What is a Blue Chip Recruit Worth? Estimating the Marginal Revenue Product of College Football Quarterbacks

Abstract

The National Collegiate Athletic Association has faced growing scrutiny due to the perceived disparity between the compensation athletes receive and their contribution to athletic revenue. Our novel use of college football game–level statistics shows a gap of millions of dollars between compensation and marginal revenue product (MRP) for elite quarterbacks, consistent with previous studies. Professional sports typically weight pay toward ex ante expected value of performance rather than incentives that pay ex post of performance. Using high school prospect rankings, we show ex ante estimates of elite quarterback expected MRP are substantially lower, roughly US$400,000, and have limited statistical significance with respect to winning or revenue. Our ex ante measurements suggest that expected player value may be closer to the value of scholarships than previous research suggests due to the difficulty in predicting which high school quarterbacks will excel in college.

Keywords

college football college sports revenue quarterback

Introduction

College football players spend nearly twice the amount of time on practice and conditioning as they do in the classroom (Jenkins, 2014). They are compensated for this effort with a grant for education, housing, and food. The National Labor Relations Board (NLRB) recently ruled that college football players should be considered employees of their university and therefore be given the right to unionize. This ruling, along with a growing belief that athletes are not compensated commensurate with their contribution, has motivated a call to increase compensation. The data trends support the idea of a growing gap, as National Collegiate Athletic Association (NCAA) football revenue grew 42% during our sample period from 2004-2012, while student-athlete compensation remained relatively constant. The NLRB ruling may signal the start of negotiations for players to receive better compensation in order to shrink this gap. Measuring compensation is fairly straightforward; however, due to the team nature of football, estimating players’ marginal revenue product (MRP) is challenging.

This study estimates MRP for college football quarterbacks from Bowl Championship Series (BCS) conferences.¹ We look specifically at quarterbacks because it is the most valuable position. From 2000-2014, of the 15 winners of the Heisman trophy,² 14 were quarterbacks. In the National Football League (NFL), quarterbacks are the highest paid position on average, and elite quarterbacks’ salaries represent up to about 8% of a team’s annual revenues, or 17% of the team’s player payroll (Becht, 2013). Our estimate of MRP for quarterbacks can be considered an upper bound for college athletes, since other positions are likely to be less valuable, and football generates the most revenue. The second reason we limit the study to one position is that performance data are more readily available for quarterbacks than other positions, which allows us to measure their contribution to team success more precisely.

We estimate MRP for an elite quarterback using a two-stage analysis, estimating first their contribution to wins and then the value of a win. The first stage of the analysis is performed both before and after the player’s college career. The ex post analysis uses a relatively new statistic called quarterback rating (QBR), which was created by Entertainment and Sports Programming Network (ESPN) and measures the quarterback’s contribution to winning based on his play. The ex ante estimate uses a quarterback’s ranking as a high school recruit to calculate expected contribution.

In the ex post analysis, we find that quarterbacks with average yearly ratings 2 SD above the mean season QBR were estimated to add roughly three additional wins per season over an average quarterback. In the second stage, we estimate the value of a win at US$740,000, including discounted revenues for the following season. Therefore, our main result is that an elite quarterback, one whose QBR is at least 2 SDs above the mean, has an estimated MRP of over US$2 million per season.

The ex ante analysis uses high school ability (as proxied by their ranking as a top 100 college recruit) to estimate future QBRs and winning percentage. Ex ante, we find that signing a quarterback with perceived high ability (based on high school recruiting ranking)—a “blue chip recruit”—adds roughly 0.3 wins per year in the third and fourth years after signing. Using the value of a marginal win (US$740,000), we estimate ex ante that signing a recruit identified as high ability is expected to add roughly US$429,000 over those 2 years. The substantially lower ex ante estimate reflects the fact that over a quarter of top quarterback recruits in our sample failed to record a qualifying game for the BCS schools that recruited them. These estimates provide a starting point for the expected value of blue chip high school quarterbacks. Furthermore, they show a gap between valuations that are performed ex post and ex ante, reflecting the inherent uncertainty in player evaluation.

Literature Review

Scully (1974) was one of the first to estimate MRP for athletes.³ He first estimated the effect of team performance statistics in Major League Baseball on total revenues and then weighted the team results by individual appearances to arrive at predicted player MRP (often referred to as the Scully method). He found that players were generally exploited to a large degree due to baseball’s reserve clause (in which player rights were retained by a team even after their contract had expired). Measuring the effect of individual players on team performance proved a difficult task without advanced metrics and statistics. Nevertheless, Scully’s work was extremely important and led the way for much of the research that has since followed.

Previous work has estimated the MRP of NCAA football players using ex post observations of NFL draft status, but statistical performance has not been used due to the difficulty in measuring an individual’s contribution in football. Brown (1993), Brown and Jewell (2004), and Brown (2010) used samples of NCAA Division 1 college football team revenue data to estimate a two-stage least squares model. The works first estimated premium-player rents by regressing the number of future professional league draftees (a proxy for premium players) on recruiting and market characteristics, then team program revenues on the number of players drafted, holding other factors constant. The MRPs were estimated at approximately US$500,000 for a premium player (a future NFL draft pick) in the early works and grew to US$1.1 million in later works, which added controls for team quality and additional data. These results far exceeded the estimated scholarship value of roughly US$25,000 (Huma & Staurowsky, 2012; Zimbalist, 2001). Other NCAA sports such as men’s basketball, women’s basketball, and men’s hockey appear to have a gap between MRP and compensation when using the draft pick measure, as shown by Lane, Nagel, and Netz (2012), Brown and Jewell (2006), and Kahane (2012), respectively. Finally, Brown (2012) added to this work by comparing player MRPs with expected NFL compensation to determine whether lost wages in college were outweighed by increased future earnings. He found that, generally speaking, they do not.

Our work provides two contributions to the previous literature. First, we strengthen the link between performance and estimated MRP. Second, we create a method for estimating the expected MRP for future NCAA athletes. Our use of QBR creates a continuous estimate allowing for comparisons of all quarterbacks, while previous works have focused on the discrete difference between drafted and undrafted players. Additionally, the NFL values some skills and attributes that may not reflect a player’s individual contribution to his team’s win percentage, as evidenced by Heisman trophy winner Jason White’s (Oklahoma, 2003) going undrafted and Troy Smith’s (Ohio State, 2006) not being drafted until the fifth round. Our second contribution is to create ex ante estimates of player value, and to our knowledge this article is the first to do so. Moving from an ex post evaluation to an ex ante measure of expected value is important, as Krautmann (1999) points out that contact negotiations typically take place before performance has been revealed.

Data

Metrics for “wins above replacement” (WAR) have been developed and used for over 20 years (Miller, 2013) to estimate the number of additional wins a player would contribute compared to a replacement player in baseball. Previous studies of college athletes’ MRPs have primarily focused on basketball and football, by far the biggest revenue producers in college athletics. Unfortunately, an adequate WAR-type statistic has not been historically available for these two sports. This makes MRP estimates difficult to obtain, though recent attempts have been made (Lane et al., 2012) in basketball. The main obstacle in developing a WAR-type statistic for football is that it is difficult to isolate an individual’s contribution to winning in team-focused sports. To bridge this gap, we use a player metric recently developed by ESPN for college football quarterbacks, which may resolve the issue of linking player performance to team win probability.

Total QBR

ESPN is a global sports and entertainment television network that reaches almost 100 million households in the United States alone (Sandomir, Miller, & Eder, 2013). In recent years, it has developed a specialized Stats and Information Group (ESPN Stats & Info). One of the first major analytic statistics it developed is total QBR. The historical NFL quarterback metric at the time, referred to as “passer rating,” had been found to be lacking in many ways.⁴ The metric measured only a few categories of quarterback performance, and, as the position evolved and included more multidimensional statistics, such as the ability to avoid sacks and run the football, passer rating became less and less relevant. QBR was introduced in 2011 for professional (NFL) quarterbacks, and the new metric had a stronger relationship to a team’s success than passer rating.

There have been earlier attempts at the NFL level to improve upon the traditional passer rating method. Berri (2007), Berri, Schmidt, and Brook (2006), and Berri and Simmons (2011) used regression analysis to develop a new rating that assigned weights to different outcomes such as yardage and turnovers. These measures, however, do not control for the contribution of other players to the outcomes (such as sack prevention and yards after the catch), while the QBR measure we utilize does. Additionally, Burke (2007) showed a 95% correlation between ratings using regression analysis (cited earlier) and the traditional passer rating at the NFL level.

The methodology behind the QBR for NFL quarterbacks estimates the team’s expected points added for each play and assigns a portion of credit to the quarterback, while also assigning a “clutch weight” based on the game situation (primarily used to de-weight plays that occur in a noncompetitive situation). After summing the plays of interest, they rescale the number to a range of 0–100 to arrive at the QBR. Over the course of 4 years and over 1,000 NFL games, ESPN found an 87% correlation with winning for games in which a team’s quarterbacks had a higher QBR than the opposing quarterback. This exceeds the correlation with the previous passer rating of 79%.⁵

In 2013, ESPN introduced the total QBR for college football, and they applied the new QBR to individual game data from 2004 onward to provide historical rating comparisons. They were able to utilize an enormous quantity of game data that had been previously captured, some of it using video-tracking technology. As Table 1 shows, a fairly strong correlation between QBR and winning appears to exist in college football as it does in the NFL. In analyzing a subset of our data, for games in which both teams had just one quarterback with a qualifying QBR, we find that the team with a higher QBR won about 83% of the time.⁶ The difference between the average QBR for a winning team (65.1) and a losing team (35.8) is statistically significant confirmed by means of a t test. The average QBR in our sample is 52.6 and the SD by game is 27.2. Of the 420 quarterback season observations (with at least 10 qualifying games), only 8 averaged above an 80 QBR over the course of the season.

Table 1.

QBR, Strength of Opponent, and Home Field.

	Mean		SD	QBR Distribution—# of Game Observations
	Mean		SD	0–20	20–40	40–60	60–80	80–100
QBR^a	52.64		27.20	1,059	1,409	1,502	1,501	1,413
	Win percentage			18%	36%	54%	75%	94%
	>25	21–25	16–20	11–15	6–10	1–5
Opponent rank^a	4,640	756	344	413	457	274
Observations (%)	67	11	5	6	7	4
	Mean
Home	0.53
Win	0.57

Note. QBR = quarterback rating.

^a N = 6,884.

Although we have QBR data for 94% of the potential games, the data we use for the game-level analysis are an unbalanced panel.⁷ The data set is unbalanced because of missing game observations, which occur because a quarterback might not have enough “action plays” to have a qualifying QBR (which require at least 20 action plays). We do not include game observations in which multiple quarterbacks on the same team had qualifying QBRs in the same game, since we have no way to allocate the impact of each of the quarterbacks on the game-level win probability.

There is a clear linear relationship between QBR and winning, as shown in Table 1. Therefore, we use a linear functional form to estimate the relationship between the two. The distribution of QBR ratings is relatively uniform, with slightly fewer QBR scores under 20. This could be because multiple quarterbacks are likely to be used in games with extremely low QBRs and there may not be a qualifying quarterback. It is also unknown whether ESPN intended the distribution to be completely uniform.

There are three potentially valid criticisms of the QBR measure.⁸ The biggest potential concern is that the QBR measure is biased by the quarterback’s teammates. That is, if having better teammates increased both QBR and the likelihood of winning, the estimated impact of QBR on winning would suffer from omitted-variable bias and overstate the effect of QBR on winning. In Appendix C, we test the relationship between offensive teammate quality and QBR. The tests support the use of QBR as a measure of ex post MRP, as a proxy for the number of high-quality offensive teammates is found to be unrelated to QBR. When we break out teammates by offensive position, we find fairly weak statistical evidence for higher quality wide receivers’ (WRs) improving a quarterback’s QBR. However, the estimated bias from omitting WRs is small relative to the variation in QBR. Additionally, other offensive positions (e.g., running back, offensive line, and tight end [TE]) do not appear to impact QBR. Given these findings, using the QBR measure seems appropriate, with an acknowledgment that there might be a slight upward bias due to the quality of WRs.

The second concern is that the formula is proprietary. Ideally, we would like to inspect the internal workings of the measure. In this article, however, we are less concerned with how the measure is constructed than with how it is associated with such outcomes as wins and team revenue. Third, QBR is composed of several statistics. It might be useful to know if two quarterbacks with the same QBR had differences in running ability, as this might matter for revenue if fans prefer teams with running quarterbacks. In that sense, we cannot look at different aspects of a quarterback’s ability that might impact revenue differently.

In addition to QBR, we use two variables to control for other factors that influence winning percentage: the strength of opponent and whether the game was played at the team’s home stadium. For ease of interpretation, we place the teams ranked in the top 25 on average⁹ during a season into five categories (top 5, top 6–10, top 11–15, top 16–20, and top 21–25), with teams not ranked all season omitted. It is also worth noting that 53% of the games were played at home, and this likely reflects the BCS schools’ paying non-BCS conference schools in order to host more home games. Similarly, BCS teams are better than non-BCS teams on average, therefore the average winning percentage in the sample is 57%.

Revenue

According to a 2012 report, the median Division I Football Bowl Subdivision (FBS) football program generated nominal revenue increased at an average annual rate of about 15% from 2004-2012, while the BCS conference revenues grew at an average rate of about 9% (Fulks, 2013). This growth is quite remarkable, considering that this period included the economic recession stemming from the 2007 financial crisis. The BCS conferences, which make up just over half of the teams in the FBS (the remainder are affiliated with other conferences or play as independents), are in especially good shape, with lucrative television network rights contracts in place through 2030 and beyond.

The most comprehensive source of institutional financial information currently available is managed by the Office of Postsecondary Education of the U.S. Department of Education. As required by the Equity in Athletics Disclosure Act (EADA), all postsecondary institutions that participate in federal student aid programs and that have an intercollegiate athletics program must submit annual financial reports, which are then made public via the EADA website. We compare a few of the EADA figures to those reported by USA Today & ESPN (separately obtained through Freedom of Information Act requests) and the NCAA (since the NCAA did provide outliers such as max revenue in their annual report) for total athletic department revenues and they appear to be consistent.

The reports from EADA do not provide a categorical breakdown of revenue within each program, but they do provide total revenue figures by school for each year as well as total athletic department revenue. Due to the inclusion of a revenue category entitled “not allocated by sport,” we construct a second version of revenue called “adjusted revenue.” We do this because different schools likely have different methods of allocating other revenue (for donations, etc.), and this other revenue may be correlated with the independent variables. In order to calculate this adjusted revenue total, we first determine the percentage weight of football revenue in terms of net total athletic department revenue. Then, we apply this weight to the not allocated by sport amount and add the result to the total football revenue to arrive at the adjusted total football revenue. Our revenue regression results are included for total revenue and total adjusted revenue. We use total revenue for our MRP estimate because the total revenue figures are more reliable and comparable between schools. Nevertheless, it is worth noting that we might be underestimating MRP because of this unallocated revenue.

There are currently 124 full members of the NCAA Division I FBS. However, there is a large disparity between the highest and lowest revenue levels. For this reason, we limit the schools used for our study to members of the “Big 6” BCS conferences: the Atlantic Coast (ACC), Big East, Big Ten, Big 12, Pac-12 (formerly the Pac-10), and Southeastern Conference (SEC).¹⁰ They are referred to as BCS Conferences because each of the conference champions receives an automatic bid to a BCS bowl game.¹¹ All of the conferences have at least 10 teams each year included in the data, except for the Big East (7–8 per year). The member schools of these conferences were fairly consistent over the period 2004-2012, with some notable changes in the last few years¹² but no major realignment. It is important to note that conference changes occurring in 2012 will not be reflected in the revenue regression results, as revenue data were available (at the time, this article was written) only for 2004-2011.

Like the game-level data, annual revenue is unbalanced panel data. First, because we account only for the BCS conferences, some teams are not included each year (i.e., if they joined or left a BCS conference between 2004 and 2011). Further, the EADA does not have data for the University of Maryland from 2005-2007.¹³ While the omission might not be completely random, only seven teams fit into this category, and the reason for missing years is strictly due to conference membership. In fact, four of those seven were included in all but 1 year because they joined the Big East in 2005. Therefore, we do not believe there is any bias.

The average inflation-adjusted football program revenue for the sample over all years is approximately US$32 million, with a fairly large variance (SD of US$18 million). The SEC had the highest average revenues for the 2011 season at US$54 million, while the Big East conference averaged only US$21 million that year. The largest outlier for the 2011 season was the University of Texas (of the Big 12 conference), bringing in US$103 million (partly due to the aforementioned Longhorn Network). Overall, average inflation-adjusted annual growth rates were fairly consistent across all conferences over the sample period, ranging from 4.3% (Big East) to 7.6% (SEC).

Blue Chip Prospects

We utilize data from the Rivals.com annual lists of top 100 prospects (inclusive of all positions), often called “blue chip” prospects, for teams from Big 6 conferences that signed blue chip quarterbacks from 2002-2009.¹⁴ Over the course of these 8 years, 64 quarterbacks were ranked on this list, but only 46 actually recorded a QBR for the team that signed them. In our sample, 16% of games were started by blue chip quarterbacks. As expected, blue chip–ranked quarterbacks who played outperformed others, with a QBR of 57 compared to 52 for those not ranked. This five-point gap is relatively small (around half a win in a 13-game season) as will later be shown in the results. This gap only applies to blue chip players who played and does not include the 18 players who did not contribute to their team.

One notable concern is that teams with blue chip quarterbacks may be historically better, thus be more likely to recruit a blue chip quarterback, so differences may reflect team quality. However, a comparison of average QBRs for a subset of schools that had at least one blue chip prospect during the sample period shows that QBRs for blue chip prospects are still 3 points higher than for non-blue chip quarterbacks (57 vs. 54) for the schools that had a blue chip quarterback during the period. Furthermore, as mentioned earlier, quality WRs may slightly bias the QBR measure. In Appendix C, we show that, on average, blue chip quarterbacks play with the same number of blue chip WRs, after controlling for team fixed effects. This supports our claim that the ex ante measure of quarterback quality is not biased by teammate quality, after we control for team fixed effects.

Econometric Framework

In this section, we present the four parts of our econometric analysis. The first three parts estimate a quarterback’s value based on ex post results and the fourth uses high school ability to proxy estimated ex ante value. In the first part, we estimate the contribution of a team’s quarterback to winning. In the second step, we estimate the value of a marginal win. In the third, we utilize the first two sets of results to estimate a quarterback’s marginal product. Finally, in the fourth step, we estimate the value of a high-ability player using his ranking as a high school recruit.

Step 1: The Win Probability Model

To calculate a quarterback’s MRP, we first need to estimate the relationship between quarterback performance and winning, while controlling for exogenous factors, such as the opponent and the game’s location. In a given season, t, team j plays G games. The equation we use to estimate win probability across j, g, and t is as follows:

P r (W_{g j t} = 1 | X) = β' X + ω_{g j t},

where $β' k X$ is

β_{0} + β_{1} Q B R_{g j t} + β_{2} O P P R N K_{g j t} + β_{3} H O M E_{g j t} + β_{4} T E A M_{g t}

The binary response variable W equals 1 if the jth team wins the gth game of season t. QBR represents the total QBR for the quarterback on the jth team in the gth game of season t.

For OPPRNK, we use five dummy variables for teams ranked on average 1–5, 6–10, 11–15, 16–20, and 21–25, using weekly BCS ranking data for the opponent in season t, with 1–5 representing the strongest opponent (an average BCS ranking in the top 5). A team ranked outside the BCS top 25 in each poll during that season has a 0 for all five dummies. HOME is a dummy variable equal to 1 for home games, excluding “home” games played at neutral sites. Finally, we run the model with and without TEAM fixed effects. The sample data for the win probability model consist of 6,884 game-level observations from 2004-2012 seasons.

To account for team fixed effects, we use dummy variables for all 68 teams. This can cause problems because of the potential for incidental parameters bias. However, we find similar results with and without team fixed effects.

Step 2: The Revenue Regression

The next step involves estimating the marginal revenue expected from an additional win. In a given season t, team j plays G games. The revenue of team j in season t is estimated as follows:

R_{j t} = α' Z + ϵ_{j t},

where $α' Z$ is:

\begin{aligned} α_{0} + α_{1} W I N_{j t} + α_{2} W I N_{j (t - 1)} + α_{3} C O N F_{j t} + α_{4} 7 H O M E G A M E S_{j t} + α_{5} Y E A R_{j} \\ + α_{6} S T A T E U N E M P_{j t} + α_{7} T E A M_{t} \end{aligned}

The continuous variable R equals the total football program revenue for the jth team in season t. As explained in the previous section, we include two versions of revenue in our regression results—total revenue and adjusted total revenue. In addition to WIN _t, the number of wins in season t, we add the number of wins in season t − 1, WIN _{t −} ₁. We include WIN _{t −} ₁ because a successful season likely has a large impact on a team’s revenues the following year, such as through increased season ticket sales. We assume that winning is linearly related to revenues, holding other factors constant. In order to ensure that marginal revenue for wins does not vary substantially between low- and high-revenue schools, we ran the regression separately for schools below and above the median revenue level and did not find statistically significant differences between the two groups.

Next, a series of CONF dummies are included to indicate conference affiliation.¹⁵ Many of the lucrative television network contracts are conference specific, and the teams benefit through revenue sharing. In fact, much of the conference realignment in college basketball and football the past few years is likely due to the financial incentives available to schools’ being offered membership in a richer conference. The 7HOMEGAMES variable is a dummy taking the value of 1 if the team had seven or more home games that season, 0 otherwise (since 89% of teams in the sample have six or seven home games). This is important because ticket sales represent a significant portion of annual generated revenues, and a difference in the number of home games impacts revenue. A YEAR dummy is included to account for the general growth in college football during the study period. STATEUNEMP, equal to the state’s unemployment rate in year t, accounts for non-football-related economic conditions in a team’s state. Finally, we run the model with and without TEAM fixed effects to control for any school-specific features that impact revenues and have not been accounted for elsewhere in the model.¹⁶ The results are fairly similar between the two models.

Step 3: Estimating MRP

The final step in the process is to estimate the MRP of an elite quarterback. To do so, we first establish the link between a change in a quarterback’s QBR and wins. The marginal effect of QBR on win probability changes based on the value of the other explanatory variables, so for our MRP calculation, we use the marginal effect of a change in QBR at the mean values of the other variables. The formula to estimate the marginal effect at a given level of QBR is:

P r (W = 1 | Q B R_{i}) = φ (β' X)

Next, we calculate the marginal effect between two values of QBR. Assuming the change is positive, the difference between the two probabilities is the increased probability of winning from the change in QBR. Then, we multiply this difference by the average number of games for a full season, G, to predict total wins added for that year:

M P_{t} = {\overline{G}}_{t} * [P r (W = 1 | Q B R_{i} = a) - P r (W = 1 | Q B R_{i} = b)],

where $0 \leq a, b \leq 100.$

To account for the effect of lagged wins on current MRP, we estimate the increase in revenue in seasons $t (α_{1})$ and $t + 1 (δ α_{2})$ , resulting from each additional win in season t by adding the coefficients from the revenue regression, discounting the lagged coefficient to account for this future revenue. Finally, we multiply the marginal revenue by the marginal product to arrive at MRP:

M R_{t} = α_{1} + δ α_{2},

where $δ = d i s c o u n t r a t e f o r t + 1.$

M R P_{t} = M R_{t} * M P_{t}

The MRP for a quarterback in season t is equal to the additional predicted wins multiplied by the sum of current (t) and discounted future ( $t + 1$ ) estimates of additional revenue per win.

As Kahane (2012) points out, an issue that can arise with this type of model is determining whether a fixed-effects or random-effects regression is appropriate. We utilized the Hausman test and concluded that the fixed-effects model is more appropriate.¹⁷ We include revenue regression results with and without team fixed effects and show there is little difference.

Step 4: Ex Ante Estimation

In this fourth step, we move from ex post estimation of value to ex ante estimation of expected value. Equation 7 shows the econometric model we use to estimate the relationship between having signed a blue chip quarterback (one rated on the rivals.com top 100 between 2002 and 2009) and observed team QBR. We also use this model to estimate the relationship between having signed a blue chip quarterback and win probability. For ease of exposition, we denote both dependent variables (QBR and win probability) as Y since the same independent variables are used.

In both cases, we use the same predictive variables as Equation 1, except we replace QBR with a series of binary variables (Top100QB) that equal 1 if a team had signed a blue chip quarterback recruit t − k years prior. In this case, k = 1 in the player’s first year of eligibility and k = 5 represents the fifth season in the case of “redshirting.”¹⁸ We also provide a reduced form of Equation 7 that combines the third and fourth years of enrollment into a single dummy variable, as those are the years a positive impact is shown. This variable captures the total impact of a top 100 quarterback. This reflects the point at which blue chip quarterbacks have an expected QBR above the average quarterback’s:

Y_{t} = α_{0} + α_{k} \sum_{k = 1}^{5} T o p 100 Q B_{g j (t - k)} + α_{6} O P P R N K_{g j t} + α_{7} H O M E_{g j t} + α_{8} T E A M_{g t}

One can examine the outcomes for blue chip quarterbacks at the individual level or the team level. At the individual level, we can examine all quarterbacks who had played enough to obtain at least one qualified QBR score and see how blue chip quarterbacks differ. However, this excludes any blue chip quarterbacks who never play in a game. Therefore, we also run regressions on the team where the variable for blue chip is coded as 1 if the team had signed a blue chip quarterback. By signing a blue chip quarterback, other quality quarterbacks may have signed elsewhere, and the team signing a blue chip quarterback who does not play may have been left with an inferior backup. In this case, we expect the value of a blue chip quarterback to be lower at the team level because we include teams that signed a blue chip quarterback, who did not record a QBR.

Results

Win Probability

The win probability probit regression results are summarized in Table 2. The estimate of the effect of QBR on win probability is statistically significant, and the positive sign on the coefficient is as expected, as a higher QBR should result in a higher win probability. At the mean QBR (52.6), an additional QBR point raises winning percentage by 1 percentage point. The QBR statistic is statistically significant at the 1% level, with and without fixed effects. It also is consistent with the descriptive statistics that suggest a similar one-to-one relationship.

Table 2.

Win Probability Model—Panel Probit Regression Results.

Variables	With Team Fixed Effects	No Team Fixed Effects
Variables	Pr(WIN)	Pr(WIN)	Marginal Effects^a
Total quarterback rating (QBR)	0.028 (0.001)***	0.028 (0.001)***	0.009 mean = 52.6
Home game dummy (HOME)	0.47 (0.04)***	0.46 (0.04)***	0.12 mean = 0.53
Average BCS OPPRNK = 1–5	−1.92 (0.13)***	−1.87 (0.13)***	−0.51 mean = 0.04
Average BCS OPPRNK = 6–10	−1.47 (0.08)***	−1.44 (0.08)***	−0.41 mean = 0.07
Average BCS OPPRNK = 11–15	−1.26 (0.08)***	−1.22 (0.08)***	−0.35 mean = 0.06
Average BCS OPPRNK = 16–20	−0.98 (0.09)***	−0.95 (0.09)***	−0.28 mean = 0.05
Average BCS OPPRNK = 21–25	−0.69 (0.06)***	−0.68 (0.06)***	−0.20 mean = 0.11
Intercept	Team dummy variables	−1.12 (0.07)***

Note. N = 6,884 Games. BCS OPPRNK = Bowl Championship Series opponent rank. Standard error is given in parenthesis.

^aMarginal effects are reported as averages.

***Significant at 1% level.

Overall, the model exhibits strong predictive ability in terms of wins and losses. In roughly 80% of the cases, the model correctly predicts a win, if Pr(W) > 50%, with similar results for losses; the predictive accuracy is only marginally improved with team fixed effects. The other control factors have the hypothesized impact. The positive sign of the coefficient on HOME is to be expected. Home teams are typically favored to defeat visiting teams in most sports, due mostly to the support of the home fans and comfort of not having to travel. Our results suggest home field advantage increases winning percentage by 12% points. The sign of the coefficients on the OPPRNK factor variables are also as expected, and the effect decreases as the opponent strength weakens ( $O P P R N K = 1 - 5 => O P P R N K = 21 - 25$ ). The best opponents (OPPRNK = 1-5) have a large negative coefficient, with a larger drop from 1–5 to 6–10 than between the rest of the opponent rank categories, showing that the truly elite teams (average of a top 5 ranking in season t) have a more substantial negative marginal impact on win probability.

Revenue Regression

The final piece of the ex post MRP equation is the marginal revenue estimate. The revenue regression results are summarized in Table 3. The coefficients on $W I N S_{t}$ and $W I N S_{t - 1}$ are statistically significant and the signs are as expected, as additional wins should result in additional revenue. An additional win is estimated to be worth approximately US$420,000, controlling for team fixed effects in the current year. Lagged wins have a slightly smaller effect (∼US$340,000) on current season revenues than current season wins, which holds with and without team fixed effects.

Table 3.

Revenue Model—Panel Regression Results.

Variables (in US$ millions)	With Team Fixed Effects		No Team Fixed Effects
Variables (in US$ millions)	Total Revenue	Adj. Total Revenue	Total Revenue	Adj. Total Revenue
Total season wins	0.42 (0.11)***	0.44 (0.13)***	0.50 (0.11)***	0.58 (0.14)***
Total season wins (lag)	0.34 (0.11)***	0.31 (0.13)**	0.41 (0.11)***	0.44 (0.14)***
Conference—Big 12	8.44 (5.36)	−0.93 (6.54)	12.22 (3.95)***	16.94 (4.54)***
Conference—Big Ten	11.91 (7.55)	−10.26 (9.21)	18.14 (4.15)***	19.95 (4.75)***
Conference—SEC	(omitted) ^a	(omitted) ^a	25.27 (4.35)***	27.81 (4.93)***
Conference—Pac-12	(omitted) ^a	(omitted) ^a	4.94 (4.17)	11.64 (4.78)**
Conference—Big East	2.87 (5.36)	2.35 (6.54)	−0.91 (3.71)	−3.29 (4.37)
Seven Home games dummy	1.07 (0.57)*	0.66 (0.69)	1.22 (0.58)**	0.94 (0.73)
Year = 2005	1.43 (0.90)	2.95 (1.10)***	1.42 (0.93)	2.95 (1.16)**
Year = 2006	2.55 (0.99)***	5.04 (1.20)***	2.41 (1.01)**	4.83 (1.27)***
Year = 2007	4.89 (0.97)***	6.87 (1.19)***	4.72 (1.00)***	6.60 (1.25)***
Year = 2008	6.07 (0.95)***	8.61 (1.15)***	5.84 (0.97)***	8.22 (1.22)***
Year = 2009	10.75 (1.47)***	13.76 (1.80)***	10.40 (1.49)***	13.12 (1.86)***
Year = 2010	12.00 (1.54)***	16.49 (1.88)***	11.65 (1.55)***	15.84 (1.94)***
Year = 2011	13.41 (1.39)***	16.16 (1.70)***	12.98 (1.40)***	15.40 (1.75)***
State unemployment rate	−75.36 (30.61)**	−100.16 (37.34)***	−71.65 (30.58)**	−92.20 (38.12)**
Intercept	20.50 (3.09)***	38.92 (3.77)***	12.30 (3.56)***	21.67 (4.20)***

Note. n = 515. SEC = Southeastern Conference. Conference dummy Atlantic Coast included in constant. Standard error is given in parenthesis.

^aSEC and PAC-12 conference dummies omitted because of fixed effects (no changes over t).

***Significant at 1% level. **Significant at 5% level. *Significant at 10% level.

As outlined previously, the MRP is calculated by multiplying marginal revenue by marginal product. Marginal revenue is a combination of the coefficients on wins and lagged wins from the revenue model, while marginal product is the difference in win probability between two values of QBR over a full season. For our sample, we find the increase in win probability between an average quarterback (QBR = 52.6) and an elite quarterback (QBR = 79.8), that lies 1 SD above the mean QBR over the course of a season. Using the estimated increased win probability of .25 over a mean number of games (12.5), we arrive at a marginal product estimate of 3.1 additional wins. The marginal revenue equals the coefficient on wins from the revenue regression plus a discounted lagged win coefficient. We use the total revenue version of the revenue regression model with team fixed effects. Applying a discount rate of 5% to the lagged win component, we find that the marginal revenue from an additional win is approximately US$740,000. Multiplying marginal revenue by marginal product gives us a MRP estimate of US$2.3 million for a 1 SD increase in quarterback quality. In Appendix C, we show weak statistical evidence that having elite receivers may bias this estimate upward, although the amount of bias is small relative to the variation in QBR. It is important to note that we have not estimated replacement player value. That is, this US$2.3 million estimate represents the marginal revenue produced by an elite quarterback over an average quarterback.

For the CONF dummies, we use the version with no fixed effects, since coefficient estimates for some conferences are not included in the fixed effects version due to static conference membership over the sample period. The results reveal a stark contrast across conferences, with large gaps between the SEC and Big Ten (over US$18 million) and the Pac-12 and Big East (less than US$5 million but with large variances)—these figures are in comparison with the ACC, which is the omitted category. Another interesting result of note is the adjusted revenue coefficient for the Pac-12. This indicates that they have large amounts of unallocated revenue, and thus football program revenue could be particularly underestimated.

The YEAR dummies show a general growth in revenues since 2004, and all but 2005 are statistically significant. The 7HOMEGAMES dummy, representing seven or more home games in a given season (vs. six or less), is consistent with the expectation that teams with an additional home game have higher revenue. Finally, the STATEUNEMP coefficient indicates some correlation between local economic conditions and program revenue, as an increase in the unemployment rate reduces expected revenue, with a 1percentage point increase in state unemployment, causing a decrease of roughly US$750,000 in revenue.

In this case, as opposed to the win probability model, team fixed effects do have some slight effect on the estimates. Because there is very little change in the conference structure during this period, the conference dummy effect mostly disappears when fixed effects are included. The year and unemployment variable coefficients are slightly larger with fixed effects, while the effect of wins (and lagged wins), and along with the home dummy, is smaller. For our final MRP calculation, we use the total revenue regression results with team fixed effects included.

Case Study: You Got Lucky

In 2009, Stanford redshirt freshman quarterback, Andrew Luck took over the starting reigns from incumbent Tavita Pritchard, who in the previous year won only five games with an average QBR¹⁹ of 47, slightly below our sample average of 53. Luck played 12 games in 2009 with an average QBR²⁰ of 71.2. Overall, he led his team to an 8-4 regular season record (they would lose their bowl game, but without Luck, as he was injured), just 1 year after they were 5-7 with Pritchard under center. Luck followed up his solid freshman season with an even more impressive sophomore year. He led the Cardinal to a 12-1 record, while averaging a remarkable 88.7 QBR over the course of the season. Luck played his final season at Stanford in 2011, finishing 11-2 and being drafted first overall in the following year’s NFL draft. During his three seasons playing for Stanford, the school’s inflation-adjusted football revenues increased at an average annual rate of 24%, much higher than the average annual growth rate from our sample over this time period (which is about 5%, inflation adjusted).

While Andrew Luck performed at an elite level over his final two seasons at Stanford, his story should be considered the exception and not the rule. Few quarterbacks in our sample had such remarkable seasons. As such, the ex post MRP estimate for an elite quarterback can be considered an upper bound for the position, as only eight quarterbacks in our sample averaged QBRs more than a single deviation above the mean (our proxy for “elite”) over the course of an entire season; Luck was the only one to have more than one such elite season. The chance of a team in our sample having one of these elite quarterbacks is less than 2%.

Estimating Quarterback Value Ex Ante

We present the results of both the individual estimates (a comparison between blue chip quarterbacks and all others) and the team estimates, which measure the effect on QBR and win probability for teams that signed a blue chip quarterback, regardless of whether he played. In our sample, 28% of the 64 blue chip quarterbacks in our sample never recorded a single QBR score for a team in a Big 6 conference.²¹

We first identify the level of experience at which blue chip quarterbacks have an above average QBR. In Part A of Table 4, we present a QBR regression at the individual level with dummies for blue chip quarterbacks in their first through fifth season after being recruited (which would include redshirt seasons, transfers, etc., as players have only 4 years of eligibility). The result is clear: blue chip quarterbacks peak in their fourth year of enrollment, which is typically their junior (if they redshirt as a freshman) or senior year. The increase in average QBR over a quarterback’s first 4 years indicates a positive relationship between experience and outcomes. The QBR increase of 6.34 points is meaningful, as it results in a 0.06 increase in winning percentage (0.79 wins per season) or US$555,000 based on the value of each additional win (calculated above). The third year of eligibility also shows a positive although not statistically significant impact on QBR. In the fifth year, the best players are likely already in the NFL, while quarterbacks starting in their first 2 years may lack experience. Moving on to the team-level analysis, because over one quarter of the top 100 quarterback recruits in our sample failed to register a single QBR, the impact of a blue chip prospect is smaller if we include both teams that signed and played a blue chip quarterback and those that signed but did not play the blue chip recruit.

Table 4.

Blue Chip Regression Results.

Key Variables	By Player			By Team
Key Variables	QBR	Pr(WIN)	Marginal Effects^a	QBR	Pr(WIN)	Marginal Effects^a
Part A: Blue chip effect on QBR and win probability by season (by QB and team)
First season	−10.46 (3.04)***	−0.250 (.17)	−0.075 (.050)	−1.29 (1.34)	−0.018 (0.074)	−0.005 (0.022)
Second season	−0.42 (1.77)	−0.070 (0.097)	−0.020 (.028)	−0.26 (1.24)	−0.189 (0.067)***	−0.056 (0.020)***
Third season	1.75 (1.56)	0.209 (0.089)**	0.062 (.026)**	0.87 (1.23)	0.095 (0.069)	0.028 (0.020)
Fourth season	6.34 (1.56)***	0.318 (0.090)***	0.094 (.027)***	2.89 (1.24)**	0.048 (0.069)	0.014 (0.021)
Fifth season	−3.01 (2.75)	−0.203 (0.144)	−0.060 (.043)	−1.84 (1.27)	−0.109 (0.070)	−0.032 (0.021)
Part B: Blue chip effect on QBR and win probability in third/fourth seasons (by QB and team)
Third/Fourth season	4.78 (1.20)***	0.305 (0.068)***	0.090 (.020)***	2.34 (1.02)**	0.090 (0.056)	0.027 (0.017)

Note. N = 6,884. QBR = quarterback rating. QBR: Included team dummies to account for team fixed effects (results not reported). Pr(WIN): Included opponent rank, home game, and team dummies (results not reported). Sixth season not included in results, as only one player from our sample had a sixth season (took 2 years off). Standard error is given in parenthesis.

^aMarginal effects are reported as averages.

***Significant at 1% level. **Significant at 5% level. *Significant at 10% level.

In part B of Table 4, we estimate the impact on the team’s QBR of signing a blue chip quarterback who would be in his third or fourth year of eligibility. We find a statistically significant increase in the team’s average QBR of 2.3. This causes an increase of about 0.023 in winning percentage, or roughly 0.29 wins over the course of a normal season, for a total of 0.58 wins over the third and fourth years (combined) from recruiting the blue chip quarterback. At a value of US$740,000 per win, 0.58 wins represent roughly US$429,000 in expected additional revenue. This 2-year total is lower than the individual results (US$555,000 in the fourth year alone), which reflects the fact that some blue chip quarterback signings do not pan out.

As a final check, we estimate the effect of signing a blue chip quarterback on team wins in the player’s third and fourth year of eligibility. The probit estimate shows the marginal effect of an added blue chip player 3 or 4 years after he signs is an increase in winning percentage of 0.027, which is not substantially different than the estimated impact above of 0.023. One difference is that the statistical significance disappears, which may stem from factors other than team fixed effects, the quarterback, the opponent, and game’s location.

Conclusions

To be sure, many factors influence both the outcome of a college football game and a quarterback’s performance. Nevertheless, the QBR developed by ESPN captures a quarterback’s performance and the impact it has on the team’s win probability with only weak evidence of bias. It also allows us to estimate a quarterback’s MRP by providing a statistical link between player performance and winning. Marginal product has historically been the most difficult part of the MRP equation to estimate accurately, and with QBR, we can have more confidence in our estimates because of the strong correlation between a quarterback’s QBR and the team’s win probability. We estimate that elite quarterbacks have a MRP of roughly US$2.3 million, although this may represent an upper bound based on the aforementioned weak omitted variable bias. We also find that quarterbacks ranked as top 100 prospects coming out of high school are expected to increase college football program revenues by around US$400,000 dollars over their careers compared to the average quarterback.

We might understate the MRP because other institutional benefits may not be captured by football program revenue. For instance, after a college has a successful season, it may have an increase in applications, potentially improving the quality of the student body. This was well documented after George Mason University made a surprise run to the Final Four of college basketball in 2006, with university officials reporting a 24% increase in freshman applicants (Carroll, 2008). Also, there may be an increase in alumni support stemming from athletic success. In September 2013, Texas A&M University reported that donations had reached a school record of US$740 million for the year, exceeding the previous high by 70% (Troop, 2013). While there were likely a variety of reasons for this, the fact that it came the year after Johnny Manziel won the Heisman Trophy should not be ignored.

On the other hand, we might overstate MRP on an ex post basis for a variety of reasons. First, we are looking only at the quarterback position and a quarterback’s success depends upon his teammates, as noted in Appendix C. If a quarterback has a highly skilled WR or running back playing alongside him, his job becomes much easier. While QBR does attempt to divide credit on each play to account for this, it might not fully account for teammates’ skill level. However, we find little evidence of this. Other team factors outside of the offense—defense, special teams, and coaching—might also have an impact on the quarterback’s MRP or on winning but not be accounted for sufficiently in the model. On the other hand, our ex ante estimates may be more precise if variation in outside factors is unrelated to quarterback quality.

Finally, more detailed financial data from NCAA member institutions would likely allow for a more precise estimate of marginal revenue. While this has been done before, most notably by the Indianapolis Star newspaper in 2006, it would be beneficial to have such highly detailed data covering many years and many schools. Hopefully, future work will address some of these issues.

Footnotes

Appendix A

Appendix B

Table B1.

Total Football Program Revenues.

	Inflation Adj. Revenues (in millions)		By Conference
	Mean	SD	ACC	BIGEAST	BIG10	BIG12	PAC12	SEC
2004	25.8	14.2	18.1	16.0	33.2	26.6	21.9	35.3
2005	27.3	15.4	19.0	16.8	35.8	26.8	23.3	38.0
2006	29.7	16.5	22.9	17.0	37.6	27.6	25.6	42.6
2007	32.2	17.6	23.1	17.8	40.5	32.7	27.3	46.1
2008	32.4	18.0	22.5	18.9	39.8	34.7	26.7	46.8
2009	34.3	20.1	21.9	19.7	42.5	37.1	25.8	53.0
2010	35.3	20.7	24.0	19.7	43.7	37.1	26.1	55.1
2011	37.0	20.2	27.5	20.7	45.7	38.9	29.9	54.0

Note. ACC = Atlantic Coast; SEC = Southeastern Conference. Program revenue data obtained via the Office of Postsecondary Education of the U.S. Department of Education (http://ope.ed.gov/athletics/).

Appendix C

Acknowledgment

The authors would like to thank Kevin Chamberlain for assistance with gathering the data for the project as well as Brandon Augustino, Scott Davis, and Samantha Romero-Duenas for their research assistance. Robert Gitter and Thomas Rhoads and seminar participants at Towson University and NAASE sponsored session at the Western Economics Association Meetings for comments on an earlier draft. All errors remain our responsibility.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

Notes

References

Becht

(2013). NFL’s average salaries by position. Sports Illustrated. Retrieved December 7, 2013, from si.com. http://sportsillustrated.cnn.com/nfl/photos/1301/nfl-average-salaries-by-position

Berri

D. J.

(2007). Back to back evaluation on the gridiron. In Albert

J. H.

Koning

R. H.

(Eds.), Statistical thinking in sport (pp. 235–256). Boca Raton, FL: Chapman & Hall/CRC.

Berri

D. J.

Schmidt

Brook

(2006). The wages of wins: Taking measure of the many myths in modern sport. Stanford, CA: Stanford University Press.

Berri

D. J.

Simmons

(2011). Catching a draft: On the process of selecting quarterbacks in the National Football League amateur draft. Journal of Productivity Analysis, 35, 37–49.

Bradbury

J. C.

(2011). What is right with Scully estimates of a player’s marginal revenue product. Journal of Sports Economics, 14, 87–96.

Brown

R. W.

(1993). An estimate of the rent generated by a premium college football player. Economic Inquiry, 31, 671–684.

Brown

R. W.

(2010). Research note: Estimate of college football rents. Journal of Sports Economics, 12, 200–212.

Brown

R. W.

(2012). Do NFL player earnings compensate for monopsony exploitation in college? Journal of Sports Economics, 13, 393–405.

Brown

R. W.

Jewell

R. T.

(2004). Measuring marginal revenue product of college athletics: Updated estimates. In Rodney

John

(Eds.), Economics of college sports (pp. 153–162). Westport, CT: Praeger.

10.

Brown

R. W.

Jewell

(2006). The marginal revenue product of a women’s college basketball player. Industrial Relations: A Journal of Economy and Society, 45, 96–101.

11.

Burke

2007. A better passer rating. Advanced Football Analytics. Retrieved March 15, 2014, from advancedfootballanalytics.com. http://www.advancedfootballanalytics.com/2007/07/better-qb-passer-rating.html

12.

Carroll

(2008, 2 24). ‘Flutie effect’ in final four. South Bend Tribune. Retrieved December 8, 2013, from southbendtribune.com. http://articles.southbendtribune.com/2008-02-24/news/26846560_1_patriots-coach-jim-larranaga-admissions-mid-major

13.

Fulks

D. L.

(2013). Revenues and expenses: 2004-2012—NCAA division I intercollegiate athletics programs report. NCAA Publications. Retrieved December 1, 2013, from ncaa.org: http://www.ncaapublications.com/productdownloads/2012RevExp.pdf

14.

Huma

Staurowsky

E. J.

(2012). The $6 billion heist: robbing college athletes under the guise of amateurism. A report collaboratively produced by the National College Players Association and Drexel University Sport Management. Retrieved December 1, 2013, from ncpanow.org

15.

Jenkins

(2014, 3 29). More questions than answers from NLRB ruling on Northwestern football players. The Washington Post. Retrieved April 1, 2014, from Washingtonpost.com, http://wapo.st/1jl6TWy

16.

Kahane

L. H.

(2012). The estimated rents of a top-flight men’s College Hockey Player. International Journal of Sport Finance, 7, 19–29.

17.

Krautmann

A. C.

(1999). What’s wrong with Scully-estimates of a player’s marginal revenue product. Economic Inquiry, 37, 369–381.

18.

Lane

Nagel

Netz

J. S.

(2012). Alternative approaches to measuring MRP: Are all men’s college basketball players exploited? Journal of Sports Economics, 00, 1–26.

19.

Miller

(2013). WAR is the answer. ESPN. Retrieved March 3, 2014, from espn.com. http://es.pn/Yj0xfO

20.

Sandomir

Miller

J. A.

Eder

(2013, 8 23). To protect its empire, ESPN stays on offense. The New York Times. Retrieved December 1, 2013, from nytimes.com: http://www.nytimes.com/2013/08/27/sports/ncaafootball/to-defend-its-empire-espn-stays-on-offensive.html

21.

Scully

G. W.

(1974). Pay and performance in major league baseball. The American Economic Review, 64, 915–930.

22.

Troop

(2013, 9 16). Texas A&M pulls in $740-million for academics and football. The Chronicle of Higher Education. Retrieved December 1, 2013, from chronicle.com. http://shar.es/11nqTd

23.

Zimbalist

A. S.

(2001). Unpaid professionals: Commercialism and conflict in big-time college sports. Princeton, NJ: Princeton University Press.