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How many wins does a million dollars of quarterback salary buy? How many points does a million bucks buy? How much should you pay a QB assuming a certain level of expected performance?

I looked at salary data from 2000 through 2009 courtesy of USA Today and compared it with stats like Win Probability Added (WPA) and Expected Points Added (EPA). For those not familiar, WPA measures the impact a player has on his team's fortunes in terms of wins. EPA measure his impact in terms of net point differential. I looked at other stats too, but EPA and WPA fit very nicely with salary, at least for QBs.

Specifically, I wanted to discover what teams are willing to pay in exchange for expected levels of performance. To find out, I plotted the salary cap values of QBs against their performance. First, I made an adjustment for year. Between 2000 and 2009, QB salaries have steadily increased. By 2009, they were about double what they were to start the decade. This fits nicely with overall team cap numbers, which approximately doubled between 2000 and 2009.

QB performance has inflated too, but I haven't yet added a correction. QB performance has increased a total of about 10% since 2000, which pales in comparison to salary. In the future I'll add a correction and it might sweeten up the results a bit.

NFL contracts are notoriously complex, with signing bonuses, guarantees for both performance and injury, roster bonuses, and performance incentives. But none of that matters to me. I just want to know how much of a team's payroll under the cap--its most precious resource--is it willing to spend. How much are they spending, and how much are they getting back? For now, I'm looking at all big-money players, whether they're draft picks or free agents.

Here is how the relationship between salary and performance shakes out. The top graph plots EPA vs. cap hit, and the second graph plots WPA vs. cap hit broken out by season. The plot filters out QBs that earned less than approximately $2M in adjusted salary.


 

The best-fit line is pretty shallow and the correlation isn't terribly strong (r = 0.26). Despite a near-zero p-value, it there is a great deal of variability in a QB's year-to-year performance and how it relates to his pay. But that's something we should expect given all the things that can happen over the course of a season and how dependent any QB is on the team around him. This plot suggests teams are getting back about 7.7 EPA and 0.17 WPA per season, for every million dollars they spend on a QB (in 2000 cap dollars).

QB performance is also highly dependent on teammates, opponents, schemes, injuries, etc. Implicit in any analysis like this is the assumption that over enough time and enough cases, those factors tend to even out. After all, the vast majority of QBs are signed to multi-year contracts, when year-to-year factors do tend to even out.

With that in mind, I plotted the data in a different way, this time aggregating career salary and career performance for the top paid QBs over the past decade. For example, in the 2000 through 2009 seasons, Brett Favre cost $61M in cap space, and returned 733 EPA and 13 WPA. I believe this method can better tell us what teams are getting in return for their cap dollars. QBs who cost less than $10M over the entire period were excluded.


 

This method provides a stronger correlation between what teams are paying and what they're getting over time (r=0.76). In this light, QBs produce about 16.8 EPA and 0.39 WPA per season per million (in 2000 dollars). The 2011 cap is almost exactly double what it was in 2000, so we could safely translate those numbers into 8.4 EPA and 0.20 WPA per million.

There are other ways to skin this cat. We can look at per game or per play measures, but they all produce roughly the same equation.

You might be asking why I don't produce a complex regression based on a jumble of stats that include passing yards, sacks, sack yards, interceptions, fumbles. The answer is that I already have. The reason I can use a simple uni-variate (single variable) regression is that the EPA and WPA frameworks already incorporate nearly all the aspects of QB play and weight them in accordance with their effect on net point production (EPA) or win production (WPA).

The replacement level QB conveniently appears to be near zero EPA. The minimum salary has doubled over the past decade, but averages near $300k per year. Players at near that salary level average near zero EPA. Across all of football, zero EPA would be the average expected outcome for all plays. But average QB play is significantly higher than zero for a couple reasons. Passing, in general, provides positive net value compared to running. Also, several other non-plays which do not involve QBs, such as false starts and other penalties, tend to be negative. Zero EPA is therefore solidly below average for a QB. This season, zero EPA/replacement level performance was achieved by the likes of Rex Grossman, Matt Moore, and Mark Sanchez.

What would this mean for Drew Brees, who is scheduled to be a free agent after the season? Over the last six regular seasons, Brees has averaged 150 EPA. Ignoring age or injury risk and using a replacement value of zero EPA combined with the slope from the aggregate plot, the numbers suggest that the market for Brees would be nearly $18M per year in 2011 money. But with Brees' scorching hot 2011 season (250 EPA) fresh in everyone's memory, it wouldn't surprise me to see him sign for more.

There is a lot of work still to be done before any of these numbers are definitive, but this kind of analysis opens a whole new window into player analysis. 

One fun game to play is most-overpaid/most underpaid. They guys above the best fit line are the bargains, and the guys below the line are the busts.