Previous post:

Next post:

How to determine the appropriate salary cap values for veterans: Part II

by Chase Stuart on April 15, 2013

in Statgeekery, Theory

In Part I, I derived a formula to translate the number of marginal wins a veteran player was worth into marginal salary cap dollars (my answer was $14.6M, but the Salary Cap Calculator lets you answer that question on your own terms). We can also translate Approximate Value into wins using a similar method.

Each NFL team generates about 201 points of Approximate Value per season, or 6,440 points of AV per season in the 32-team era. I ran a linear regression using team AV as the input and wins as the output, which produced a formula of

Team Wins = -9.63 + 0.0876*AV

This means that adding one point of AV to a team is expected to result in 0.0876 additional wins. In other words, for a 201-AV team to jump from 8 to 9 wins, they need to produce 11.4 additional points of AV.

A player who can deliver 11.4 marginal points of AV is therefore worth one win to a team, or 14.6 million marginal salary cap dollars (or whatever number you choose). Alternatively, you can think of it like this: a player who is worth $1.277M marginal dollars should be expected to produce 1 additional point of AV and 0.0876 additional wins. In case the math made you lose the forest for the trees, this is all a reflection of the amount of wins we decide the replacement team is worth, as the formula is circular: if a team spends all of its $72.877M marginal dollars, they should get 57.07 marginal points of AV, or 5 extra wins, the amount needed to make a replacement team equal to an average team.

Next we need to focus just on Veterans, defined as players in their fourth year or later. The table below shows how much AV is provided by all players in the NFL by year, as a percentage of league-wide AV. The right column shows the amount of cumulative AV provided by all players that year and younger:

Year
% of Lg AV
Cumulative %
18.8%8.8%
212.3%21.1%
312.6%33.7%
412.2%45.9%
511.4%57.3%
610%67.3%
78.6%75.9%
87.1%83%
95.3%88.3%
104%92.3%
112.9%95.3%
122%97.2%
131.2%98.4%
140.7%99.2%
150.4%99.6%
16+0.4%100%

Players in their first three seasons provide over one-third of the average team’s value, while nearly half of a team’s AV comes from players in their first four seasons. In 2012, for example, Veterans produced 3958 points of AV. Since we have theorized that all Veterans produce a total of 160 marginal wins, or 5 marginal wins per team, you might think we just want to divide 3958 by 160, but that’s not exactly right because it ignores the concept of marginal AV. Doing so would suggest that one win was worth 24.7 points of AV, and we just determined that one win was worth slightly fewer than half as many points of AV.

This makes sense — a player with one or two points of AV isn’t really doing much, and certainly isn’t doing much that isn’t easily replaceable. What we need to do is subtract a certain number of points from each player to reduce the total pile of points of AV from Veterans from 3958 to 1824 (11.4 * 160). I’ll spare you the complicated math, but that number turns out to be 3.36 points of AV from each player in 2012. What this means is that every Veteran with 3 or fewer points of AV is therefore worth $850K salary cap dollars (our average Veterans minimum). For Veterans with 4 or more points of AV, we subtract 3.36 points of AV to figure out their amount of marginal AV provided, and multiply that number by $1.277M to give us the amount of marginal salary cap dollars they were worth. Add $850K to that number, and you get that player’s salary cap dollar value for 2013 assuming they produce exactly as they did in 2012. I have included a list of the top 100 or so Veterans at the bottom of this post.

But first, let’s take a step back and remember how AV was created. There are many situations, including this one, where we need a metric that is capable of comparing players across positions. In baseball and basketball, lots of stats have been cooked up to do this, and analytics folks have done so with a reasonable degree of precision. In football, no such stat existed prior to Doug’s creation of AV. In most cases, people used “starter” or “number of years as a starter” or “number of pro bowls” as the metric when they had to compare across positions.

AV was intended to be an improvement over those metrics, and nothing more. It is not Not NOT an ubermetric whose purpose is to decide once and for all who the best players in the NFL are. So I should not Not NOT rank all the players in the NFL according to AV, translate those AV values into salaries, and present them in a list. To do so would be to imply that I’ve done something I haven’t done. To do so would be to invite links from team message boards where the first post is “some guy posted a list saying Charles Tillman is worth Seventeen Million Dollars!” and the second post is “I stopped reading as soon as I saw Cameron Wake ranked ahead of Aaron Rodgers. What a bozo!”

I now present to you a list of the amount of Salary Cap Dollars that the top Veterans are worth based on their performance last season:

Name	                Team	Pos	AV	MarAV	Wins	Salary (in millions)
Adrian Peterson	        MIN	RB	19	15.64	1.37	$20.82
Tom Brady	        NWE	QB	18	14.64	1.28	$19.55
Julius Peppers	        CHI	RE	18	14.64	1.28	$19.55
Matt Ryan	        ATL	QB	18	14.64	1.28	$19.55
Cameron Wake	        MIA	RDE	18	14.64	1.28	$19.55
Aaron Rodgers	        GNB	QB	17	13.64	1.20	$18.27
Charles Tillman	        CHI	RCB	16	12.64	1.11	$16.99
Vince Wilfork	        NWE	DT	16	12.64	1.11	$16.99
Peyton Manning	        DEN	QB	15	11.64	1.02	$15.72
Drew Brees	        NOR	QB	15	11.64	1.02	$15.72
Eli Manning	        NYG	QB	15	11.64	1.02	$15.72
Wes Welker	        NWE	WR	15	11.64	1.02	$15.72
Marshawn Lynch	        SEA	RB	15	11.64	1.02	$15.72
Patrick Willis	        SFO	ILB	15	11.64	1.02	$15.72

NOTE FOR PEOPLE WHO SKIPPED STRAIGHT DOWN TO THE LIST WITHOUT READING THE POST: the author who generated this list does not agree with the entirety of this list. He, in fact, acknowledges that it’s obviously wrong in spots. He does think it’s pretty respectable, given the difficulty of comparing players across positions using only objective data without just saying that Tom Brady and Peyton Manning are worth 10 wins each. He also thinks it’ll give us something to talk about here in April.

We now return to the list.

Name	                Team	Pos	AV	MarAV	Wins	Salary (in millions)
Andre Johnson	        HOU	WR	14	10.64	0.93	$14.44
Tony Romo	        DAL	QB	14	10.64	0.93	$14.44
Roddy White	        ATL	WR	14	10.64	0.93	$14.44
Brandon Marshall	CHI	WR	14	10.64	0.93	$14.44
Jahri Evans	        NOR	RG	14	10.64	0.93	$14.44
Calvin Johnson	        DET	WR	14	10.64	0.93	$14.44
Ryan Clady	        DEN	LT	14	10.64	0.93	$14.44
Max Unger	        SEA	C	14	10.64	0.93	$14.44
Champ Bailey	        DEN	LCB	13	9.64	0.84	$13.16
Tim Jennings	        CHI	LCB	13	9.64	0.84	$13.16
Haloti Ngata	        BAL	DT	13	9.64	0.84	$13.16
Joe Flacco	        BAL	QB	13	9.64	0.84	$13.16
Ray Rice	        BAL	RB	13	9.64	0.84	$13.16
Josh Freeman	        TAM	QB	13	9.64	0.84	$13.16
Matthew Stafford	DET	QB	13	9.64	0.84	$13.16
Tony Gonzalez	        ATL	TE	12	8.64	0.76	$11.89
London Fletcher	        WAS	MLB	12	8.64	0.76	$11.89
Justin Smith	        SFO	RDE	12	8.64	0.76	$11.89
Matt Schaub	        HOU	QB	12	8.64	0.76	$11.89
Vincent Jackson	        TAM	WR	12	8.64	0.76	$11.89
Eric Weddle	        SDG	FS	12	8.64	0.76	$11.89
Ahmad Brooks	        SFO	OLB	12	8.64	0.76	$11.89
Chad Greenway	        MIN	OLB	12	8.64	0.76	$11.89
Elvis Dumervil	        DEN	RDE	12	8.64	0.76	$11.89
Joe Staley	        SFO	LT	12	8.64	0.76	$11.89
Ed Reed	                BAL	FS	11	7.64	0.67	$10.61
Lance Briggs	        CHI	OLB	11	7.64	0.67	$10.61
DeMarcus Ware	        DAL	ROLB	11	7.64	0.67	$10.61
Jay Cutler	        CHI	QB	11	7.64	0.67	$10.61
Ahmad Bradshaw	        NYG	RB	11	7.64	0.67	$10.61
Lawrence Timmons	PIT	RILB	11	7.64	0.67	$10.61
Dashon Goldson	        SFO	FS	11	7.64	0.67	$10.61
Joe Thomas	        CLE	LT	11	7.64	0.67	$10.61
Jerod Mayo	        NWE	ILB	11	7.64	0.67	$10.61
Duane Brown	        HOU	LT	11	7.64	0.67	$10.61
Clay Matthews	        GNB	ROLB	11	7.64	0.67	$10.61
Reggie Wayne	        IND	WR	10	6.64	0.58	$9.33
Steve Smith	        CAR	WR	10	6.64	0.58	$9.33
Paris Lenon	        ARI	ILB	10	6.64	0.58	$9.33
Larry Foote	        PIT	LILB	10	6.64	0.58	$9.33
Brandon Lloyd	        NWE	WR	10	6.64	0.58	$9.33
Jason Witten	        DAL	TE	10	6.64	0.58	$9.33
Philip Rivers	        SDG	QB	10	6.64	0.58	$9.33
Carson Palmer	        OAK	QB	10	6.64	0.58	$9.33
Ben Roethlisberger	PIT	QB	10	6.64	0.58	$9.33
Jared Allen	        MIN	RDE	10	6.64	0.58	$9.33
Chris Snee	        NYG	RG	10	6.64	0.58	$9.33
Ryan Fitzpatrick	BUF	QB	10	6.64	0.58	$9.33
Frank Gore	        SFO	RB	10	6.64	0.58	$9.33
Chris Clemons	        SEA	RDE	10	6.64	0.58	$9.33
Marques Colston	        NOR	WR	10	6.64	0.58	$9.33
Johnathan Joseph	HOU	RCB	10	6.64	0.58	$9.33
Antonio Cromartie	NYJ	CB	10	6.64	0.58	$9.33
Brandon Mebane	        SEA	RDT	10	6.64	0.58	$9.33
Matt Forte	        CHI	RB	10	6.64	0.58	$9.33
Martellus Bennett	NYG	TE	10	6.64	0.58	$9.33
Arian Foster	        HOU	RB	10	6.64	0.58	$9.33
Jairus Byrd	        BUF	FS	10	6.64	0.58	$9.33
Michael Crabtree	SFO	WR	10	6.64	0.58	$9.33
Sebastian Vollmer	NWE	RT	10	6.64	0.58	$9.33
Jeff Saturday	        GNB	C	9	5.64	0.49	$8.06
John Abraham	        ATL	RDE	9	5.64	0.49	$8.06
Ryan Clark	        PIT	FS	9	5.64	0.49	$8.06
Brett Keisel	        PIT	DE	9	5.64	0.49	$8.06
Anquan Boldin	        BAL	WR	9	5.64	0.49	$8.06
Karlos Dansby	        MIA	MLB	9	5.64	0.49	$8.06
Jonathan Babineaux	ATL	DT	9	5.64	0.49	$8.06
Kevin Burnett	        MIA	LOLB	9	5.64	0.49	$8.06
Derrick Johnson	        KAN	RILB	9	5.64	0.49	$8.06
Heath Miller	        PIT	TE	9	5.64	0.49	$8.06
Logan Mankins	        NWE	LG	9	5.64	0.49	$8.06
Lance Moore	        NOR	WR	9	5.64	0.49	$8.06
Andrew Whitworth	CIN	LT	9	5.64	0.49	$8.06
D'Qwell Jackson	        CLE	MLB	9	5.64	0.49	$8.06
LaRon Landry	        NYJ	S	9	5.64	0.49	$8.06
Stephen Nicholas	ATL	OLB	9	5.64	0.49	$8.06
Nick Roach	        CHI	OLB	9	5.64	0.49	$8.06
David Harris	        NYJ	ILB	9	5.64	0.49	$8.06
Alan Branch	        SEA	LDT	9	5.64	0.49	$8.06
Greg Olsen	        CAR	TE	9	5.64	0.49	$8.06
Sidney Rice	        SEA	WR	9	5.64	0.49	$8.06
Marshall Yanda	        BAL	RG	9	5.64	0.49	$8.06
Jermon Bushrod	        NOR	LT	9	5.64	0.49	$8.06
Chris Johnson	        TEN	RB	9	5.64	0.49	$8.06
Jamaal Charles	        KAN	RB	9	5.64	0.49	$8.06
Steve Johnson	        BUF	WR	9	5.64	0.49	$8.06
Jermichael Finley	GNB	TE	9	5.64	0.49	$8.06
Jo-Lonn Dunbar	        STL	OLB	9	5.64	0.49	$8.06
Wesley Woodyard	        DEN	OLB	9	5.64	0.49	$8.06
Sam Baker	        ATL	LT	9	5.64	0.49	$8.06
Tyler Polumbus	        WAS	RT	9	5.64	0.49	$8.06
Percy Harvin	        MIN	WR	9	5.64	0.49	$8.06
Brian Hartline	        MIA	WR	9	5.64	0.49	$8.06
James Laurinaitis	STL	MLB	9	5.64	0.49	$8.06
Michael Johnson	        CIN	RDE	9	5.64	0.49	$8.06
Evander Hood	        PIT	DE	9	5.64	0.49	$8.06
Ryan Wendell	        NWE	C	9	5.64	0.49	$8.06
William Beatty	        NYG	T	9	5.64	0.49	$8.06

{ 14 comments… read them below or add one }

James April 15, 2013 at 9:58 am

Chase, potentially dumb question: Have you or anyone else looked to see if AV is consistent from season to season, especially for players who switch teams?

With the notable exception of Brady, I notice that the QBs who recently signed new contracts, Peyton, Brees, Romo, Flacco, and potentially Ryan and Rodgers soon, are all overpaid by $3-4 million a year. This could mean 1) QBs deserve more AV, 2) this was a down year for those QBs, 3) teams overvalue QBs, 4) AV misses some component of a QB’s value (the ol’ jerseys argument), or potentially other answers. My money’s on 1 or 3, but I’m not sure.

This also means that others have to be underpaid. Do we know if this underpayment is distributed evenly, or is it focused on one particular position?

Reply

JeremyDe April 15, 2013 at 10:42 am

Good comments/questions. I think I remember someone (either here or at the football-reference blog) looked at the correlation of AV from season-to-season, although at the moment, I am not awake enough to remember whether that was the reason for the post, or if it was related to some other curiosity.

I was thinking along the same lines (either 1 or 3), but the thought occurred to me…could QBs be appropriately valued in AV, but the scarcity of quality level starters, and the difference between a starter and a replacement level QB account for QBs being overvalued?

Also, not sure if it would be worthwhile exercise, but with 2012 salary data, one could see which players are most over/under-valued (according to this concept), as well as which franchises get the best value for their dollars.

Reply

Chase Stuart April 15, 2013 at 10:50 am

You have asked all the right questions. One of the main reasons I blog is to receive the type of feedback that helps me clarify my own thoughts.

Re: the consistency of AV, I touched on that last week: http://www.footballperspective.com/which-positions-are-most-consistent-from-year-to-year/

Re: QBs, I suppose there are several schools of thought:

1) If you don’t pay Manning/Brees/Romo/Flacco/Ryan/Rodgers because you think you have to “overpay” to keep them, you basically fall to “praying that a non-elite QB prospect pans out” or “entering the Kolb/Campbell/Palmer/Flynn/Alex Smith” sweepstakes. And you could argue that all of those players are overpaid, too. So it might just be the case that all QBs are overpaid, and that the elite ones aren’t “overpaid” any more than the non-elite ones. Let’s not forget that Sanchez and Stafford (admittedly on old rookie cap deals) are both making absurd money this year (Stafford is costing over $20M in cap dollars).

2) It’s possible that QBs deserve more AV, but you need to be careful. Turn that dial up, and that means offensive linemen or wide receivers need to be downgraded. It’s tempting to want to keep turning the QB dial higher, but there is a limit.

On the other hand, one could argue that great QBs unlock the value of other positions. A bad QB turns Larry Fitzgerald or a great OL into a waste, while a great one can make Wes Welker a 120-catch player. That bumps up the AV of someone like Welker, so that adds value; in 2007, Matt Light had an AV of 21. Without Brady, he’s not there. It might be better to think of it as AV is linear but QB values are non-linear. In any event, it needs more thought.

3) I do think QBs are probably overpaid somewhat and your #4 point probably has some merit. There’s also the GM’s risk-averse tendency to simply pay the QB and build around him.

I do not know who is underpaid or how such underpayment is distributed. But it’s the right question to ask.

Reply

James April 15, 2013 at 5:27 pm

0) Ha, I knew that was a dumb question. I read that article less than a week ago and knew it was a precursor to this post and still forgot about it.

1) In Stafford’s defense his contract’s average annual value (AAV) is only $12.3M, so it’s the Lions fault for backloading the cap hit to the final three years of the contract. Matt Ryan has essentially the same rookie contract with an AAV at $11.3M, but his largest cap hit was last year’s $13.5M because the Falcons spread the hit out evenly. Sanchez, on the other hand, was given a completely stupid extension and is simply horribly overpaid.

However, that led me to another realization: the QBs I mentioned are only overpaid based on their face-value AAVs, but we know that almost no top players actually receive anything close to their full contract values. So while Romo’s face-value AAV is $17.1M, maybe in the end he’ll be cut before the final two seasons, dropping him down to $15.9M. That’s already half of the difference between his ‘appropriate’ salary cap value and his actual.

2) Perhaps the problem here is the difference between ‘value’ and ‘true talent’. AV determines the total number of AV points to give out based on the points scored by the team per drive, but that doesn’t necessarily measure the “true talent” of the players involved. For instance, say two teams had 20 FGA from the 25 yardline, but one had terrible luck and missed all of them, while the other had excellent luck and made all of them. We know from numerous studies that after controlling for distance and weather field goal attempts are almost entirely random, but AV would look at those two teams and say the latter was much better than the former. This is especially true for defensive field goals, and I remember something like Ravens’ opponents missed only one field goal against them all season. It might be worth it to try and recalculate AV based on EPA instead of Points per Drive while still using the same positional percentages.

3) Anyone know of a good database for player salaries? Of course, I doubt anyone is going to take the time to match names from the two databases. We need a common player ID among NFL players like the baseball saber guys just created.

Reply

JeremyDe April 16, 2013 at 10:02 am

Have not found a good NFL database for salaries. Hoopshype.com has an NBA salary database (http://hoopshype.com/salaries.htm), which is laid out nicely. Haven’t been able to find a comparable NFL database.

How did the baseball guys create their player ID? Do you have a link? I googled and found various discussion about it, but didn’t get end results.

Reply

James April 16, 2013 at 10:12 am

I heard about this through the tangotiger.com blog: http://chadwick-bureau.com/the-register/

Reply

Chase Stuart April 16, 2013 at 10:42 am

Overthecap.com is a great resource for player salaries.

Reply

Richie April 16, 2013 at 2:50 pm

This site seems to have pretty good salary data: http://www.spotrac.com/nfl/ At least for looking up individual salaries. I don’t know if they have any easy way to download the data for all players at once.

Reply

Richie April 16, 2013 at 2:59 pm

Some random thoughts about QB value.

I think teams might “overpay” QB’s because there is some additional marketing value from having franchise-caliber QBs. So even though Matt Stafford might be paid $4M more than his wins-added is worth, he creates additional value in giving Lions’ fans hope beyond his 0.94 wins.

QB’s have a larger sample size of objective data than any other position, so it might be slightly more likely that a QB’s stats relate to his true ability. And somewhat related, poor QB play is so obvious for fans and front office to see. So when you have a QB who is NOT bad, you want to keep him, and willing to pay for it. But poor play at other positions, such as Center, is not even visible to casual fans, and difficult for hard core fans to see and probably fairly difficult for front office/coaches to see. So, if your center sucks, it’s not obvious, and therefore replacing him with the best center won’t be obviously the correct move, and probably won’t make huge changes in team performance.

Reply

JeremyDe April 15, 2013 at 10:30 am

“This bozo thinks Tom Brady is better than Tony Ro…..errr…oh yeah.”

Chase, people will come, Chase. They’ll come to the internet for…porn, usually…and for reasons they can’t even fathom. They’ll click on your URL, not knowing for sure why they’re doing it. They’ll arrive at your blog through team messageboards, as innocent as homers, longing for the past. “Of course, we won’t mind if you have a look around,” you’ll say. “It’s free if you look at our ads.” They’ll pass over their time without even thinking about it; for it is time they have and understanding they lack.

And they’ll click into your archives, and sit in stained pajamas in the middle of the night. They’ll find they have reservations about anything you say about their team, as they post with the grammatical skills of children with traumatic head injuries and defend their heroes. And they’ll read your post, and it’ll be as if they’d smoked bath salts. The crimson fury will be so thick, they’ll have to brush it away from their faces.

People will come, Chase.

The one constant through all the years of the web, Chase, is trolls. The web has rolled by like an army of steamrollers. It’s been erased like a wikipedia post, re-written, and erased again. But trolls have marked the time. This URL, this web, is a part of our past, Chase. It reminds us of all that once was good, and it could be again. Oh, people will come, Chase. People will most definitely come.

Reply

Shattenjager April 15, 2013 at 1:23 pm

That was fantastic.

Reply

Richie April 16, 2013 at 2:38 pm

Each NFL team generates about 201 points of Approximate Value per season

Best I can tell there is no way to extract team AV totals from PFR. Do you have that ability? I’d love to see a list of some of the best and worst all-time team AVs for a season, and also the best and worst from 2012.

Reply

Chase Stuart April 16, 2013 at 2:44 pm

For the most part, AV just corresponds to scoring, so that list will largely mirror the teams with the largest points differential

But as for 2012, I did publish those: http://www.footballperspective.com/the-youngest-and-oldest-nfl-teams-in-2012/

Reply

Richie April 16, 2013 at 2:53 pm

Cool. I read that post, but since it was about team ages, it didn’t register in my memory that you had team AVs there.

Reply

Leave a Comment

You can use these HTML tags and attributes: <strong> <em> <pre> <code> <a href="" title="">

{ 3 trackbacks }