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?