How Much Does A Win Cost?

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.

Texans Shut Down Dalton By Shutting Down Green

The Cincinnati Bengals were supposed to be one of football's worst teams in 2011, but nobody told Andy Dalton and A.J. Green. Thanks to a surprisingly competent Bengals passing game -- Cincinnati's 6.0 adjusted yards per attempt ranked 16th in the league -- the Bengals' offense was just good enough to power them to a 9-7 record and a playoff berth.

Green, in particular, was the big play threat and clearly the best player on the offensive side of the ball in Cincinnati. The fourth overall draft pick finished 6th in total WR WPA and 9th in total WR EPA. He was Cincinnati's passing offense, earning substantially more EPA (55.4) and WPA (1.98) than Dalton (27.5 and -0.23 respectively). That is, when Dalton wasn't throwing to Green he was a mediocre quarterback at best. When the ball headed towards number 18, the Bengals offense clicked like a finely tuned machine.

Saturday against Houston, the Bengals offense was completely stifled. For the first time, a team was able to completely neutralize A.J. Green, and the Bengals were left completely stunned.

Deadspin/Slate Roundtable: Fourth Downs Galore

Here's a contribution I had to the weekend's recent discussion at Slate and Deadspin. I looked at some how a few critical 4th downs made the difference in two of the wildcard games and consider some of the factors that are causing the game to evolve.

There are many doubters when it comes to four-down football. If you’re in that camp, indulge me in a quick thought experiment. Let’s imagine a football world where the punt and field goal had never been invented. (Sorry, Ray Guy and Jan Stenerud.) In this universe, there would be no second-guessing: Teams would go for it on every fourth down.

Then one day, some smart guy invents the punt and approaches a head coach with his new idea. “Hey coach,” he’d say, “instead of trying for a first down every time, let’s voluntarily give the ball to the other team.” Our coach would be incredulous at this suggestion. “You want me to give up 25 percent of our precious downs for just 35 yards of field position? Do you have any idea how difficult it would be for us to score?” And the coach would be right.

Catch it here at Deadspin or here at Slate.

Punting "Mainly Blows"

...that is, according to a recent in-depth analysis.

"I've found that, throughout the course of a football game, having the ball is really important and good," said Patriots head coach Bill Belichick, widely regarded as the league's greatest football mind. "Given that the idea behind punting is to willingly and knowingly give the ball away, one would not expect it to be a very popular thing to do. Understood?"

The funny thing is, this Onion article perfectly captures the state of punting in the NFL. Offenses have become good enough to tip the balance further and further toward going for it. Having the ball is good. Not having it is bad. It even discusses the fact that the kickoff following a score has to be factored into the equation.

"You have to give the ball away after you score by kicking it off, and no one likes that, but that's different from punting," Steelers head coach Mike Tomlin said. "For one thing, you're in a good mood because you just scored. And you can't score more than one touchdown each time you have the ball—that's the rule. So you have to kick the ball away, but it's sort of okay, since you can't really do anything else."

Helmet-knock to Eddy Elfenbein for the link.

More Falcons' 4th-Down Decisions

Earlier this year, the Falcons were criticized for going for it on 4th down and failing to convert against the Saints in OT.  Mike Smith was crucified for his "incorrect" decision.  But, as Brian wrote, his decision was correct.  A decision cannot be evaluated based on the outcome, but rather the theoretical expectation of the choice itself.  This week against the Giants, Mike Smith was faced with several 4th-down decision throughout the course of the game.  The first came at the end of a 14-play, 66-yard drive at the start of the 2nd quarter.  Using our Markov model, we can look at how the drive developed:

WP: Redskins' Off-Season Needs

This week's post at the Washington Post's Redskins Insider site takes a look at the Redskins needs based on a position-by-position analysis of player EPA.

2011 Regular Season Play-by-Play Data

Now uploaded. Find it here. Happy cruching.

Wildcard Game Probabilities

Weekly game probabilities are available now at the nytimes.com Fifth Down. This week I share some statistical tidbits on all four of the match-ups.