1. NFL Quarterback Salary and Passer Rating
Brandon R & Devon F

2. Abstract We are conducting a study on NFL quarterbacks.
We are interested if there is a relationship between a quarterback’s salary and their passer rating.
We believe that the higher the quarterback’s salary is, the higher their rating should be.

3. Abstract (cont.)
We collected the salaries and passer ratings of the starting quarterbacks for the 32 NFL teams for the 2009 season.
We conducted a linear regression t-test. It produced a p-value of Therefore, we cannot say that there is a significant relationship between a quarterback’s salary and their passer rating.

4. Similar Studies
The Sports Guru conducted a similar study for NFL quarterbacks in the 2009 season. The plot was very scattered and did not appear to show significant correlation.

5. A website called Advanced NFL Stats conducted a study to see if there was a relationship between an NFL team’s payroll (the sum of every player’s salary on the team) and the number of games that team won. They found significant evidence to say that the higher the payroll, the more wins the team had over a six-year period. This relates to our study in that it also relates salaries to success in the NFL.

6. The Study
We will take the salaries and passer ratings for the 2009 NFL season for the 32 starting NFL quarterbacks.
Salary is x; passer rating is y.

7. Quarterback Team 2009 Passer Rating 2009 Salary ($) Jay Cutler
Chicago Bears
76.8
14,944,090
Peyton Manning
Indianapolis Colts
99.9
14,000,000
Brett Favre
Minnesota Vikings
107.2
12,000,000
Carson Palmer
Cincinnati Bengals
83.6
9,500,000
Donovan McNabb
Philadelphia Eagles
92.9
9,200,000
JaMarcus Russell
Oakland Raiders 50
7,805,880
Eli Manning
N.Y. Giants
93.1
7,500,000
Matt Schaub
Houston Texans
98.6
6,950,000
Marc Bulger
St. Louis Rams
70.7
6,500,000
Philip Rivers
San Diego Chargers
104.4
6,000,000
David Garrard
Jacksonville Jaguars
83.5
5,475,000
Matt Hasselbeck
Seattle Seahawks
75.1
5,250,000
Matt Cassel
Kansas City Chiefs
69.9
5,000,000
Tom Brady
New England Patriots
96.2
Matt Ryan
Atlanta Falcons
80.9

8. Quarterback Team 2009 Passer Rating 2009 Salary ($) Ben Roethlisberger
Pittsburgh Steelers
100.5
4,750,000
Drew Brees
New Orleans Saints
109.6
4,487,500
Kurt Warner
Arizona Cardinals
93.2
4,000,000
Jake Delhomme
Carolina Panthers
59.4
3,200,000
Matthew Stafford
Detroit Lions 61
3,100,000
Jason Campbell
Washington Redskins
86.4
2,857,500
Mark Sanchez
N.Y. Jets 63
2,545,000
Vince Young
Tennessee Titans
82.8
2,160,000
Alex Smith
San Francisco 49ers
81.5
2,000,000
Ryan Fitzpatrick
Buffalo Bills
69.7
1,820,000
Joe Flacco
Baltimore Ravens
88.9
1,535,000
Kyle Orton
Denver Broncos
86.8
995,000
Aaron Rodgers
Green Bay Packers
103.2
680,000
Brady Quinn
Cleveland Browns
67.2
655,000
Tony Romo
Dallas Cowboys
97.6
620,000
Chad Henne
Miami Dolphins
75.2
385,000
Josh Freeman
Tampa Bay Buccaneers
59.9
310,000

10. Descriptive Statistics
µsalary = 4,882,030.31
σsalary = 3,859,759.57
µrating = 83.4
σrating = 15.8

11. Significance Test We will conduct a linear-regression t-test.
Null Hypothesis
Ho: β = 0
Ho: The true slope of the regression line is 0 because there is no linear relationship between a quarterback’s salary and their passer rating.
Alternative Hypothesis
Ha: β ≠ 0
Ha: The true slope of the regression line is not 0 because there is a linear relationship between a quarterback’s salary and their passer rating.

12. Significance Test (cont.)
We will set the significance level at α = .05
t = (b – β1)/(Sβ)
df = n – df = 32 – 2 df = 30
There are 30 degrees of freedom
t = 1.32
The slope of the regression line is x 10-7, so b = x 10-7.
The standard error of the slope (SEB) is x 10-7.

13. Significance Test (cont.)
The p-value is approximately
Since the p-value, , is greater than the significance level (0.05), we do not have significant evidence to reject the null hypothesis and accept the alternative hypothesis, since it is greater than the significance level of .05.
Therefore, we do not have significant evidence to say that there is a relationship between a quarterback’s salary and their passer rating.

14. Discussion Some weaknesses of our study are:
Since we took the starting quarterbacks in our sample, we may have left out other quarterbacks with less playing time that could significantly change the results of our study.
Also, by taking the 2009 salary for the quarterbacks, some of the data may be somewhat misleading, because many of the quarterbacks that switched teams received huge salaries and bonuses.
We cannot extrapolate our results because our study included the entire population of NFL quarterbacks and it is the only football league that uses this specific formula for finding passer rating.
Further work on this topic could include comparing salaries of NFL players at different positions with a relevant statistic that can show their performance, such as a running back’s salary and the number of yards they run for.

15. Conclusion
After conducting this study to determine if there is a relationship between a NFL quarterback’s salary and his passer rating, we have concluded that there is not a significant relationship between the two, since the linear regression t-test we conducted gave us a p-value of at a significance level of .05.