Determining The Value Of NFL Quarterbacks - Purdue · PDF file1 Determining The Value Of NFL Quarterbacks Economics Honors Thesis Steve Alexander 2008

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Determining

The Value Of

NFL Quarterbacks Economics Honors Thesis

Steve Alexander

2008

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Table of Contents

Variable Reference Guide

Introduction

Related Research

Results

Conclusion

Summary Statistics

Appendix

Works Cited

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Variable Reference Guide

(Every statistic is specific to a particular season/year)

Ht Height in inches

Wt Weight in pounds

Age Age in years

Exp Years of NFL experience (Equals 1 if player is a rookie)

G Games attended (Quarterback did not necessarily play)

GS Games where Quarterback was designated as a starting player

Pcomp Number of pass completions

Patt Number of passes attempted

PcompPct Pcomp/Patt

Pyds Number of passing yards

PTD Number of passing touchdowns scored

Interceptions Number of interceptions thrown

Sck Number of times sacked

SckY Number of yards lost as a result of being sacked

Rate Passer Rating (this is explained elsewhere in the paper)

Ratt Number of rushing attempts

Ryds Number of rushing yards

RTD Number of rushing touchdowns scored

Fum Number of fumbles

FumL Number of fumbles lost

BaseSalary Annual base salary in dollars (there is a minimum salary level explained later)

SignBonus Signing bonus in dollars as a lump sum in the year it was negotiated

OtherBonus Roster, report, workout, and other bonuses in dollars

TotalSalary BaseSalary + SignBonus + OtherBonus

CapValue BaseSalary + OtherBonus + Pro‐Rated Signing Bonus

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Introduction

This study is comprised of several closely related goals. First and foremost, an attempt

will be made to predict the future earnings of National Football League quarterbacks based on

their performance in previous seasons, as judged by multiple key statistics. With these

statistics, efforts will also be made to predict a team’s future record and to see exactly how vital

these players are to their teams. The reader is assumed to have a basic understanding of the

game of football.

The quarterback position is unique. Historically, it has been regarded as the most

critical role. The pay many of these players receive reflects that fact well. The quarterback is

the first player to receive the football when it is put into play and the decisions he makes can

alter the team’s odds of success or failure drastically. He must be hyper‐aware of every one of

the other 21 players on the field—genetically gifted super‐athletes with lightning‐quick speed.

He can throw the ball, run with the ball, or give the ball to another player. From memory, he

can call and execute the complex plays the coach has chosen, or he can modify these calls after

evaluating the opposing defense with audibles. Quarterbacks represent the majority of Most

Valuable Player Award recipients and are remembered for years after the rest of their

teammates have been forgotten.

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One would therefore imagine that a quarterback’s pay would be highly sensitive to his

on‐field performance, and perhaps the performance of his team would be affected likewise.

The players whose perceived values are most directly related to measurable statistics are

probably quarterbacks. For instance, this study would be difficult or impossible if it concerned

offensive linemen because their performance is not easily quantifiable. Other positions can be

similarly confounding, such as defensive backs. A great defensive back may not have

outstanding statistics, such as a high amount of interceptions, because the ball will not often be

thrown in their direction. For these reasons, I have chosen to study the quarterback position

over all others.

I compiled a list of every quarterback on the NFL’s payroll from the 2000 season to the

end of the most recent (2007) season. I then gathered their individual statistics for each season

from the official NFL records database. Next, using U.S.A Today’s database, I was able to find

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figures for each player’s annual compensation and bonuses. Finally, using the STATA program, I

attempted to create meaningful regressions.

Primarily, four methods were used to regress these time‐series panel data. To control

for such a high level of endogeneity and fluctuation of the variance of the error term, the fixed

effects method was employed. Three dummy‐variable approaches were also utilized. The first

used a dummy variable representing each year (season). The second involved 96 dummy

variables, each assigned to a specific quarterback. The third used 32 dummy variables, each

assigned to a specific team.

Before the results of this study are shown, it is necessary for a quick primer on NFL pay

schemes. Each player receives an annual salary, and there are minimum salary levels that vary

with the number of years a player has been in the NFL. This minimum level is determined by

the Collective Bargaining Agreement (CBA), which is negotiated by the NFL Players Association,

a union of which every NFL player is a member.

Years of Experience Minimum Salary

0 $285,000

1 $360,000

2 $435,000

3 $510,000

4‐6 $595,000

7‐9 $720,000

10+ $820,000

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Players may also receive signing bonuses when they commit to a contract and other

performance‐based bonuses. This makes a player’s total salary numbers fluctuate wildly from

year to year, as signing bonuses can be very large and are counted as a lump‐sum payment in

the year they were signed for. For this reason I have chosen to use the CapValue variable as my

main salary statistic rather than the TotalSalary variable. The CapValue variable pro‐rates the

amount of any signing bonuses over the years for which the player has contractually agreed to

play. An NFL team may not pay more than a certain level of compensation to its players as a

whole. This level is called the salary cap, and the CapValue statistic is the amount of

compensation used for the purposes of calculating whether a team is at or under the cap.

Because choosing to pay a quarterback more means choosing to pay other players less, the

CapValue statistic gives an accurate measurement of the degree to which a team values their

quarterback.

Quarterbacks who have been drafted but have not yet played in their first season are

allowed to negotiate their compensation only with the team that drafted them. For this

reason, pay levels for rookies tends to be extremely low relative to more experienced

quarterbacks who have negotiated another contract.

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Related Research

During the course of this study, some academic research that is directly relevant was

found. Far more research was found that was tangentially relevant, but still interesting.

When dealing with rookies, Hendricks, DeBrock, and Koenker found that the sooner

draftees were allowed to negotiate with other teams, the lower the demand for athletes with

more uncertain futures. These athletes might include players from lesser‐known schools or

players with a history of injuries. These researchers also found that the visibility of the football

program that a player came from was significant and positively correlated with their success in

the draft. However, players from less visible programs seemed to have better careers over the

long term, as their salaries were less likely to fall over time. These players received less pay

initially, though. In my research I expected to find large returns to experience.

Clark and Hall found that teams with a greater number of veteran players were of a

better quality and had more success. The number of veterans was positively correlated with

the level of competition between teammates. This is because the more veterans a team has,

the less the likelihood of an open position. The increased competition for the spot drives the

starter and the backups to perform better than they otherwise would. Clark and Hall also

found that the preseason (which is not discussed in this study due to its nature) is a good thing,

as it increases competition between teammates and therefore improves team quality. To

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perform their research, these individuals used a team‐dummy method identical to the method

performed in this study.

To discuss the research done by Leeds and Kowaleski, it is necessary to again refer to

the CBA. The current CBA went through a major overhaul in 1993. These researchers found

that dramatic shifts in quarterback pay resulted. After this overhaul, the top quartile of

quarterbacks (ranked according to pay) was rewarded more for starting games than for their

performance in those games. In other words, performance was de‐emphasized relative to

merely starting in games. For the lowest quartile of quarterbacks, however, the basis of pay

stayed basically the same as before the new CBA. For these quarterbacks, there was a far

greater emphasis on performance than for the higher‐ranked players. These low‐ranked

quarterbacks could dramatically improve their pay by performing better. In my research I

expected to find a large return to starting games, as this study might suggest.

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Results

Determining Cap Value as a Result of Passing Touchdowns Scored

The primary way a quarterback scores points is by passing the football. Thus, the PTD

statistic should prove especially relevant in determining the value of the quarterback. My first

approach was via the fixed effects method.

1.

CapValue Coefficient Std. Error P>|t|

L1.PTD 108,527.1 15,302.3 0.000

R2=0.4692

#Obs=367

#Groups=84

I started simply by regressing the number of passing touchdowns scored in the previous

season (L.PTD) on the cap value of the quarterback in the next season. With a high level of

significance, it can be said that scoring one extra passing touchdown is predicted to increase a

quarterback’s compensation in the next season by approximately $108,527. So a very large

premium is placed on scoring an additional passing touchdown. The current record for the

most passing touchdowns scored in a single regular season is 50, set in the 2007 season by New

England Patriots quarterback Tom Brady.

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2.

CapValue Coefficient Std. Error P>|t|

L1.PTD 64,066.31 17,442.06 0.000

L2.PTD 100,066.7 16,769.26 0.000

R2=0.5361

#Obs=281

#Groups=71

Here, I also control for the number of passing touchdowns scored two seasons ago

(L2.PTD). As expected, the R‐squared value increases favorably. This regression indicates that

an extra touchdown scored two seasons ago is predicted to add $100,066 to a quarterback’s

pay today, while an extra touchdown scored one season ago is predicted to add only $64,066 to

a quarterback’s pay today.

Adding the passing touchdowns scored in even earlier seasons to the regression

resulted in terribly insignificant p‐values or a lower adjusted coefficient of determination, so for

the sake of brevity these regressions will not be shown.

3.

CapValue Coefficient Std. Error P>|z|

L1.PTD 181,995.5 12205.54 0.000

R2=0.4943

#Obs=367

#Groups=84

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+6 Time Dummies

In this regression, I abandoned the fixed‐effects approach for the time‐dummy

approach. Again I started simply by using the passing touchdowns scored in the previous year

and the quarterback’s cap value in the current year. An additional passing touchdown in the

previous season was predicted to increase the quarterback’s compensation in the current

season by $181,995. As expected, this is a very large figure. This regression shows a slightly

higher r‐squared than the fixed effects method, but this is due to the inclusion of six more

variables. The adjusted r‐squared actually decreased. So the time‐dummy approach is a less

than optimal method in this case.

This is fairly conclusive evidence that passing touchdowns play a large role in

determining quarterback salary. Although this statement may seem intuitive or obvious, at

least there is now evidence to back up that intuition.

Determining Cap Value as a Result of Quarterback Passer Rating

As stated before, passing ability is likely the greatest factor in judging a quarterback’s

performance. To this end, statisticians have devised a system for ranking quarterbacks called

the Passer Rating (Rate). Although the methods of calculating this number shall not be

divulged here, suffice it to say that it includes the percentage of passes completed, the average

yards gained per pass completion, the average number of touchdowns scored per pass attempt,

and the average number of interceptions thrown per pass attempt. It is a very useful statistic,

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yet it does not include sacks, rushing ability, or intangibles. Still, it should be a better measure

of overall performance than passing touchdowns.

The fixed effects method gave very poor results with low R‐squared values and high p‐

values. The fixed effects regressions will not be included in this section for this reason. The

time‐dummy method gave a poor r‐squared value, and the player‐dummy method gave a poor

adjusted r‐squared. The best method proved to be the team‐dummy approach.

4.

CapValue Coefficient Std. Error P>|z|

L1.Rate 20,254.68 3,819.688 0.000

R2=0.2873

#Obs=367

#Groups=84

+31 Team Dummies

Here, each additional point of passer rating a quarterback earns is predicted to increase

his value by $20,254.68 in the next season. A player who goes from an abysmal rating of 50 to

an elite rating of 100 will receive an estimated $1,012,734 more in his next season.

Determining Cap Value as a Result of Age and Experience

One would predict that age and experience should increase a quarterback’s

performance to a point, after which performance suffers. Rare players, like Brett Favre, who

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played well into his late thirties, seem to defy this prediction. Nonetheless, since diminishing

returns to age and experience are expected, the variables AgeSQ (age‐squared) and ExpSQ

(experience‐squared) were added to the models in the following regressions.

Using fixed effects, regressing age and age‐squared on cap value prove inconclusive. So

experience and experience‐squared were substituted:

5.

Log(CapValue) Coefficient Std. Error P>|t|

L1.Exp 0.440962 .0392241 0.000

L1.ExpSQ ‐0.0239457 .0027393 0.000

R2=0.1752

#Obs=365

#Groups=84

This regression has a rather low R‐squared, but that is somewhat expected because

experience is certainly not the biggest factor in determining quarterback salary. There are

many seasoned veterans who are backups and do not receive compensation like the starting

players receive. LCapValue is the log of CapValue. So we do observe a diminishing returns

effect when dealing with experience.

The massive return to experience is somewhat expected, based on the findings of

previous researchers. It shows that rookies and inexperienced players (who cannot negotiate

with teams other than the team that drafted them) do indeed make far less than more

seasoned quarterbacks.

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Using time‐dummies, experience was again superior to age. However, the fixed effects

method provided a more meaningful regression.

Using the team‐dummy and player‐dummy methods, age was mostly a worthless

variable and the effect of experience was virtually identical to the time‐dummy and fixed

effects methods. Every regression showed a prominent diminishing returns to experience

effect.

Determining Cap Value as a Result of Games and Games Started

Being a starter should be fairly relevant to a quarterback’s salary. Backup quarterbacks

are little‐known and receive, on average, far less pay than their superiors. As the number of

games started increases (to a maximum of 16), I predict that expected compensation will rise.

Being present for a game, regardless of starter status, should also have a positive correlation,

but will likely not be as strong.

6.


L1.GS .0602965 .0081548 0.000

R2=0.5035

#Obs=365

#Groups=84

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In this regression, the log of cap value was regressed on the number of games started in

the previous season. Starting one additional game is predicted to increase the next year’s

salary by about 6%.

Using the time‐dummy approach, a 9% increase in cap value was predicted as a result of

starting an additional game in the previous season, but adjusted r‐squared was low.

Though the regressions will not be shown here, a 9% effect was also shown using the

team‐dummy approach, but a 6% effect was shown using the player‐dummy approach.

Perhaps the true figure is in between 6% and 9%.

To account for games attended (G), I created a new variable: PctOfGamesStarted,

which is simply GS divided by G:

7.


L1.PctOfGamesStarted 0.7105315 .137685 0.000

R2=0.3698

#Obs=317

#Groups=81

Here we see that a player who starts all 16 regular season games is predicted to have a

71% higher value than a player who is not a starter. This is a large and significant difference.

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Determining Cap Value as a Result of Height and Weight

Quarterback heights were very closely clustered with a mean of 74.9 inches. Weights

had more variance and a mean of 224 pounds. Here I used normal regressions. R‐squared

values for both height and weight were extremely miniscule. It appears as though height and

weight have very little to do with being a good quarterback. Fifty percent of quarterbacks were

between 74 and 75 inches tall, with no one shorter than 71 inches. It seems as though there is

a certain minimum height required to see over the heads of the massive linemen. The low R‐

squared associated with weight is also not surprising, since traditionally the quarterback

position has not been a brutally physical one. Quarterbacks do not usually take large amounts

of physical punishment relative to their teammates so high weight is not that important.

Conversely, light weight (normally associated with speed) is not extremely valuable either, since

speed is not as vital for a quarterback as it is for a defensive back or running back. Here are the

results of the regressions:

8.


Ht .0617184 .0375106 0.101

R2=0.0058

#Obs=464

9.


Wt .0118269 .004162 0.005

R2=0.0172

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#Obs=464

Determining Cap Value as a Result of Interceptions

Until this point, the independent variables used in the regressions have added value to a

quarterback. Now the independent variable, Interceptions, is expected to decrease value.

Throwing an interception is certainly a very bad thing as it gives possession of the football back

to the opposing team. Surprisingly, however, using the Interceptions variable almost always

showed a positive correlation to cap value. This was likely due to the fact that the highest paid

quarterbacks threw many passes, a few of which were of course intercepted, while the lowest

paid quarterbacks did not even receive any playing time and therefore never had the chance to

throw an interception. I created a variable, InterceptionAvg, that I believed would suit the

needs of this study better. This statistic is simply Interceptions divided by Patt. It shows how

often, on average, a quarterback throws an interception when he throws a pass. This way, the

quarterbacks who do not play and therefore do not throw passes are eliminated from the

equation. The coefficient on this variable was negative in all regressions, but with unacceptable

p‐values up to 0.6. I then restricted the regressions to include only quarterbacks who had

started at least one game, and finally to include quarterbacks who had started at least half of

the games during the regular season. The coefficient on Interceptions continued to be positive

with high significance and the coefficient on InterceptionAvg continued to be negative with

unacceptable significance.

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10.

Log(CapValue) Coefficient Std. Error P>|z|

L1.Interceptions .0189017 .0101443 0.062

L1.PTD .0434145 .0071356 0.000

R2=0.4129

#Obs=173

#Groups=55

+6 Time Dummies

Here is an example of one of the better regressions involving interceptions. It employs

the time‐dummy method, includes only quarterbacks who started 8 games or more (half of the

season), and also controls for passing touchdowns. I controlled for passing touchdowns

because while the coefficient on Interceptions was consistently positive, it was less than half of

the value associated with the “good” statistic, PTD. Perhaps there is a positive return for

making risky passes which are sometimes intercepted, and this accounts for the way that the

seemingly “bad” statistic adds value.

Finally, using team‐dummy variables and controlling for the number of games started in

the previous year, I was able to generate a regression that looks more like one might expect:

11.

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L1.Interceptions ‐.0303574 .0126393 0.016

L1.GS .1176726 .0138604 0.000

R2=0.5454

#Obs=365

#Groups=84

+31 Team Dummies

Here it is shown that throwing an additional interception in the previous season is

predicted to decrease cap value in the current season by about 3%.

Multiple Regression Models with Cap Value as the Dependent Variable

12.


L1.Exp .3627602 .0426122 0.000

L1.ExpSQ ‐.0188704 .0028811 0.000

L1.PcompPct .3464153 .3267147 0.289

L1.Pyds .0002402 .000106 0.023

L1.PTD .0002593 .0112537 0.982

L1.Interceptions ‐.0088807 .010640 0.404

L1.Sck ‐.0017347 .0048105 0.718

R2=0.8063

#Obs=303

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#Groups=78

+96 Player Dummies

In these multiple regression analyses, I began to put together all of the more simple

regressions I had done in order to find the absolute best model to predict quarterback

compensation. The goal was to see how different statistics interacted with each other and to

control for all relevant variables in hope of finding elasticities. The player‐dummy approach

yielded the best results for the model specified above. I included all variables pertaining to the

passing game from the previous year and also experience. The diminishing returns to

experience were discovered once again, with high significance. The way in which passing yards

contribute to compensation was also determined with accuracy far better than the desired 10%

level. Every additional 100 yards a quarterback passed for during the previous season was

estimated to increase cap value by about 2.6% in the current season. The p‐values associated

with the other variables indicate that they are not statistically significant, but the coefficients

associated with the other variables are what one might expect. For example, touchdowns add

to compensation while throwing an interception and being sacked decrease compensation.

13.


L1.Exp .360661 .0424637 0.000

L1.ExpSQ ‐.0189453 .0028701 0.000

L1.PcompPct .3756269 .3259106 0.250

L1.Pyds .0000914 .0001388 0.511

L1.PTD ‐.0002735 .0112141 0.981

L1.Interceptions ‐.0132091 .0109181 0.228

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L1.Sck ‐.0048875 .0051582 0.344

L1.GS .0462967 .0280463 0.100

R2=0.3791

#Obs=303

#Groups=78

Here we have a fixed effects regression using the same variables as before but also

controlling for the number of games started in the previous year. This statistic is almost

significant at the 10% level, and so this regression has been included. It appears as if the

estimated return to starting one additional game in the previous season is a 4.6% increase in

cap value.

Though the regressions will not be shown here, I began replacing the statistics from the

previous year (the variables with the L.‐prefix) with statistics from two years ago, three years

ago and so forth. I found that the R‐squared values as I went further back in time decreased

drastically and the variable coefficients lost significance. This seems to indicate that when this

many variables are accounted for, more recent performance outweighs past performance when

determining compensation.

The time‐dummy approach worked best when the rushing statistics were introduced

into the model. Number of rushing touchdowns and number of rushing yards were added to

the previous regression. Traditionally, rushing ability has not been extremely vital for the

quarterback position. Some uncommon players, such as the Atlanta Falcons’ Michael Vick, can

run with the football or pass it with equal skill. Players like this are a double threat, and this

versatility has proven value—Michael Vick had the highest cap value of any player at any

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position in the 2005 season. The results are somewhat confounded by the fact that possessing

these dual abilities is extremely rare and by the fact that Michael Vick had a rather short stint in

the NFL due to legal issues. Though the p‐values on the rushing statistics are high, one can see

that, on average, scoring rushing touchdowns decreases cap value. This may be due to the fact

that rushing touchdowns are usually better attempted by rushing specialists—not every

quarterback is a Michael Vick. A quarterback who rushes and is then tackled has a higher risk of

injury, which will hurt future performance and possibly cause him to miss games.

14.


L1.Exp .2837511 .0366806 0.000

L1.ExpSQ ‐.0158642 .0024127 0.000

L1.Rate .0021731 .001125 0.053

L1.Sck ‐.0041898 .0051741 0.418

L1.GS .0751387 .012307 0.000

L1.RTD ‐.0228148 .0350197 0.515

L1.Ryds .0003807 .0005437 0.484

L1.RegSeasonWins .0245214 .0119926 0.041

R2=0.5726

#Obs=365

#Groups=84

+6 Time Dummies

Here I have also replaced the variables pertaining to the passing game with the

quarterback passer rating, which was briefly described earlier. It includes elements of all the

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variables that were removed. In the regression above, the number of wins the quarterback’s

team had in the previous season are also accounted for. This is attempting to control for the

team’s performance as a whole as well as the individual quarterbacks’ performances. The

coefficient on RegSeasonWins is both positive and significant at the 5% level. If a quarterback’s

team goes from winning half of the regular season games (8) to winning all of the regular

season games (16), his cap value is estimated to increase by about 19.6%. This was the best

model that I was able to specify for the regular season, after much deliberation.

15.


L1.Exp .2233226 .0435665 0.000

L1.ExpSQ ‐.0126701 .0027003 0.000

L1.Rate .0026633 .0013548 0.049

L1.Sck ‐.0085052 .0057719 0.141

L1.GS .0960592 .0132456 0.000

L1.RTD ‐.0232805 .0392978 0.554

L1.Ryds .000808 .0005548 0.145

L1.RegSeasonWins .0291631 .0137586 0.034

L2.WonSuperBowl .1422508 .2025955 0.483

R2=0.6035

#Obs=279

#Groups=71

+5 Time Dummies

Here, the WonSuperbowl variable was added to control for post‐season performance.

The best regression containing this variable used the time‐dummy approach and considered

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only the effect of winning the Superbowl 2 years ago. Winning the Superbowl in any other year

had inconclusive effects. It could be that there is a time‐delay effect in receiving extra

compensation for being a Superbowl‐winning quarterback. The variable has low statistical

significance but has a large positive coefficient. A quarterback who won the Superbowl 2 years

ago is predicted to reap a 14.2% benefit today from doing so.

Estimating Team Performance as a Result of Quarterback Performance

It was stated before that quarterbacks are very important to their teams. But just how

important is this position? While the primary goal of this study was to determine how a

quarterback’s measurable qualities contribute to his monetary value, the secondary goal was to

see how these qualities affect the performance of his team.

16.

RegSeasonWins Coefficient Std. Error P>|z|

PTD .1804051 .0270309 0.000

R2=0.4643

#Obs=200

#Groups=60

Restriction: GS greater than or equal to 8

+31 Team Dummies

The best results were obtained by using the team‐dummy method and specifying that to

be included in the model, a quarterback must have started at least half of the games during the

regular season. This is an effective way to eliminate second‐ and third‐string quarterbacks who

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confound the results. Though the coefficient on PTD appears small, it is significant, and it

indicates that passing for an extra 11 touchdowns is estimated to increase an entire team’s

record by about 2 wins. Two wins can make the difference between a chance at going to the

playoffs and being uninvited to the post‐season tournament.

17.

Log(RegSeasonWins) Coefficient Std. Error P>|z|

Rate .0185015 .0026498 0.000

R2=0.4352

#Obs=200

#Groups=60

Restriction: GS greater than or equal to 8

+31 Team Dummies

This regression demonstrates how powerfully the passer rating, as a measure of a

quarterback’s ability, affects a team’s regular season wins. Here I used the log of

RegSeasonWins, LRegSeasonWins. This shows that if a quarterback were to add 50 points to

his passer rating (say for example, he doubles it from a score of 50 to a score of 100), the

percent of games his team won would be predicted to almost double. This shows the

difference between having a mediocre quarterback as a starter and having an elite quarterback

as a starter. It is substantial.

18.


Exp ‐.0200178 .0284501 0.482

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ExpSQ .000605 .0017967 0.736

Rate .0151807 .0025851 0.000

Sck ‐.011551 .0027757 0.000

RTD ‐.0213521 .0186355 0.252

Ryds .0003679 .0002519 0.144

GS .0669841 .0109636 0.000

R2=0.5645

#Obs=200

#Groups=60

Same restrictions apply

+31 Team Dummies

Here, many more variables are controlled for in order to isolate a ceteris paribus effect.

The effect of passer rating decreases slightly but maintains high significance. There appears to

be a strong positive return to having a quarterback who is a consistent starter, as indicated by

the GS coefficient. Every other correlation matches with what one might expect except for the

reversal of the diminishing returns effect discussed earlier with Exp and ExpSQ. The

significance of these values, however, is very poor.

19.


Exp ‐.0978946 .0510495 0.055

ExpSQ .0042126 .0026727 0.115

Rate .0094647 .0036782 0.010

Sck ‐.0158034 .0041549 0.000

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RTD .0219416 .0266615 0.411

Ryds .0002524 .0003816 0.508

GS .0673368 .0146347 0.000

L3.WonSuperbowl .2685658 .192206 0.162

R2=0.7553

#Obs=103

#Groups=40

Same restrictions apply

+31 Team Dummies

The only variable added here is WonSuperbowl. Except for winning the Superbowl 3

years ago, winning the Superbowl in every other year was extremely statistically insignificant. It

appears as though winning the Superbowl 3 years prior has the most significant effect on

regular season wins, with an estimated increase in wins of 26% if true.

Estimating Team Performance as a Result of Compensation

Surprisingly, none of the measures of compensation used in this study had any

conclusive effect on team performance. All regressions were awful, with insignificant p‐values

and r‐squared values lower than 1 percent. This indicates that paying a quarterback more does

not necessarily increase team performance in the regular season. Perhaps quarterbacks at the

professional level are in a position so advanced that their incentives to perform better (their

internal drive to win) cannot be influenced by merely attempting to motivate them with

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money. There are ten other players on the offensive side of the ball who must also perform

well to win games, although the quarterbacks’ performance seems to matter to a

disproportionately high degree. It is not possible to be a more successful team by giving your

quarterback more money.

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Conclusion

Overall, the goals of this study have been achieved. With few surprises, the effects of

quarterback statistics are what one would probably expect. With so many measurable factors,

controlling for as many variables as possible without generating a meaningless regression

proved difficult at times. Sometimes the results of each of the four methods were nearly

identical, and other times they were drastically different. To write a somewhat concise paper,

only the “best” regressions (as determined by adjusted r‐squared and F‐tests) were shown.

This study has shown that the effects of “good” statistics on quarterback value are

positive and of a magnitude consistent with their commonly accepted importance , while the

effects of “bad” statistics on quarterback value are negative and of a magnitude consistent with

their commonly accepted importance. While this may seem mundane, nothing should be

assumed without empirical evidence, and that is what is provided here. For instance, there is

some degree of evidence for the idea that throwing risky passes (thereby increasing

interceptions) may increase quarterback value, although to a lesser degree than more

commonly accepted “good” statistics.

The fixed‐effects method seemed to work best for the regressions involving one

independent variable of interest. The other methods tended to reduce the adjusted r‐squared

value while inflating the r‐squared value. This was, of course, due to the drastically increased

degrees of freedom when using the dummies. The team‐dummy method was noticeably

31

preferable to all other methods when there were many independent variables of interest. They

usually provided the best estimate of the elasticities.

The statistics that were most important and that were not direct measures of on‐field

performance were experience and games started. Being a consistent starter was extremely

valuable year after year. The huge effect of experience on compensation was mostly due to the

better negotiating ability achieved after the first few years of professional play. For direct

measures of on‐field performance, I had expected passing touchdowns to have the greatest

effect. Although a large positive effect was confirmed using simple linear regression analysis

with fixed effects, when controlling for more variables the significance of passing touchdowns

became inferior to the passer rating statistic. So for the multiple regression models, which I

believe were the best predictors of compensation, passer rating seemed to be the most

important measure of direct on‐field performance.

The results of this study were consistent with the findings of other researchers that

dealt with related topics. Some of the regressions performed strongly reinforce the assertions

made by these researchers.

Both measurable and intangible qualities were controlled for, and I believe some good

information was found.

32

Summary Statistics

Variable Obs Mean Std. Dev. Min Max

fuml 466 1.890558 2.10244 0 9 fum 466 4.375536 4.483969 0 23 rtd 466 .6416309 1.317502 0 10 ryds 466 69.79828 126.9199 -13 1039 ratt 466 18.66524 21.37015 0 123 rate 466 64.71953 34.59824 0 156.9 scky 466 93.26609 92.13887 0 424 sck 466 14.60515 14.48376 0 76intercepti~s 466 6.845494 6.682488 0 29 ptd 466 9.17382 10.00719 0 50 pyds 466 1512.7 1475.598 0 4830 patt 466 219.0837 206.4902 0 652 pcomp 466 132.0773 126.9787 0 440 gs 466 6.729614 6.478074 0 16 g 466 8.203863 6.046706 0 16 exp 466 5.371245 3.917091 1 21 age 466 27.88841 4.239141 21 44 wt 466 223.7639 12.72809 196 285 ht 466 74.87339 1.419927 71 78

wonsuperbowl 466 .0321888 .176691 0 1regseasonl~s 466 7.914163 2.991949 0 15regseasonw~s 466 8.081545 2.989192 1 16 capvalue 466 2597211 2832639 0 1.54e+07 totalsalary 466 3027277 3926658 66176 3.50e+07 otherbonus 466 538608.8 1643858 0 1.23e+07 signbonus 466 1494023 3311007 0 3.45e+07 basesalary 466 1190329 1562312 0 1.10e+07

33

Appendix

1.

F test that all u_i=0: F( 83, 282) = 2.73 Prob > F = 0.0000 rho .48063419 (fraction of variance due to u_i) sigma_e 1847200.7 sigma_u 1776989 _cons 1914881 176411.1 10.85 0.000 1567632 2262131 L1. 108527.1 15302.3 7.09 0.000 78405.84 138648.3 ptd capvalue Coef. Std. Err. t P>|t| [95% Conf. Interval]

corr(u_i, Xb) = 0.5536 Prob > F = 0.0000 F(1,282) = 50.30

overall = 0.4692 max = 7 between = 0.7170 avg = 4.4R-sq: within = 0.1514 Obs per group: min = 1

Group variable: obs Number of groups = 84Fixed-effects (within) regression Number of obs = 367

. xtreg capvalue l.ptd ,fe

2.

F test that all u_i=0: F( 70, 208) = 2.91 Prob > F = 0.0000 rho .51120839 (fraction of variance due to u_i) sigma_e 1733970.4 sigma_u 1773286.1 _cons 1631497 256585.7 6.36 0.000 1125655 2137339 L2. 100066.7 16769.26 5.97 0.000 67007.18 133126.2 L1. 64066.31 17442.06 3.67 0.000 29680.43 98452.2 ptd capvalue Coef. Std. Err. t P>|t| [95% Conf. Interval]

corr(u_i, Xb) = 0.4510 Prob > F = 0.0000 F(2,208) = 28.34



. xtreg capvalue l.ptd l2.ptd ,fe

34

3.

rho .16889926 (fraction of variance due to u_i) sigma_e 1751372.5 sigma_u 789524.41 _cons 575559.4 355044.3 1.62 0.105 -120314.7 1271433 y07 1025555 392056.8 2.62 0.009 257137.6 1793972 y06 1094537 394331 2.78 0.006 321662.2 1867411 y05 439813.4 402574.6 1.09 0.275 -349218.3 1228845 y04 190079.5 414823.9 0.46 0.647 -622960.4 1003120 y03 798669 425670.2 1.88 0.061 -35629.28 1632967 y01 -522170 469627.4 -1.11 0.266 -1442623 398282.8 L1. 181995.5 12205.54 14.91 0.000 158073.1 205917.9 ptd capvalue Coef. Std. Err. z P>|z| [95% Conf. Interval]

corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000Random effects u_i ~ Gaussian Wald chi2( 7) = 235.85


Group variable: obs Number of groups = 84Random-effects GLS regression Number of obs = 367

note: y02 dropped because of collinearitynote: y00 dropped because of collinearity. xtreg capvalue l.ptd y00 y01 y02 y03 y04 y05 y06 y07

4.

rho .38473986 (fraction of variance due to u_i) sigma_e 1954847.2 sigma_u 1545848.9 _cons 5238504 1206533 4.34 0.000 2873742 7603266 dredskins -3731496 1393326 -2.68 0.007 -6462365 -1000627 dtitans -3429250 1497973 -2.29 0.022 -6365224 -493276.4 dbuccaneers -4415544 1434426 -3.08 0.002 -7226968 -1604120 drams -4268885 1402118 -3.04 0.002 -7016986 -1520784 dseahawks -3900727 1341221 -2.91 0.004 -6529471 -1271983 d49ers -4660108 1442309 -3.23 0.001 -7486981 -1833235 dchargers -2186909 1499619 -1.46 0.145 -5126108 752290.9 dsteelers -3988432 1579748 -2.52 0.012 -7084682 -892181.7 deagles -3703831 1507980 -2.46 0.014 -6659418 -748244.1 draiders -3043044 1607036 -1.89 0.058 -6192777 106689.9 djets -5003556 1445665 -3.46 0.001 -7837007 -2170104 dgiants -3146108 1472795 -2.14 0.033 -6032734 -259482.4 dsaints -4651285 1515097 -3.07 0.002 -7620820 -1681750 dpatriots -3679358 1506940 -2.44 0.015 -6632906 -725810.3 dvikings -4079960 1363923 -2.99 0.003 -6753200 -1406719 ddolphins -4843109 1424244 -3.40 0.001 -7634576 -2051642 dchiefs -4154680 1457836 -2.85 0.004 -7011985 -1297374 djaguars -5775319 1498789 -3.85 0.000 -8712891 -2837747 dcolts -1512382 1644751 -0.92 0.358 -4736034 1711271 dtexans -2514947 1857192 -1.35 0.176 -6154976 1125082 dlions -4544148 1439423 -3.16 0.002 -7365366 -1722931 dbroncos -3411288 1469921 -2.32 0.020 -6292280 -530296.8 dcowboys -3884920 1561670 -2.49 0.013 -6945737 -824103.3 dravens -3757052 1450133 -2.59 0.010 -6599260 -914842.8 dbengals -2411496 1490864 -1.62 0.106 -5333536 510543.7 dbears -4731928 1685671 -2.81 0.005 -8035783 -1428073 dpanthers -5444537 1673851 -3.25 0.001 -8725225 -2163850 dbills -4339563 1758252 -2.47 0.014 -7785673 -893452.2 dfalcons -2596233 1687118 -1.54 0.124 -5902923 710457.3 dcardinals -4270060 1457252 -2.93 0.003 -7126221 -1413899 dbrowns -3839118 1391916 -2.76 0.006 -6567224 -1111012 L1. 20254.68 3819.688 5.30 0.000 12768.22 27741.13 rate capvalue Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: dpackers dropped because of collinearity> s d49ers dseahawks drams dbuccaneers dtitans dredskins> ers dtexans dcolts djaguars dchiefs ddolphins dvikings dpatriots dsaints dgiants djets draiders deagles dsteelers dcharger. xtreg capvalue l.rate dbrowns dcardinals dfalcons dbills dpanthers dbears dbengals dravens dcowboys dbroncos dlions dpack

35

5.

F test that all u_i=0: F( 83, 279) = 9.96 Prob > F = 0.0000 rho .72583324 (fraction of variance due to u_i) sigma_e .56348094 sigma_u .91683304 _cons 13.07829 .1191112 109.80 0.000 12.84382 13.31277 L1. -.0239457 .0027393 -8.74 0.000 -.029338 -.0185533 expsq L1. .440962 .0392241 11.24 0.000 .3637493 .5181748 exp lcapvalue Coef. Std. Err. t P>|t| [95% Conf. Interval]

corr(u_i, Xb) = -0.1298 Prob > F = 0.0000 F(2,279) = 67.13



. xtreg lcapvalue l.exp l.expsq ,fe

6.

F test that all u_i=0: F( 83, 280) = 3.14 Prob > F = 0.0000 rho .59513203 (fraction of variance due to u_i) sigma_e .62614982 sigma_u .75915108 _cons 13.95662 .0666776 209.31 0.000 13.82536 14.08787 L1. .0602965 .0081548 7.39 0.000 .0442439 .076349 gs lcapvalue Coef. Std. Err. t P>|t| [95% Conf. Interval]

corr(u_i, Xb) = 0.5721 Prob > F = 0.0000 F(1,280) = 54.67



. xtreg lcapvalue l.gs ,fe

7.

F test that all u_i=0: F( 80, 235) = 3.66 Prob > F = 0.0000 rho .61485897 (fraction of variance due to u_i) sigma_e .62573563 sigma_u .79062173 _cons 14.07673 .0987915 142.49 0.000 13.8821 14.27136 L1. .7105315 .137685 5.16 0.000 .4392769 .981786pctofgames~d lcapvalue Coef. Std. Err. t P>|t| [95% Conf. Interval]

corr(u_i, Xb) = 0.4728 Prob > F = 0.0000 F(1,235) = 26.63



. xtreg lcapvalue l.pctofgamesstarted ,fe

36

8.

_cons 9.563875 2.808704 3.41 0.001 4.044457 15.08329 ht .0617184 .0375106 1.65 0.101 -.0119941 .135431 lcapvalue Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 607.077729 463 1.311183 Root MSE = 1.143 Adj R-squared = 0.0037 Residual 603.541125 462 1.30636607 R-squared = 0.0058 Model 3.53660431 1 3.53660431 Prob > F = 0.1006 F( 1, 462) = 2.71 Source SS df MS Number of obs = 464

. reg lcapvalue ht

9.

_cons 11.53885 .9324726 12.37 0.000 9.706436 13.37126 wt .0118269 .004162 2.84 0.005 .0036482 .0200056 lcapvalue Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 607.077729 463 1.311183 Root MSE = 1.1364 Adj R-squared = 0.0151 Residual 596.649224 462 1.29144854 R-squared = 0.0172 Model 10.4285052 1 10.4285052 Prob > F = 0.0047 F( 1, 462) = 8.08 Source SS df MS Number of obs = 464

. reg lcapvalue wt

10.

rho .36215413 (fraction of variance due to u_i) sigma_e .5519512 sigma_u .41590058 _cons 13.89946 .1780126 78.08 0.000 13.55057 14.24836 y07 .3985979 .1844948 2.16 0.031 .0369946 .7602011 y06 .4587249 .1782349 2.57 0.010 .109391 .8080588 y05 .1705334 .1789033 0.95 0.340 -.1801105 .5211774 y04 .0153469 .1751459 0.09 0.930 -.3279327 .3586266 y03 .1016172 .1819525 0.56 0.577 -.255003 .4582375 y01 -.2847873 .1875889 -1.52 0.129 -.6524548 .0828803 L1. .0434145 .0071356 6.08 0.000 .0294291 .0574 ptd L1. .0189017 .0101443 1.86 0.062 -.0009808 .0387841intercepti~s lcapvalue Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: y02 dropped because of collinearitynote: y00 dropped because of collinearity. xtreg lcapvalue l.interceptions l.ptd y00 y01 y02 y03 y04 y05 y06 y07 if gs>=8

11.

37

sigma_u .4700485 _cons 14.60054 .3730729 39.14 0.000 13.86933 15.33175 dredskins -.7226087 .4333973 -1.67 0.095 -1.572052 .1268345 dtitans -.6604002 .4663019 -1.42 0.157 -1.574335 .2535348 dbuccaneers -1.271332 .4453714 -2.85 0.004 -2.144244 -.3984203 drams -.9228794 .4372712 -2.11 0.035 -1.779915 -.0658435 dseahawks -.8032136 .4181844 -1.92 0.055 -1.62284 .0164128 d49ers -.9936043 .4480642 -2.22 0.027 -1.871794 -.1154146 dchargers -.5936432 .467485 -1.27 0.204 -1.509897 .3226105 dsteelers -1.585512 .487937 -3.25 0.001 -2.541851 -.6291728 deagles -1.085783 .4693304 -2.31 0.021 -2.005654 -.1659123 draiders -.9411509 .498073 -1.89 0.059 -1.917356 .0350542 djets -1.217716 .4516811 -2.70 0.007 -2.102995 -.3324377 dgiants -.9373878 .4563711 -2.05 0.040 -1.831859 -.0429169 dsaints -.8983575 .4723382 -1.90 0.057 -1.824123 .0274083 dpatriots -1.079872 .4670408 -2.31 0.021 -1.995255 -.1644888 dvikings -.9855204 .4239892 -2.32 0.020 -1.816524 -.1545169 ddolphins -1.174528 .4444627 -2.64 0.008 -2.045658 -.3033968 dchiefs -.9744763 .4526173 -2.15 0.031 -1.86159 -.0873626 djaguars -.9119642 .4696097 -1.94 0.052 -1.832382 .0084538 dcolts -.5702867 .5102558 -1.12 0.264 -1.57037 .4297963 dtexans -1.158997 .5763073 -2.01 0.044 -2.288538 -.0294552 dlions -1.203488 .4475691 -2.69 0.007 -2.080708 -.3262689 dbroncos -.610266 .456446 -1.34 0.181 -1.504884 .2843517 dcowboys -.4087923 .488364 -0.84 0.403 -1.365968 .5483835 dravens -.7727529 .4515109 -1.71 0.087 -1.657698 .1121922 dbengals -.4961707 .4645388 -1.07 0.285 -1.40665 .4143086 dbears -1.202484 .5251186 -2.29 0.022 -2.231697 -.17327 dpanthers -.9680404 .5222009 -1.85 0.064 -1.991535 .0554547 dbills -1.04008 .5480824 -1.90 0.058 -2.114302 .0341416 dfalcons -.7104435 .523095 -1.36 0.174 -1.735691 .3148037 dcardinals -.9939535 .4521004 -2.20 0.028 -1.880054 -.107853 dbrowns -.9756889 .431719 -2.26 0.024 -1.821843 -.1295351 L1. .1176726 .0138604 8.49 0.000 .0905068 .1448385 gs L1. -.0303574 .0126393 -2.40 0.016 -.05513 -.0055847intercepti~s lcapvalue Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: dpackers dropped because of collinearity> eelers dchargers d49ers dseahawks drams dbuccaneers dtitans dredskins> os dlions dpackers dtexans dcolts djaguars dchiefs ddolphins dvikings dpatriots dsaints dgiants djets draiders deagles dst. xtreg lcapvalue l.interceptions l.gs dbrowns dcardinals dfalcons dbills dpanthers dbears dbengals dravens dcowboys dbronc

12.

> d74 d75 d76 d77 d78 d79 d80 d81 d82 d83 d84 d85 d86 d87 d88 d89 d90 d91 d92 d93 d94 d95 d96> d44 d45 d46 d47 d48 d49 d50 d51 d52 d53 d54 d55 d56 d57 d58 d59 d60 d61 d62 d63 d64 d65 d66 d67 d68 d69 d70 d71 d72 d73 > d14 d15 d16 d17 d18 d19 d20 d21 d22 d23 d24 d25 d26 d27 d28 d29 d30 d31 d32 d33 d34 d35 d36 d37 d38 d39 d40 d41 d42 d43 . xtreg lcapvalue l.exp l.expsq l.pcomppct l.pyds l.ptd l.interceptions l.sck d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13

L1. -.0017347 .0048105 -0.36 0.718 -.0111631 .0076937 sck L1. -.0088807 .0106404 -0.83 0.404 -.0297355 .011974intercepti~s L1. .0002593 .0112537 0.02 0.982 -.0217977 .0223162 ptd L1. .0002402 .000106 2.27 0.023 .0000326 .0004479 pyds L1. .3464153 .3267147 1.06 0.289 -.2939338 .9867644 pcomppct L1. -.0188704 .0028811 -6.55 0.000 -.0245173 -.0132236 expsq L1. .3627602 .0426122 8.51 0.000 .2792418 .4462786 exp lcapvalue Coef. Std. Err. z P>|z| [95% Conf. Interval]




38

rho 0 (fraction of variance due to u_i) sigma_e .5214263 sigma_u 0 _cons 13.21509 .5233163 25.25 0.000 12.18941 14.24077

13.

F test that all u_i=0: F( 77, 217) = 4.15 Prob > F = 0.0000 rho .65953644 (fraction of variance due to u_i) sigma_e .51937562 sigma_u .72287905 _cons 12.87554 .2167161 59.41 0.000 12.4484 13.30267 L1. .0462967 .0280463 1.65 0.100 -.0089814 .1015748 gs L1. -.0048875 .0051582 -0.95 0.344 -.0150541 .0052791 sck L1. -.0132091 .0109181 -1.21 0.228 -.0347281 .00831intercepti~s L1. -.0002735 .0112141 -0.02 0.981 -.0223761 .0218291 ptd L1. .0000914 .0001388 0.66 0.511 -.0001822 .000365 pyds L1. .3756269 .3259106 1.15 0.250 -.2667287 1.017982 pcomppct L1. -.0189453 .0028701 -6.60 0.000 -.0246021 -.0132884 expsq L1. .360661 .0424637 8.49 0.000 .2769669 .444355 exp lcapvalue Coef. Std. Err. t P>|t| [95% Conf. Interval]

corr(u_i, Xb) = -0.0041 Prob > F = 0.0000 F(8,217) = 18.33



. xtreg lcapvalue l.exp l.expsq l.pcomppct l.pyds l.ptd l.interceptions l.sck l.gs ,fe

14.

39

rho .44208302 (fraction of variance due to u_i) sigma_e .50365711 sigma_u .44833444 _cons 12.55499 .1674532 74.98 0.000 12.22679 12.88319 y07 .3330096 .1304998 2.55 0.011 .0772348 .5887844 y06 .1979179 .1258871 1.57 0.116 -.0488163 .4446521 y05 .1503134 .1239032 1.21 0.225 -.0925325 .3931593 y04 .0955666 .124395 0.77 0.442 -.1482432 .3393764 y03 .2530758 .1246211 2.03 0.042 .0088229 .4973287 y01 -.0257068 .1369846 -0.19 0.851 -.2941917 .2427781 L1. .0245214 .0119926 2.04 0.041 .0010162 .0480265regseasonw~s L1. .0003807 .0005437 0.70 0.484 -.0006849 .0014463 ryds L1. -.0228148 .0350197 -0.65 0.515 -.0914522 .0458226 rtd L1. .0751387 .012307 6.11 0.000 .0510173 .0992601 gs L1. -.0041898 .0051741 -0.81 0.418 -.0143309 .0059513 sck L1. .0021731 .001125 1.93 0.053 -.0000318 .004378 rate L1. -.0158642 .0024127 -6.58 0.000 -.0205929 -.0111355 expsq L1. .2837511 .0366806 7.74 0.000 .2118585 .3556436 exp lcapvalue Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: y02 dropped because of collinearitynote: y00 dropped because of collinearity. xtreg lcapvalue l.exp l.expsq l.rate l.sck l.gs l.rtd l.ryds l.regseasonwins y00 y01 y02 y03 y04 y05 y06 y07

15.

40

rho .21225072 (fraction of variance due to u_i) sigma_e .50391917 sigma_u .26157212 _cons 12.56888 .2074093 60.60 0.000 12.16237 12.9754 y07 .3742909 .1371455 2.73 0.006 .1054907 .6430912 y06 .2352229 .1355663 1.74 0.083 -.0304822 .500928 y05 .1673362 .1369741 1.22 0.222 -.1011282 .4358005 y04 .0671194 .1415351 0.47 0.635 -.2102842 .344523 y03 .247729 .1424452 1.74 0.082 -.0314584 .5269165 L2. .1422508 .2025955 0.70 0.483 -.2548291 .5393306wonsuperbowl L1. .0291631 .0137586 2.12 0.034 .0021968 .0561295regseasonw~s L1. .000808 .0005548 1.46 0.145 -.0002794 .0018955 ryds L1. -.0232805 .0392978 -0.59 0.554 -.1003027 .0537418 rtd L1. .0960592 .0132456 7.25 0.000 .0700983 .1220202 gs L1. -.0085052 .0057719 -1.47 0.141 -.0198179 .0028074 sck L1. .0026633 .0013548 1.97 0.049 7.99e-06 .0053187 rate L1. -.0126701 .0027003 -4.69 0.000 -.0179626 -.0073776 expsq L1. .2233226 .0435665 5.13 0.000 .1379338 .3087113 exp lcapvalue Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: y02 dropped because of collinearitynote: y01 dropped because of collinearitynote: y00 dropped because of collinearity> y07. xtreg lcapvalue l.exp l.expsq l.rate l.sck l.gs l.rtd l.ryds l.regseasonwins l2.wonsuperbowl y00 y01 y02 y03 y04 y05 y06

16.

41

rho .05692792 (fraction of variance due to u_i) sigma_e 2.3735634 sigma_u .58316445 _cons 5.036159 1.184958 4.25 0.000 2.713683 7.358635 dredskins -.88162 1.612956 -0.55 0.585 -4.042955 2.279715 dtitans .6501697 1.286229 0.51 0.613 -1.870793 3.171132 dbuccaneers -.5671619 1.370503 -0.41 0.679 -3.253299 2.118975 drams -1.16893 1.366791 -0.86 0.392 -3.847791 1.509931 dseahawks .453696 1.338168 0.34 0.735 -2.169065 3.076457 d49ers 1.009167 1.61154 0.63 0.531 -2.149394 4.167728 dchargers .586182 1.388213 0.42 0.673 -2.134665 3.307029 dsteelers .7614854 1.448989 0.53 0.599 -2.078481 3.601452 deagles 1.620261 1.349605 1.20 0.230 -1.024916 4.265439 draiders -1.158669 1.587116 -0.73 0.465 -4.269359 1.952021 djets -1.143425 1.334023 -0.86 0.391 -3.758063 1.471213 dgiants -1.573288 1.494993 -1.05 0.293 -4.503421 1.356844 dsaints .4716759 1.742061 0.27 0.787 -2.9427 3.886052 dpatriots 2.150056 1.323021 1.63 0.104 -.4430176 4.74313 dvikings -.1314502 1.416055 -0.09 0.926 -2.906867 2.643967 ddolphins -2.931395 1.488615 -1.97 0.049 -5.849026 -.0137636 dchiefs .2492065 1.495999 0.17 0.868 -2.682898 3.181311 djaguars 1.093331 1.530055 0.71 0.475 -1.905523 4.092184 dcolts .3609777 1.411115 0.26 0.798 -2.404757 3.126712 dtexans -2.246461 1.67217 -1.34 0.179 -5.523855 1.030932 dlions -1.152624 1.397487 -0.82 0.409 -3.891649 1.586401 dbroncos -2.468439 1.512685 -1.63 0.103 -5.433247 .4963684 dcowboys .9138654 1.736475 0.53 0.599 -2.489564 4.317295 dravens 1.024919 1.474692 0.70 0.487 -1.865424 3.915262 dbengals -2.15358 1.326885 -1.62 0.105 -4.754226 .4470664 dbears 2.384208 1.582736 1.51 0.132 -.717898 5.486313 dpanthers -1.873512 1.482343 -1.26 0.206 -4.77885 1.031826 dbills -.7204439 1.780537 -0.40 0.686 -4.210233 2.769345 dfalcons -.4393028 1.398919 -0.31 0.753 -3.181134 2.302529 dcardinals .5468973 1.326908 0.41 0.680 -2.053795 3.147589 dbrowns -1.210322 1.341551 -0.90 0.367 -3.839714 1.419069 ptd .1804051 .0270309 6.67 0.000 .1274255 .2333848 regseasonw~s Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: dpackers dropped because of collinearity> hargers d49ers dseahawks drams dbuccaneers dtitans dredskins if gs>=8> packers dtexans dcolts djaguars dchiefs ddolphins dvikings dpatriots dsaints dgiants djets draiders deagles dsteelers dc. xtreg regseasonwins ptd dbrowns dcardinals dfalcons dbills dpanthers dbears dbengals dravens dcowboys dbroncos dlions d

17.

42

rho .29730397 (fraction of variance due to u_i) sigma_e .3153457 sigma_u .20511788 _cons .6169718 .3054938 2.02 0.043 .018215 1.215729 dredskins -.12063 .2962498 -0.41 0.684 -.7012688 .4600089 dtitans .0076742 .2491229 0.03 0.975 -.4805978 .4959462 dbuccaneers -.180036 .2514342 -0.72 0.474 -.672838 .3127659 drams -.3766757 .2711652 -1.39 0.165 -.9081497 .1547982 dseahawks -.0349606 .2377384 -0.15 0.883 -.5009194 .4309982 d49ers -.010978 .2764847 -0.04 0.968 -.5528781 .5309221 dchargers -.0464107 .2775081 -0.17 0.867 -.5903165 .4974951 dsteelers -.2042278 .286444 -0.71 0.476 -.7656478 .3571922 deagles .1215891 .2833584 0.43 0.668 -.4337831 .6769613 draiders -.2598571 .2793882 -0.93 0.352 -.8074478 .2877337 djets -.3865581 .254382 -1.52 0.129 -.8851376 .1120214 dgiants -.1935594 .2842079 -0.68 0.496 -.7505966 .3634778 dsaints -.0230991 .3058804 -0.08 0.940 -.6226137 .5764155 dpatriots .0721761 .2697232 0.27 0.789 -.4564716 .6008238 dvikings -.0895699 .2627777 -0.34 0.733 -.6046047 .4254648 ddolphins -.4095488 .2626931 -1.56 0.119 -.9244179 .1053203 dchiefs -.0601978 .3214248 -0.19 0.851 -.6901789 .5697833 djaguars .0443465 .2831561 0.16 0.876 -.5106292 .5993221 dcolts -.0638885 .3161445 -0.20 0.840 -.6835204 .5557433 dtexans -.5486389 .3190813 -1.72 0.086 -1.174027 .0767489 dlions -.0361522 .2565305 -0.14 0.888 -.5389426 .4666383 dbroncos -.4082978 .284227 -1.44 0.151 -.9653724 .1487769 dcowboys -.0185914 .3100152 -0.06 0.952 -.6262101 .5890273 dravens .0822455 .280479 0.29 0.769 -.4674832 .6319742 dbengals -.387051 .2573132 -1.50 0.133 -.8913755 .1172735 dbears .3157724 .2836575 1.11 0.266 -.240186 .8717309 dpanthers -.3832408 .271264 -1.41 0.158 -.9149085 .1484269 dbills -.1261122 .3184502 -0.40 0.692 -.7502632 .4980388 dfalcons -.180657 .2641275 -0.68 0.494 -.6983374 .3370235 dcardinals -.0572861 .2532998 -0.23 0.821 -.5537447 .4391724 dbrowns -.2082741 .2531486 -0.82 0.411 -.7044362 .287888 rate .0185015 .0026498 6.98 0.000 .013308 .023695 lregseason~s Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: dpackers dropped because of collinearity> dchargers d49ers dseahawks drams dbuccaneers dtitans dredskins if gs>=8> dpackers dtexans dcolts djaguars dchiefs ddolphins dvikings dpatriots dsaints dgiants djets draiders deagles dsteelers . xtreg lregseasonwins rate dbrowns dcardinals dfalcons dbills dpanthers dbears dbengals dravens dcowboys dbroncos dlions

18.

43

dredskins -.0573071 .2734202 -0.21 0.834 -.5932008 .4785866 dtitans .0840737 .2236808 0.38 0.707 -.3543327 .52248 dbuccaneers -.05001 .2241611 -0.22 0.823 -.4893577 .3893377 drams -.0214787 .2440969 -0.09 0.930 -.4998997 .4569424 dseahawks .1579454 .2131944 0.74 0.459 -.2599079 .5757987 d49ers .2460976 .2526856 0.97 0.330 -.2491571 .7413523 dchargers -.0663288 .2466082 -0.27 0.788 -.5496719 .4170144 dsteelers .032353 .2595417 0.12 0.901 -.4763395 .5410455 deagles .2600247 .2547739 1.02 0.307 -.2393231 .7593724 draiders -.1204437 .2531647 -0.48 0.634 -.6166375 .37575 djets -.0945079 .2289799 -0.41 0.680 -.5433004 .3542845 dgiants -.1065287 .2489577 -0.43 0.669 -.5944768 .3814194 dsaints -.026323 .2722946 -0.10 0.923 -.5600106 .5073646 dpatriots .1663909 .2341795 0.71 0.477 -.2925925 .6253743 dvikings .0484898 .2405346 0.20 0.840 -.4229493 .5199289 ddolphins -.2324319 .2391436 -0.97 0.331 -.7011448 .2362811 dchiefs .0420877 .2676383 0.16 0.875 -.4824737 .5666492 djaguars .1663781 .2483173 0.67 0.503 -.3203148 .653071 dcolts -.1143498 .2696525 -0.42 0.672 -.642859 .4141594 dtexans -.4984856 .2820265 -1.77 0.077 -1.051247 .0542763 dlions .0518478 .235885 0.22 0.826 -.4104782 .5141738 dbroncos -.3917313 .2579886 -1.52 0.129 -.8973796 .113917 dcowboys .1409161 .281334 0.50 0.616 -.4104885 .6923206 dravens .1903495 .2560168 0.74 0.457 -.3114342 .6921332 dbengals -.2778486 .227862 -1.22 0.223 -.7244499 .1687527 dbears .3019682 .2573444 1.17 0.241 -.2024177 .806354 dpanthers -.3617107 .2436637 -1.48 0.138 -.8392827 .1158613 dbills .0589324 .2901562 0.20 0.839 -.5097633 .6276282 dfalcons -.2008257 .2469289 -0.81 0.416 -.6847975 .283146 dcardinals .0307806 .228223 0.13 0.893 -.4165282 .4780894 dbrowns .0076087 .2324205 0.03 0.974 -.4479272 .4631446 gs .0669841 .0109636 6.11 0.000 .0454959 .0884723 ryds .0003679 .0002519 1.46 0.144 -.0001258 .0008615 rtd -.0213521 .0186355 -1.15 0.252 -.0578771 .0151729 sck -.011551 .0027757 -4.16 0.000 -.0169912 -.0061108 rate .0151807 .0025851 5.87 0.000 .010114 .0202475 expsq .000605 .0017967 0.34 0.736 -.0029164 .0041264 exp -.0200178 .0284501 -0.70 0.482 -.075779 .0357434 lregseason~s Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: dpackers dropped because of collinearity> draiders deagles dsteelers dchargers d49ers dseahawks drams dbuccaneers dtitans dredskins if gs>=8> ns dcowboys dbroncos dlions dpackers dtexans dcolts djaguars dchiefs ddolphins dvikings dpatriots dsaints dgiants djets . xtreg lregseasonwins exp expsq rate sck rtd ryds gs dbrowns dcardinals dfalcons dbills dpanthers dbears dbengals drave

19.

44

rho .16848734 (fraction of variance due to u_i) sigma_e .25628941 sigma_u .11536654 _cons 1.127414 .4297942 2.62 0.009 .2850325 1.969795 dredskins (dropped) dtitans -.048114 .2266213 -0.21 0.832 -.4922837 .3960556 dbuccaneers .0235807 .2397807 0.10 0.922 -.4463809 .4935422 drams .0281761 .2301507 0.12 0.903 -.422911 .4792633 dseahawks .2517392 .1985793 1.27 0.205 -.137469 .6409474 d49ers -.0148283 .2759735 -0.05 0.957 -.5557265 .5260698 dchargers -.1095333 .230542 -0.48 0.635 -.5613873 .3423208 dsteelers .1513948 .3570334 0.42 0.672 -.5483779 .8511675 deagles .2693371 .2517683 1.07 0.285 -.2241196 .7627938 draiders -.2780264 .3272844 -0.85 0.396 -.9194921 .3634392 djets -.0393572 .2159081 -0.18 0.855 -.4625293 .383815 dgiants -.1137503 .2403596 -0.47 0.636 -.5848464 .3573457 dsaints .2019396 .2729145 0.74 0.459 -.332963 .7368423 dpatriots .1090676 .2570223 0.42 0.671 -.3946867 .612822 dvikings -.0847136 .3150534 -0.27 0.788 -.7022068 .5327797 ddolphins -.1456616 .2489925 -0.59 0.559 -.6336779 .3423547 dchiefs .3092648 .2285346 1.35 0.176 -.1386549 .7571845 djaguars .1125682 .2401711 0.47 0.639 -.3581585 .5832949 dcolts .0662275 .2375632 0.28 0.780 -.3993879 .5318428 dtexans -.597166 .3069655 -1.95 0.052 -1.198807 .0044753 dlions -.1918851 .2699186 -0.71 0.477 -.7209159 .3371457 dbroncos .0797176 .3449221 0.23 0.817 -.5963172 .7557524 dcowboys .1259591 .2848702 0.44 0.658 -.4323763 .6842945 dravens -.0274463 .3464091 -0.08 0.937 -.7063957 .6515031 dbengals -.09739 .2148152 -0.45 0.650 -.5184201 .32364 dbears .3162462 .3405066 0.93 0.353 -.3511345 .9836268 dpanthers .0228089 .2782492 0.08 0.935 -.5225495 .5681674 dbills (dropped) dfalcons -.0113941 .3054718 -0.04 0.970 -.6101077 .5873196 dcardinals .0565413 .2368391 0.24 0.811 -.4076548 .5207374 dbrowns -.1216714 .2501946 -0.49 0.627 -.6120439 .3687011 L3. .2685658 .192206 1.40 0.162 -.108151 .6452826wonsuperbowl gs .0673368 .0146347 4.60 0.000 .0386534 .0960203 ryds .0002524 .0003816 0.66 0.508 -.0004955 .0010004 rtd .0219416 .0266615 0.82 0.411 -.0303139 .0741971 sck -.0158034 .0041549 -3.80 0.000 -.0239468 -.00766 rate .0094647 .0036782 2.57 0.010 .0022556 .0166738 expsq .0042126 .0026727 1.58 0.115 -.0010259 .0094511 exp -.0978946 .0510495 -1.92 0.055 -.1979498 .0021605 lregseason~s Coef. Std. Err. z P>|z| [95% Conf. Interval]




note: dpackers dropped because of collinearity> s dgiants djets draiders deagles dsteelers dchargers d49ers dseahawks drams dbuccaneers dtitans dredskins if gs>=8> s dbengals dravens dcowboys dbroncos dlions dpackers dtexans dcolts djaguars dchiefs ddolphins dvikings dpatriots dsaint. xtreg lregseasonwins exp expsq rate sck rtd ryds gs l3.wonsuperbowl dbrowns dcardinals dfalcons dbills dpanthers dbear

Works Cited

USATODAY Player Salaries Database. Retrieved throughout February 2008.

(http://content.usatoday.com/sports/football/nfl/salaries/)

45

Official NFL Players Database. Retrieved throughout February 2008.

(http://www.nfl.com/players/)

NFL Team History Database. Retrieved throughout February 2008.

(http://www.nflteamhistory.com/nfl_team_history.html)

Salary Cap Frequently Asked Questions. Retrieved throughout March 2008.

(http://askthecommish.com/salarycap/faq.asp)

Hendricks, Wallace; DeBrock, Lawrence; Koenker, Roger. “Uncertainty, Hiring, and Subsequent Performance: The NFL Draft.” Journal of Labor Economics, October 2003, v. 21, iss. 4, pp. 857‐86

Craig, Lee A.; Hall, Alastair R. “Trying Out for the Team: Do Exhibitions Matter? Evidence from the National Football League.” Journal of the American Statistical Association, September 1994, v. 89, iss. 427, pp. 1091‐99

Leeds, Michael A.; Kowalewski, Sandra. “Winner Take All in the NFL: The Effect of the Salary Cap and Free Agency on the Compensation of Skill Position Players.” Journal of Sports Economics, August 2001, v. 2, iss. 3, pp. 244‐56

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