Caponomics Part I

Guest Column by Bruce Stram

Now is the time for NFL fans to ponder those two little words that have ruined the sport with the sweaters and sticks: salary cap. Economists try to learn lessons about the real world by looking at relatively simplistic mathematical models of reality. These simple models have proven valuable in uncovering how markets work, and so I've built a simple model to explain the market for NFL talent: "Caponomics."

In my simple model, two numbers describe players: actual salary and ability level . Actual salary is of course a concrete number, and is known. The true ability of a player (also a number for the sake of this argument) is not known with certainty, and teams may differ in their ability to assess this number accurately. Uncertainty about this number decreases the more time the player spends in the league. Teams may also increase this number through coaching and development of individual players. It also often increases with experience and declines with age. Teams bid for players under NFL rules with one exception: for simplicity, I assume each team spends the salary cap, nothing more and nothing less, each year.

In this model, if player ability were known by everyone, and unchanging, there would evolve a market for ability that would establish a fixed proportionate relationship between ability level and salary level, and each team would have the same level of total ability. This is of course one of the objectives of the salary cap design. Under these circumstances, every team is expected to finish 8-8, and strategy and luck determine differences in won-loss records. (Economists will quibble with me here: I'm also assuming that the gain in terms of winning from higher skill level of a given player increases uniformly regardless of skill level.)

Since I've instead assumed that player ability is not known with certainty, teams are also competing both in their judgment of talent and in their ability to develop talent. Teams that are (relatively) good at this sign up talent at less than the market ratio, and will tend to have a better won-loss record to the extent they sign up talent at a cost below the market level. Pretty simple right?

Here are two perhaps surprising (and I think, realistic) conclusions that can be drawn from this model. The first is that if one team is underpaying for talent, at least one other must be overpaying. More precisely, the sum of net bargains (salary below market value) must equal the sum of busts (salary above market value.). (This is in fact the consequence of what mathematicians call a tautology; the tautology here is the sum of abilities multiplied by the value of abilities must equal the sum of salaries, which is a number fixed by the salary cap.) This observation underscores the extreme competitive nature of the NFL under the salary cap: probably half the teams are paying too much for the talent under contract. And it might also give pause to the most rabid fans -- if 32 such fans sat around a table and concluded that their team had better than average talent, it's mathematically certain at least one of them is wrong, and likely around half of them are wrong.

The second conclusion is a little more fun: a team that pays market value for all its players would be expected to finish 8-8. (Strictly speaking, another assumption or two is needed to make this true, such as: teams are normally distributed around the mean sum of luck and strategy skill.)

This implies that paying a veteran (or any player, for that matter) his true market value is actually a commitment to an 8-8 record. Or, more precisely, the team's talent advantage, if there is to be one, must come from the other players on the roster. So a team should never sign a veteran at market value, right? Well, that would be too strong a conclusion for this simple model, but this makes it clear that such a signing is not automatically a net plus. It also points out that a player-for-player trade represents equal value only if each player represents an equal bargain, not equal player skill. Thus a trade of a high salary cap veteran for a cheap diamond in the rough is very unfavorable to the team getting the veteran.

There are a several countervailing factors related to the signing of veteran free agents which could tend to lead to above- or below-market offers. Two obvious sources of bargain players are the draft and cheap free agent signings. But incumbent teams do have at least one advantage in signing (or not signing) their veterans: they have greater knowledge regarding that player's true ability. Perhaps offsetting this is something called the "winner's curse [1]". The idea is that in an auction (i.e. free agent bidding) for something of uncertain value, the bidder who makes the greatest valuation error on the high side wins the auction, assuming every bidder offers to pay an amount equal to his valuation of the player (Exhibit A: Deion Sanders and the Redskins). This analysis says to go ahead and bid for the veteran, but make sure you've got a fixed idea of his value and bid below that.

This analysis also supports the notion of a "franchise" player (a player who is key to the team as opposed to the NFL franchise tag) as follows: some very uniquely talented players, who are paid a great deal, may nonetheless not ever be fully paid according to their ability level. Other teams may be too cautious to bid them up. More likely, the player's unique abilities permit a team to get more productivity (this is going beyond the simple assumptions in the model: I've heretofore implicitly assumed that a team's total ability is strictly determined by the sum of individual player abilities.) from less able players. Therefore a team seeking to bid away the franchise player faces the prospect of reforming their whole team to realize his full value, even if they are aware of his value. Acquiring such a player could require at minimum unwinding some valuable long-term contracts for players who don't mesh well with the franchise player, which could be risky. So the unique player's ability will not be bid up to its value to his present team. To give some real world examples: I would, as an avid Packer fan, have put Reggie White and Brett Favre in that category. Peyton Manning is also a prime example.

One important corollary of the franchise player concept is that you have to be careful not to double pay for performance. Since by definition the franchise player makes the performances of others look better, those other players are being overpaid if they are paid a league norm according to that performance level. Now, it's going to be pretty hard to tell a free agent who led the league in receptions that he's only going to be paid the league average because that's his ability level and his stats have been inflated by the presence of the franchise quarterback. And a likely result is that he will find another team to bite on the stats and go elsewhere. But if that assessment about his talent level is right, then he should be replaceable with an average receiver developed from the draft or acquired as a cheap free agent from a program that deflated that player's performance level with a bad quarterback. How is Az Hakim these days?

It's All Relative

Speaking more generally, the best use of this model is to help a fan (or GM if he's not already of this mindset) think about player acquisition situations more clearly. The key question is not how good a player is, but what his ability and cost are relative to other players that might be available to replace him. Here's a neat example from fairly recent history: suppose as GM of the 49ers, Joe Montana is your quarterback coming up on free agent status, and Steve Young is on the bench. (Congratulations on great planning and execution by the way.) Your evaluation is that Steve is at least almost as good as Joe, and maybe even better, especially given Joe's age. Joe is going to be marked close to his true value by FA status. Steve is relatively cheap, both because he's under contract and his skills are less well known. Do you trade Steve and keep Joe, or let Joe move on and use Steve, or keep both?

Getting rid of that last option is easy: you can't afford to keep two top quarterbacks even if one is underpriced. I think it's clear the best decision is to let Joe go and play Steve. If you keep Joe, he's being paid market value (approximately) so the team has no net gain in bargain value associated with Joe. By trading Steve, a player becomes available who probably has greater bargain value than Steve sitting on the bench. However, the player acquired in a trade is unlikely to be as big a bargain as Steve as a starter. Because other teams don't know that Steve is as good as he really is, it's unlikely he'll command appropriate value in a trade. Consequently, more net value is left for the team by keeping Steve and letting Joe move on. (Ironically, the more well known a player's value, the more likely it is a team should let him go once he reaches free agency.)

Obviously, coaching prowess might affect these considerations. The ability of a coaching staff to develop players, to understand how a high priced free agent might improve the performance of those around him (and therefore justify a salary that looks out of proportion to his performance), or to recognize how player skills might fit together -- all of these issues affect whether or not a team gets "bang for the buck". (Why do the words "Bill Belichick" echo here?) What I'm doing is giving fans an additional metric to measure the performance of their team's management.

For example, as a Packer fan, I am well aware that Tom Rossley has built an excellent offense (ranked 4th by conventional NFL ratings in 2003 and 3rd this year). As a Caponomic analyst, I also have to note that it's a pretty expensive offense, with a very highly paid quarterback, a well-paid running back, and a well-paid offensive line. They should be good. Green Bay allocates quite a bit more of its salary cap to offense when compared with the average NFL team.

On the other hand, the defense is not nearly so well paid. By traditional performance measures, the Packers got an average (i.e. 16th ranked) performance out of their defense last year. Knowing that, I'd say Ed Donatell did a pretty good job. DVOA measures Green Bay as 8th in offense last season [2], 9th in offense this season [3]. But the defense rated 9th in DVOA last season [4], 29th in DVOA this season [5]. Compare those ratings with the amount of salary cap Green Bay spends on each unit and it suggests that Ed Donatell, though fired, clearly did a better job than Tom Rossley. For what it's worth, my Caponomic analysis suggests that the Donatell firing last year was likely to turn out to be a mistake and that Mike Sherman was unlikely to find anyone better. Unfortunately I was right.

How Valuable Are Draft Picks?

In the salary cap world, the importance of the NFL draft is highly discounted. For reasons I don't fully understand, teams who have acquired exclusive rights (at least for one year, which may be the key) to negotiate with high draft prospects nonetheless pay them "proven veteran" salaries. Caponomics suggests that a player's contribution to net winning (i.e. better than a .500 record) is a consequence of how much a team underpays him, so the advantage of a top draft choice is largely a wash. For example, several years ago the Packers traded for a relatively high draft choice, used it to choose defensive end Jamal Reynolds, and paid him a big bonus and salary. The following year they signed Joe Johnson, at the time one of the top defensive linemen in the league, for pretty much the same money they paid Reynolds. (Ironically both turned out to be busts) If Reynolds had turned out to be as good as Johnson, the pick would have been deemed a big success. But they got Johnson -- without a "valuable" high draft choice -- for the same money they had to pay high draft choice Reynolds. So tell me again why the high draft choice was so valuable?

For another example, look at two wide receivers chosen high in recent drafts. According to ESPN, Larry Fitzgerald was signed by Arizona for $60 million over 6 years, with $20 million guaranteed, after being taken with the third pick in the 2004 draft. At the same time, Philadelphia traded for Terrell Owens and signed him to a contract extension of $42 million over 7 years. It's possible that Owens got more guaranteed money so his contract is in fact richer despite what the numbers say. But still we're talking the same ballpark here. Why was the high draft choice so valuable?

One counter-argument against this reasoning is that Reynolds and Fitzgerald are younger and therefore potentially have their best years ahead of them, with their current teams. This doesn't hold water. Those future years -- after the first contract runs its course -- belong to Reynolds and Fitzgerald, not the team that drafted them. A veteran would probably follow his current contract with retirement, but a younger player like Reynolds or Fitzgerald becomes a free agent at the end of his first contract. Either way, the end of the contract leaves a hole on the roster of the team, and requires the team to pay to fill that hole, whether they are paying a new player or re-signing a now-veteran Reynolds or Fitzgerald. (Actually, both Reynolds and Johnston were cut prior to 2004 training camp, so we'll have to see how Owens and Fitzgerald do in future seasons.)

I think high salaries paid to very high draft picks are an example of the "winner's curse" run rampant. First, a rookie's quality is more uncertain than a veteran's quality -- a key component of a team fooling itself regarding value. Second, the rookie can choose not to sign and re-enter the draft the following year (arguably this creates similar conditions as a competitive auction; I'm not sure I believe that). Third, management just can't live with the idea of "wasting" a valuable high draft choice that, almost by definition, represents a poor team's hope for the future. The last issue is probably the driving factor behind submission to high salary demands.

What about acquiring a franchise player, such as Peyton Manning? Doesn't that suggest high draft choices have great value? Perhaps, but Manning coming into the league was an unknown factor to a degree. The Colts were paying big money and taking a significant risk on whether or not he would pan out. If he had not, the Colts would have been in a very poor position to "recover" from the salary cap bust. And of course Ryan Leaf was in fact a bust in the very same draft. If we had somehow known before the draft that only one of the two quarterbacks would become a success, the total money paid to both quarterbacks would not be worth the value of one highly-drafted successful quarterback.

In any case it's quite clear the draft is not nearly as significant as it was years ago, when players couldn't move from team to team. Then, a team could theoretically afford to have the very best player available at every position, because each player had no alternative but to sign with the team that "owned" his contract. The only thing preventing a team from attaining such a lofty status was the luck and skill necessary to acquire those players. Under such a governing regime, the draft gives weaker teams preferred access to new talent that should enable them to improve as long as they have high drafts and decent management. That no longer seems to be the case.

To maximize gain from the draft, I'd propose an alternative strategy: trading away high picks for a bunch of lower round picks. Play the numbers game. The chance of one of these lower round picks succeeding is much lower, of course. But the high round pick costs plenty if he busts and adds little bargain value if he succeeds. The low round picks that fail are simply cut at little or no salary cap loss, and the rare success is a huge bargain for a number of years. More picks add up to more chances for a success.

NEXT WEEK IN PART TWO [6]: Expanding our economic model to include bonus payments and amortized money, and addressing the salary cap issues faced over the past season by the Indianapolis Colts.

Bruce Stram has a PhD in economics from the University of Maryland, was an executive for a major U.S. corporation for a number of years, and now works in business development. He's been a Packer fan since birth in Green Bay, where his mother rocked his cradle while whispering of the long ago glory days of Vince Lombardi. Bruce can be reached at Bruce_Stram@sbcglobal.net [7]. If you have an idea for a guest column, something that analyzes the NFL from a distinctive point of view, please email us at info@footballoutsiders.com.