PERFORMANCE EVALUATION IN THE NFL: A STUDY OF PROFESSIONAL QUARTERBACKS
A THESIS
Presented to
The Faculty of the Department of Economics and Business
The Colorado College
In Partial Fulfillment of the Requirements for the Degree
Bachelor of Arts
By
Tyler Warren Fox
May/2008 PERFORMANCE EVALUATION IN THE NFL: A STUDY OF PROFESSIONAL QUARTERBACKS
Tyler Warren Fox
May, 2008
Mathematical Economics
Abstract
Previous research has shown the difficulty and inconsistency in drafting new talent into professional sports leagues, especially at the quarterback position in the NFL. This study attempts to determine what makes quarterbacks successful at the professional level and how to find these athletes in the NFL draft. The abundance of data in the NFL makes this investigation aptly suited for econometric analysis. This study incorporates a systems model to test the player, team, and coach specific variables that influence quarterback success. The implications of this research are valuable to NFL executives as they try to build a successful team around the quarterback position.
KEYWORDS: (National Football League, Performance Evaluation, Quarterbacks) ON MY HONOR, I HA VE NEITHER GIVEN NOR RECEIVED UNAUTHORIZED AID ON THIS THESIS
TABLE OF CONTENTS
ABSTRACT .. '" ...... 11
ACKNOWLEDGEMENTS ...... , ...... '" ...... , . .. IX
I INTRODUCTION ...... '" ...... " ...... '" ...... " . ... 1
II LITERATURE REVIEW ...... " ...... , ...... 3 Incentives for Success...... 4 Managerial Quality...... 6 Ability to Find Talent...... 8 The NFL Draft...... 11 The NFL Combine ...... " . .. 15 Non-NFL Scholarly Literature...... 16 Conclusion ...... , .... " . ... 19
III THEORy...... 20 Quarterback Success as a Production Function...... 20 Output Optimization and Deriving Demand...... 22 Theoretical Determinants of NFL QB Success...... 23 NFL Draft...... 24 Physical Attributes...... 25 Character...... 26 Intelligence...... 27 College Success...... 27 NFL Quarterback Success...... 30 Coach...... 31 Age...... 32 Rank of Opposing Defense...... 32 Rank of Team Defense...... 33 Rank of Team Offense...... 34 Offensive System...... 35 NFL Perfonnance Measures...... 35 Conclusion ...... " ...... 36
IV DATA AND METHODOLOGy...... 38 Data and Sources...... 38 Dependent Variables...... 40 Equations...... 41 Independent V ariab 1es...... 41 Player Specific Variables...... 42 Coach Specific Variables...... 44 College Player Specific Variables...... 44 Team Specific Variables...... 46 Methodology...... 47 Estimation Procedure...... 48
V RESULTS AND CONCLUSIONS...... 51 Two-Stage Least Squares Regression...... 51 Econometric Issues...... 53 The Coefficients...... 56 Fit of the ModeL...... 60 Conclusions ...... " ...... , ...... " . ... 60 Future Research...... 61 Implications...... 63
APPENDIX...... 64 SOURCES CONSULTED...... 70 LIST OF TABLES
4.1 Variable Definitions and Descriptive Statistics...... 48
4.2 Two-Stage Least Squares Instrumental Variables and Description...... 49
5.1 Two-Stage Least Squares Regression Results...... 52
5.2 Two-tailed Serial Correlation Test...... 55 LIST OF FIGURES
2.1 NFL Scholarly Literature ... , ...... , ...... " ...... 5
3.1 Detenninants of NFL Quarterback Success...... 24
3.2 Physical Make-Up...... 25
3.3 Collegiate Success...... 28 ACKNOWLEDGEMENTS
I would like to thank Professor Aju Fenn for his effort and advice throughout the entire process of senior thesis. Professor Fenn made my thesis experience productive and enjoyable, and continually pushed for new avenues of research. I would like to thank Robin Satterwhite as well for her assistance with formatting, citations, and research. CHAPTER I
INTRODUCTION
In the 2004 National Football League (NFL) draft, Eli Manning and Philip Rivers were the first two quarterbacks selected, with the first and fourth picks, respectively. I
Both players have made playoff appearances in their short careers, and Eli Manning already has a Super Bowl ring. It seems that these two quarterbacks are on a track for success. However, not all drafts have been this successful, with highly-touted college quarterbacks being busts in the NFL. Ryan Leaf, a great college player out of
Washington State, is now synonymous with bust in the football world. These two examples demonstrate the amount of inconsistency in the draft, making the ability to find talent all that more important, especially at the quarterback position.
Eleven players comprise an offensive unit in the NFL, yet none are deemed more important than the quarterback. He is credited for victories when the team wins, yet scrutinized on a national level when the team losses. The fate of a team lies in the hands of the quarterback, and with this responsibility comes great rewards and heavy burdens.
Optimization of quarterback success has long been a key concept for successful teams at the college and professional levels. Greatness and success occurs when a player produces in important situations and continually leads his team to victories. How he does this, however, varies from player to player based on their individual skill set and surrounding
I "NFL Drafts," Available from http://www.nfl.comldraftlhistory.
1 2 players. Because generating wins is a team concept, the quarterback's role is different depending on who he plays with and what abilities he brings to the field. There is no perfect model for finding great quarterbacks, but the goal is to get closer to a model that can predict success at the professional level. A great quarterback is essential because winning matters in the NFL on financial, social, and psychological levels. Winning
2 games has positive social externalities for cities, fans, players, and coaches. It also determines the tenure of head coaches and players' individual contracts.3 This paper will attempt to generate a quarterback success model based on the theory of the firm production function. Since several inputs, namely quarterback performance measures, go into final quarterback success or output, this is a logical connection between economic optimization and football production.
This paper will proceed as follows. The second chapter will discuss past and current research in the field of performance evaluation in sports. This review will bring the reader up to date on the literature relating to professional drafts, player production, and win optimization. Chapter three will present and discuss production theory as it pertains to firms and the NFL. The fourth chapter will explain the data set and the empirical methodology used to test the theoretical model. The final chapter will report the results and conclusions of this study, along with any limitations, and lastly develop the framework for future research.
2 Wladimir Andreff and Stefan Szymanski, ed. Handbook on the Economics ofSport, (Northampton, MA: Edward Elgar Publishing, 2006)
3 Gerald W. Scully, "Managerial Efficiency and Survivability in Professional Team Sports," Managerial and Decision Economics 15, no. 5, Special Issue: The Economics of Sports Enterprises (Sep. - Oct. 1994): 403-411. CHAPTER II
LITERATURE REVIEW
The purpose of this chapter is to review the literature on perfonnance evaluation in professional sports, specifically with regard to production in the National Football
League (NFL). The NFL is a business where job security is virtually nonexistent,! and each member of an NFL organization is expected to perfonn at the highest level in an effort to breed success. NFL coaches and staff are responsible for utilizing and motivating their players in order to win games. Players, in tum, must effectively execute their duties. When collegiate players are drafted into the NFL each year, competition for starting positions escalates, and players are forced to earn their spot on the team. The first section of this chapter discusses incentives for success and the motivation for player perfonnance. Next, managerial quality and the ability to discover new talent are outlined by reviewing published literature and discussing significant perfonnance statistics in the
NFL. Section three sheds light onto uncertainty in the NFL draft as well trends in the draft. Finally, the chapter concludes with a discussion of perfonnance evaluation measures in leagues other than the NFL.
I Gerald W. Scully, "Managerial Efficiency and Survivability in Professional Team Sports," Managerial and Decision Economics 15, no. 5, Special Issue: The Economics of Sports Enterprises (Sep. - Oct. 1994): 403-411.
3 4
Incentives for Success
The NFL is a billion dollar business that prevails as the most popular American
sport today. This success can be attributed to the fact that "many ofthe NFL's
fundamentals are similar to that of any other profitable firm or industry: its internal
incentives point in the right direction; it has had good leadership for a long time; it has
been lucky; and it has followed a sensible growth strategy.,,2 These fundamentals have
kept competitive balance in tact, revenues high, fans loyal, and most importantly, players
and teams striving for success. However, the NFL is the only league that does not guarantee contracts to players under the labor agreement. The reasoning behind this lies in the aggressive nature of football and the common occurrence of injuries. NFL owners are adamant about not guaranteeing contracts because they do not want to pay athletes who are not playing. Signing bonuses are the only form of guaranteed money, so if at any time management deems a team member ineffective, he can be cut and his contract and salary are negated. This means that players are in a constant state of anxiety over being cut for salary cap reasons or lack of production. Not only is quality performance essential in creating a grand legacy in the NFL, which is a strong incentive itself, but it is also important for their job security and financial well being.
Player contracts also include incentives for making the Pro Bowl, the equivalent of an NBA or MLB all star game. Financial bonuses, greater marketability, and higher exposure all come from performing at a top level and being selected for this game.
Additionally, each player on the winning team receives $30,000, while the losing team participants take home $15,000. Although this amount of money is small compared the payment players receive in their contracts, New Orleans special teams player Fred
2 "In a League of its Own," Economist 379, no. 8475 (04/292006): 63-64. 5
McAfee comments, "fifteen-thousand is $15,000. I don't care if you're a housewife or a
CEO ofa large company, $15,000 is $15,000.,,3 Financial incentives, along with personal
and team goals, motivate individual players to perform. It is important now to evaluate
performance, given a number of variables, to assess how individual players contribute to
a team.
FIGURE 2.1
NFL Scholarly Literature
Managerial Quality l Ability to Find Performance --" Talent Evaluation 1 The NFL Draft Trends 1 NFL Combine .. Scouting Ranking Players
3 "With Cash on the Line, Players Pick it Up a Notch," Associated Press Newswire, January 29 2003 2003, 6
Managerial Quality
Player and team success is often a function of the head coach's managerial
efficiency. The head coach is responsible for preparing and motivating his players,
strategizing, play calling, and most importantly, maximizing win percentage. The ability to translate player talent into points scored and team wins is the ultimate goal of management.
Hadleyet al. examine the efficiency of coaching in the NFL by analyzing data for all NFL teams from the 1969-1970 season up until the 1992-1993 season. Performance of NFL teams and head coaches is measured by Poisson regression estimates of offensive and defensive variables that contribute to team wins. Hadley et al. examine the mean performance index for the entire sample of NFL teams and conclude that efficient head coaches make significant contributions to team performance. More specifically, efficient head coaches can gain three to four more victories for a team given the same player talent as average head coaches.4 The paper also shows that more experienced coaches tend to be more efficient. It is clear that player performance and team wins are greatly affected by the coaching system and management.
The difference between the 2006 and 2007 Dallas Cowboys illustrates the effect of different coaching philosophies on team performance. It also demonstrates the pressure even the most adept and proficient coaches are under to win every year. Bill
Parcells led the team to an 8-8 record in the 2006 season, while his replacement, Wade
Phillips, led the team to a 13-3 record in 2007. Although no one rightfully doubts
Parcells' ability as a head coach, his style did not fit the team. Wade Phillips' laid back
4 Lawrence Hadley et aI., "Perfonnance Evaluation of National Football League Teams," Managerial and Decision Economics 21, no. 2 (Mar. 2000): 63-70. 7
approach and defensive tactics has clearly impacted the Cowboys in a positive way. Few
changes were made in personnel between the 2006 and 2007 campaign, and while some
may argue Phillips simply inherited a great team that Bill Parcells built, the results speak
for themselves.
Although Hadley et al. find more experienced coaches are more successful in the
NFL, there is one major exception. Experienced college coaches attempting to make the transition to the NFL have been far from successful: "a good coach might be a good
coach, but the currents of the NFL can make a good coach drift."s The NFL game is more complex, players are faster and stronger, and as Colt's President Bill Polian notes,
"It is a completely different game .. .It would take a college coach a year, maybe more, to get used to the league and the pace that is required at this level,,6. Additionally, the 'any given Sunday' mentality in the NFL, which is the attitude that any team can win against any opponent, puts added pressure on coaches to prepare teams to play at high levels every game. This outlook has far less weight in college as the parity is nothing compared to that of the NFL. Other prominent differences include longer seasons, roster limitations, and players who are stereotypically less coachable in the NFL. Players are set more in their ways, harder to mold, and have already established themselves as prominent players. NFL players have the millionaire superstar mind frame and it is oftentimes hard to adjust attitudes and egos. In college, the players are younger, need more guidance, and are usually more willing to buy into a coach's system or philosophy.
The differences in the game and player attitudes have made this transition difficult.
5 Dan Pompei, "Coaches: Look before You Leap to the NFL," Sporting News 229, no. 3 (01121 2005): 40- 40.
6 Ibid. 8
Grady Jackson, a defensive lineman for the Jacksonville Jaguars, notes, "it's going to be pretty hard now for someone to say, 'Let's give this college coach a chance.' You never know. Could he handle it? He was dealing with kids in college. Now, he's dealing with grown men.,,7 In fact, the results show that "of the past 15 NFL coaching hires who came directly from college jobs, nine had records below .500 in their first NFL jobs. Overall, their combined winning percentage was .467,,8. It is no wonder coaches like Bobby
Petrino, Nick Saban, and Pete Carroll all returned to college after short stints in the NFL.
It is clear from these examples that the coaching system and managerial quality can have a large influence on production in the NFL on a team and individual basis.
Ability to Find Talent
Allen St. John examines how productive NFL executives are in finding future stars. Ofthe 80 position players who made All-Pro teams since 2002, 44 percent were not drafted in the first round.9 This means, surprisingly, that almost every NFL team passed on these potential stars at least once. This implies that future superstars are available in the second and third rounds of the draft, so it is just a matter of finding them.
Joe Montana, perhaps the best quarterback of all time, was selected in the third round of the 1979 draft with the 82nd pick. Terrell Davis, a 6th round draft pick out of the
University of Georgia, had a brilliant career as a running back for the Denver Broncos.
Although some would argue any running back can rush effectively in the Broncos
7 "College Coaches Rarely Succeed in NFL - USATODAY.Com," [cited 2007]. Available from http://www.usatoday.com!sports/footbaI1J2007-12-13-4190722396_x.htm.
8 Pompei, Coaches: Look before You Leap to the NFL, 40-40.
9 Allen St. John, "Playing the NFL Draft," Wall Street Journal- Eastern Edition 249, no. 98 (04/272007): W9C. 9 system, no one has done it as well or as consistently as Terrell Davis did. He was a Super
Bowl MVP in 1997, rushed for over 2,000 yards in 1998, yet was drafted as the 196th pick in 1995. Potential superstars are evidently dispersed throughout all rounds of the draft and the free agent market, and although the earlier rounds usually produce more talented players, picking up a gem in the later rounds can make a monumental difference to a team. This is why NFL executives so heavily value scouting and why they are so attentive to activities such as the NFL Combine, individual workouts, and pro days.
Berri et al. examine player talent through a basic model of quarterback productivity. This study details the impact of a quarterback's performance on the overall outcome of a game and total points scored. Bern et al. use the relative value of yards, plays, interceptions, and fumbles lost to encompass an overall QB score. The QB score is calculated as All Yards - 3 x Plays - 50 x All Turnovers. \0 This measure incorporates factors that influence a team's offensive ability as well as defensive capability. Bern et al. use QB score, along with other commonly used measures, to assess how well quarterbacks contribute to a team. Although assigning wins and losses to quarterbacks is fairly common, this study shows that a quarterback's contribution is often overvalued.
Football is a team sport, and although no player has more responsibility than the quarterback, it is important to analyze surrounding players in evaluating team and player performance.
Boulier et al. evaluate the ability of football executives to identify and select promising athletes from the NFL draft. Boulier et al. use data from NFL drafts from
1974 through 1995, and use a variety of measures to determine the success of
10 David Berri, Martin Schmidt, and Stacey Brook, "How are Quarterbacks Like Mutual Funds," in The Wages o/Wins (Stanford, CA: Stanford University Press, 2006), 164. 10 quarterbacks and wide receivers. He compares the order in which they were drafted with their subsequent performance over the entirety of their careers.
The success of quarterbacks was measured by three indicators: number of years played, passing yards, and quarterback rating. The number of years played demonstrates how long a quarterback was able to perform at a high level as well as his durability.
Passing yardage, although somewhat a product of the offensive system a quarterback is in, is a strong indicator of overall contribution to a team. Finally, the quarterback rating is the prevailing determinant of efficiency, as it encompasses completions, yards per attempt, touchdowns per attempt, and interceptions per attempt. I I For the wide receiver position, performance was evaluated based on number of years played and pass reception yards.
The methodology for this study includes analysis of individual draft years as well as pooled draft data. Boulier finds support for his hypothesis that football executives, on average, are quite adept at recognizing talent. The regression results imply that managers can effectively rank both future performance of quarterbacks and wide receivers relative to other players at these positions. However, there is no perfect formula for predicting future performance and mistakes have been made. Many successful players are overlooked in the draft and many highly touted players are simply overrated. Ryan Leaf is the most notable example of a talented college quarterback who was drafted in the first round but never produced in the NFL. Ryan Leaf had a great college career at
Washington State, impressed scouts with his physical ability and athleticism, and was the second overall pick in the 1998 draft behind Peyton Manning. Leaf's time in the NFL,
II Boulier, Bryan and H. O. Steckler, "Evaluating National Football League Draft Choices: The Passing Game," Working Paper, Department of Economics. George Washington University, Washington, D.C. 11
despite his potential and optimism, was short-lived. His tendency to blame teammates
for his shortcomings, a series of injuries, and poor media relations cut his career short. A
12 panel of ESPN analysts even declared him the biggest sports flop from 1979-2004. It is clear that talent and potential stars are everywhere in the draft. It is just a matter of finding them.
The NFL Draft
There are seven rounds to the NFL draft, with a total of 32 teams selecting players. The draft order is determined based on the previous year's team performance.
The team with the worst record drafts first and the Super Bowl winner selects last. This format helps to maintain parity in the NFL by allowing less successful teams the right to the most talented incoming pool of players. When a player is drafted, he may only play for the team that has selected him unless his rights are traded or relinquished. If a player is not selected after the final round of the draft, he is considered a free agent and may negotiate with any team in the league.
Hendricks et al. examine the impact of uncertainty on the hiring process as it relates to the NFL draft. Their empirical work focuses on risk aversion and option value effects evident in different rounds of the NFL draft. The NFL draft is an opportunity to add new talent, make trades, fill positional needs, and most importantly, improve productivity and overall team performance now and in the future. However, every draft pick carries a certain amount of unpredictability. Individual teams spend large amounts of time and money scouting players, analyzing past performance, interviewing, and
12 "ESPN.Com - ESPN 25 - ESPN25: The 25 Biggest Sports Flops of 1979-2004," [cited 2007]. Available from http://sports.espn.go.comiespniespn25/story?page=listranker/25biggestflops. 12 administering a series of examinations to gauge player potential. This work is done in order to rank the available talent and select the best player for a team given its draft position. No matter what ranking system scouts use, only time will tell how ultimately productive a player will be. Hendricks et al. first use 1996 NFL data to conclude that risk aversion prevails in early rounds while option value becomes more important in later rounds of the draft. In other words, as the number of candidates who meet minimum playing standards decreases, choosing from a higher variance or riskier group becomes more attractive because of the chance of finding a star player. J3 However, when teams are choosing between two athletes in the opening rounds, the player from the more visible football program is generally selected because teams drafting tactics are risk averse.
If we examine trends in the NFL draft over the past ten years, the positions most likely to be filled in the first round have been cornerbacks and wide receivers, with 41 and 43 selections, respectively.14 NFL front offices, despite their attitude that games are won in the trenches, draft very few linemen and opt for players out on the flanks. Allen
Barra suggests this is because skilled cornerbacks are a rare commodity in the draft because college defenses rarely emphasize man to man coverage. IS Wide receivers get more exposure and plays in the highlight films. Note as well that these positions have more apparent performance measures than linemen, who are often not credited as much because it is difficult to assess their individual contributions. Dan Pompei, a senior writer
13 Wallace Hendricks, Lawrence DeB rock, and Roger Koenker, "Uncertainty, Hiring, and Subsequent Perfonnance: The NFL Draft," Journal ofLabor Economics 21, no. 4 (Oct. 2003): 857-886.
14 Allen Barra, "Crunchtime for Bonzo: The NFL Draft," Wall Street Journal- Eastern Edition 249, no. 96 (04/252007): D9.
15 Ibid. 13 of Sporting News, advises teams to give cornerbacks the cold shoulder during the draft.
He argues the cornerback position has been devalued with the way the NFL is now enforcing pass interference, and that elite cornerbacks no longer have a large advantage over average skilled corners. 16 Pompei also sites several instances where wide receivers dominate the alleged best cornerbacks in the NFL.
The 2006 draft presented some controversy as the Houston Texans took Mario
Williams, a defensive end from NC State, with the first pick rather than playmaker and
Heisman Trophy winner Reggie Bush. Bush was flashy, quick, and frequented the ESPN top 10 plays almost every week. Even despite the need for an all purpose back like Bush, the Texans opted for a defensive lineman predicted to make an immediate difference in the trenches. It is difficult to compare success at different positions, but when Bush and
Williams were compared to other players at their respective positions, Bush was more successful than Williams in their rookie years. This, however, was a function of the system Bush was in. He was not the featured back in his rookie year and was used more as a utility player like he was at USC. Bush lined up at several different positions to spread the offense and Deuce McCallister took the majority of carries. However, with
McCallister out this year, Bush was forced into the starting running back position, and although his individual rushing production was similar to the previous year, his receiving efficiency dropped off considerably and his team has suffered. The Saints had the same number of losses through Week 11 in 2007 as they did in the entire regular season in
2006. The Texans and Mario Williams, on the other hand, are having a much better year than in 2006. Part of this success is due to the emergence of Mario Williams as a great
16 "Offseason Advice: Pass on the Comers: Teams that Woo Cornerbacks Like Valentine's Dates Will End Up Heartbroken I Sporting News, the I Find Articles at BNET.Com," [cited 2007]. Available from http://findarticles.comlp/articles/mi_mI20S/is_6_229/ai_ n9770770. 14 pass rusher. After just 4 sacks throughout his entire rookie campaign, he already has 13 sacks through week 15 in 2007. These top draft picks illustrate two great points with regard to NFL performance. First, even the most highly touted rookies can struggle adjusting to the NFL yet still be successful in later years, and secondly, success is as much a product of individual skill as it is a function of the surrounding players and the system.
Sam Walker takes an overall look at the NFL draft and examines why so many draft picks become benchwarmers at the elite level. Top executives will often draft based on potential rather than on college performance. This is because, as Colts president Bill
Polian states, "The distance between the college and pro game has never been greater.,,)7
The college game is simply a different style of football than the pro game, and great college performers will often be flops in the NFL. Eric Crouch, for example, was the
2001 Heisman Trophy winning quarterback out of the University of Nebraska. He thrived as an option running quarterback in college and set numerous school and NCAA records; however, he was a better runner than passer and deemed too short to play quarterback in the NFL. He never started a game at quarterback and failed at an attempt to convert to wide receiver. Nonetheless, NFL scouts must not overlook players who fail to fit the mold of a prototypical quarterback, or any other position for that matter. People believed Joe Montana was too small, yet he is arguably the best quarterback the NFL has ever seen. To make educated selections in the draft, teams must rely on scouting and events such as the NFL combine.
17 Sam Walker, "Why the NFL is Drafting Benchwarmers," Wall Street Journal- Eastern Edition 247, no. 99 (04/28 2006): Wl-W6. 15
The NFL Combine
The NFL Scouting Combine, also know as the National Invitational Camp, is held every February to analyze the nation's top prospects for the incoming NFL draft class.
Players are chosen to attend the combine by a selection committee of scouting professionals, and the intent is to extend invitations to every player who is predicted to be drafted. Note however, that, many athletes have successful NFL careers without attending the combine. Top executives, coaching staffs, and medical personnel from all
32 teams are present to further evaluate the future NFL players. Athletes treat the four day event like a professional job interview as they showcase their skills and prove their worth to NFL teams. Players undergo several medical exams, along with physical workouts, position specific drills, mental and psychological tests, and interviews with team executives.
What do NFL scouts look for as they rank players and attempt to predict their success at the elite level? NFL scouts grade each player on position specific criteria as well as general standards, which include height, weight, speed, quickness, agility, balance, intelligence, strength, explosion, flexibility, character, and production. Scouts delve deep into these categories in order to fully examine player talent. For example, if a player is well below the average height at his position, scouts look at how he makes up for this deficiency in order to determine if it is a cause for concern. Pro Day workouts are another way NFL prospects showcase their talent. These workouts are held at the individual's university and usually produce better results because of the familiar setting.
Another test of player ability by McDonald Mirabile relates quarterback intelligence and both collegiate passing performance and rookie year NFL compensation. 16
Intelligence is measured by the Wonderlic Personell Test (WPT), a timed 50 question assessment that gauges an athlete's general cognitive ability. Mirabile hypothesizes that that high Wonderlic scores indicate greater quarterback success as well as higher rookie year compensation. IS This contention was empirically tested using data on 84 NFL quarterbacks drafted between 1989 and 2004. Ordinary Least Squares (OLS) regression analysis shows no statistically significant relationship between Wonderlic scores and collegiate passing performance, all other things held equal. 19 Additionally, no statistically significant relationship was found between intelligence and rookie year compensation. The 1998 NFL draft supports this assertion if we look at the careers of
Peyton Manning and Ryan Leaf. Manning and Leafhad similar Wonderlic scores (28 and 27 respectively), yet their football careers are polar opposites. Peyton Manning is arguably the best current quarterback in the NFL and tops many of the NFL's most prestigious passing categories, while Ryan Leaf struggled with several different teams and was out of football at age 25.
Non-NFL Scholarly Literature
Lawrence Kahn investigates the impact of managerial quality on team success and individual player performance in Major League Baseball. The paper uses data from 1969 through the 1987 baseball season to determine how managers convert player inputs into wins as well as improve player performance. The extensive collection of performance measures makes this study well suited for empirical investigation. Kahn cites multiple
18 McDonald Mirabile, "Intelligence and Football: Testing for Differentials in Collegiate Quarterback Passing Perfonnance and NFL Compensation," The Sport JournalS, no. 2 (2005)
19 Ibid. 17 papers, such as Mintzberg (1973), Porter and Scully (1982), and James (1984) to create a comprehensive break down of the role of executives.2o These functions include acting as a leader, liaison to those outside the organization, monitoring subordinates, disseminating information, and making critical decisions. In economic terms, "managers may enable firms to produce more efficiently and may improve information flow within the firm,,?l
In addition to encompassing all of the qualities listed above, baseball managers must specifically focus on opponent match-ups, lineup construction, defensive alignments, and timely player substitutions. Many characteristics of baseball managers can also be seen in business executives or NFL head coaches.
Kahn uses a market related approach that approximates managerial quality as a function of predicted salary. Predicted salary, which is used because only 1987 salary data was available, takes into account experience, winning percentage, and a dummy variable for league. Managerial quality is thus a measure of predicted salary standardizing for league. 22 This variable is then used in regression equations that evaluate team and individual performance. The effect of managers on team success, given player performance, measures the manager's strategic ability. Additionally, the effect of managerial quality on individual player performance relative to his career average captures the motivational impact of their leadership. Kahn concludes that managerial quality has a positive and significant effect on team winning percentages as
20 Lawrence M. Kahn, "Managerial Quality, Team Success, and Individual Player Performance in Major League Baseball," Industrial and Labor Relations Review 46, no. 3 (Apr. 1993): 531-547.
21 Ibid.
22 Ibid. 18 well as individual player performance. An implication of the study is that players may be willing to take a lower initial salary to play for a better manager.
Stephen Spurr analyzes the ability to find talent in the major league baseball draft.
He questions whether baseball success, as measured by a player reaching the majors, varies with position, across different baseball clubs, or with the level of schooling attained by the player. Data was used from the first baseball draft in 1965 until the 1983 draft. Like the NFL draft, selections are made in reverse order ofteam records in the previous season. Uncertainty plagues baseball as well, and to a much greater degree, as only 63 percent of players drafted in the first round from 1965 to 1985 eventually reached the major leagues. 23 Spurr finds no statistically significant difference between clubs in terms oftheir ability to find major league talent. The study also shows higher overall draft position and greater probability of reaching the major leagues if the player is in college, and better yet, attending an elite baseball program.
Berri et al. predict the NBA draft by examining the effects that specific performance statistics, college experience and competition, race, and physical attributes have on player draft position. Berri et al. determine which performance measures are rewarded and which are overlooked. Player productivity in the NBA is difficult to ascertain because the relative value of each performance statistic is hard to compare. Is one point worth more than one rebound? Previous literature suggests that although scoring consistently tops player talent evaluations, factors that influence number of team
23 S. J. Spurr, "The Baseball Draft: A Study of the Ability to Find Talent," Journal ofSports Economics 1, no. 1 (022000): 66-85. 19 possessions, such as rebounds and steals, are surprisingly trivial. 24 Berri et al. analyze these assessments using seven years ofNBA data from 1999 through 2005. He finds evidence that supports previous literature and concludes that above all else, college point scoring has the greatest impact on higher draft position. Assists and blocked shots were significant as well. Although these performance statistics differ from those in the NFL, this article illustrates the value of certain performance measures over others.
This sports literature shows that finding potential star athletes and managing them efficiently is a goal that extends beyond the NFL. The constant search for new talent exists in all sports as teams strive for future success.
Conclusion
This study will fuse elements of NFL literature as well as output maximization models to predict performance in the NFL. The purpose is to determine better drafting tactics based on what makes individuals and teams more successful at the elite level. The
NFL draft, and all job hiring processes, are filled with uncertainty and based on perceptions of talent by professional scouts. Minimizing this uncertainty is essential to building a stronger and more dominant NFL team in future years. The model will build on the methodology and research done by Berri et al. and Boulier et al. and attempt to better predict success in the NFL.
24 David Berri, Stacey Brook, and Aju Fenn, "From College to the Pros: Predicting the NBA Amateur Player Draft," Working Paper, Department of Applied Economics. California State University, Bakersfield, CA. CHAPTER III
THEORY
The purpose of this chapter is to explain the theory that accounts for quarterback success in the NFL. There are several different gauges of a quarterback's ability, yet predicting success in the NFL is still considered an inexact science. The first part of this chapter will analyze quarterback success as a classic production function. Next an output maximization model will be set up to derive demand for various success measures for quarterbacks in the NFL. Finally, the latter half ofthis chapter will discuss theoretical determinants of NFL quarterback success.
Quarterback Success as a Production Function
Analyzing the results of our quarterback production function will add further insight into reducing the uncertainty associated with picking a successful quarterback in the NFL. Both profit seeking firms and NFL teams demand high levels of production to attain the greatest levels of success. It is important to remember that like most firms,
NFL teams are concerned with hiring the best employees or players and applying their skills to help advance productivity and their efficiency. The typical production function of a firm usually takes on the following form:
20 21
Y=f(K,L) (3.1)
where output, or Y, is detennined by a specific combination of capital and labor. It relates the quantity of inputs, which are constrained by costs and availability, to the quantity of output produced. I
Modifying the classic production function to account for football perfonnance allows for an investigation into the nature of production by NFL players. The theory behind a finn's production function is actually quite similar to that of an NFL quarterback. It involves deriving the demand for a good, be it apples or quarterback output measures, and modeling that demand based on a number of variables affecting total production. Just as a finn uses its resources, such as labor and capital, to produce goods and services, an NFL team utilizes statistical inputs, such as touchdowns and team defensive ranks, to generate a measure of quarterback output. Although worker output measures are quite different in the business world and the NFL, the theory behind them has certain parallels.
The general fonn of a production function for NFL output might be specified as follows:
Success = f(NFL Players (-), NFL Coaches) (3.2)
where success is a specific measure of output or productivity. Success is dependent on the types of players and coaches in an organization. NFL player success is dependent on
I Gregory Mankiw, Essentials a/Economics, 3d ed. (Mason, Ohio: South-Western College, 2004) 22
several inputs are that are player, team, and coach specific variables. Like the firms
production function, a quarterback's function will also be subject to constraints outlined
in the next section on optimization. The production function draws on a deep
understanding of competition in the NFL as well as detailed player performance statistics.
Output Optimization and Deriving Demand
This section outlines output optimization and deriving demand for productivity based on certain cost constraints. The goal is to maximize output given cost constraints on NFL players and coaches. Given the production function as follows:
(3.3)
where Y is output, z is the numeraire good with Pz =1, XI represents NFL players, and X2 represents NFL coaches. The parameters of the production function are ai, a2, b, b l , and b2. The production function is subject to a cost constraint, where,
(3.4)
We set up the Lagrangian in order to determine the first order conditions of optimization.
These conditions are then set equal to zero, rearranged and manipulated, and finally used to determine the demand for NFL players and NFL coaches in terms of prices of the two goods. The first order conditions are as follows: 23
(3.5)
Once demand is found for Xl and X2, these equations can be plugged into the initial production function. A complete derivation can be found in the appendix.
Theoretical Determinants ofNFL QB Success
This section will examine the many factors that contribute to quarterback success in the NFL. Variables are included based on previous empirical research as well as personal knowledge ofthe sport. Figure 3.1 offers a graphical representation of the attributes and statistical categories that influence a quarterback's success. This study will incorporate a two-stage model. The first stage will use college performance measures, a conference dummy variable, and physical player characteristics to predict the NFL draft.
This NFL draft variable will subsequently be used to forecast NFL success in the second stage of the model. The theoretical reasoning behind the inclusion of each variable will be provided in the following subsections to specifically delineate each element of quarterback success. 24
FIGURE 3.1
Determinants of NFL Quarterback Success
Physical Character Intelligence College Attributes Success
NFL Quarterback Success Coach
Age
NFL Draft
The annual NFL draft is a chance for teams to make improvements and prepare for the future by selecting young talent from the pool of players. Great college 25
quarterbacks are usually highly sought after in the draft because of their potential to make
a positive and immediate impact on team success. Also, there are generally very few
quarterbacks in a given draft year with the ability to start in the NFL, making them highly
desirable commodities. The quarterback is arguably the most important position on the
field, as it is their responsibility to execute plays and lead the team to victory. A
quarterback's draft position reflects how well scouts and executives believe he will
perform in the NFL. In order to make educated draft choices, players are evaluated on their past performance as collegiate athletes, their physical make up, and by how well they perform at the NFL combine or on their respective pro days.
Physical Attributes
The physical make up of players entering the NFL has long been studied as one of the many indicators of future success. Although certain characteristics prevail across all positions, there are specific traits scouts look for at the quarterback position. Height and weight are important factors in assessing talent at quarterback.
FIGURE 3.2
Physical Make-Up
Height Weight 26
In the National Football League, taller quarterbacks have a distinct advantage
over smaller quarterbacks. Taller quarterbacks can more effectively see over their
offensive linemen and thus have better opportunities to read defenses and analyze
coverage. The ability to make quick and accurate reads is an important step toward
effectively executing the offense, completing passes, and making sound decisions.
Another advantage with greater height is that taller quarterbacks generally have less
passes tipped or batted down at the line of scrimmage. Although this is partially a matter
of the quarterback's delivery, being taller certainly helps. NFL quarterbacks tend to also
fall within a specific weight range, one that allows for enough mobility and quickness as
well as durability and toughness. The heavier end ofthe weight range is usually
preferable, especially if quickness is not compromised, because quarterbacks need to be
able to take hits throughout a game without sustaining injury. Heavier quarterbacks are
oftentimes harder to tackle as well and can fight through potential sacks to make plays.
This is not to say that smaller or lighter quarterbacks cannot be successful; rather, they must overcome their disadvantage through other skills, such as arm strength, vision, mobility, and leadership ability.
Character
The character of a quarterback in the NFL is an important determinant of his ability to be successful. As a leader of the team, the quarterback is responsible for motivating players, leading by example, and focusing his energy on team success. Off the-field issues can damage a player's reputation and negatively affect their performance on the football field. Distractions from football often hurt a player's focus and channel 27
unwanted attention to the team. Michael Vick is now the classic example of a talented
quarterback who let his team down by engaging in illegal activities outside of football.
Quarterbacks are interviewed as a part of the NFL combine so that NFL executives have
a better grasp of a player's character. Although it is difficult to measure character, a
quarterback with fewer off-the-field problems should perform better than one with
criminal charges or legal issues.
Intelligence
The intelligence of a quarterback has long been studied as an indicator of a quarterback's ability at the professional level. The Wonderlic Test, a timed 50 question exam that measures an athlete's general cognitive skills and basic knowledge, is used as a pre-draft gauge of a player's IQ. Because quarterbacks need to make quick decisions on the field in order to be successful, a player's intelligence should be highly valued.
Although higher scores should theoretically yield better quarterbacks, several sources cited in the Literature Review chapter show no correlation between the Wonderlic and player ability.
College Success
Past college performance is a prominent factor in determining how well quarterbacks will do as they advance to the NFL. NFL scouts evaluate potential draft choices largely on how they have performed in college, paying special attention to their final season before the draft. Although the college game is considerably different than 28 the NFL, and success in college by no means automatically translates to success in the
NFL, performance measures in college are important to evaluate because they showcase a player's ability to operate during pressure-filled situations. It is through college experience that quarterbacks are molded and shaped into professional league stars.
Figure 3.3 shows the specific variables that help determine collegiate success.
FIGURE 3.3
Collegiate Success
YP A Final Season CMP Final Season Conference
College Success
Each of the three variables represent different aspects of college football experience and success. Yards per attempt captures a quarterbacks efficiency as well as his overall passing performance. The number of completions a quarterback makes not only sheds light into his passing skills, but it also gives a glimpse of the of system the quarterback operated in at the college level. Lastly, the conference variable takes into account the level of competition and the pressure and exposure that comes from playing against the best collegiate athletes on the biggest stage. 29
Yards per attempt in a quarterback's final season is a measure of production in a
player's last year before the NFL draft. This measure illustrates a quarterback's
efficiency by incorporating every passing attempt into the statistic. A quarterback may
throw for a staggering 400 yards a game, but it may take him 60 passing attempts each
game to reach this total. The 400 yards a game is certainly impressive, but the number of
attempts discounts this total because of a lack of efficiency. Yards per attempt is also a
fairly strong gauge of throwing accuracy and arm strength. This statistic demonstrates
many aspects of a quarterback's passing capability and his overall ability to lead a
successful offense at the college level. Thus, we should expect strong yards per attempt
numbers to translate into some form of success in the NFL.
Players electing to leave college after their junior season are also included in the
yards per attempt statistic for their final year. Athletes must be three years removed from
high school to be eligible for the NFL draft. Although quarterbacks who attend all four
years of college are theoretically more prepared for the NFL because of their college
experience, players leaving early usually have great potential or talent that attracts scouts.
For this reason, this study contains data for final year yards per attempt from both types
of quarterbacks.
The second variable used as an indicator of college success is completions. This is measured as the number of total passing completions by a quarterback in his final season in college. Players that have high numbers of passing completions should theoretically be better fits in the NFL. Many college quarterbacks are excellent athletes, but prefer running the ball over passing. They can get away with this style in option oriented offenses that take advantage of their team speed relative to the defense. In the 30
NFL, however, quarterbacks cannot afford taking hits trying to run the ball. The athletes are so adept at their positions that the quarterback is simply responsible for getting them the ball and then letting them operate. Pocket passers who can scramble if necessary are the types of quarterbacks scouts look for. Therefore, it seems that higher numbers of completions translate to more confident and willing passing quarterbacks that can compete at the NFL level.
Lastly, a dummy variable for conference is used to distinguish the level of competition a quarterback faces in college. This variable will account for mid-major conferences as well as the six Bowl Championship Series (BCS) conferences. The BCS conferences include the ACC, Big 12, Big East, Big Ten, Pac-10, and the SEC. The mid major conferences include Division I FBS schools that are not apart of the BCS conferences, Division I FCS schools that play non scholarship football, and Division I
FBS independents.2 These conferences include Conference USA, Mountain West, Sun
Belt, Western Athletic, and the IVY league to name a few. The higher level of competition within the major conferences provides a better idea of how productive quarterbacks are when they face great oppositions. Great performances in the mid-major conferences should not be overlooked, yet certainly discounted for the degree of competition. This variable allows for just that.
NFL Quarterback Success
This study incorporates a model that will attempt to predict NFL quarterback success according to a number of variables. Quarterback success will be measured by
2 Notre Dame is considered an Independent in NCAA football. However, they are still eligible for BCS bowls and are thus treated as a major conference school. ' 31
number of wins in games played. The variables attempting to explain quarterback
success include NFL draft position, which is accounted for with physical characteristics
and college statistics, as well as variables relating to coaches, age, opposing and team
defensive ranks, offensive team rank, and various quarterback performance measures in
the NFL.
Coach
Coaches in the NFL are responsible for developing player talent and giving teams the best opportunities to be successful. Even the best coaches have their jobs on the line
every year because the demand for success in the NFL is so high. As quarterbacks enter the NFL, coaches playa pivotal role in helping them learn the offensive system, understand different defensive coverages, and make a smooth transition into the NFL. As noted earlier, the college game differs heavily from the professional level because the strategies are more complex and the players are more experienced. Coaches must help quarterbacks adapt to this new style of play while still utilizing the player's talent in the most effective way. Whether a head coach is more of an offensive or defensive specialist is irrelevant, yet his ability to lead a team to victory is significant. More successful coaches, as measured by career winning percentage, are more likely to produce more wins and better players. 3 Theoretically, successful coaches should produce successful quarterbacks.
3 Gerald W. Scully, "Managerial Efficiency and Survivability in Professional Team Sports," Managerial and Decision Economics 15, no. 5, Special Issue: The Economics of Sports Enterprises (Sep. - Oct. 1994): 403-411. 32
Age
When quarterbacks are drafted into the NFL, few are expected to start right away
while many others will not see their first NFL snap for several years. It takes time to
develop the skill set necessary to perform at high levels in the NFL. Players need time to
adjust to life as an NFL player, learn the offensive system, improve technique and
strength, and gain valuable insight from veterans. Every added year of experience is a
form of increasing human capital in the NFL. Age is simply another measure of
exp.erience, and should be an important factor in examining the success of quarterbacks.
Older quarterbacks should theoretically be more successful because they have more
experience at the professional level. However, at some point in their careers,
quarterbacks skills begin to deteriorate. Around this time, many quarterbacks retire and
leave football at the top of their game, so we can still theoretically say that older
quarterbacks are more successful than younger ones.
Rank of Opposing Defense
When analyzing any performance measure of a quarterback, whether it is
quarterback rating, touchdowns, interceptions, or passing yards, we must factor in the level of competition he faces. The opposing team defense can have a major affect on the way a quarterback performs. Some quarterbacks may produce huge numbers against lowly ranked defenses, yet cannot perform at the same level when challenged by the better defending teams. Better defenses put the. quarterback under more pressure, disrupt the flow of the offense, force faster decisions, and make executing plays more difficult.
Thus, the true measure of a successful quarterback is when he can perform against the 33
best defensive teams with a certain amount of consistency. Just as the competition levels
vary between conferences in college football, they vary as well among defensive teams in
the NFL. Defensive ranks in this study are measured by total points allowed. By
including this variable, quarterback performance becomes a relative measure of the
strength of his opponents.
Rank of Team Defense
They say offenses wins games but defenses win championships. In the NFL,
although offenses get the most credit for scoring points, defenses are usually a crucial
element in generating these scoring opportunities. Defenses can have a major effect on the outcome of a game by putting the offense in great field position or by making a key interception, fumble recovery, or tackle. Great defenses also allow the offense more chances for success. By continually stopping the opposing offense, the defense generates more possessions for the quarterback to make plays. Having a great defense can also relieve the pressure a quarterback is under by setting up easy scoring chances or shutting out the opposing offense. Quarterbacks will make mistakes, but if they have a good defense to back them up, they will usually be more successful. Conversely, if a quarterback has a less than average defense, he must operate under more intense pressure because he knows that any mistake he makes could cost the team points. Accounting for the rank ofthe team defense gives a better representation a quarterback's ability to perform and be successful. 34
Rank of Team Offense
The offensive rank of a team has a major impact on a quarterback's ability to
produce in the NFL. A quarterback simply cannot be successful without the support,
talent, and ability of his other offensive players .. The offensive line, arguably the greatest
contributor to a quarterback's success, is respoI)sible for protecting the quarterback and
allowing him sufficient time to complete passes and make accurate throws. Additionally,
the offensive line blocks for wide receivers and quarterbacks on specified plays, such as
screens or quarterback draws. More regularly, however, they create running lanes for
tailbacks and fullbacks to successfully penetrate the defensive front. The successes of running backs, in tum, also contribute to a quarterback's performance. First, a solid running attack sets up play action fakes, which when successfully executed, can result in huge plays for the offense. A good running game also puts pressure on the defense to bring more players up to the line of scrimmage. This allows for more one-on-one match ups for receivers, who theoretically have better chances of performing when in isolated coverage. Better receivers also make the quarterback's job easier because they can often make errant throws into competitions. The combination or synergy ofthese positions leads to a complete offensive package. The offensive rank is measured as total points scored. 35
Offensive System
There are several different offensive systems in the NFL, notably the West Coast,
Air Coryell, Run and Shoot, and Erhardt-Perkins offenses.4 Depending on the type of
system used, quarterbacks may have more opportunities for success. For example, the
West Coast offense is built around short, accurate passing plays that rely on quick-
thinking and timing by the quarterback; however, the Erhardt-Perkins strategy relies
heavily on the running game to set up pass plays.5 It is clear that the offensive system
could affect a quarterback's performance simply by the number of passing plays that are
called.
NFL Performance Measures
Several NFL performances measures for quarterbacks will be included in the
theoretical model. These statistics are a direct result of how well a quarterback is
performing on the field. Unlike many other measures which indirectly influence a
quarterback, these numbers give an accurate assessment of his actual production. Yards
per attempt, just as it is in college, is a strong measure of efficiency on passing attempts.
The greater this value, the better a quarterback is performing and running a strong
offensive system. Touchdown percentage, or the number of touchdown throws per passing attempt, should theoretically boost a quarterback's success the higher its value.
Interception percentage, on the other hand, hinders a quarterback's success. By turning the ball over to the opposing team, a quarterback is putting his team in a compromising
4 "American Football Strategy," Available from http://en.wikipedia.org/wikilAmerican_football_strategy#Specific _offensive_strategies.
5 Ibid. 36
position. Ball control is a huge part of not only individual success, but team success as
well. Sack percentage, which is the number of sacks when attempting to pass, is another
variable that should theoretically impact a quarterback's success. The more often a
quarterback is sacked, the more likely he is to make mistakes trying to rush throws or
elude defenders. Higher sack percentages also increase the likelihood of injury, which
can severely alter a quarterback's ability to be successful. All of these NFL statistical
measures will be incorporated into a model that predicts certain measures of quarterback
success.
Conclusion
This chapter has provided the theory behind a quarterback's ability to perform in
the NFL. Modeling quarterback success as a classic production function allows for an
output maximization model that can derive demand for success. The theoretical
determinants of NFL success will be tested in the chapters to come. Specifically,
touchdown percentage, yards per attempt, career win percentage of head coach, and the
average rank of defenses faced should all be positively correlated with strong NFL
quarterback performance. Interception percentage, team defensive rank, draft pick, and
sack percentage should all impact quarterback success negatively. Lastly, the relationship between quarterback success and age is inconclusive. The empirical model in the following chapter will be used to test the hypotheses regarding each ofthese independent variables. 37
This concludes the discussion of the theoretical detenninants of NFL quarterback success. The next chapter will give a thorough description of the data set, sources, and econometric techniques used to estimate the final regression equation. CHAPTER IV
DATA AND METHODOLOGY
The purpose of this chapter is to discuss the data set that will be used to empirically test the model that was outlined in the Theory Chapter. Each variable included in the regression model will be addressed in this section, including the source and reliability of the data. After reviewing the data set, the empirical model will be constructed and the methodology used to test the model will be explained. The outcome of the empirical tests will be presented in the Results and Conclusions Chapter.
Data and Sources
The empirical model will be tested using a pooled data set that has been collected for quarterbacks in the National Football League for the 2002 through 2007 NFL seasons.
The data set includes all quarterbacks who played during at least one season and threw a minimum of 100 passing attempts during the regular season. I Quarterbacks from all 32
NFL teams are accounted for in this study. No figures for pre-season or postseason play are included, however, as the data set uses statistics gathered from the regular season games each quarterback competed in. Annual summaries of each statistic are then used in the regression equation. Starting quarterbacks, back-ups, and even third string
I 100 passing attempts qualified for inclusion in the data set because this number was used by other sources and demonstrates that a quarterback is playing a prominent role in the offense in a given season.
38 39 quarterbacks are accounted for, with passing attempts being the minimum standard for inclusion in the data set. College performance data is also included for each player's final year in NCAA football.
Statistics and player information on each quarterback were collected from pro football reference2 and the ESPN College Football Encyclopedia. 3 For the few quarterbacks who attended smaller colleges, data for their final year performance was gathered from various online sources.4
From 2002 through the 2007 season, 273 observations were collected in the data set for 100 different quarterbacks. The variables used for the study include: win percentage in games played, age, touchdown percentage, interception percentage, yards per attempt, sack percentage, team defensive ranks, coach career winning percentage, average rank of opponents defense, draft pick, college conference, college yards per attempt (final season), college completions (final season), height, and weight.
This study will use a two-stage least squares technique to evaluate the empirical model. Thus, there will be multiple dependent variables will be explained in the next part of this chapter. This is because the two stage procedure will first estimate fitted values for a dependent variable that will subsequently be used as an independent variable.
2 "Pro-Football Reference.Com," Available from http://www.pro-football-reference.coml.
3 Michael Maccambridge, ed. ESPN College Football Encyclopedia, ESPN, 2005)
4 Information was gathered from several different online pages, including college pages, yahoo, and espn. 40
Dependent Variables
The first dependent variable for quarterback success, wpctgp in equation 4.2, is the win percentage of a quarterback in games played. Win percentage is a strong measure of a quarterback's productivity. Although many other players contribute to wins, the quarterback takes on the most responsibility during a game. It is his duty to lead the team to victory, control the offensive possessions, and ultimately score points for the team. Because all quarterbacks in the data set did not play in every game during a given season, game logs from pro-football reference were consulted to determine outcomes of games in which the quarterback had at least one passing attempt.
The next dependent variable comes from a model that attempts to predict the NFL draft. Drfpick, which appears in both equation 4.1 and 4.2, is the pick a player is selected with in the NFL draft. It appears in both models because the two-stage least squares regression technique is employed to test the theoretical model. This estimation procedure is explained in more detail in the latter part of this chapter.
The order of selection in the draft is predetermined by the previous years winning percentage. Trades, however, can alter the number and position of draft picks a team has in each round. The total number of draft rounds has changed throughout the history of the NFL. From 1977 to 1992, selection of draft picks lasted through 12 rounds. This changed in 1993 to 7 rounds and has stayed that way ever since. The change in number of rounds also altered how many players were selected in the draft. Currently, 255 selections are made through the 7 rounds ofthe draft,S so all undrafted players in the data set are therefore assigned a numerically value of 256 for drfpick. Players drafted before
1993 who were also selected past pick 255 are also entered as selection 256. Doug
5 "NFL Drafts," Available from http://www.nil.comldraftlhistory. 41
th Flutie, for example, was drafted in the 11 th round of the 1985 draft with the 285
selection. He is treated as an undrafted player by today's standards and is entered in the
data set as a 256th pick.
Equations
DrjPick =c+ /30 Height + /31 Weight + /32ConjDummy + /3 CmpFyc + 3 (4.1) /34YrdPerAttFyc + 8 0
WinPctGp =c + aoAge + a1TdPct + a 2IntPct + a 3YrdPerAtt
+ a 4DejRank + asOppAvDejRank + a 6DrjPick (4.2)
+ a 7 SkPct + agCarWinPct + 8
Independent Variables
The majority of independent variables used in this study are player specific for both college and the NFL, along with coach and team specific variables as well. Player specific variables include age, yards per attempt, and touchdown percentage to name a few. The coach specific variable captures the career winning percentage of the head coach. Team specific variables relate to offensive and defensive ranks. 42
Player Specific Variables
The first player specific variable in equation 4.2 is age. This variable simply
determines how old a player is during a given season. It is a measure of a quarterback's
experience in the NFL and generally shows how long a player has had to make the
transition into the NFL. The older a quarterback is, the more time he has had to learn
offensive systems, practice reading defenses, an get an overall feel for the speed of the
professional level. On the other hand, as quarterbacks age past their prime, their skills
diminish and their productivity and win percentage usually fall. Thus the expected sign
is inconclusive on the variable age.
The next player specific variable is yrdperatt in equation 4.2, which is the yards per passing attempt for each quarterback included in the data set for each season. It is
calculated by dividing total passing yards by the number of passing attempts. This
statistic is a measure of a quarterback's efficiency and productivity over a season. It takes into account every passing attempt by a quarterback, and thus captures how well a quarterback performs, on average, on any given passing play. The expected sign for this variable is positive, as higher values of yrdperatt demonstrate better quarterback performance.
Percentage of touchdowns thrown when attempting to pass, tdpct in equation 4.2, is another variable that appears on the right-hand side of the regression equation. This is the number of touchdown passes divided by the number of passing attempts times 100.
Like yrdperatt, this statistic is another measure of efficiency for NFL quarterbacks. High values for touchdown percentage means the quarterback is consistently able to lead his team on successful offensive drives. It is another variable that should be positively 43
related to success measures. This statistic also speaks to how well a quarterback can read
defenses and learn an offensive playbook. If a quarterback is reading defenses well and
knows his receivers precise routes, he should generate high values for touchdown
percentage.
Another player specific explanatory measure, intpct in equation 4.2, is the
percentage of interceptions thrown when attempting to pass. Interceptions are costly
turnovers in the NFL and are expected to be negatively related to a quarterback's success.
This measure is calculated as the number of interceptions thrown divided by the number
of passing attempts times 100. It shows how likely a quarterback is to tum the ball over when passing the ball. The lower these values, the better a quarterback is controlling the ball, reading defensive coverages, and communicating well with his receivers.
Although drfpick is also used as a dependent variable, it is used in the final regression equation as an independent variable. Lower numbered draft picks are
expected to perform better in the NFL, and therefore are predicted to have better success than higher numbered draft picks. The expected sign for dr/pick is therefore negative.
See the dependent variable section for further explanation.
The percentage of times a quarterback is sacked when attempting to pass, Skpct in equation 4.2, is another independent variable in the regression equation. It is calculated as the number oftimes sacked divided by the sum of total pass attempts and number of times sacked, all multiplied by 100. Sacks do not count as passing attempts, so to accurately generate Skpct, the equation must include times sacked in the numerator and denominator. This variable demonstrates a quarterback's elusiveness and the quality of his offensive line and blockers. Lower values of Skpct usually translate into higher levels 44
of quarterback success because better blocking and elusiveness allow the quarterback
more time to make passes and breakdown the defense. Thus this expected sign is
negative.
Coach Specific Variable
The carwinpct independent variable in equation 4.2 is a coach specific measure of
a head coach's career win percentage prior to a given season. This is measured as total
number of wins going into an NFL year divided by the total number of games coached
before that year times 100. Coaches that had no prior work as an NFL head coach were
assigned a value of zero. For teams that changed coaches mid-season, an average head
coach career win percentage was calculated between the newly hired coach and the
recently fired coach. More successful coaches should theoretically produce better players
and more wins, making this expected sign positive.
College Player Specific Variables
The data set also includes player specific variables from a quarterback's final
season performance in NCAA football. Height and Weight in equation 4.1 are
independent variables that take into account players physical characteristics. Coaches
prefer taller quarterbacks so they can see over the offensive line, read defenses, and
decrease the number oftipped balls at the line of scrimmage. Height is therefore expected to be positively related to draft position. Weight, on the other hand, is a bit inconclusive. In the NFL, quarterbacks must weigh enough to take hits, but they also 45
must maintain their agility to avoid pass rushers. The variable weight could be either
positively or negatively related to draft position.
The next explanatory variable for draft position is confdummy in equation 4.1.
This dummy variable factors in the differences in competition between major conferences
and mid-major conferences. Quarterbacks who competed in the 6 major BCS
conferences are entered in as a value of 1. Players from mid-major conferences are
entered as a value of O. Quarterbacks who face greater competition in college are usually
deemed more ready for the NFL by scouts and executives. The expected sign for
confdummy is negative because quarterbacks in major conferences are usually drafted
earlier than mid-major quarterbacks.
The last player specific college variables include measures of quarterback productivity in their final season. CmpfYc in equation 4.1 is the number of pass completions a quarterback has in his final year of college. The number of completions is preferred to completion percentage for predicting draft order because of the nature of
NFL football. In the NFL, quarterbacks are expected to be pocket passers who run very few running plays throughout a game. In college, many quarterbacks are option runners and can utilize their speed more effectively with the slower pace of NCAA football. A college quarterback may have a high completion percentage, but they throw relatively few passes in their system. A high number of completions usually mean that the quarterback is more comfortable and adept at passing the ball. CmpfYc is expected to be negatively related to draft position, with high passing completions translating into earlier draft selection. Yrdperattfyc in equation 4.1 measures the yards per passing attempt for quarterbacks in their final season of college. This is an efficiency statistic that captures a 46 quarterback's ability to move the ball on any given pass play. Its expected sign is also negative.
Team Specific Variables
The defensive rank of a team, defrank in equation 4.2, should also have a negative relationship with quarterback success. The lower the defensive rank, the better the defense and the less points the team allows. A strong defense should theoretically contribute to greater quarterback success because it gives the quarterback more opportunities to perform. Better defenses cause more turnovers, create good field position for the offense, and generate more time of possession for the offensive unit to operate with. Although team variables do not directly affect a quarterback's ability, they certainly lead to better chances for success.
The final team specific variable is the average rank of an opponent's defense, oppavdefrank in equation 4.2. This variable accounts for the quality of defenses that quarterbacks face over a season. It is calculated dividing the sum of opponent defense ranks by the number of games played. For this statistic, NFL game logs were referenced to see what defensive teams a quarterback faced in a given year. As oppavdefrank decreases, quarterbacks are facing tougher competition that usually diminishes their success. This variable, therefore, has an expected positive sign.
This concludes the discussion of the various parts of the data set that is used in the empirical testing of the quarterback production model. The regression equation does not include every theoretical determinant outlined in the Theory Chapter. This was due to 47
the fact that data was either unavailable, specific measures did not exist, or variables were
highly correlated with each other. 6 The following section will discuss the econometric
methodology used in this study.
Methodology
Since the estimation procedure is a two-stage least squares, equation 4.1 shows
the first stage which generates the predicted values for drfpick. This model is displayed
in equation 4.1. The second stage now uses the fitted values of dr/pick as an independent
variable. The basic empirical model is displayed in equation 4.2 mentioned above.
TABLE 4.1 provides a brief description of each of the variables in the regression
equation, along with the mean and standard deviation of each of the variables.
6 Character, Intelligence, Offensive Team Rank, and Offensive System were not included in the final regression equation. See Results and Conclusions for areas of future research. 48
TABLE 4.1
Variable Definitions and Descriptive Statistics
Variable Description Mean Standard Deviation age The age ofa 28.67 4.38 quarterback in a given season tdpct Percentage of 3.94 1.39 touchdowns thrown per pass attempt intpct Percentage of 3.25 1.16 interceptions thrown per pass attempt yrdperatt Yards per pass attempt 6.71 0.86
defrank Defensive rank of 16.98 9.16 quarterback's team oppavdefrank Average defensive rank 16.39 2.78 of opponents faced drfpick Selection number in the 97.79 97.09 NFL draft skpct Percentage of times 6.60 2.62 sacked when attempting to pass carwinpct Career winning 0.47 0.20 percentage of head coach prior to a given season
Estimation Procedure
This study uses a two-stage least squares (2SLS) technique to estimate the win percentage of quarterbacks in games played. This estimation procedure is used to make certain that the drfpick variable is not correlated with our error term, which in tum ensures that our variables are consistent and unbiased. When right-hand side variables 49
are correlated with the error term, the fundamental assumption of regression analysis is
violated.? The method of two-stage least squares involves using instrumental variables to
first obtain fitted values for the endogenous variable (drfpick), and then using these fitted
values in the final regression equation. The instrumental variables do not appear in the
final regression equation, but they are correlated with the endogenous variable and are thus used to determine the fitted values. 8 In the first stage, instrumental variables are regressed against drfPick as a dependent variable. The second stage then uses drfPick as
an independent variable that is used to explain variations in quarterback win percentage.
The instrumental variables that were used in the first stage of regressions are listed in
TABLE 4.2.
TABLE 4.2
Two-Stage Least Squares Instrumental Variables and Descriptions
Variable Description
height Height of quarterback in inches
weight Weight of quarterback in pounds
confdummy Conference Dummy Variable (major= 1, mid-major=O) cmpfyc Number of passing completions in final NCAA season
yrdperattfyc Yards per Attempt in final NCAA season
7 Damodar Gujarati, Basic Econometrics, 4d ed. (Boston, Massachusetts: McGraw Hill, 2003)
8 Ibid. 50
This chapter has outlined the data set, sources consulted, the empirical model, and the methodology for estimating the final regression equation. The detailed explanations of variables and expected signs should allow for knowledgeable interpretations of the end results. The following chapter will report the outcome of the regression analysis, discuss implications and conclusions, and finally acknowledge limitations and directions for future research. CHAPTER V
RESULTS AND CONCLUSIONS
This closing chapter will discuss the results from the regression analysis of the empirical model introduced and detailed in the Data and Methodology Chapter. Results will be evaluated for the quarterback success model using the Two-Stage Least Squares
(TSLS) technique. After presenting the regressions and results of this model, discussion will be directed at the accuracy ofthe model and any econometric issues that must be addressed. Conclusions and implications of the study will follow in the next section of the chapter. Finally, attention to the limitations of this study and future research will conclude the discussion of this topic.
Two-Stage Least Sq uares Regression
TABLE 5.1 summarizes the results of the regression equation that were estimated using the two-stage least squares procedure. The t-statistics are displayed in parentheses below the coefficients of each independent variable. R-squared values, adjusted R squared values, and F-statistics are also displayed in the table.
51 52
TABLE5.l
Two-Stage Least Squares Regression Results
Dependent Variable - Variable WINPCTGP
C 35.25 (3.18)* AGE -0.46 ( -2.29)** TDPCT 2.87 (3.29)* INTPCT -3.06 (-4.02)* YRDPERATT 6.30 (4.56)* DEFRANK -0.10 (-10.48)* OPPAVDEFRANK 0.69 (2.28)** DRFPICK -0.018 (-1.99)** SKPCT -1.66 i-4.83)* CARWINPCT -3.62 (-0.82)
R-squared 0.64 Adjusted R-squared 0.63 F-statistic 50.16
t-statistics in parenthesis *indicates significance at the 1% significance level **indicates significance at the 5% significance level 53
Econometric Issues
Heteroskedasticity was the first econometric problem that was addressed in the model. It occurs when the variance of the error term, given the explanatory variables, is not constant.' Ifhomoskedasticity, or constant variance, is violated, then our least squares estimators become inefficient and are no longer minimum variance. 2 There are multiple ways to test whether or not a model exhibits heteroskedasticity. The graphical approach involves using the fitted values of the dependent variable and plotting them against the residuals. If this residual plot exhibits some sort of cone shape rather than an even spread, heteroskedasticity may be an issue. The White test is also used to determine whether heteroskedasticity is a problem in the model by using the N*R-squared chi- square statistic. 3 The appropriate R-squared is generated by regressing the residuals squared against all of the independent variables, their squares, and their cross products.
To preserve degrees of freedom, the White test can be carried out by regressing the residuals squared against the fitted values and the fitted values squared. Keep in mind that squaring the fitted values will still yield a function with the squares and cross products of the independent variables. The empirical model exhibited an N*R-squared value less than our chi-square statistic, thus leading to the assumption that homoskedasticity was not violated.
Another econometric issue to test for is the normality of the error term. In order to ensure the validity of our t-statistics, R-squared values, and f-statistics, the assumption
1 Damodar Gujarati, Basic Econometrics, 4d ed. (Boston, Massachusetts: McGraw Hill, 2003)
2 Jeffrey Wooldrige, Introductory Econometrics: A Modern Approach, 3d ed. (Mason, Ohio: Thomson South-Western, 2006)
3 Ibid. 54 that the error tenn is nonnally distributed must hold true.4 This assumption can be graphically tested by looking at a histogram of the residuals. If the histogram looks like a nicely shaped bell curve, the error tenn is most likely follows a nonnal distribution.
Additionally, if the Jarque-Bera statistic is smaller than a chi-square with two degrees of freedom (5.99 at 95% confidence), then the nonnality assumption is valid.s The Jarque
Bera statistic in the empirical model was 4.482639. Therefore, the reliability of our test statistics should not be called into question.
Serial correlation is another econometric issue to take into account. This occurs when the error tenns are correlated in different time periods. This problem is common in time series data and is usually solved by adding a year variable to the regression equation.
Any oscillating or distinct patterns in the residuals over time indicate that serial correlation exists. To test for this condition, the Durbin-Watson statistic is generated by a given fonnula and then compared to the upper and lower values of this statistic. 6 The upper and lower values are dependent on the number of observations in the data set and the number of explanatory variables. If the Durbin-Watson statistic falls within a certain range, then there is no serial correlation. Table 5.2 shows the ranges of the two-tailed test.
4 Gujarati, Basic Econometrics
5 Ibid.
6 Ibid. 55
TABLE 5.2
Two-tailed Serial Correlation Test?
If dw
- 4-dL Serial correlation exists
If dw between dL and du or Inconclusive test if dw between 4-du and 4-dL No serial correlation If dw between du and 4-du
The Durbin-Watson statistic for the two-stage least squares regression was 1. 993185.
With 273 observations and 9 dependent variables or estimators, the Durbin-Watson table
shows values for du and dL as 1.73 and 1.86, respectively8. This implies that since dw is in the range between du and 4-du that there is no evidence of serial correlation. In the case that serial correlation does exist, this econometric problem is easily handled by adding an auto-regressive term to the regression equation. By including this term, the model captures the relationship between error terms in different periods. Since the data set in this study spans only 6 years and past year performance does not necessarily translate into current year performance, serial correlation is not an issue in the model.
Lastly, multicollinearity is an econometric problem that occurs when multiple independent variables are correlated with each other. When variables on the right hand side of the equation are related, it skews the data by artificially raising the R-squared value, and inflating the standard errors of the coefficients. This in turn diminishes the
7 Ibid.
8 Ibid. 56
significance of many of the variables as seen by dropping t-statistics.9 The only issue with multicollinearity in this model was with the variable offrank, which is the rank of a team's offense based on points scored. By running a correlation matrix of all of the independent variables, it is easy to see which factors have a strong relation to one another. A general rule of thumb is that if any values in the correlation matrix are above
.5 (excluding diagonal terms), then the model should be closely examined for the effects of multicollinearity. Offrank was highly correlated with both tdpct and yrdperatt because the quarterback has such a large impact on the offensive's ability to score points.
Although including this variable increased the R-squared value, it took away significance from many variables that should theoretically be significant. Because offrank is encompassed in many of the quarterback's individual statistics, it was removed from the model to ensure multicollinearity did not inflate the standard errors and R-squared. Note that even though the correlation matrix also showed some correlation between tdpct and yrdperatt, both of these estimators were still included in the model. This is because the significance of the other variables was kept in tact, and both variables are powerful performance measures that should not be omitted.
The Coefficients
As expected, the coefficients on many of our variables are significant at very high confidence levels. This is consistent with much of the theory chapter, which outlined which factors or variables should playa role in determining quarterback success. The
9 Wooldrige, Introductory Econometrics: A Modern Approach 57
following section will analyze the individual variables and comment on the results from
the final regression equation.
The coefficient for the quarterback's age is negative and significant at the 5
percent significance level. This implies that, on average, younger quarterbacks have a
slightly higher winning percentage in a given season than older quarterbacks. This result
shows that as quarterbacks age one year, win percentage in games played falls
approximately .457 percentage points. This is not a large amount, although it is still
significant. The age variable in this model speaks to the variation in winning percentage
among different aged quarterbacks. Some quarterbacks are successful from a very young
age when their bodies are healthiest, while others gain success over time as their experience grows.
Touchdown percentage, as expected, is significantly positive at the 1 percent significance level. The most points that can be scored on any given play in the NFL is 6 points from a touchdown. It seems logical that high touchdown percentages correlate with higher levels of success for quarterbacks. This variable also encompasses the offensive unit as a whole. No matter how strong or accurate a quarterback is, he needs his receivers to catch his passes in order to register touchdowns. This explains why the offensive rank variable, which was excluded due to issue with multicollinearity, is so strongly related to touchdown percentage.
Interception percentage, on the other hand, significantly depresses a quarterback's winning percentage in games played. This variable, like touchdown percentage, is significant at the 1 percent significance level. The powerful negative relationship with this variable speaks to the value of ball control in the NFL. Giving up team possessions 58
and putting the opponent in better positions to win is a recipe for disaster. Quarterbacks
cannot survive in the NFL with high interception percentages because they are far too
costly to the overall success of a team. As interception percentage rises one point, win
percentage falls a little over 3 percent.
The yards per attempt of a quarterback in the NFL have a positive impact on his
success. This variable was also significant at the 99 percent confidence level, and had the
largest coefficient of any independent variable, excluding the constant term. Just as
college success at the quarterback position is influenced by yards per attempt, so is
success at the NFL level. Yards per attempt is an important statistic because of how it
factors into many facets ofthe game. Not only does is represent a quarterback's
efficiency as a passer, but it also shows an offensives ability to maintain ball control and time of possession. All of these intangibles in NFL games help teams to victory.
Another important player specific variable is sack percentage. This is negatively related to win percentage in games played and for obvious reasons. Simple put, quarterback's perform better when they have time to pass and when they are protected by their offensive line. High sack percentages affect the timing and rhythm of the game by making quarterbacks uneasy in the pocket and forcing off-balance or rushed pass attempts.
The draft pick variable is also negatively associated with win percentage at the 5 percent significance level. This implies that earlier selections in the draft yield better win percentages in the NFL in a given year. The coefficient on drfPick, however, is a mere -
.0175, meaning as draft position changes by one spot, win percentage changes by only 59
.0175 percentage points. This speaks to the fact that although this variable is significant,
the consistency of executives in drafting great quarterbacks is still questionable.
The team specific variable measuring defensive rank is important in discounting
the success attributed to a quarterback. The team defensive rank has a negative impact on
win percentage in a given year. In other words, the better a team's defense, the more
likely a quarterback will be able to lead his team to victory. This makes intuitive sense
and is supported by the data and regression results at a high confidence level.
Another significant team specific variable is the opponent's average defensive rank. When quarterbacks face strong defensive units and still lead the team to a win, his
success and performance is all the more spectacular. As the average rank of the opponent's defense rises, the competition becomes easier and win percentage escalates.
This variable follows the theoretical interpretation of its affect on win percentage.
The final variable in question is career win percentage of the head coach. This is the only variable that was not statistically significant. In fact, the expected sign on this variable was the opposite of what the theory chapter described. The sign on the coefficient is negative, which would asset that the higher a coaches career winning percentage, the lower the win percentage is in games played by specified quarterbacks.
The possible explanations for this relate to a player's influences at the NFL level. It is clear that the head coach usually has a noteworthy impact on his players, and it seems special attention should be paid to the quarterback. However, quarterback coaches, offensive coordinators, and other veteran players are also usually responsible for molding the quarterback into a professional. Keep in mind as well that NFL coaches move around 60
the league a lot, so they have less time to influence players when their job security is in
an almost constant state of flux.
Fit of the Model
To evaluate how well the empirical model explains variation in the dependent variable around its mean, we look at the R-squared and adjusted R-squared values. These values are 0.639 and 0.626, respectively. This is a decent fit for a model, but shows that there is still plenty of variation in the dependent variable that is not explained by the theoretical determinants of quarterback success. A possible explanation for the R squared values is that our measure of success for quarterbacks is usually considered more of a team statistic. Although team variables are accounted for in the model, it is hard to attribute wins specifically to a quarterback's production. The F-statistic, which tests the joint significant of the independent variables, is also well above the critical level. This means we can reject the null hypothesis and confidently say that the coefficients are jointly different from zero.
Conclusions
This study has attempted to answer questions about quarterback performance in
National Football League games by estimating the demand for success and examining several independent variables. The production function approach suggests that in order to obtain the desired output, specific levels of different inputs must be used in a cost- 61
effective way. The purpose of this thesis was to test the NFL inputs, or theoretical
determinants of quarterback success.
While there have been many studies that have attempted to examine the
inconsistency in the NFL draft and subsequent player performance in the NFL, none have
identified an exact formula to find great talent. This paper has summarized the main
findings of prior research and extended it to a more current data set and more recent
theoretical determinants of success.
To test the theoretical model empirically, data was collected on quarterbacks for
the 2002 through 2007 NFL seasons. The data set was limited to quarterbacks who
played during at least one season and threw a minimum of 100 passing attempts during the regular season. The data set is a pooled set comprised of quarterbacks from all 32
NFL teams. A two-stage least squares (2SLS) estimation technique, which incorporates instrumental variables, was used to determine quarterback success in the model. The model finds several statistically significant indicators of quarterback success, namely touchdown percentage, interception percentage, yards per attempt, defensive rank, opponents average defensive rank, sack percentage, and draft pick.
Future Research
The first avenue for future research would be to obtain more detailed college performance statistics. The NFL records comprehensive and thorough statistics on each quarterback, from touchdowns thrown to red zone completion percentage. This data allows for more in-depth research and analysis, and usually yields more meaningful results. The NCAA, however, does not make this information readily available. Finding 62
and integrating this infonnation into future draft pick models would substantially increase
the value of the model.
A second major improvement would be to expand the theoretical model to include
proxy variables or specific measures of character, intelligence, and a team's offensive
system. It would be interesting to obtain personal infonnation on quarterbacks relating to
their off-the-field activities. Closely tracking a quarterback's legal issues or misconduct
could shed light into how he will carry himself as a professional athlete. Developing a
proxy variable for intelligence would also be an improvement on the model. The
Wonderlic is far too inconsistent to accurately assess intelligence, so creating a different
parameter or proxy could be more effective. Lastly, including college and professional
offensive systems into the regression equation would help detennine how well
quarterback's perfonn under different offensive schemes.
Another avenue for future research could analyze different success measures for quarterbacks. An investigation of player salaries, post-season awards, and even sponsorships or commercial deals could highlight various definitions of success. Keep in mind that a player's value to a team can go beyond the football field in the fonn of exposure and publicity.
A final opportunity for future studies would be to expand perfonnance evaluation to other team sports. Analyzing how different position players contribute to team wins or individual success could be valuable to executives looking for talent. These suggestions for future research extend beyond the scope of this investigation and merely address some of the limitations of this study. 63
Implications
This study has some important implications for NFL executives. The model produced in this investigation could serve as a basis for drafting new talent and analyzing subsequent performance in the NFL. By no means is this model perfect, but it provides a starting point for future research and more in-depth analysis of player performance.
Because ofthe uncertainty in drafting college players into the NFL, models that move closer to reducing this uncertainty are critical to all NFL teams.
In conclusion, this study provides a strong base for evaluating performance in the
NFL. The results suggest that the success of NFL quarterbacks is dependent on several player, coach, and team specific variables. As the detail and availability of player data increases, as mentioned above, more significant results could be obtained and implemented into drafting strategy. It will be interesting to see if drafting talent will ever be the result of an econometric model or formula, or whether player performance uncertainty will always persist in the NFL. This study provides a starting point for the examination of player performance in professional sports. APPENDIX
Regression Results
Dependent Variable: WINPCTGP Method: Two-Stage Least Squares Date: 05/02/08 Time: 12:38 Sample: 1 273 Included observations: 265 Excluded observations: 8 Instrument list: C CONFDUMMY HEIGHT WEIGHT CMPFYC YRDPERATTFYC AGE TDPCT INTPCT YRDPERATT DEFRANK OPPAVDEFRANK DRFPICK SKPCT CARWINPCT Variable Coefficient Std. Error t-Statistic Prob. C 35.24543 11.07746 3.181724 0.0016 AGE -0.457666 0.199877 -2.289740 0.0229 TDPCT 2.865915 0.869787 3.294960 0.0011 INTPCT -3.064939 0.762495 -4.019617 0.0001 YRDPERATT 6.304002 1.382295 4.560533 0.0000 DEFRANK -0.996621 0.095119 -10.47757 0.0000 OPPAVDEFRANK 0.686083 0.301226 2.277638 0.0236 DRFPICK -0.017582 0.008842 -1.988520 0.0478 SKPCT -1.655550 0.342936 -4.827584 0.0000 CARWINPCT -3.616796 4.395757 -0.822793 0.4114 R-squared 0.639051 Mean dependent var 45.75481 Adjusted R-squared 0.626312 S.D. dependentvar 21.67056 S.E. of regression 13.24722 Sum squared resid 44749.69 F-statistic 50.16343 Durbin-Watson stat 1.993185 Prob{ F-statistic} 0.000000
64 65
Correlation Matrix
WINPCTGP AGE TDPCT INTPCT YRDPERATI WINPCTGP 1.000000 -0.027192 0.564790 -0.415556 0.546317 AGE -0.027192 1.000000 0.016831 -0.119025 0.144913 TDPCT 0.564790 0.016831 1.000000 -0.224496 0.677572 INTPCT -0.415556 -0.119025 -0.224496 1.000000 -0.312479 YRDPERATI 0.546317 0.144913 0.677572 -0.312479 1.000000 DEFRANK -0.582024 0.016756 -0.234797 0.226583 -0.211965 OPPAVDEF 0.202810 0.096683 0.188773 -0.148983 0.199859 RANK DRFPICK -0.128297 0.276028 0.045294 0.052598 0.017849 SKPCT -0.335107 -0.163156 -0.336055 0.146046 -0.165312 CARWINPCT 0.165537 0.037129 0.148230 -0.085927 0.132253
DEFRANK OPPAVDEFR DRFPICK SKPCT CARWINPCT ANK WINPCTGP -0.582024 0.202810 -0.128297 -0.335107 0.165537 AGE 0.016756 0.096683 0.276028 -0.163156 0.037129 TDPCT -0.234797 0.188773 0.045294 -0.336055 0.148230 INTPCT 0.226583 -0.148983 0.052598 0.146046 -0.085927 YRDPERATI -0.211965 0.199859 0.017849 -0.165312 0.132253 DEFRANK 1.000000 -0.045518 0.098155 0.088303 -0.211429 OPPAVDEF -0.045518 1.000000 0.089871 -0.026485 -0.000734 RANK DRFPICK 0.098155 0.089871 1.000000 -0.042258 -0.043102 SKPCT 0.088303 -0.026485 -0.042258 1.000000 -0.190447 CARWINPCT -0.211429 -0.000734 -0.043102 -0.190447 1.000000 66
Histogram Plot
24 Series: Residuals :- r- Sample 1 273 20 -n Observations 265 - 1-1 I 1 16 --- Mean 1.96E-14 '.
~ Median -0.263585 Maximum 31.13935 12 .. - Minimum -43.62945 I I ! ..... r- Std. Dev. 13.01946 8 ~ - 1 Skewness -0.220135 c ·· - Kurtosis 3.460584 - ' 4 r-- r-rl r- Jarque-Bera 4.482639 I rfl rf f-- I 1-I ' Probability 0.106318 o I -37.5 -25.0 -12.5 0.0 12.5 25.0 67
Derivation
subject to
z = composite numeraire good :. p z =1
X J = NFL Players
x 2 = NFL Coaches
Eq.1
Eq.2
Eq.3
EqA
From Eq.3: A = 1
Substituti ng in for Eq .1 and Eq.2 :
2b2 (x J - a J ) + 2b(a2 - x 2 ) _ - 0 2 2 - ) _ ) PJ- 2(bJb2 b 2(bJb2 b
2bJ (x2 -a2 )+ 2b(a J -xJ ) _ =0 2 2 - ) _ ) P2 2(bJb2 b 2(bJb2 b 68
Re arranging: 2 2b2xI - 2b2al + 2ba2 - 2bx2 = 2(blb2 - b )PI Eq.5 2 2blx2 -2bla2 +2bal -2bxI =2(blb2 -b )P2 Eq.6
Multiply Eq.5 by b : 2 2 2 2b2bxI -2bb2al +2b a2 -2b x2 =2b(blb2 _b )pI Eq.7
Multiply Eq.6 by b2 : 2 2blb2x2 - 2blb2a2 + 2bb2al - 2bb2xI = 2b2(b lb2 - b )P2 Eq.8
Now Add Eq. 7 and Eq.8 2 2 2 2 2b a2 -2b x2 +2blb2x2 -2blb2a2 =2b(blb2 _b )pI -2b2(blb2 -b )P2
Group terms: 2 2 2 2 2x2(blb2 -b )+2b a2 -2blb2a2 =2b(blb2 _b )pI -2b2(blb2 -b )P2
Rearrange: 2 2 2 2b(blb2 _b )pI -2b2(blb2 -b )P2 2blb2a2 -2b a2 x2 = --'---'--=----2-=-(b-=-l--2 -_-=-b-=-2-=-)-"-----=--=--- + 2(b b b2) b I 2 -
Complete same process for XI and begin with Eq. 5 and 6
Multiply Eq.5 by bl : 2 2b2blxI -2blb2al +2bbla2 -2bblx2 =2bl(blb2 _b )pI
MultiplyEq.6byb : 2 2 2 2blbx2 -2blba2 +2b al -2b xI = 2b(blb2 -b )P2 69
Now Add the two equations l l 2bl b)x) -2bl b)a) +2b a) -2b x) =2bJb)bl _bl)p) -2b(b)bl -bl)Pl
Group terms: l l 2x)(b)bl -b )+2b a) -2bl b)a) = 2bJb)bl _bl)p) -2b(b)bl -bl)Pl
Rearrange: l l l 2b) (b)bl - b )p) - 2b(b)bl - b )Pl 2b)bl al- 2b a) x = --...!....:.-!.--=----=-=---!...--....:.-!.--=----=-=--=--l + 1 ) 2(b)bl - b ) 2(b)bl - b )
Now plug x) and Xl int 0 original equation
(b2 (a) +b)p) -2bpl _a)l +b) (al +bp) -2bl Pl -al )2) Y =z+ l + 2(b)bl _b ) b(a)(al +bp) -2b2P2)+a2(a) +b)p) -2bp2)-(a) +b)p) -2bp2)(a2 +bp) -2b2P2)-a)aZ ) 2 b)b2 _b SOURCES CONSULTED
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