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Aaron Rodgers' contract extension fell right in line with what many expected. But even at an annual average of $22 million, he's well below his worth. Our contributing author, through using an advanced statistical model, explains why.

The Green Bay Packers extended the contract of Aaron Rodgers this offseason by five years for a total value of $110 million, or an average of $22 million per season. Before Rodgers' extension, the five highest-paid quarterbacks, based on average annual earnings, were, in order, Joe Flacco, Drew Brees, Peyton Manning, Tony Romo and Eli Manning at $18.33 million collectively.

As the contracts of the star quarterbacks continue to rise, the question becomes what is an accurate value of their contributions?

League contracts are mostly negotiated based on the market value, or "going rate," for similar players, not directly based on the player's total worth or value-add to the team.

Based on the five highest-paid quarterbacks mentioned, Rodgers' extension would be measured as standard or near standard considering that he is regarded as either the best or close to the best passer in the league. However, this conjecture does not tell the entire story of Rodgers' worth to the Packers, and as a result, it does not properly evaluate whether the Packers are either overpaying or receiving a bargain on Rodgers.

The role of advanced statistics in football (the football equivalent of baseball sabermetrics) has increased greatly over the past decade, particularly for the in-game decision-making process for coaches. More teams are turning toward statistics to make the most efficient decisions possible to win games. However, the process of winning games happens both in the actual playing of the game and in the salary cap management and valuing of individual players.

Of the "new" statistics across the league is the phenomenon of Expected Points, first generated by former NFL quarterback Virgil Carter. Expected Points is a net measurement of the average points that will be scored over the next two possessions in a game. The term measures what the offensive team will score, on average, based on the down, distance and field position, and subtracts what the defensive team will score, on average, on their following offensive possession based on their down, distance and field position to form the net calculation.

To put it into perspective, a team with a first-and-10 on its 10-yard line has a net EP of minus-0.21. That figure rises to 0.90 on their 30, 2.04 on the 50, 3.32 on the opponent's 30 and 4.74 on the opponent's 10. Expected Points are part of the advanced statistics that are used in determining QBR, or Total Quarterback Rating, a measure often used by ESPN.

One of the new ways of measuring player productivity is through the use of EP. Suppose the Packers have a first-and-10 on their 10 and Rodgers completes a 40-yard pass. That play would bring the Packers' EP from minus-0.21 to 2.04, a 2.25-point increase. The 2.25 would be added to Rodgers' EP for the season and each individual player's EP total for the season. Expected Points also accounts for negative plays, such as incomplete passes, sacks and interceptions. Basically EP is a total measure of all of a player's contributions to his team over the course of the season.

Over the past three seasons, Rodgers has averaged an EP total of 195.8 points per a 16-game season, which is tops in the NFL. For players with at least 20 starts over the last three seasons, Rodgers is followed by Tom Brady (195.2), Brees (181.5), Peyton Manning (159.0) and Matt Ryan (147.5).

The next step is determining the point value of a win. This is a necessary step to know exactly how much a team should be willing to spend based on the productivity it is receiving in return. Running a regression analysis for the entire league from 2007 through 2012 using team wins as the dependent variable and point differential as the independent variable, it turns out that a team with a point differential of zero can expect to win approximately 7.99 games per season. Likewise, a team with a point differential of 100 can expect to win 10.69 games per season, a 2.7-win increase. Dividing the change in point differential of 100 by the difference in wins of 2.7 brings us to final result of 37.04 points. This figure represents the point value of a win, meaning for every 37 points added to a team's point differential, it will win one more game than it would without the additional 37 points.

Knowing that every 37.04 points is worth one win in the NFL, Rodgers' average contributions of 195.8 EP added per season adds 5.3 wins to the Packers' record above what a quarterback with zero EP would add to a team's record (such as Kevin Kolb and Mark Sanchez, who have averaged 7.6 and minus-14.9 EP per season over the last three years). The term used for such players as Kolb and Sanchez is "replacement player." A replacement player is a player that can be picked up for the minimum salary. This term will become important in the last step of this process, which is applying the current salary cap to the players' contracts.

The salary cap for the 2013 season is $123 million. Imagine a team full of replacement-level players making near the minimum salary, which varies based on player experience, but assume an average salary of $500,000. Fifty-three players making $500,000 would total $26.5 million for a team full of scraps that would likely go about 1-15 with a point differential of around minus-260.

Essentially, each team starts out spending $26.5 million for one win and has $96.5 million left to spend on players, hoping to win at least 11 games to get into the playoffs. Assuming each team sets its sights on 11 wins per season, each team has $96.5 million to "buy" 10 additional wins, or $9.65 million per win. If Rodgers is adding 5.3 wins to the Packers on an annual basis above what a replacement player would add, his total worth to the Packers should be $51.1 million. In fact, all of the top quarterbacks across the league are getting underpaid greatly based on this exercise.

Why aren't these quarterbacks paid like this if this is their dollar worth in contributions to their teams? There are a few reasons why they are not.

The first reason is the seemingly parallel decision that most quarterbacks make to value long-term financial security over the opportunity to become the guy to break the chain. Of the $110 million included in Rodgers' contract extension, $54 million of it — just less than half — is fully guaranteed. From Rodgers' perspective, why would anyone want to take on a risk of injury that would cost at least $54 million and up to $110 million? The chance of seeing the value of the contract double is simply not worth the risk of losing it all due to injury.

The second reason is the salary floor across the NFL. With a salary cap comes a maximum and minimum number of dollars that teams can spend on its players. In 2013, the salary floor is 89 percent of the maximum salary cap of $123 million, which equates to $109.47 million. What ends up happening is that because every team is required to spend $109.47 million each season, rarely if ever does a team have $30 million to $50 million in cap space to spend on free agents while maintaining their current roster and signing all rookies.

Therefore these elite quarterbacks end up not having much of a choice but to re-sign with their current teams for a fraction of what they are actually worth because they cannot get more money elsewhere. In theory, a team could strategically set up their contracts to have a bunch of expiring deals in the same year, giving it the opportunity to make a never-before-seen offer to a quarterback on the market. The problem is that almost none of the elite guys worth the money hit the market, and even if they did, a slew of bidders could enter, making the entire strategic process an illogical one.

Reason No. 3 is the way their contracts are negotiated by teams and agents. The negotiators on both sides focus on the going rate for similar players and not the total value added to the team, as the latter is more difficult to measure. In essence, part of the reason that players like Rodgers are underpaid is because neither Rodgers, his agent, nor the market fully understands what he is worth. The same applied in Flacco's contract situation. Thus, Rodgers' contract happened to magically fall just ahead of the previous top-paid quarterback in annual earnings. Both Flacco's and Rodgers' contracts were negotiated based on what players had gotten in previous years for having similar seasons.

Reason No. 4 is the nature of the game of football and its ambiguity in measuring player worth and value. Unlike baseball, where sabermetrics were founded thanks to Bill James, football is a much more clustered game. Baseball is statistically friendly due to the isolated and individualized nature of the sport.

In baseball, there is a single pitcher throwing to a single batter with a single fielder making a play on any ball hit into play. In football, there are 22 players involved in every single play, each with a separate responsibility on the play. A 40-yard touchdown pass involves a quarterback completing an accurate pass, a receiver successfully creating enough separation from the coverage and coming down with the catch, and an offensive line providing the quarterback with enough time to complete a pass deep down the field.

With relation to EP, both the quarterback and receiver would receive equal credit for the play. Expected Points is a statistic, meaning it can show what happened and when it happened, but it cannot show why it happened or how it happened. Every 40-yard touchdown is a different play, with different credit going to different players based on what happened on the field. There is no perfect measurement to properly asses the credit for a single play. Yet over the course of time, with increased sample size, statistics like EP prove to be trustworthy.

General managers are likely to use the last argument against quarterbacks, who negotiate to be paid like they are worth based on the exercise. After all, the chart with the quarterback value based on EP makes the assumption that every player is playing in the same system, for the same coaches, with the same additional players. Everything else is being held constant, aside from the quarterback's net production to the team, a weakness of EP.

However, certain instances with quarterback-receiver relationships will show that the passer is a lot more important than the receiver. Larry Fitzgerald is widely regarded as one of the top receivers in the game, perhaps the best at certain points. He played alongside Kurt Warner for five years (2005-2009) in Arizona. In those five years, Fitzgerald averaged 49.6 EP per season. In the four years he did not play with Warner (which were 2004 and 2010-2012), Fitzgerald averaged a dreadful minus-0.85 EP per season. In 2012, Fitzgerald had a catch rate (receptions/targets) of 45.5 percent, which ranked 74th among 76 qualifying receivers.

To put Fitzgerald's dreadfulness into deeper perspective, drop-happy Packers tight end Jermichael Finley had a catch rate of 70.9 percent in 2012 and has a career rate of 69.5 percent, both astronomically higher than Fitzgerald's 2012 rate. Another example lies in the webbed hands of Calvin Johnson. Matthew Stafford was unable to stay healthy for an entire season until 2011, and he hasn't missed a start since. In the last two years, Johnson has 179 EP. In his first four years (2007-2010) while playing with mediocre and poor quarterbacks, Johnson had only 110.8 EP.

It is most likely a safe assumption that even in this day and age of "monster" quarterback contacts, quarterbacks are underpaid across the NFL. The Packers should be thrilled to have locked up Rodgers for less than half of what he is worth to the team based on the findings of this exercise.

It would be fascinating to see a team build a roster with several expiring contracts in the same spring as an elite quarterback hitting the free agent market. It appears that most teams operate under the premise that "we have to have our guy at quarterback to make us successful." These teams are able to "have their guy" for a fraction of what they are worth. What would be fascinating is the negotiating and auctioning that would take place over a quarterback that can make an 8-8 team a 12-4 or 13-3 team, with several teams offering upward of $30 million to $40 million per season. While it is unlikely to happen anytime soon with the current NFL structure, Packers fans can enjoy Rodgers knowing that he is suiting up at a half-off "discount."

Note: All statistics and information related to expected points retrieved from

Mike Bursik is a senior economics major at Butler University in Indianapolis. He is an avid follower of the game of football and has a deep passion for statistics.

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