One of the imperfect markets in an economy is the market for quarterback (QB) services in the National Football League (NFL). The relationship that is shown between a quarterback and manager or owner of NFL is typically oligopolistic though bilateral in operations. There is the upstream oligopolist, represented by the quarterback and the downstream oligopolist, who is the team owner. Due to the imperfections that are in the market, it emerges that there are differences in payments for the quarterbacks. Some get reasonably high pays while others get much lower payments compared to the market standards. However, the reason for the difference is not yet clear as some attribute it to the varied pool of talent available while others on a host of factors. Through the development of a model, the research will identify the key determinants of NFL QB salary.
The study on salary determinants in professional team sports has not been exhaustively covered with just a few studies done covering the last ten years. Most of the works that have been done concentrated on identification of the performance parameters that affect the mean salaries paid in a team, while the recent studies are looking at the factors that determine the salary of a single player position in a team sport. It is worth noting that for a long time, most of the studies have primarily focused on professional baseball. The main reason for the biases of the studies on baseball can be attributed to the distinct and measurable performance variable for every player. Some of the variables that can easily be looked at include the home runs, the mean batting and runs batted when gauging the performance of a hitter, the strike-outs and the earned run average are used to gauge the performance of a pitcher. Even though some studies have expanded to cover sports such as hockey and football, it has not been easy as the measurement variables are not clear and in themselves affected by certain factors. Therefore, most of the studies that have been done are so much concentrated on player-related variables with little attention given to factors such as revenue or monopoly power of the owner.
Different from the previous studies, this research will regress the average annual salary for an NFL quarterback against the different player and team related variables. The variables used in the study include team revenue, winning percentage, payroll costs. Through this, the study will help find out the determinants of an NFL QB Salary.

Literature Review
Even though it is widely acknowledged that there is growing literature in regards to factors that affect payments of quarterbacks in team sports, most of the researches done concentrate largely on the performance of the team and the mean salaries that players earn. Very few studies have attempted to take an individualistic player approach on this matter. In a study done by Scoville , regression analysis for NFL team salaries for 1970 was done against the winning chances in the previous three years. To ensure that there are no extremes, the author used dummy variables to represent the growing and upcoming teams and the Green Bay packers on the other hand to represent the dominant team . The results obtained from the study showed that the significant factor that affect the team salaries is their frequency of wins. From the results it can be inferred that players were rewarded just because the team had posted better results.
To respond to the study done by Scoville (1974), Scahill (1985) made an effort to establish the marginal revenue product of individual players in a team sport . However, the study would face a challenge on the best way to quantify the contribution of a player to the team’s success. In fact, quantifying the contribution was a serious problem for players on the defensive and offensive lines. To outlive the challenge, Scahill (1985) came up with several proxies for individual performance and included them in the regression models. The proxies included the number of appearances that a player has had for the team. This would help showcase the player’s experience. The second proxy is the position that a player is given as a show of the player’s potential and the last proxy is the number of times a player is selected to play vis-à-vis his or her peers. This would show the player’s stature. While conducting her study, the team salaries were regressed on the mean number of appearances by a player, the average round for which they were selected and the winning proportion of the team (covering five to ten years). Even though from the results obtained, it was shown that there was a positive correlation between salary and the proportion of wins, it was however realized that the winning proportion was not statistically significant. Looking at the three variables, it was only the chances of pro-teams being significant. From the study, it was concluded that performance of the team was insignificant in determination of player salaries.
Even though the study that was commissioned by Scahill concentrated on the mean team salaries, it is easily assumed that quarterback has the most direct effect hence the higher duty to win or lose games compared to any other position in NFL . What this means is that the quarterback serves on the roles of a manager and must be ready to take up the larger share of blame in case of unproductivity while be credited for productivity.
Nonetheless, the most informative research in the field was done by Jones and Walsh (1988) where they had a regression model relating the salaries of every pay to the skills they had, the discrimination meted on a player and then powers of the National Hockey League (NHL) . The study concluded that skills are critical determinant of salary for all players without their position playing a role. The study also established that monopoly of the club ownership had positive effect on the individuals playing at the forward position. The players at the defense position are likely to face more discrimination than others. The results obtained are in synch with the neoclassical price theory, which captures that without discrimination, skills are the key determinants of salary differences.
Methodologies of Forming Models
The methodology that are applied when forming the models is so important for this study. For Jones and Walsh, they included the values of both extreme values and then ran it against salary data from an estimated 300 players.
For the study done by Ahlburg and Dworkin (1991), factors that dictate the salaries in the NFL was done . In fact, at one point, there was misunderstanding on the determinant of player salaries. According to the players, the salaries given were pegged on years of experience, the position one plays and the frequency of selection. According to the authors, performance of the team played less role or rather none when deciding the salaries to be paid. For the team owner players salary level cannot be talked about without tying it to the performance of the team.
To get a clear understanding of the situation, a model that checks on salary determinants was run for the data from 1982, 1986 and 1987. Given that the player positions are often filled by specialists, the authors ensured that position specific performance measures. Through application of the factor analysis, different 21 performance measures were drafted for the quarterback position. After running the model, the arguments for both sides were nearly same.

Economic Theory
When hiring a quarterback into a team, there are certain financial as well as the performance variables that must be considered when signing a contract. Some of the most significant elements include player payroll, the revenue of the team, the franchise value affect the salary decision for a team. It is against this backdrop that the following theoretical model is developed through equation approach. The equation has several performance variables both on-field and team related ones.
Below is a representation of the equation:
Vvap = (A1, A2,…An, Y1, Y2, …..Yn),
Vvap = mean yearly salary
A1..An = combination of on-field performance variables
Y1..Yn = Combination of on-field and off-field variables
In this study, the author uses salary data from 32 NFL quarterback players.
To back up the equation above, there are three sets of simultaneous equations that will be applied. The application is agitated by the fact that the existing link between the explanatory variables and the error term is not stochastic in nature. This if not checked would violate the assumption that is held under ordinary least squares.
For the model, the following equations will adopted
Equation 1
Cj=fc(Aj, Bj) + ej, where
C= total completed passes in previous season
A= attempted passes in previous season
B= duration in years with NFL
ej= the error term
From the equation one gets to understand the anticipated success arising from number of completions and experience.
Equation 2:
Rk=fR(Dk, Tk, Ik, Ok) +ek, where
R= rating of quarterback
D= yard per completion of the quarterback
T= touchdowns the quarterback thrown
I= interceptions the quarterback thrown
O= the completion percentage
ek= the error term
From the equation one gets to comprehend the successes in terms of the touchdowns, yards, and completion percentage while failures achieved through the interceptions when a quarterback is signed in a team. All the values are pegged on previous years
Equation 3:
Sl=fS(Xl, Yl, Zl , Cl, , Ll , Rl , Fl , Gl) + el , where

S= mean yearly salary
X= revenue accrued for team
Y= yearly total costs for signings (keen on talent degree of the team)
Z= wins signing team had
C= anticipation of pass completion (fitted value from Equation 1)
L= win-loss proportion during quarterback’s career
R= anticipated rating (fitted value from Equation 2)
F= Selection through peer recognition
G= Previous team winning NFL championship
el= the error term
From this equation there will be a correlation achieved between the salary of quarterback and the performance in the field as well as some measures of the team when signed.

Data Collection
The data that is applied in the study covers the duration of 1987 to 1993. The choice is mainly dictated by several occurrences in the same period that relate to NFL. Most of the happenings related to their salary and training environment. The data used for this study largely relied on the contract signings of each quarterback as identified in the newspapers.

Empirical Investigation
Equation 1:

Variable X Coefficient Standard Error t-statistic
Pass Attempts 0.598 0.020 30.428
Years in NFL 2.154 0.919 2.216

In the equation, 32 set of data was applied. The R2 is .919. The significance level for t-statistic for both variables (pass attempts and years in NFL) is at 5% level.
Equation 2:
Variable X Coefficient Standard Error t-statistic
Yards/Completion 2.009 0.406 4.952
Touchdowns 0.867 0.088 9.901
Interceptions -1.261 0.117 -10.819
Percentage Completed 144.271 12.016 12.007
A data set of 32 was used and the result was an R2 of .963 for t-statistic of all the variables at 5% significant level. The correlation statistic as determined by Durbin-Watson statistic was 2.01 hence no significant correlation.
Equation 3:
Variable X Coefficient Standard Error t-statistic
Team Revenue 0.076 0.029 2.572
Player Costs 0.027 0.022 1.213
Team Wins -0.135 0.099 -1.361
Completions 0.010 0.003 3.636
Career Win-Loss 5.186 1.90 2.733
Rating Previous
Year 0.016 0.020 0.787
Pro Bowl Selection 0.749 0.678 1.104
NFL Champions -0.031 0.806 -0.039
From the third equation, it is evident that a set of data containing 32 observations were used. The results show that the R2 at .731 with the t-statistics for revenue accrued by the team, the total passes completed, the performance of player in terms of losses and wins all at 5% significance level. The other variables had their t-statistics as not significant. Sign of NFL was negative even though the estimate was statistically insignificant. No statistical significance.

Sports Economic Policy
From the results that have been obtained one can reach the following statistical interpretations. First, the remuneration of the quarterback is mostly affected by the factors while on the field playing and to some extent by the variables that relate to where he or she gets a play contract. The variables are divided into two groups; players’ perspective and team’s perspective. What matters most from the side of the player is his or her record in terms of win-loss and the number of passes that the player completes in the previous season. From the results, it is shown that a player gets rewarded most when he or she has better completions and better win record.

The variables that affect the performance of a quarterback include his or her record in terms of win-loss and the number of passes that the player completes in the previous season. From the study, it is worth noting that it becomes so much difficult to cover the qualitative aspect of the study as much as it may also affect the outcome. Therefore, it is not within the scope of this study qualitative contributions. Even though variables such as courage and intelligence affect and are integrated among the factors, not much can be done as they are not measurable. As much as revenue may be a pointer or a factor in determining the salary of a quarterback, it is not clear to a specific player. The revenue may increase after a quarterback is signed but this could be due to several other factors. The causal relationships under this kind of circumstances would be difficult to define.
The successive efforts between different sections of the teams such as defensive and offensive may not warrant an indication on the level of salary earned by a quarterback. The victory of a team mostly relies on the coordination of the different sections and players but then that would not point to salary increment or reduction. The model applied captures the talent level of the players that support quarterback through the inclusion of player costs variable. The effect is that all the teams that pay their players well generally attract very talented players. Nonetheless, the variable was not statistically significant

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