## Win Values for the NFL

Jimmy Graham's contract values him at about 0.9 wins per season. Here's how I came to that estimate.

In 2013 the combined 32 NFL teams chased 256 regular season wins and spent \$3.92 billion on player salary along the way. In simple terms, that would make the value of a win about \$15 million. Unfortunately, things aren't so simple. To estimate the true relationship between salary and winning, we need to focus on wins above replacement.

Think of replacement level as the "intercept" term or constant in a regression. As a simple example think of the relationship between Celsius and Fahrenheit. There is a perfectly linear relationship between the two scales. To convert from deg C to deg F, multiply the Celsius temperature by 9/5. That's the slope or coefficient of the relationship. But because the zero point on the Celsius scale is 32 on the Fahrenheit scale, we need to add 32 when converting. That's the intercept. 32 degrees F is like the replacement level temperature.

No matter how teams spend their available salary, they need to have 53 guys on their roster. At a bare minimum, they need to spend 53 * \$min salary just to open the season. We can consider that amount analogous to the 32-degrees of Fahrenheit. For 2013, the minimum salaries ranged from \$420k for rookies to \$940k for 10-year veterans. To field a purely replacement level squad, a franchise could enlist nothing but rookies. But to add a bit of realism, let's throw in a good number of 1, 2, and 3-year veterans in the mix for a weighted average min salary of \$500k per year. The league-wide total of potential replacement salary comes to:

32 *53 * \$500k = \$848 million

Which, in turn, leaves available a salary-above-replacement of:

\$3.92 B - \$848 M = \$3.068 billion

Now what about wins above replacement? How many games would this hypothetical all-replacement level team win in a season? This question is a bit open to interpretation, but I'll offer my own opinion. In baseball, it's more straight-forward. Analysts can look directly at the stats of guys who make the minimum salary and total up their equivalent wins produced. Unfortunately, there's no (quantitative) way to separate football players' contributions from each other. However, we can contemplate how many wins a pure replacement team would produce.

I say such a team would win ZERO games. Well, statistically it's probably something between 0 and 1, but I think it's a lot closer to 0. The baseball guys might be surprised by this, because in MLB a replacement team has about a .250 winning percentage. But in the NFL, the better team wins far more often than in MLB. Plus, team performance in football is not the sum of individual performance as in baseball. Football team performance is the product of player interactions--It's largely multiplicative rather than additive.

You might be able to recall several journeymen or lowly-drafted rookies who came out of nowhere to play very well, at least for a season. Kurt Warner is a great example. But for every Kurt Warner making the minimum salary in 1999, there are hundreds of other minimum salary guys who we've never heard of, many of whom are actually below replacement level.

Consider a team with a replacement-level QB but is average in all other respects. I can tell you from an analysis of WPA that a team like that would win an average of about 4 games. Now imagine that team with an offensive line made of nothing but replacement level cast-offs. How many wins would that team have? Now imagine a replacement level receiving corps...secondary...defensive line...Now how many wins would they have? You get the picture.

Still, reasonable minds can disagree, so I'll calculate things based on a replacement level of 0 team wins and of 1 team win as bounds for the final result. For a 0-win replacement level, that means all 256 games are available to be won, and for a 1-win replacement level, 256 - 32*1 = 224 wins are available.

The NFL Win Value is therefore:

\$3.068 billion / 256 = \$12.0 million per win

or, alternatively (for 1-win repl lvl)

\$3.068 billion / 224 = \$13.7 million per win

You might take things a step further and consider playoff games. Franchises are paying players for more than just accumulating regular season wins. Playoff wins could be considered as valuable as multiple regular seasons wins. But if we simply weighted them equally to regular season wins, the total wins available becomes 267, and the Win Value drops slightly to \$11.5 million per win. Counting playoff wins double puts the Win Value about \$11 million per win.

The really cool thing about arriving at Win Values is that teams are communicating their estimates of player value in terms of contract values. Consider NO TE Jimmy Graham's new contract for 4 years/\$40 million. NFL contracts are often written with back-loaded based salaries which are almost never fulfilled. But Graham's contract is different. With a \$12 million signing bonus, his deal is worth \$21 million over 2 years and \$30 million over 3 years. That's a contract with even cash flow, written to be fulfilled to the end. In short, the Saints are implying that Graham is worth just under 1 win (above replacement) per season.

That's interesting because now we have a Rosetta Stone of player win values. We can translate any player's contract into an equivalent WAR. For example, the Saints' star offensive lineman Jahri Evans is making about \$8.1 million/yr, which means his contract values him at about 0.7 wins/season.

This analysis is mostly a back-of-the-envelope exercise, but I don't think we're very far from the right answer. We can go further and refine the estimates by discounting future years according to inflation. (In this case, with salary cap inflation rather than the usual monetary kind.) We could also break out draft pick salaries. Because those are largely predetermined by the CBA, and usually provide surplus win values when compared to free agent values, the market is deformed slightly. There is more money available to purchase wins with veteran free agents than there otherwise would be.

This kind of analysis is prescriptive rather than descriptive. In other words, it tells us what teams should be spending per win, and not necessarily how they actually behave. Ultimately, contracts boil down to supply and demand within the constraints of the CBA. So Win Values can help tell us where the market opportunities are, Moneyball-style. In other words, which positions and skills are overvalued, and which are undervalued?

### 9 Responses to “Win Values for the NFL”

first - i love your blog. it's a wonderful mix of nerdery and sports.

second - ie've been considering a lot of similar ideas because of a calcutta-style auction league for nfl teams that we do. we auction off each team before the season. 50% of the pot is awarded to the 256 regular season wins, the other 50% is paid for making and winning playoffs games, increasing progressively toward the super bowl So we ponder the questions "how many games will this team win?" and "will they potentially make the playoffs?" and then create a formula to determine our spending line. The real trick, however, is trying to figure out what the total pot will be and change your projections accordingly (there are a lot of factors at play: auction order of teams, people waiting to spend til late, homerism, etc.) it's pretty fun!

2. Anonymous says:

This proves my theory that the top QBs are severely underpaid. Rodgers, Manning, Brees, and possibly Brady would make 40+ million in a free market. Thanks for the article.

3. Phil Birnbaum says:

So, how does it work? If you figure expected salary wins and compare to real wins (or, even better, Vegas pre-season estimates), how does it do?

Oh, wait ... it looks like they all spent about the same. Never mind.

4. Dave says:

If you ever want to hear someone who does not understand replacement level, listen to Bob Ryan rant about WAR.

5. Daniel Tilkin says:

I think that a replacement-level team would be significantly WORSE than 0 wins, in the sense that you could add significant talent to them and still get a team you'd expect to win 0 games.

If a team with a replacement-level QB but otherwise average would win 4 games, then this average QB would be 4 WAR. But if a replacement team is 0 wins, then adding this QB to the replacement team should give a 4-win team. But I can't imagine a team which is replacement-level in everything except QB getting 4 wins.

Not entirely sure what the answer is. One possibility is to call the replacement team "-N wins", for some N. Then any team with <0 wins would be expected to get 0 wins. Or, some sort of nonlinear equation. (It's obviously non-linear at some point, even an all-star team can't have more than 16 wins in a season)

6. JMM says:

Interesting analysis, but....

Given:

There is a minimum spend on salaries above 53*500 set by the collective bargaining agreement.

Roughly 50% of the outcome of a game is luck. (I read that somewhere on the internet...)

Coaching (game theory) matters. (I also read that somewhere on the internet...)

Then the actual replacement level wins could easily be above 1. A well coached, minimum salary/talent level roster could easily expect to win 3 , 4 or even 5 games at a minimum with better than average luck.

7. Jeremy Billones says:

Daniel,

The Indianapolis Colts probably come pretty close to a test case.

8. Will says:

@Phil Welcome to the wonderful world of the NFL salary cap!

9. Anonymous says:

This analysis is flawed. It assumes that like baseball, the team performance is the sum of the player performances.

The relationships are highly non-linear. A great QB might make his O-line look good by getting rid of the ball fast, but without some receiving talent it might not matter that much (Peyton). An amazing offensive line might make a decent QB look fantastic (Green, Chiefs of yesterear).

A QB upgrade might be worth 8 wins in one situation, and only 3 or 4 in another. An O-line filled with pro bowlers might be worth 4 wins in one situation, and only 1 or 2 in another.

Due to all of this, win values of this sort are going to be pretty much useless in the NFL.