. As I quoted Bill James in the last post: "These approximations are not intended to tell you anything at all about the player that you do not already know." They're not supposed to teach us new things; they're merely supposed to codify the things we already know, so it's OK to cook the books a little bit until they do tell us what we already know. The problem here is that none of us really knows how to compare Tarik Glenn's 2006 to Gary Clark's 1991. And to the extent that we do "know," we all "know" different things. The point is: while I do think we need some sort of theory to get us started in certain areas, I won't be too apologetic about making some arbitrary changes if a strict application of the theory leads us to "wrong" answers.
• The reason I write a blog instead of writing books --- well, one of them --- is because I'm not the kind of guy who thinks everything through completely before running the numbers and writing it up. I'm the kind of guy who comes up with a vague idea, gets excited about it, and tries to get to (and share) some preliminary results as soon as possible, occasionally making a few admittedly half-hearted choices along the way. There are some calculations below that I know are wrong. But I think they're close enough that they won't do any real damage to the conclusions. I'll go back and re-examine them later.
• A reminder that this method is for the purpose of establishing approximate value. From yesterday's post, this is James: "The approximations are intended only to distinguish as quickly and reliably as possible between large contributions, very large contributions, gigantic contributions, medium-sized contributions, small, smaller, and negligible contributions." I bolded "as possible" to remind us that there's only so much we're going to be able to do. We're not going to be able to give Hines Ward the credit he allegedly deserves for blocking. We're not going to be able to distinguish between a tight end who posted 20/110/1 because he stunk and another who posted 20/110/1 because he was basically a third tackle. If a team has a very good right guard and a very bad left guard, we're not going to be able to distinguish them unless the good one makes the pro bowl. Is this unfortunate? Yes. Does it make this whole exercise useless? That's for you to decide. But if you think it does, there's not much point in reading on. So if you're still here, remember: I will liberally and sometimes arbitrarily play the "we're keeping it simple" card. Daniel Graham and Steve Tasker will simply have to accept my apologies.
• At least for now, I'm only going to attempt to rate players from 1978--2006 (I'm still filling in a few stats from '07). First, lots of things changed with the rule changes that preceded the 1978 season. They have continued to change since then, of course, but I'm fairly comfortable assuming that 78--06 constitutes an era. Also, games started will be a key part of the metric, and GS data gets a little sketchy in my database right around 1978.

OK, here goes.

The metric for measuring team offense

At least for now, I'm going to go with offensive points per drive, which is a stat I should have thought to compute a long time ago, but didn't. Unless I'm missing something, every drive ends with either a rushing touchdown, a passing touchdown, a field goal attempt, a punt, a turnover, a failed fourth down conversion attempt, or the end of a half. On the team level, the new database has touchdowns, field goals, punts, and turnovers. The other two I don't have data for. A half-ending possession that doesn't result in one of the four main outcomes probably wasn't much of a possession anyway, so I don't mind not counting those. I wish I had turnover-on-downs data, but given the relative rarity of these kind of possessions, I'm not too uncomfortable excluding them. So we'll just call it offensive points per estimated drive:

OPPED = ( 7*TDs + 3*(field goals made) ) / ( TDs + FG attempts + punts + turnovers )

Now divide the team's OPPED by the league OPPED, multiply by 100, and that's how many points a team's offense has to distribute. So an average offensive team will necessarily have 100 points. The 1982 Chargers, 2000 Rams, and 1984 Dolphins all have about 170. The 1992 Seahawks have about 44 and the 2006 Raiders have 47.

Dividing up the points

Here's where it's going to get a little controversial.

In the comments to yesterday's post, Neil outlined an idea that is probably better than mine:

I tried to look at salaries to see how GMs value each position. For instance, QBs made 17% of the salary cap # devoted to offensive players from 2000-07, so I allocated 17% of “Offensive Wins” to the QB position; RBs were paid 12% so they got 12% of wins, etc

If I had that data, and if I'd thought of it, that's probably what I'd use. But I don't and I didn't. I did, however, realize that last April I ran a study that can provide a similar theoretical basis for allocating the points. I calculated the percentage of draft value chart "points" that NFL teams have historically used on each position. Here is the chart:

```qb    7.4
rb   12.5
wr   11.7
te    3.9
ol   15.5
dl   19.3
lb   13.2
db   15.8
pk    0.5
pn    0.3
```

Assuming teams actually believe the pick value chart, and assuming they know what they're doing, then it might make sense to make it a goal to set up our system so that, in the long run, the number of total points awarded to players at each position matches the above distribution. We're going to start with that idea and work from there.

I wish I had a RB/FB breakdown, but I don't. I'm just going to make one up: 80/20. So we have this:

```qb    7.4
rb   10.0
fb    2.5
wr   11.7
te    3.9
ol   15.5
```

Looking at just QB, RB, WR, TE, and OL, it adds to 51. Our task is essentially to divide that 51 into four buckets: (1) blocking, (2) running, (3) pass throwing, (4) pass catching. Let's make the following assumptions, which I do know are not exactly right:

• an OL's job is 100% blocking
• an average QB's job is 95% pass-throwing and 5% running
• an average RB's job is 70% running and 30% pass-catching
• a WR's job is 100% pass-catching (sorry Hines)
• an average TE's job is 70% pass-catching and 30% blocking (yes, I know this varies a lot from TE to TE, more on that later)
• an average fullback's job is 10% running, 20% catching, and 70% blocking.

So, for blocking we have 100% of 15.5, 30% of 3.9, and 70% of 2.5.

For running we have 5% of 7.4, 70% of 10.0, and 10% of 2.5.

For pass-throwing we have 95% of 7.4.

For pass-catching we have 100% of 11.7, 30% of 10.0, 20% of 2.5, and 70% of 3.9.

Blocking: 18.42
Running: 7.62
Throwing: 7.03
Catching: 17.93

So the proportions are:

Blocking: 36.1%
Running: 14.9%
Throwing: 13.8%
Catching: 35.2%

I really, really like the above method. The problem is that it just doesn't seem to work. Offensive linemen turn out to be undervalued by just about anyone's standards. In a preliminary version of this method using these percentages, Jon Ogden came in right between Brian Sipe and Ronnie Harmon in terms of total career approximate value. So let's tweak up the blocking percentage just a bit and keep the remaining relationships fixed. Here's one that I think works pretty well.

Blocking: 45.5% <--- that's 5/11
Running: 12.8%
Throwing: 11.8%
Catching: 29.9%

OK, so an average team will have 45.5 points to split among the blockers. The 1982 Chargers will have about 77. The 2006 Raiders will have about 22. Here's how we'll split it:

1. Every lineman, fullback, and tight end gets 1 pre-point for each game played and an additional 5 pre-points for each game started.
2. Tackles get their pre-points multiplied by 1.3, fullbacks by .7, and tight ends by .3.
3. Pro bowl linemen (not tight ends or fullbacks) get their pre-points multiplied by 1.7.
4. Every OL, FB, and TE gets points proportional to his percentage of the team's total pre-points.

Now we move on to the skill guys. The percentages above dictate that an average team should have 23.5% of its remaining points devoted to running, and 76.5% devoted to throwing and catching. [Here come a couple of calculations that I think are basically in the ballpark, but could use some improvement...] For each team, we take its ratio of rushing yards to total yards and divide it by the league average ratio. This gives a number like 1.15 for a run-heavy team or .93 for a team with a slight tendency toward the pass. Then we multiply that number by 23.5 to see what percentage of that team's non-blocking points will go to runners. Now we know how many points to give the runners, and how many points to give the passers/receivers.

Remember from last time, I declared that the passer/receiver split should stay constant from team to team. So passers get 11.8/(11.8+29.9) = 28.3% of the passing game points and receivers get the other 71.7%. Remember, there are a lot more people that have to split the receiving points.

The individual runners get points proportional to their share of the team's rushing yards. We're keeping it simple here. Likewise with the individual passers (passing yards) and receivers (receiving yards).

That's it. Now let's look at some results and see if it's believable. Here are the top two and bottom two offensive teams of the era, along with a couple of average-ish teams:

```sdg 1982 172.8
--------------
Dan Fouts               21
Wes Chandler            20
Kellen Winslow          19
Doug Wilkerson          15
Russ Washington         14
Billy Shields           14
Chuck Muncie            13
Ed White                10
Charlie Joiner          10
Don Macek               10
James Brooks             7
Eric Sievers             5
John Cappelletti         2
Pete Holohan             2
Chuck Loewen             2
Andrew Gissinger         2
Bob Rush                 2
Dwight Scales            2
Bobby Duckworth          1
Dennis McKnight          1
Scott Fitzkee            1

mia 1984 171.6
--------------
Dan Marino              22
Mark Clayton            15
Ed Newman               14
Dwight Stephenson       14
Jon Giesler             14
Mark Duper              14
Cleveland Green         11
Tony Nathan             11
Roy Foster              10
Dan Johnson              9
Woody Bennett            6
Nat Moore                6
Bruce Hardy              5
Joe Carter               5
Eric Laakso              3
Joe Rose                 3
Jeff Toews               2
Jimmy Cefalo             2
Pete Johnson             2
Jim C. Jensen            2
Ronnie Lee               2
Steve S. Clark           1
Andra Franklin           1

nyj 2001 100.1
--------------
Curtis Martin           15
Vinny Testaverde        11
Laveranues Coles         9
Kevin Mawae              8
Jason Fabini             8
Ryan Young               8
Wayne Chrebet            7
Richie Anderson          7
Kerry Jenkins            6
Anthony Becht            5
Randy Thomas             4
LaMont Jordan            3
Kevin Swayne             2
James Dearth             1
David Loverne            1
Jerald Sowell            1

oti 2000 99.7
--------------
Eddie George            14
Steve McNair            12
Frank Wycheck            9
Bruce Matthews           8
Derrick Mason            8
Fred Miller              7
Benji Olson              5
Chris Sanders            5
Kevin Long               5
Erron Kinney             3
Lorenzo Neal             2
Yancey Thigpen           2
Carl Pickens             2
Neil O'Donnell           2
Rodney Thomas            1
Kevin Dyson              1
Zach Piller              1
Mike Leach               1
Jason Mathews            1

rai 2006 47.0
--------------
Justin Fargas            4
Doug Gabriel             4
Ronald Curry             4
Langston Walker          4
Jake Grove               3
Aaron Brooks             3
Kevin Boothe             3
Randy Moss               3
Andrew Walter            3
Robert Gallery           2
Zack Crockett            2
LaMont Jordan            2
Paul McQuistan           2
Courtney Anderson        2
Barry Sims               2
ReShard Lee              1
Alvis Whitted            1
Corey Hulsey             1
Randal Williams          1

sea 1992 43.2
--------------
John L. Williams         6
Chris Warren             5
Stan Gelbaugh            3
Andy Heck                3
Ray Roberts              3
Kelly Stouffer           2
Darrick Brilz            2
Tommy Kane               2
Bill Hitchcock           2
Joe Tofflemire           2
Paul Green               1
Ronnie Lee               1
Louis Clark              1
John Hunter              1
Robb Thomas              1
Ron Heller               1
James R. Jones           1
Trey Junkin              1
David Daniels            1
```

Here's the total career approximate value list. Players whose careers started before 1978 (and hence whose complete careers are not counted) are asterisked:

``` Dan Marino               225
Jerry Rice               223
Brett Favre              212
John Elway               207
Bruce Matthews           176
Anthony Munoz            176
Warren Moon              172
Emmitt Smith             171
Steve Young              165
Joe Montana              161
Lomas Brown              157
Marshall Faulk           156
Vinny Testaverde         154
Peyton Manning           153
Mike Kenn                152
Drew Bledsoe             147
Boomer Esiason           146
Barry Sanders            141
Willie Roaf              140
Shannon Sharpe           139
Gary Zimmerman           139
Dave Krieg               138
Marcus Allen             136
*Jackie Slater            136
Richmond Webb            136
Will Shields             134
Marvin Harrison          134
Randall Cunningham       133
Curtis Martin            133
Thurman Thomas           132
Jim Kelly                132
*Dan Fouts                132
Steve McNair             132
Randall McDaniel         131
Troy Aikman              130
Tim Brown                129
James Lofton             128
Mark Brunell             126
Rich Gannon              125
Orlando Pace             125
Tarik Glenn              123
Bruce Armstrong          122
*Mike Webster             122
Stan Brock               122
Art Monk                 121
Phil Simms               121
Cris Carter              121
Ricky Watters            120
Andre Reed               120
Henry Ellard             120
Jim Everett              119
Steve DeBerg             119
Will Wolford             117
Tony Gonzalez            117
*Walter Payton            116
Michael Irvin            116
Edgerrin James           116
Chris Hinton             114
John L. Williams         114
*Steve Largent            113
Rod Smith                112
Max Montoya              112
Terrell Owens            112
Joe Jacoby               111
Jonathan Ogden           111
Tiki Barber              110
Isaac Bruce              109
Steve Wisniewski         109
Tom Nalen                109
*Tony Dorsett             109
Jerome Bettis            109
Jimmy Smith              108
Ozzie Newsome            108
Jim Harbaugh             108
Walter Jones             108
Luis Sharpe              108
Eric Dickerson           107
Bob Whitfield            107
Trent Green              107
Tony E. Jones            106
Mike Munchak             106
Kerry Collins            105
Willie Anderson          105
Jake Plummer             104
Chris Chandler           104
Warrick Dunn             104
Roger Craig              104
Todd Steussie            102
Earnest Byner            102
*Joe Theismann            101
Larry Centers            100
```

The best single seasons of the period form an interesting collection that will surely spark some discussion:

```Orlando Pace          2000       23
Marshall Faulk        1999       23
Dan Marino            1984       22
Priest Holmes         2002       22
Steve Young           1993       22
Steve Young           1992       21
Tarik Glenn           2004       21
Dan Fouts             1982       21
Terrell Davis         1998       21
Steve Young           1994       21
Emmitt Smith          1995       21
Marshall Faulk        2000       20
Peyton Manning        2004       20
Steve Wallace         1992       20
Peyton Manning        2006       20
Daunte Culpepper      2004       20
Wes Chandler          1982       20
Edgerrin James        1999       20
Kurt Warner           2001       20
Barry Sanders         1994       20
Rich Gannon           2000       20
Daunte Culpepper      2000       20
Kellen Winslow        1982       20
```

Finally, here are the approximate top performers of 2006:

```LaDainian Tomlinson   2006       23
Peyton Manning        2006       20
Tarik Glenn           2006       19
Steven Jackson        2006       17
Tiki Barber           2006       17
Antonio Gates         2006       17
Philip Rivers         2006       17
Larry Johnson         2006       17
Marcus McNeill        2006       16
Marvin Harrison       2006       16
Reggie Wayne          2006       15
Carson Palmer         2006       15
Matt Light            2006       15
Michael Vick          2006       15
Frank Gore            2006       15
Drew Brees            2006       15
Jon Kitna             2006       14
Brian Westbrook       2006       14
Willie Anderson       2006       14
Jeff Saturday         2006       14
Jammal Brown          2006       14
Marc Bulger           2006       14
Chris Samuels         2006       13
```

You may agree with these lists in spots and strongly disagree in others. That's OK. But it's worth pausing for a minute to remind ourselves just how impossible the task we've undertaken is. All we're using is passing yards, rushing yards, receiving yards, games, games started, position played, and pro bowl status. And we're only using the pro bowls when we really have to (for linemen). Given that that's all we have to work with, I happen to think the method does a pretty good job of getting close to an assessment of approximate value that most people would generally agree with.

Kinds of players who are over-valued:

• On the career list, quarterbacks who played for a long time. That's unavoidable, given that QB is the most important position on the field, quarterbacks tend to have long careers, and this is a career total metric. But it does raise some questions. Namely, if a team has a terrible offense and/or a terribly inefficient passing game, why are we giving the quarterback any points at all? Stan Gelbaugh got three points for compiling dreadful stats on the worst offensive team of the last 30 years. Why aren't we giving him negative points? I'm not sure I have a good answer for that, except that I don't see how to do it in a way that would keep the method for QBs consistent with the rest of the positions and I'm not quite ready to have totally different sets of rules for different positions. And I definitely don't want to go the route of making this a metric where an average player is zero and a below average player has negative points.
• Post-James Wilder era running backs, compared to pre-James Wilder era backs. Wilder was the first true workhorse back. Before him, no coach ever attempted to let a single RB get 80--90% (or more) of the RB work on a team. I'm not completely comfortable with Shaun Alexander having three seasons as good as Earl Campbell's best one, simply because Tim Wilson was getting some touches.
• I was hoping to avoid this, but I may have to re-work the running game / passing game percentages, creating a slightly different set for pre-1985ish versus post-1985ish.

• Bad offensive tackles. Of course, they won't generally be on good teams and/or won't stick around long anyway. So I don't see this as a major issue.
• Offensive linemen who make the pro bowl based on reputation long after their best years are behind them.
• Offensive linemen (especially tackles) who were the only pro bowl lineman on a very good offensive team. Orlando Pace and Tarik Glenn have probably been overcredited a little.
• Guys whose nominal position is fullback, but who don't do as much blocking as a real fullback. Yes, Mike Alstott, I'm talking about you. Probably Larry Centers too. They get as big a share of the blocking credit as Dan Kreider and Lorenzo Neal do, but they don't do near as much actual blocking.

Kinds of players who are under-valued:

• Good blocking tight ends and wide receivers.
• Linemen (especially guards and tackles) who were good, but not good enough to make the pro bowl.

Next, we move to the defensive side of the ball. That may happen this week, or it may be next week.