Hypothetical: If you had been given the opportunity to start an NFL expansion team before the 2012 season, how would you allocate your $120.8 million salary cap to your new roster? Would you use $13.25 million (nearly 12%) on a wide receiver, like the Cardinals? Or $19.035 million (over 15%) on a defensive end, like the Colts?

Strategically structuring contracts to maximize the talent on NFL rosters is an art in itself. Each owner, general manager, and coach have their own opinions on how money should be spent. Yet, most teams seemingly agree that the quarterback position should have the most money per player allocated to it.

Yet, how do you evaluate the success of an investment in a quarterback?

You evaluate quarterbacks relative to their peers, and you pay them according to that success relative to their peers.

The quarterback is the most highly valued position in the game, and thus, quarterbacks are paid on average more than any other position in the league. Fortunately, due to the NFL’s salary cap rules, teams may sign players with a signing bonus that may be prorated across the life of the contract. Thus, the amount of money allocated to the salary cap is not always the amount of money a player was actually paid that year. This allows teams to offer players a large sum of money up front without the salary cap taking a “hit” for the signing bonus in its entirety. For example, in July of 2012, Drew Brees signed a 5-year contract worth $100 million with a $37 million signing bonus. Here is what Brees is scheduled to actually receive each year under this contract:

But, since the Saints may prorate the signing bonus across the life of the contract, here’s the actual “hit” the Saints’ salary cap is taking from Brees’ contract:

This mechanism allows teams to maneuver contracts and “even” out the Cap Hit to fit the salary cap. The 2012 NFL salary cap was $120.6 million. Thus, the Saints had $110.2 million to allocate to the rest of the team for this past season. Keep in mind that if the Saints were forced to use the amount they actually paid Brees in 2012, it would remove $40 million from the team’s 2012 salary cap instead of $10 million.

The reason the Cap Hit is more important in this analysis than (1) the amount a player was actually paid or (2) the average salary they will be paid over the course of a contract is that the Cap Hit is specifically representative of the cap room a player is taking up in a given year. Thus, it informs us as to the amount of money that is available to allocate to other players on a specific team.

So, now that we’re all salary cap experts, let’s talk about a valuation process for the most pivotal position on the field: the kicke… quarterback. The Quarterback.

There is no exact method in determining a quarterback’s performance over the course of a year. In 1971 the NFL came up with the “Passer Rating,” which rated quarterbacks on a scale of 0 to 158.3. The formula for this rating was:

Passer Rating = [ (4.16667 x [ ( 20 x Completions ) + Yards + ( 80 x Touchdowns ) - ( 100 x Interceptions ) ] ) / Attempts ] + 2.083

This rating system contained some major flaws. To illustrate these flaws, here’s 3 examples:

1. Quarterback A throws 10 passes. He completes 5 of the passes for a total of 100 yards with 0 touchdowns and 0 interceptions.

A's Passer Rating = [ (4.16667 x [ ( 20 x 5 ) + 100 + ( 80 x 0 ) - ( 100 x 0 ) ] ) / 10 ] + 2.083

A's Passer Rating = 85.4 (Rounded to the nearest tenth)

2. Quarterback B throws 10 passes. He completes all 10 of the passes for a total of 50 yards with 0 touchdowns and 0 interceptions.

B's Passer Rating = [ (4.16667 x [ ( 20 x 10 ) + 50 + ( 80 x 0 ) - ( 100 x 0 ) ] ) / 10 ] + 2.083

B's Passer Rating = 87.5 (Rounded to the nearest tenth)

3. Quarterback C throws 10 passes. He completes 8 of the passes for 90 yards with 1 touchdown scored on a 62-yard screen play to the running back and 2 interceptions, which both are returned for touchdowns.

C's Passer Rating = [ (4.16667 x [ ( 20 x 8 ) + 90 + ( 80 x 1 ) - ( 100 x 2 ) ] ) / 10 ] + 2.083

C's Passer Rating = 97.9 (Rounded to the nearest tenth)

At a glance…

As is evident in the examples, this passer rating gives too much weight to completion percentage. It also accounts for specific occurrences that are not attributable to the quarterback, such as an on-target pass that goes through the hands of the receiver and is intercepted or an 80-yard touchdown that was scored on a shovel pass to the running back.

So in an effort to create a more reliable quarterback rating system, ESPN teamed up with AdvancedNFLStats.com and FootballOutsiders.com to create the Total Quarterback Rating (“QBR”). QBR takes into account the “contexts and details of throws” and is scored on a scale of 0 to 100, where the average NFL quarterback would be a 50. While QBR is not perfect, it is a far better representation of a quarterback’s performance than the classic passer rating, so we’ll use it to measure quarterback performance.

Here are the 36 quarterbacks that played enough during the 2012 NFL season to qualify for ESPN’s QBR, along with their respective cap hits:

Logically, the best quarterback in the league is worth the most money, so a team should be willing to allocate the highest percentage of their salary cap to the best quarterback. Along the same logic, in a perfect world the second best quarterback should have received the second highest salary (or respective cap hit). But it’s not a perfect world, so in order to illustrate this relationship, I ranked 2012’s highest QBRs and Cap Hits from 1 to 36:

Using the table above, I created a scatter plot, with the X-axis representing QBR and the Y-axis representing the Cap Hit. Once all of the points were on the chart, I had excel create a “trend line” to represent the average relationship between Salary Cap Hit and QBR. Interestingly, an exponential relationship exists between Cap Hit and QBR. This is due to teams’ willingness to pay exponentially more money for the more elite quarterbacks. The trend line can be seen in the scatter-plot chart below:

As you can see, the trend line’s formula in the chart is:

y = 3,214.6(x)2 - 51,907x - 419,885

To demonstrate the applicability of this formula, here’s an example:

In 2012 Jake Locker had a QBR of 48.1. Since QBR is the X-axis of the chart, we’ll plug Locker’s QBR into the formula to determine how large of a salary cap hit his performance warranted:

Salary Cap Hit = (3,214 x (48.1)2) - (51,907 x 48.1) - 419,885

…I hate to ruin the fun as you scramble to find your old TI-83 calculator, but here’s the answer:

Salary Cap Hit = $5,360,489

In other words, relative to other quarterbacks in the NFL, Jake Locker’s performance at quarterback was worth a team taking up to a $5,360,489 cap hit for him, thus I deemed this amount a player’s “Cap Hit Value” for a given year. Here’s the “Cap Hit Value” for all 36 quarterbacks in 2012:

Obviously, some of these quarterbacks were paid much less than their Cap Hit Value, while some were paid much more. I’m going to call the difference between a player’s Cap Hit Value and their actual Cap Hit “Net Value.” While the Cap Hit Value represents the average amount teams paid for a particular QBR, the Net Value represents whether teams actually gained money or lost money on their investment.

For instance, the Seattle Seahawks took a $544,850 Cap Hit for Russell Wilson, yet he played up to the market value of a quarterback worth $12,379,195. Thus, his Net Value for the Seattle Seahawks was $11,834,345. While on average other teams had to pay an additional $11.8 million in 2012 to receive the caliber of play Russell Wilson provided the Seahawks with, Seattle was able to use that $11.8 million elsewhere. In essence, Net Value is simply how overvalued or undervalued a quarterback was in a particular year.

Here’s all 36 quarterbacks in order by their Net Value in 2012:

*Made playoffs as a starting QB (Alex Smith made playoffs, but not as a starting QB)

The most fascinating part of this chart is that every one of the top 8 quarterbacks, with respect to their net value, made the playoffs. This illustrates the principle that teams who effectively evaluate talent and draft or sign quarterbacks (or really any position) for lower than their eventual performance on the field have more money to spend in other areas, and thus, more overall talent on their roster. While this conclusion is a simple generalization, common sense seems to deem it meritorious.

To close quite simply, Colin Kaepernick, Russell Wilson, Robert Griffin III, Tom Brady, and Andrew Luck gave their teams the most “bang for their buck” in 2012, while Matt Cassel, Mark Sanchez, Michael Vick, Sam Bradford, and Philip Rivers played far below their pay grade.

But Philip Rivers, if you’re reading this, don’t despair… in 2010 Jamarcus Russell did not play a down for the Oakland Raiders and was paid $19.92 million for a Net Value of $(19,919,100), all of which was applied to the cap (thankfully for the Raiders, it was an uncapped year). Let’s just hope Jamarcus Russell makes this return he’s talking about, so that I can do this next year, and he can shatter any semblance of a record low that you may currently hold, Philip.

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By: Tyler Raborn