Is Defense Decisive? An Examination of the National Football League Salary Structure and Game Outcomes

Eric Ness

Professor Peter Arcidiacono, Faculty Advisor

Honors Thesis submitted in partial fulfillment of the requirements for Graduation with Distinction in Economics in Trinity College of Duke University.

Duke University Durham, North Carolina 2010

Table of Contents

Acknowledgements………………………………………………………………………..3

Abstract…………………………………………………………………………………....4

1. Introduction…………………………………………………………………………...... 5

2. Literature Review…………………………………………………………………….....9

3. Theoretical Framework……………………………………………………………..…13

4. Data……………………………………………………………………………………14

5. Empirical Specification...……………………………………………………………...19

6. Results………………………………………………………………………………....21

7. Discussion……………………………………………………………………….…….33

8. Conclusions...………………………………………………………………………….36

Appendix A: Sample Salary Data……………………………………………….……….39

Appendix B: Initial Regression Results………………………………………………… 42

Appendix C: 2008 Variable Data and Winning Percentage……………………………..43

Appendix D: Implied Strategies by Team and Opponent………………………………..48

References………………………………………………………………………………..49

Data Sources…………...……………………………………………………….………. 52

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Acknowledgements

This paper would not have been possible without Professor Peter Arcidiacono, my faculty

advisor, who gave extremely helpful advice at each step of the research process. I am

also indebted to Professor Kent Kimbrough for his thorough analysis and constructive

criticism, as well as my fellow students in the Economics Honors Seminar for their

creative ideas, many of which were used in this paper. Finally, I am grateful for my

family, who not only assisted me with creating a tedious and complex data set, but

provided me with emotional support both during the research process and my entire

career at Duke University.

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Abstract

Professional sports constitute an enormous industry. Maximizing a team’s victories generates substantially increased revenue. A common maxim in sports is “defense wins

championships.” The National Football League is an ideal venue to test this adage. A

conditional logistic model was used to determine the effect of the percentage of team

payroll spent on defense on the probability of victory. In most cases, no evidence

suggested that the defense’s share of team payroll had a significant effect on a game’s

outcome. However, the percentage of defensive payroll paid to starting players was

consistently significant and sizably increased the probability of victory.

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1. Introduction

The ability to predict the outcome of professional sporting events, particularly

National Football League (NFL) games, is a skill that many pundits, gamblers, and laypersons desire to possess. The NFL is an enormous entity composed of 32 teams located in all areas of the United States, each of which is worth hundreds of millions of dollars. Every year, the NFL generates $6 billion of revenue (Plunkett Research, Ltd.,

2009). Its championship game, known as the Super Bowl, is watched by over 90 million viewers and generates over $250 million for the broadcasting company (Fixmer, 2009).

When football fans argue for the supremacy of their sport, facts like these are often cited as evidence that football has replaced baseball as the new national pastime.

One of the aspects of the National Football League that attracts many fans and allows the league to generate such a large amount of revenue is the level of parity in the league. Many teams that perform poorly in one season have a winning season the next year, and vice versa. Parity exists in the NFL for several reasons. One of these is the revenue sharing system, which was established in 1961 by former Commissioner Pete

Rozelle. Since then, the National Football League has acted as a single entity in many important respects, including sharing revenue generated by the sale of television rights and merchandise equally among all of the teams (Mason, 2004). Without this system, the richer teams located in larger television markets would gain a financial advantage from having more viewers for their games, which would inevitably translate into a competitive advantage. By inheriting largely equal revenue, each team has roughly equal resources to commit to signing players.

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In addition to revenue sharing, many pundits point to the NFL’s strict salary cap, initially imposed in 1994, as a contributing factor to the league’s parity. Unlike Major

League Baseball, which has a “soft” salary cap that can be exceeded with the relatively light penalty of a luxury tax, the NFL has a “hard” salary cap that cannot be exceeded without incurring steep penalties. In professional baseball, large-market teams, such as the New York Yankees, frequently exceed the cap and pay their players as much as five times more than other teams (Associated Press, 2009). These large-market teams are able to outbid the smaller-market teams and drain the finite talent pool such that smaller- market teams are unable to compete. NFL franchises, on the other hand, are restricted by the salary cap and must make wise personnel decisions to gain an edge over their opponents (Einolf, 2004). No single team is able to corner the market on blue-chip players because they are eventually outbid for talent by another team with more room under its salary cap.

Another unique characteristic of the National Football League and football in general is the universal use of specialists in each player position. In almost all other sports, individual players frequently play both offense and defense according to the flow of play and the demands of the moment. At the least, players in other sports have widely varying roles within the offense or defense. Football players, however, almost never play both roles. In fact, not only do they play only “one side of the ball,” but they frequently play the same position and line up in the same place for every play. Because of this clear distinction between offensive and defensive specialists, it is possible to examine their contributions to overall team success independently.

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The existence of revenue sharing, a hard salary cap, and the specialization of player positions make it possible to use the National Football League to explore one of the most well-known adages in sports: defense wins championships. This phrase is frequently cited, especially when a sports team with a particularly stingy defense wins a title. Many journalists and fans, however, have questioned the accuracy of this statement by arguing that no matter how well the defense plays, the offense must score points in order for the team to win, and thus, the offense plays at least an equal role in attaining victory. In fact, some football teams specifically emphasize their offense under the business assumption that fans prefer to watch higher-scoring games and are more likely to attend if their team scores more often (a corollary to the defensive maxim is, “offense sells tickets”). While numerous attempts to correlate defensive performance to team performance have frequently been made by journalists in newspapers and on websites, the literature is lacking a thorough analysis of preference for a good defense and its relationship to the outcome on the field.

The purpose of this paper is to measure the probability that a team will win a game given the proportion of salary cap space it devotes to defensive and offensive players. First, a measure of a team’s spending preferences will be found by calculating the proportion of its payroll it devotes to defensive players (defensive lineman, linebackers, and the secondary) and offensive players (quarterback, running backs, offensive linemen, and wide receivers). Here, the specialization inherent in football is crucial because it allows for the money spent on defensive and offensive players to be specifically isolated and compared to the whole. Special teams players, such as kickers

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and punters, will be placed into the offensive and defense categories, respectively. Then, a regression will be run to determine the relationship between these proportions and the outcome on the field on a game-by-game basis.

An assumption that must be made before a more detailed analysis can occur is that more money spent on defensive players correlates directly to better defense and, thus, is a good instrument for defensive prowess (and vice versa for the offense).

Certainly other factors affect the defense in addition to salary allocations. Over the course of a season, injuries to players are common, and the absence of players who improve the defense or offense should be factored into calculations. Furthermore, research suggests that wage equity has a positive correlation with success on the field and needs to be included in the regressions (Mondello and Maxcy, 2009; Borghesi, 2008).

Also, a good team is not necessarily one with all of the best players at each position (i.e., an all-star team) but rather is composed of players who work together well. This element is difficult to capture in statistical analysis, although one potential measure of team dynamics is the time each player has been with the team, assuming that a team that has fewer personnel changes is more cohesive and functions more effectively. While these factors will be accounted for as much as possible, the main focus of the paper is on the potential effect of salary allocations to defensive and offensive players on the outcome of the game.

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2. Literature Review

The issues of competitiveness and the outcome of games in professional sports leagues have been studied thoroughly. Several studies have shown that competitive games lead to higher attendance in Major League Baseball, particularly when the home team is slightly favored (Rascher, 1999; Meehan et al., 2007). This result makes sense because fans are more willing to pay to watch an entertaining game as opposed to a rout.

Higher attendance, in turn, leads to higher revenue for the home team and the league in general. This finding is important because it demonstrates that owners of professional sports clubs should seek to field a team that is competitive with other teams in their league in order to maximize profits. The choice that owners are sometimes said to face between fielding a successful team and a profitable team is therefore a false choice.

Other studies address the effect of a salary cap in professional sports. Before discussing this literature, a look at the National Football League’s salary cap is useful.

To field a successful team, management must be able to negotiate a salary cap that has a number of complex rules, the basic principles of which will be described here. To determine the salary cap of a season, the projected total revenue from all revenue streams for the entire league is calculated. Then, this number is multiplied by a negotiated percentage according to the Collective Bargaining Agreement (CBA) between the NFL

Players’ Association and the owners. In 2006, this number dropped to 57% from 64.5%

(Lackner, 2009; NFL CBA, 2006). This figure is then divided by the number of teams in the league to obtain the official salary cap. While this number is the team payroll ceiling, a floor also exists. Beginning in 2006, the team payroll must be at least 84% of the salary

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cap; this number was increased to 86.4% in each of the subsequent seasons but cannot exceed 90% of the salary cap (Lackner, 2009; NFL CBA, 2006). Additionally, players can be paid in two ways: bonuses, and regular salary. The bonuses are given in one year, but spread evenly over the lifetime of the contract, while the regular salary paid to a player can vary from year to year. A common financial method used to take maximum advantage of the system is to pay a player a bonus for signing the contract and then pay him very little in regular salary, with most of the regular salary in the last year or years of the contract. Thus, if the player is not as valuable to the team as expected, the player can be cut, with the team only owing the portion of the bonus allocated to the remaining years of the contract (Lackner, 2009; NFL CBA, 2006).

Separate studies by Lee and by Larsen et al. found that the institution of the salary cap measurably increased competitiveness, or parity, in the NFL (Lee, 2009; Larsen et al., 2006). Parity in this sense refers to the principle that a team that performs poorly one year can make improvements and perform well the next year with the right management.

Lee found that turnover in team rankings increased after the salary cap was introduced.

Larsen et al. used a version of the Herfindahl-Hirshman Index, a common measure of market concentration, to find a similar result. As a result of this increased parity, the salary cap has been effective in raising NFL revenue.

While the National Football League might have parity as an objective, the league still possesses certain systemic issues that can cause deviations. A 2007 study by W. A.

Hamlen delved into this topic and identified two significant departures from parity

(Hamlen, 2007). First, while most revenue is shared, money derived from premium

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seating, such as luxury boxes, is exempt from the parity rules. Second, coaches’ salaries are not subject to a cap. Large-market teams, with an incentive to leverage their larger fan base (and corresponding greater revenue stream) over small-market teams, therefore attempt to designate more seating as premium and spend as much as needed to secure the best available coaches for the team; this leads to significant advantages over their small- market competitors in both revenue and leadership personnel quality.

According to a study by Hadley et al., effective coaching can result in three or four additional victories in a single season (Hadley et al., 2000). This result is highly significant given that the entire regular season comprises only sixteen games; thus, differences in coaching can turn a potentially unsuccessful season into a successful one, or vice versa. A study by Scully demonstrated that coaching success (winning) and coaching tenure are correlated (Scully, 1994). Thus, an efficient way to measure the quality of the coach of a given team is to take into account the length of time he has been coaching. Given Hadley et al.’s findings and Hamlen’s conclusions, the location (or market size) of the team must also be considered in order to avoid bias stemming from unequal coaching abilities or disproportionate revenue streams.

Many studies have focused on the effect of wage inequity in professional sports in general, and the National Football League in particular. A recent article by Mondello and

Maxcy found that teams that had more incentive pay in contracts with its players, i.e., payment related to job performance, and lower wage dispersion, i.e., differences in wages across the team, outperformed their competitors on the field (2009). Furthermore, a very useful study was performed by Richard Borghesi and published in November 2008. He

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used a linear regression to determine the correlation between performance and a number of other factors with an emphasis on pay equity variables on an individual basis. In other words, he determined the effect of wage inequity on individual statistics. His results expanded those of Mondello and Maxcy. While he, too, found that compensation equity results in increased performance relative to the competition, he also determined that this remains true even when salary inequity could be justified by differences in skill

(Borghesi, 2008).

The present study is an extension of Borghesi’s work with two different focuses.

First, defensive players will be grouped together as a unit, and indicators of unequal pay will be removed in favor of other variables that isolate the effect of spending on defensive players on team performance. Second, the regression model is altered to predict game outcomes based on the level of defensive spending for a particular team.

Generating predictions for the outcome of NFL games, as well as determining the effectiveness of commonly used predictors, have both been done using many different variables and economic techniques. Boulier and Stekler measured the predictive power of the New York Times ranking system for NFL teams and the accuracy of predictions of the newspaper’s sports page. The study found that the ranking system was a reasonably effective predictor of game outcome and was much more accurate than the Times ’ own sports editor (Boulier and Stekler, 2003). In addition, David Harville was one of many to attempt to predict game outcomes based on algorithms. His algorithm, which was based on points scored at home and away for each team and the effect of home field advantage, predicted game outcomes about as well as the betting line (Harville, 1980). Many papers

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have analyzed the effectiveness of betting lines in predicting game outcomes (e.g. Zuber,

Gandar, and Bowers, 1985; Gandar et al., 1988; Golec and Tamarkin, 1991); they conclude that, while economic biases occur in betting lines (resulting in profitable betting strategies for bettors), the lines themselves are effective predictors of the outcomes of

NFL games.

The contribution of this paper to the literature is to take into account salary statistics at the defensive and offensive unit levels in order to determine how they correlate with team success and, therefore, test the claim made by coaches, players, columnists, and fans alike that defense wins championships.

3. Theoretical Framework

The data is analyzed using a conditional logistic model, which determines the probability of an outcome in settings where the data are matched in pairs and only the relative difference in their characteristics are important. Thus, when examining two different teams, only the differences in the characteristics of each team are significant.

According to the previously discussed literature, variables that are significant under the conditional logit model include the coach’s tenure as head coach, the standard deviation of defensive salaries, spending on starters, and the number of injuries sustained by the team. If a conditional logit model were implemented with all of these measures, then they would be expected to have a statistically significant effect on the game outcome and change the probability that a team wins. However, the literature lacks predictions of how and to what extent salary statistics, i.e., unit-level spending on defense or offense,

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affect game outcomes. Thus, there is little guidance as to how these characteristics will affect the probability that a particular team has. The hypothesis is that the difference in salary devoted to defense between two teams affects the probability of victory in favor of the team that spends more on defense. This hypothesis stems from the common assumption that defense is more important to winning a game than offense. Evidence in favor of the hypothesis would consist of regressions in which the variables that measure the percent of salary cap devoted to defense and the variables measuring the percent of payroll devoted to defense are significant with positive coefficients. It is further hypothesized that a unique maximum will exist such that the quadratic variables’ coefficients will be negative while the linear variables will have positive coefficients.

This hypothesis stems from the idea that devoting nearly all of a team’s payroll to either defense or offense will, at some point, be so detrimental to the other unit that the payroll allocations become suboptimal.

4. Data

Relevant data was obtained from several sources and carry important caveats.

Salary data and a set of rosters for each season and team were obtained from USA

Today’s online salary database and accessed through sports economist Rodney Fort’s personal website (www.rodneyfort.com). Because only a very incomplete set of salary data is available for 1994, the first year under the salary cap, that year is excluded from the regression. The regression includes the years up to and including 2008. To control for salary inflation during the time period used in the study, the standard deviation of the

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defensive payroll was calculated, then divided by the team’s payroll. A second set of player rosters, complete with each player’s position, the number of games they played and the number of games they started, was obtained from Sport Reference LLC’s website pro-football-reference.com . One important issue concerning these two sources is that the rosters did not always match exactly. USA Today’s salary lists include payments to players that are not listed in Sport Reference LLC’s rosters, which in turn list other players for whom no salary data is listed by the USA Today rosters. As a result, a portion of each team’s annual payroll is devoted to players whose position and impact on the team are not readily available. Conversely, some players are listed for a team, but no publicly accessible data exists regarding how much they were paid for that particular season. As an example, for the 1995 season, combining the two rosters results in a list of

1,945 player names. Of these, 237 have salary data but no position or playing time information, and 104 players, including at least ten listed more than once with different teams, have position and playing time information but no salary data, even though they are listed as playing, or even starting, more than one game for each team. Out of the years 1995-2008, the 1995 data has the most anomalies of this type. After this year, the number of these errors decreases significantly. For the purpose of this study, players who are listed as having a salary from a team will have that salary added to the team’s total payroll, even if no position or playing time data is available. The effect is the same as assuming that all these players are neither offensive nor defensive specialists. Because of the infrequency of the errors, however, it is highly unlikely that they will have any meaningful effect on the regressions.

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It is noteworthy that many teams do not spend the exact amount allocated by the salary cap on players. This might occur for several reasons, one of which is to make it easier to create room under the salary cap in the following offseason in order to sign a better player who will demand more money in his contract. Because of the complex nature of the NFL salary system and the lack of availability of precise data, this paper considers the total salary paid to a player in a particular year, which may lead to some teams appearing to exceed the salary cap.

To determine how much money was spent on players who spent the most time on the field, a special “starting salary” was determined for each player. Each player’s salary was multiplied by the number of games they started and then divided by the number of games in a season (sixteen). The resulting number represents the portion of the player’s salary that was paid to him as a starter. Because the extra amount that starters play over their backups is not fixed, simply labeling one person as a starter and another as a backup is not the most complete measure of time spent on the field. However, given data and time constraints, it is an effective solution. Using this method, the 1995 Arizona

Cardinals spent about 71.5% of their total payroll on starters and 75% of defensive payroll on defensive starters. While these numbers are not necessarily standard for the league (they are, in fact, close to the league high for that year), they are representative of the nature of data.

Coaching and playoff data were obtained from pro-football-reference.com .

Relevant data for each team included their coaches’ ability and whether or not the team made the playoffs the previous year. To measure coaching ability, the number of years

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that the head coach has held a head coaching position in the NFL entering the season under study was determined. The outcome of each game from each team’s perspective was also recorded. That means that for every one game, two pieces of data were collected.

Sample cross sections of salary data are located in Appendix A. The first two charts listed are defensive and offensive salary statistics for all teams in the year 1995.

As might be expected in a “copycat league,” where teams imitate successful rivals, and a league with many rules in place to enforce parity, several of the variables contain somewhat limited variation. For example, in 1995, all total defensive payrolls are within about $5 million of each other (between about $13 and $18 million), with offensive payrolls having only a slightly greater range. Correspondingly, unit spending as a percentage of salary cap is also limited in its variation. Greater fluctuation exists for the percentage of unit spending on starters as well as unit spending as a percentage of total team payroll; this result is expected because payrolls are not static like the salary cap.

For most teams, more was spent on offensive players than defensive players, with more variation in the offensive statistics. While an average of 44.60% of payroll was allocated to defensive players, 49.23% was given to offensive players, with standard deviations of

4% and 4.4%, respectively.

The second set of charts in Appendix A describes the spending habits, with standard deviation unadjusted, of the Arizona Cardinals from 1995 to 2008. While occasionally drastic differences exist from year to year, such as in 2001, the data is relatively steady for several successive years. In 2001, defensive spending dropped from

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45.51% to 27.77%, while offensive spending increased dramatically from about 53% to over 69%. No obvious reason exists for this occurrence, although the signing of a marquee offensive player carrying a substantial contract has the ability to alter the balance between offense and defense. The next year, the spending levels reverted to close to those in 2000.

Injury data was obtained from NFL injury reports provided on the website jt- sw.com . Because of the way injuries are reported (or not reported), it would be extremely difficult to completely and accurately catalogue the number of player-games lost to injury by a team in a particular year. The likelihood that a player with an injury will play is listed before games as “probable,” “questionable,” “doubtful,” or “out,” with only those designated as “out” definitely not playing in the game. Therefore, to achieve a workable estimate for the purposes of the study, those players designated as “out” or “doubtful” are counted as lost to the team for the game. The number of players a team lost due to injury each game using this method is generally a number between 0 and 4. There are a number of different patterns in the data. Some teams have a stagnant number of player-games lost, be it high or low, while other teams have a relatively high number one week and a low number the next. Often, a team has several players lost to injury at the beginning of the season, but gradually the number decreases. Perhaps this last phenomenon is due to long-term injuries sustained prior to the season during preseason training camp or the exhibition games that eventually heal. These patterns are not expected to have an impact on the regression except for the effect of the quantity of the injuries themselves.

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5. Empirical Specification

The empirical method to be used for this study is a conditional logit model, which is written as follows:

P(Team A) = exp(XAβ )/(exp( X A β )+ exp( X B β ))

This equation can be rewritten as:

((− )β ) P(Team A) = 1 / (1+ e XB X A )

Both of these equations represent the probability that Team A will defeat Team B.

The variables XA and X B are not important individually; rather, it is the difference between them that matters. XA and X B are vectors of variables that include salary statistics and other statistics. Salary statistics comprise the percent of payroll devoted to defense and offense, the percent of the salary cap devoted to defense and offense 1, the standard deviation of the defensive and offensive salaries as a measure of wage equity, and the percent of defensive and offensive salaries allocated to starters. Other statistics include the number of players lost to injury for that game, the tenure of the team’s head coach, and an indicator variable for whether or not the team made the playoffs. In addition, a team fixed effects variable is included in order to correct for market size.

Finally, some salary statistics are also included in a quadratic format to account for a potential “unique maximum” that may exist for these variables. The dependent variable is the outcome of the game between Team A and Team B from Team A’s perspective. A win for Team A is labeled with 1, a loss is designated as 0, and a rare tie is treated as half

1 It has been suggested that including both percent of payroll and percent of salary cap devoted to payroll is superfluous and could cause collinearity in the regression. In addition to being evaluated in tandem, both will be used individually.

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of a win, or 0.5. It is expected that injuries are negatively correlated with victory, while coaches with a longer tenure win more often and have a positive correlation. The teams that qualify for the playoffs are selected based primarily on the number of wins; thus, the playoff variable will almost certainly have a positive correlation with victories.

Additionally, the optimal spending strategy may differ based on the quality of the opponent; for example, increased defensive spending may be crucial when facing a playoff-caliber opponent, but not as important when competing against a weak opponent.

It is predicted that both the percent of payroll and percent of salary cap devoted to defense will have a positive correlation with victory, while the standard deviation of defensive salaries will garner a negative correlation. The percent of defensive and offensive payrolls devoted to starters is more difficult to predict. Starters are obviously more important to the outcome of the game than their backups, but starters do not play the entire game. Thus, while spending more on starters may help at some level, there may be a point at which it is counterproductive because a high percentage of salary devoted to starters will, by definition, increase wage inequity. Therefore, it is difficult to predict the direction of the correlation of the variable.

Through the regression, a series of coefficients for the tested variables is generated. Then, the coefficients are analyzed to determine their statistical significance by calculating the Z-value for each coefficient. Finally, the magnitude of the effect of each coefficient on the dependent variable of Team A winning the game is examined.

Because the conditional logit regression being used in this study is not linear, the

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magnitude of the effect of each coefficient is determined by computing the effects of marginal changes in the independent variables on the dependent variable.

6. Results

The results to the initial regressions can be seen in Appendix B. A conditional

(fixed-effects) logistic regression was used to measure the effect of each of these variables on the probability of a victory in a particular game. Using offensive variables, the percent salary cap variables were found to be significant, with the linear variable having a positive coefficient and the quadratic variable a negative coefficient, giving the idea of a “unique maximum.” However, the percent salary cap variable for offense was found to be insignificant. Using defensive variables, the percent salary cap variables were also insignificant. The percent payroll variables, unlike in the offensive regressions, were significant. However, the linear variable had a negative coefficient and the quadratic variable had a positive coefficient, yielding the prospect of a “unique minimum.” This result directly contradicts the result found by using offensive variables and is illogical.

These results prompted a reorganization of the data. In addition to the already existing variables, two new indicator variables were created. The first was a variable that indicated whether or not a team spent 95% or more of its salary cap allotment. The second identified whether or not a team allocated more of its payroll towards offensive or defensive players. Also, several interaction terms were created. The first two interacted the indicator variable for the team making the playoffs the previous year with the percent

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of salary cap space spent on defense and percent payroll spent on defense, respectively.

These were included to determine if having success in the previous year would expand or mute the effect of extra defensive spending. The next three interaction terms use the number of injuries in combination with the percent of payroll on defense, percent of defensive spending on starters, and the indicator for whether or not the team used all of its salary cap allotment. It was anticipated that increased spending on defense might change the effect of injuries. Spending more defensive money on starters is expected to exacerbate the negative effect of injuries because, presumably, the players who are being paid a much higher share than their teammates are more important to the team’s success.

Also, spending to the salary cap would alleviate the effect of an extra injury because the team could have more effective backups that can take over the injured players’ assignments.

Table 1 lists summary statistics for the data according to the two new indicator variables. Teams that are at the salary cap have a higher winning percentage than those below the salary cap, with teams that spend more on defense having a slightly higher winning percentage than those who favor offense. One notable statistic is that teams at the salary cap who spend more on offense have a much higher chance of having been to the playoffs the previous year than teams with different characteristics.

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Table 1. Summary Statistics According to Percent of Salary Cap Spent and Allocation to Offense or Defense.

At Cap (>=.95 Below Cap of Cap) (<.95) More on More on More on More on Variable Offense Defense Offense Defense Winning % 0.527380952 0.534970238 0.478 0.482 Winning % Against At Cap 0.504596527 0.509339975 0.411842105 0.470954357 Winning % Against Below Cap 0.559201141 0.573012939 0.509057971 0.485981308 Winning % Against More on Offense 0.534552846 0.537748344 0.476830087 0.475258918 Winning % Against More on Defense 0.517241379 0.531409168 0.481121899 0.489019034 Playoffs Previous Year 0.485714286 0.321189591 0.390566818 0.319381842 Coaching 6.620833333 7.427710843 6.150662252 5.898840206 Std. Dev. Offense Spending 2,366,418.19 1,574,594.45 1,319,303.99 958,521.94 Std. Dev. Defensive Spending 1,621,615.29 2,111,396.74 976,501.49 1,339,630.54 % Offense Spending on Starters 0.651442654 0.596375697 0.61868333 0.581789041 % Defense Spending on Starters 0.628833564 0.664445695 0.644115345 0.645990799

# of Entries 1680 1346 2417 1553 NOTE: – the Standard Deviation Variables are in U.S. Dollars.

In order to obtain usable and relevant results, the conditional logistic regressions used earlier were repeated using different sets of variables and with different caveats.

The first series of regressions comprised only games between two teams at the salary cap; the second series of regressions contained data from games between two teams below the salary cap; and the third series of regressions analyzed games between a team at the salary cap and a team below the salary cap. Further analysis of the results, including their specific effects and implications, can be found in the previous discussion.

Table 2 lists the results of the first set of regressions. The first regression includes percent spending on defense, the variable of interest, as well as coaching experience and

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injuries, variables considered uncontroversial given previous results. The percent spending variable is included in the regression only in order to avoid the same problems that plagued the initial regressions. The succeeding regressions added an extra variable until Regression 5, in which 3 of the 4 relevant interaction variables were added (because every team is at the salary cap, the injuries*at cap variable was withheld due to collinearity). For this set of regressions, the percent of payroll devoted to defense is clearly insignificant, while coaching experience, the number of injuries, and playing at home were all significant and possessed the expected sign – positive for coaching and home-field advantage and negative for injuries. Also of note is the injuries and defensive starter variable, which is positive and significant. This indicates that spending more on defensive starters might actually soften the blow caused by injuries rather than the expected amplification.

Table 3 lists results for games between two teams spending below the salary cap.

Unlike teams above the salary cap, the percentage of spending on defensive players for teams below the cap is significantly correlated with victory, but negative. Given the construction of the variable, this result indicates that offense is the important unit for an increased chance of success in this case. Also dissimilar to the results from the teams at the cap is the coaching variable, which is positive but not consistently significant. In addition, the standard deviation of the payroll ratio is positive and significant, which means that increasing the disparity of pay between players increases the odds of victory, a result contrary to previous literature findings.

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Table 2. Conditional Logit Regression of Teams At the Salary Cap Variable 1 2 3 4 5 6 Pct Payroll Defense -.608 -.750 -.785 -.800 -.0468 .015 (-.94) (-1.10) (-1.14) (-1.15) (-.04) (.01) Coaching .0277*** .0275*** .0277*** .0221** .0223** .0206** (2.90) (2.86) (2.88) (2.25) (2.25) (2.08) Def. Injuries .102 .105 .111 .113 .124 .078 (1.38) (1.42) (1.49) (1.51) (1.64) (.99) Total Injuries -.187*** -.186*** -.195*** -.205*** -.016 -.543* (.3.53) (-3.51) (-3.67) (-3.79) (-.07) (-1.75) Home .293*** .302*** .297*** .306*** .306*** .320*** (4.25) (4.30) (4.22) (4.28) (4.28) (4.44) Pct. Def. Spending on .373 .144 .663 .628 .553 Starters (.66) (.25) (1.09) (1.03) (.91) Std. Dev. Def. Payroll/Total 8.85 8.24 7.53 7.56 Payroll (1.24) (1.13) (1.03) (1.03) Playoffs Previous Year .373*** -.344 -.033 (3.49) (-.33) (-.03) Pct Cap Defense * Playoffs .651 .234 Previous Year (.87) (.31) Pct. Payroll Defense * .006 .242 Playoffs Previous Year (.00) (.18) Total Injuries * Pct. Payroll -.417 -.102 Defense (-.89) (-.21) Total Injuries * Pct Def. .659** Spending on Starters (2.45) Total Injuries * At Cap Pseudo R2 .0344 .0348 .0369 .0475 .0488 .0539 Observations 1780 1780 1768 1758 1758 1758 Log Likelihood -595.672 -595.451 -590.117 -580.324 -579.518 -576.421

* Significant at 90% confidence level ** Significant at 95% confidence level *** Significant at 99% confidence level NOTE. – Standard errors are listed in parentheses.

Another interesting significant variable is the interaction variable between percent salary cap on defense and playoffs the previous year, which was significant and positive.

This piece of data suggests that teams that made the playoffs last year are better off favoring defense rather than offense. Also, the interaction between percent payroll on defense and injuries suggests that defensive spending helps to offset the negative effects

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of injuries. Unlike teams at the cap, teams below the cap seem not to have a significant benefit from coaching experience. The total injuries, home-field advantage, and interaction between defensive starters and injuries variables are all significant as they were with teams at the cap.

Table 3. Conditional Logit Regression of Teams Below the Salary Cap Variable 1 2 3 4 5 6 Pct Payroll Defense -1.117* -1.363** -1.350* -.995 -1.948 -1.996* (-1.74) (-2.10) (-1.86) (-1.35) (-1.63) (-1.67) Coaching .0156* .0151* .0179* .0136 .0162 .0145 (1.74) (1.68) (1.71) (1.25) (1.46) (1.34) Def. Injuries -.044 -.035 .0207 .0337 .-269 .002 (-.70) (-.56) (.30) (.47) (-.37) (.03) Total Injuries -.053 -.0477 -.0593 -.0480 -.388 -.728** (-1.25) (-1.13) (-1.25) (-.98) (-1.61) (-2.35) Home .357*** .387*** .374*** .375*** .375*** .383*** (6.40) (6.81) (5.78) (5.66) (5.63) (5.73) Pct. Def. Spending on 1.764*** .860 .647 .537 .487 Starters (3.34) (1.40) (1.03) (.85) (.77) Std. Dev. Def. Payroll/Total 9.691** 9.895** 9.620** 9.535** Payroll (2.35) (2.35) (2.28) (2.25) Playoffs Previous Year .361*** -1.45 -1.44 (3.66) (-1.16) (-1.15) Pct Cap Defense * Playoffs 2.165* 2.136* Previous Year (1.79) (1.77) Pct. Payroll Defense * -.196 -.192 Playoffs Previous Year (-.13) (-.13) Total Injuries * At Cap Total Injuries * Pct. Payroll .720 .919* Defense (1.42) (1.76) Total Injuries * Pct Def. .445* Spending on Starters (1.76) Pseudo R2 .0286 .0346 .0310 .0395 .0434 .0456 Observations 2722 2722 2126 2050 2050 2050 Log likelihood -916.363 -910.704 -713.985 -682.434 -679.652 -678.079

* Significant at 90% confidence level ** Significant at 95% confidence level *** Significant at 99% confidence level NOTE. – Standard errors are listed in parentheses.

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Table 4. Conditional Logit Regressions for Games Between a Team At the Salary Cap and a Team Below the Salary Cap Variable 1 2 3 4 5 6 Pct Payroll Defense .491 .384 .430 .669 2.133** 2.131** (.85) (.65) (.71) (1.07) (1.99) (1.97) Coaching .0191** .0184** .0189** .0129 .0151* .0138 (2.37) (2.27) (2.30) (1.53) (1.77) (1.61) Def. Injuries .0288 .0342 .0197 -.00416 -.006 -.024 (.44) (.52) (.29) (-.006) (-.09) (-.34) Total Injuries -.0684 -.0680 -.0708 -.0683 .172 -.541* (-.150) (-1.49) (-1.49) (-1.41) (.79) (-1.83) Home .320*** .329*** .312*** .313*** .317*** .339*** (5.41) (5.53) (5.00) (4.91) (4.94) (5.22) At Cap .266*** .257*** .263*** .252*** .215* .263** (4.53) (4.36) (4.26) (3.98) (1.64) (1.99) Pct. Def. Spending on .709 .553 .512 .545 .537 Starters (1.46) (1.09) (.99) (1.04) (1.02) Std. Dev. Def. -1.323 -.580 -1.694 -4.130 Payroll/Total Payroll (-.22) (-.10) (-.27) (-.66) Playoffs Previous .399*** -.585 -.339 Year (4.25) (-.70) (-.40) Pct Cap Defense * 1.810*** 1.545** Playoffs Previous (2.89) (2.45) Year Pct. Payroll Defense * -1.618 -1.613 Playoffs Previous (-1.30) (-1.29) Year Total Injuries * AtCap -.0632 -.105 (-1.00) (-1.63) Total Injuries * Pct -.467 -.033 Payroll Defense (-1.06) (-.07) Total Injuries * Pct .893*** Def Spending on (3.61) Starters Pseudo R2 .0378 .0391 .0386 .0524 .0610 .0698 Observations 2456 2456 2264 2222 2222 2222 Log likelihood -818.988 -817.917 -754.344 -729.733 -723.097 -716.368 * Significant at 90% confidence level ** Significant at 95% confidence level *** Significant at 99% confidence level NOTE. – Standard errors are listed in parentheses.

Table 4 lists results for regressions performed using only the games in which one team was spending at the salary cap and one team was below the salary cap. In this series of regressions, the indicator variable of a team spending at the salary cap was added to the variables already being used. Here percent spending on defense is significant and

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positive. Coaching experience is insignificant, as for teams below the cap. Injuries and home-field advantage were again significant in their usual directions. The indicator for teams at the salary cap is extremely significant and positive, showing that teams using all of their salary allocation have a distinct advantage over those who are not. Two interaction terms, percent of cap on defense and making the playoffs in the previous year, as well as total injuries and percent defensive spending on starters, are significant. They have the same sign as the teams below the salary cap for equivalent reasons.

A second set of regressions was then conducted in a similar manner. In this set of regressions, making the playoffs the previous year was the variable used to divide the data. The first series of regressions consists of games between two playoff teams from the previous year; the second series uses games between two teams that did not make the playoffs the previous year; and the third series consists of games between one playoff team and one non-playoff team.

Table 5 lists results for regressions between two teams that made the playoffs the previous year. This series is notable more for what variables are not significant rather than those that are: coaching, injuries, spending to the salary cap, and the interaction between injuries and defensive starter spending, all of which were significant in previous regressions, were insignificant in this series, as well as percent payroll on defense. Only home-field advantage was found to be a significant variable for games between two playoff teams. In the final regression, the injuries and percent payroll on defense interaction variables are omitted due to their collinearity with the percent payroll on defense.

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Table 5. Conditional Logistic Regression for Games Between Two Teams that Made the Playoffs the Previous Year Variable 1 2 3 4 5 Pct Payroll Defense .213 .0991 .125 - -.992 (.23) (.11) (.13) (-.65) Coaching .018 .0164 .0232 .024 .023 (1.33) (1.19) (1.54) (1.61) (1.52) Def. Injuries .144 .149 .177 .174 .167 (1.40) (1.44) (1.58) (1.55) (1.46) Total Injuries -.0667 -.065 -.064 -.410 -.526 (-.94) (-.91) (-.82) (-1.25) (-1.12) Home .345*** .355*** .312*** .316*** .319*** (3.83) (3.90) (3.17) (3.19) (3.20) At Cap .480*** .483*** .15*** .320 .330 (3.18) (3.19) (3.25) (1.22) (1.25) Pct. Def. Spending on Starters .596 .0997 .028 .044 (.81) (.12) (.03) (.05) Std. Dev. Def. Payroll/Total Payroll 11.922 11.724 11.811 (1.55) (1.50) (1.51) Pct Cap Defense * Playoffs Previous .617 .550 Year (.81) (.70) Pct. Payroll Defense * Playoffs -1.00 - Previous Year (-.66) Total Injuries * At Cap .0638 .062 (.62) (.60) Total Injuries * Pct Payroll Defense .669 .735 (1.00) (1.06) Total Injuries * Pct Def. Spending on .133 Starters (.35) Pseudo R2 .0401 .410 .0448 .0477 .0479 Observations 1076 1076 932 932 932 Log likelihood -357.957 -357.631 -308.542 -307.603 -307.542 * Significant at 90% confidence level ** Significant at 95% confidence level *** Significant at 99% confidence level NOTE. – Standard errors are listed in parentheses.

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Table 6. Conditional Logistic Regression for Games Between Two Teams that Did Not Make the Playoffs Variable 1 2 3 4 5 Pct Payroll Defense 1.011 .555 .512 -1.141 -1.240 (1.62) (.87) (.76) (-1.16) (-1.26) Coaching .0154* .016* .0178** .0182** .0162* (1.84) (1.89) (2.01) (2.06) (1.82) Def. Injuries -.0833 -.072 -.090 -.096 -.142** (-1.31) (-1.12) (-1.33) (-1.42) (-2.04) Total Injuries -.058 -.050 -.051 -.550** -1.265*** (-1.33) (-1.14) (-1.10) (-2.32) (-4.18) Home .328*** .373*** .367*** .371*** .383*** (5.70) (6.32) (5.89) (5.93) (6.06) At Cap .147 .0763 .0652 .165 .189 (1.49) (.76) (.62) (1.11) (1.26) Pct. Def. Spending on Starters 2.52*** 2.270*** 2.303*** 2.07*** (4.82) (3.91) (3.96) (3.51) Std. Dev. Def. Payroll/Total Payroll 1.352 1.722 1.177 (.27) (.34) (.23) Pct Cap Defense * Playoffs Previous - - Year Pct. Payroll Defense * Playoffs - - Previous Year Total Injuries * At Cap -.0536 -.0805 (-.82) (-1.21) Total Injuries * Pct Payroll Defense 1.083** 1.549*** (2.26) (3.08) Total Injuries * Pct Def. Spending on .903*** Starters (3.96) Pseudo R2 .0337 .0471 .0467 .0504 .0608 Observations 2560 2560 2292 2292 2292 Log likelihood -857.359 -845.434 -757.229 -754.297 -746.088 * Significant at 90% confidence level ** Significant at 95% confidence level *** Significant at 99% confidence level NOTE. – Standard errors are listed in parentheses.

Table 6 lists results for the series of regressions between two non-playoff teams.

Percent spending on defense is negative, but insignificant. Coaching, total injuries, and home-field advantage are significant, as usual, while the coefficients for defensive injuries are significant for the first time and negative. Thus, for non-playoff teams, defensive injuries are more damaging to a team’s success than offensive injuries. The interaction terms between injuries and percent payroll on defense and percent of

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defensive payroll on starters variables are both positive and significant, as they have been in some previous regressions. The percent of defensive spending on starters variable is significant and positive, which indicates that increasing the portion of defensive spending devoted to those who start the game on the field increases the probability of victory. This result seems to match the earlier findings that spending more money on those who start the games increases the team’s chance of winning games by diluting the injury effect. It also builds on that logic by suggesting that, in this case, spending more correlates with a higher defensive output and a greater probability of victory. In this series of regressions, the two interaction variables that used the indicator variable for making the playoffs the previous year were not used; all teams had “0”s for those variables because they did not make the playoffs.

Table 7 lists results for games between a playoff team and a non-playoff team.

Percent spending on defense is insignificant, as is total injuries. However, defensive injuries are significant and positive. The logical explanation for this result is that teams consistently underestimate their defensive backups and instead play inferior players more often; however, given the stronger results that indicate paying those “overrated” players more leads to a greater probability of victory, that explanation seems unlikely, and that the result can be seen as an aberration. Coaching experience and home-field advantage are positive and significant, as usual. In addition, the variable for teams at the cap is highly significant and positive, again showing that teams using all of their salary allotment have an advantage over teams that do not do so. However, some of this advantage is potentially mitigated by injuries, as demonstrated by the injuries and at cap

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interaction variables. The fact that it is significant and negative shows that teams at the cap suffer more from injuries than teams below the cap, a finding contrary to expectation and without an immediate explanation. The percent of cap on defense and playoffs the previous year interaction variable, as well as the total injuries and percent of defensive spending on starters interaction variable, are both positive and significant for similar reasons to those described above.

Table 7. Conditional Logistic Regression for Games Between Playoff Teams and Non-Playoff Teams Variable 1 2 3 4 5 Pct Payroll Defense -.774 -.819 -.863 .622 .704 (-1.49) (-1.54) (-1.55) (.61) (.69) Coaching .0135* .0133* .0138* .0151* .0145* (1.79) (1.75) (1.71) (1.87) (1.78) Def. Injuries .0512 .0531 .110* .129** .107* (.90) (.93) (1.79) (2.09) (1.71) Total Injuries -.129*** -.129*** -.158*** .323* -.063 (-3.21) (-3.20) (-3.68) (1.75) (-.25) Home .331 .334*** .310*** .325*** .336*** (6.27) (6.27) (5.47) (5.66) (5.82) At Cap .272*** .271*** .275*** .503*** .519*** (3.09) (3.07) (2.98) (3.62) (3.73) Playoffs Previous Year .358*** .359*** .356*** -.510 -.394 (6.60) (6.62) (6.16) (-.48) (-.57) Pct. Def. Spending on Starters .194 -.215 -.229 -.208 (.44) (-.45) (-.48) (-.43) Std. Dev. Def. Payroll/Total 7.904* 7.816* 7.168 Payroll (1.68) (1.66) (1.51) Pct Cap Defense * Playoffs .960** .843* Previous Year (2.00) (1.75) Pct. Payroll Defense * Playoffs -.134 -.167 Previous Year (-.12) (-.15) Total Injuries * At Cap -.196*** -.217*** (-3.48) (-3.78) Total Injuries * Pct Payroll -.865** -.646 Defense (-2.22) (-1.60) Total Injuries * Pct Def. Spending .505** on Starters (2.25) Pseudo R2 .0569 .0570 .0588 .0700 .0727 Observations 3166 3166 2806 2806 2806 Log likelihood -1034.774 -1034.679 -915.294 -904.396 -901.832 * Significant at 90% confidence level ** Significant at 95% confidence level *** Significant at 99% confidence level NOTE. – Standard errors are listed in parentheses.

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7. Discussion

In order to examine the magnitude and meaning of the results, the 2008 season was analyzed. The year 2008 was chosen because it was the most recent year of data used in the study, and the number of teams that were at the salary cap was representative of the data at large. Variables used in the regressions were tabulated for each team, and the median for each variable was found. A hypothetical team with all characteristics at the median level was then devised, and the probability of victory against each actual team in the league was calculated. These probabilities were added together to find the total number of expected wins in a mythical season in which the median team would play all teams involved. For this analysis, the number of injuries was assumed to be at the median level. From this number, the expected winning percentage of the median team was found. Then, the variables were slightly tweaked to find the magnitude of a realistic change for each significant variable in the series of regressions. These variable changes influenced the probabilities of victory, which in turn influenced the total number of expected wins and the expected winning percentage. These winning percentages were placed into charts, which can be seen in Appendix C along with the raw data for each team from the 2008 season. The charts are organized by whether the median team is at the cap, below the cap, a playoff team, or not a playoff team. The horizontal lines are placed at intervals of 0.0625, which is the amount that the expected winning percentage would have to increase to represent one extra expected win.

For teams at the salary cap, the first noticeable trend is the effect that home-field advantage has on expected winning percentage. If a team at the cap were able to play

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every single game at home, its winning percentage would increase by about 8 to 10%, whether or not their opponents spent to the salary cap, which represents a full extra expected win. However, NFL teams are required to play eight home games and eight away games, so this result does not bear any policy implications beyond hoping that the best opponents are scheduled for home games. Another notable trend is that spending more or less of the payroll on defense does not alter the expected winning percentage against other teams at the salary cap but does increase the number of expected wins when opponents do not spend to the salary cap. Injuries are costly: for either type of opponent, having one more injury than the opponent equates to a drop of slightly less than one-half in expected wins. However, the injury effect can be neutralized by increasing the portion of defensive payroll on starters when playing teams at the cap by 5%, and increasing percent starter spending by 10% from the median leads to almost a full extra expected win. Meanwhile, one extra year of coaching made only a slight difference and was only significant against other teams at the cap. The results suggest that in order for extra coaching experience to win an additional football game, it would take a coach with 13 years of experience over the median of 5 – coaches in the league rarely have that much experience. In fact, no coaches in the entire league had that much experience in the 2008 season. This trend was constant throughout all other analyses. Thus, it seems that the most effective strategies for maximizing expected wins as a team spending at the salary cap limit would be to increase defensive spending on starters and defensive spending as a portion of payroll (to a lesser extent) and minimize injuries.

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For teams below the salary cap, increasing the percent of defensive spending is a viable strategy, although only for opponents at the salary cap because the variable was insignificant against other teams below the salary cap. Furthermore, the positive effect only exists when combined with an extra injury compared to the opponent. Increasing the percent of payroll on defense by 10% is almost enough to generate an extra expected win against teams at the salary cap, but is not a significant factor against teams below the salary cap. An unusual trend for teams below the cap is that making the playoffs the previous year leads to disastrous results the next year, especially in concert with adjusting the level of defensive spending. Even injuries are not nearly as costly as they were for teams at the cap unless they are combined with making the playoffs the previous year.

Overall strategies for a team below the salary cap vary depending on the expected number of injuries for the season: if the team is particularly injury-plagued, it should increase spending on defensive starters and possibly increase overall defensive spending if it has many opponents who are spending to the limit. Additionally, teams that make the playoffs in a particular year should not let total spending fall far below the salary cap because no good strategy exists for playoff teams when they are below the cap.

For teams who made the playoffs the previous year, two predominant strategies exist: spend to the salary cap and increase percent defensive spending on starters.

Increasing the percent of defensive payroll on starters by 10% translates to an entire extra expected win. Additionally, spending to the salary cap increases the number of expected victories by almost one-half game if the opponents were not playoff teams. Although a

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“side effect” to spending at the cap is an increased injury effect, spending at the cap is still a net benefit.

The data from teams that did not make the playoffs the previous year contain a distinct trend for injuries to defensive players and injuries at large. When facing a non-playoff opponent, having an extra injury to a defensive player when the portion of defensive payroll was increased 5% caused about a half-game lower number of expected wins than a non-defensive injury. This trend appeared when the median team was both at the cap and below the cap. To further complicate matters, defensive injuries actually caused the number expected wins to increase when facing playoff teams, a result that lacks good explanation. Continuing the findings from other analyses, increasing the portion of defensive payroll devoted to starters increased the expected number of wins significantly, particularly against other non-playoff teams.

8. Conclusions

Appendix D shows the implied strategies for a team given its characteristics and those of its opponents. Given the results detailed above, several important conclusions can be reached. First, there is no evidence to suggest that increased spending on defense significantly improves the probability of winning a particular game, independent of the circumstances. However, in certain situations, particularly in games between a team at the salary cap and a team below the salary cap, increasing the portion of payroll devoted to defensive players increased the probability of victory. However, in games between two teams below the salary cap, the percent of payroll devoted to defense was negatively

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correlated with victory, which indicates that, in those cases, offensive spending was an important factor. Coaching was found to be significantly correlated with victory, although further analysis suggested that its effects described in previous literature may be overstated, given that a median team would have to have a head coach with 13 extra years of experience in order to gain a single expected win for the season. For the most part, injuries were significant and had a downward effect on the probability of victory; their effect on expected wins over the course of a season depended on the opponent but was generally large enough to conclude that teams with several injuries are at a distinct disadvantage to their opponents. This injury effect could, however, be negated in several situations by increasing the portion of defensive spending paid to starting players. In fact, the percentage of defensive payroll spent on starters was the most consistently significant of all spending variables in the study; in almost all situations, teams could increase the amount of defensive money given to their starters and see their expected win total for a season improve. The exact amount by which the number of expected wins increases depends on the characteristics of the team and its 16 opponents in a season and is difficult to decipher precisely. However, given that winning one extra game could be the difference between going to the playoffs and finishing last in the division, the effect of increasing the portion of defensive spending on starters can be considered significant.

Therefore, instead of the common adage “defense wins championships,” a more correct maxim would be “defensive starters win championships.”

The results of this analysis suggest several areas of study for the future. First, additional study could more fully explore the ramifications of increased spending on

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defensive starters. One way in which it could do this is by breaking down the effect by position to see if starting linebackers are a better investment than starting defensive lineman or cornerbacks. Second, future studies could incorporate a time lag on several pieces of data beyond making the playoffs. Time lags could determine the benefit or detriment of not spending to the salary cap in a particular year in order to sign more talented players for next year. Finally, a fixed effect could be included in the regressions in order to account for some differences in management between franchises over a period of time. This analysis finds that increasing salary allocations to defensive starters as a portion of overall defensive spending has a positive effect on the probability of victory, which is perhaps good news for high quality defensive players. Further study may generate additional significant findings about professional football salary strategies.

Eric Ness was a four-year letter winner for Duke's Swimming and Diving Team, setting a team record in the 200 yard butterfly his junior year. He will be attending the

University of Virginia School of Medicine in the fall and can be reached at [email protected] .

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Appendix A. Sample Salary Data

1995 Defensive Unit Salary Statistics Total Unit Salary for % of % of Cap % on Team Salary Std. Dev. Starters Payroll ($37.1M) Starters Arizona $18,544,900.00 $836,491.63 $13,939,368.75 54.37% 49.99% 75.17% Atlanta $18,434,900.00 $648,223.01 $12,161,818.75 50.95% 49.69% 65.97% Buffalo $17,809,600.00 $797,552.35 $13,000,331.25 49.84% 48.00% 73.00% Carolina $14,984,500.00 $695,212.00 $11,101,506.25 49.41% 40.39% 74.09% Chicago $14,137,500.00 $447,325.02 $9,701,762.50 42.92% 38.11% 68.62% Cincinnati $13,567,100.00 $639,259.68 $8,637,718.75 39.39% 36.57% 63.67% Cleveland $13,718,600.00 $473,690.18 $9,797,150.00 46.14% 36.98% 71.42% Dallas $14,741,800.00 $567,346.29 $8,714,862.50 42.01% 39.74% 59.12% Denver $15,297,800.00 $594,079.11 $10,162,843.75 45.60% 41.23% 66.43% Detroit $14,382,800.00 $563,658.98 $10,787,987.50 40.07% 38.77% 75.01% Green Bay $15,176,300.00 $938,862.33 $12,075,681.25 46.31% 40.91% 79.57% Houston $13,498,000.00 $566,568.01 $9,124,787.50 41.51% 36.38% 67.60% Indianapolis $15,665,900.00 $690,405.00 $11,619,031.25 46.20% 42.23% 74.17% Jacksonville $13,354,500.00 $531,098.68 $9,097,256.25 44.75% 36.00% 68.12% Kansas City $17,285,000.00 $788,993.12 $13,548,706.25 48.32% 46.59% 78.38% Miami $14,904,500.00 $501,295.00 $10,771,512.50 42.20% 40.17% 72.27% Minnesota $13,972,000.00 $532,566.93 $9,757,700.00 39.33% 37.66% 69.84% New England $14,100,800.00 $536,409.62 $9,350,993.75 42.40% 38.01% 66.32% New Orleans $13,938,300.00 $574,645.63 $9,491,550.00 43.67% 37.57% 68.10% New York Giants $14,235,900.00 $433,416.98 $9,709,087.50 40.31% 38.37% 68.20% New York Jets $14,981,400.00 $435,101.99 $9,504,625.00 48.06% 40.38% 63.44% Oakland $14,628,700.00 $445,334.91 $9,509,731.25 41.67% 39.43% 65.01% Philadelphia $14,529,300.00 $631,913.30 $10,121,462.50 41.50% 39.16% 69.66% Pittsburgh $16,868,900.00 $764,210.16 $10,588,093.75 47.10% 45.47% 62.77% San Diego $16,246,400.00 $931,766.20 $13,910,750.00 46.26% 43.79% 85.62% San Francisco $13,268,000.00 $475,961.09 $9,845,812.50 37.80% 35.76% 74.21% Seattle $14,725,700.00 $675,169.59 $10,799,012.50 40.73% 39.69% 73.33% St. Louis $16,694,400.00 $641,592.92 $11,844,456.25 48.60% 45.00% 70.95% Tampa Bay $15,432,900.00 $422,665.00 $9,265,481.25 44.17% 41.60% 60.04% Washington $16,345,100.00 $730,622.00 $12,833,425.00 46.43% 44.06% 78.52%

Minimum $13,268,000.00 $422,665.00 $8,637,718.75 37.80% 35.76% 59.12% Maximum $18,544,900.00 $938,862.33 $13,939,368.75 54.37% 49.99% 85.62% Average $15,182,383.33 $617,047.89 $10,692,483.54 44.60% 40.92% 70.29% Std. Dev. $1,483,590.28 $145,342.12 $1,571,304.62 3.95 4.00 6.01

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1995 Offensive Unit Salary Statistics Total Unit Salary for % of % of Cap % on Team Salary Std. Dev. Starters Payroll ($37.1M) Starters Arizona $14,137,800.00 $699,937.42 $10,460,718.75 41.45% 38.11% 73.99% Atlanta $15,638,200.00 $608,531.44 $10,993,750.00 43.22% 42.15% 70.30% Buffalo $15,838,300.00 $703,132.43 $10,503,018.75 44.33% 42.69% 66.31% Carolina $12,193,400.00 $455,939.47 $5,859,768.75 40.21% 32.87% 48.06% Chicago $15,613,700.00 $616,136.99 $9,185,856.25 47.41% 42.09% 58.83% Cincinnati $17,577,500.00 $867,022.24 $11,796,781.25 51.04% 47.38% 67.11% Cleveland $14,841,600.00 $503,043.28 $8,879,037.50 49.92% 40.00% 59.83% Dallas $16,950,800.00 $819,267.61 $13,835,518.75 48.31% 45.69% 81.62% Denver $17,566,100.00 $969,134.11 $13,324,493.75 52.36% 47.35% 75.85% Detroit $19,878,900.00 $938,395.71 $15,969,543.75 55.38% 53.58% 80.33% Green Bay $14,492,900.00 $718,471.29 $10,502,806.25 44.23% 39.06% 72.47% Houston $15,785,600.00 $557,880.56 $7,517,981.25 48.54% 42.55% 47.63% Indianapolis $17,024,700.00 $728,521.05 $10,671,818.75 50.21% 45.89% 62.68% Jacksonville $14,295,400.00 $544,481.98 $6,682,956.25 47.91% 38.53% 46.75% Kansas City $15,919,300.00 $504,544.22 $9,543,112.50 44.50% 42.91% 59.95% Miami $18,592,100.00 $863,254.44 $13,061,575.00 52.64% 50.11% 70.25% Minnesota $19,847,200.00 $837,655.56 $13,403,887.50 55.87% 53.50% 67.54% New England $18,399,400.00 $896,865.41 $11,402,293.75 55.32% 49.59% 61.97% New Orleans $16,424,100.00 $664,244.31 $12,007,331.25 51.46% 44.27% 73.11% New York Giants $19,385,200.00 $665,972.42 $13,442,956.25 54.89% 52.25% 69.35% New York Jets $14,189,000.00 $587,915.25 $7,137,962.50 45.52% 38.25% 50.31% Oakland $17,287,800.00 $631,699.42 $11,627,612.50 49.25% 46.60% 67.26% Philadelphia $18,268,700.00 $801,115.98 $10,737,475.00 52.18% 49.24% 58.78% Pittsburgh $17,791,900.00 $663,989.10 $11,287,875.00 49.68% 47.96% 63.44% San Diego $16,869,100.00 $617,486.46 $11,117,425.00 48.03% 45.47% 65.90% San Francisco $20,370,900.00 $955,695.28 $13,554,087.50 58.04% 54.91% 66.54% Seattle $17,726,300.00 $845,556.26 $11,701,093.75 49.03% 47.78% 66.01% St. Louis $16,863,500.00 $500,402.19 $10,251,112.50 49.09% 45.45% 60.79% Tampa Bay $17,965,500.00 $735,134.42 $12,780,887.50 51.42% 48.42% 71.14% Washington $15,978,100.00 $621,356.32 $7,509,175.00 45.39% 43.07% 47.00%

Minimum $12,193,400.00 $455,939.47 $5,859,768.75 40.21% 32.87% 46.75% Maximum $20,370,900.00 $969,134.11 $15,969,543.75 58.04% 54.91% 81.62% Average $16,790,433.33 $704,092.75 $10,891,663.75 49.23% 45.26% 64.37% Std. Dev. $1,927,077.79 $146,754.41 $2,363,457.84 4.39 5.19 9.43

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Arizona Cardinals Defensive Unit Salary Statistics Total Unit % on Team Salary Std. Dev. % of Payroll % of Cap Starters 1995 $18,544,900.00 $836,491.63 54.37% 49.99% 75.17% 1996 $20,374,500.00 $1,104,202.55 54.61% 49.97% 84.34% 1997 $20,013,100.00 $1,059,757.17 53.21% 48.28% 76.00% 1998 $23,412,900.00 $1,133,587.27 46.14% 44.69% 53.76% 1999 $26,753,200.00 $1,167,755.07 48.73% 45.85% 48.79% 2000 $26,672,500.00 $965,339.98 45.51% 42.90% 59.95% 2001 $20,800,709.00 $661,353.28 27.77% 30.86% 48.82% 2002 $31,656,465.00 $1,897,446.75 47.27% 44.52% 55.48% 2003 $29,041,612.00 $1,186,393.24 35.84% 38.72% 53.19% 2004 $41,370,856.00 $1,934,005.77 52.39% 52.51% 66.02% 2005 $30,073,665.00 $1,547,531.31 39.29% 35.17% 66.05% 2006 $36,706,699.00 $1,405,371.44 34.73% 38.84% 69.61% 2007 $42,956,057.00 $1,547,697.22 43.52% 39.41% 57.76% 2008 $53,455,110.00 $2,043,413.65 43.78% 46.08% 68.46%

Arizona Cardinals Offensive Unit Salary Statistics Total Unit % on Team Salary Std. Dev. % of Payroll % of Cap Starters 1995 $14,137,800.00 $699,937.42 41.45% 38.11% 73.99% 1996 $16,214,700.00 $707,346.74 43.46% 39.76% 61.24% 1997 $17,028,500.00 $768,401.00 45.27% 41.08% 65.07% 1998 $26,617,000.00 $992,442.46 52.45% 50.81% 70.01% 1999 $27,488,300.00 $1,220,072.40 50.07% 47.11% 59.31% 2000 $31,103,600.00 $1,401,145.49 53.07% 50.03% 56.86% 2001 $51,766,438.00 $2,817,581.49 69.12% 76.80% 70.01% 2002 $34,392,075.00 $1,410,248.75 51.36% 48.37% 54.08% 2003 $49,831,947.00 $2,056,988.39 61.49% 66.44% 58.69% 2004 $35,948,289.00 $1,782,582.35 45.53% 45.63% 64.97% 2005 $43,219,996.00 $1,916,461.94 56.47% 50.55% 65.25% 2006 $66,423,733.00 $3,410,061.21 62.85% 70.29% 72.85% 2007 $54,648,480.00 $2,379,304.80 55.37% 50.14% 59.87% 2008 $67,240,400.00 $3,572,429.95 55.07% 57.97% 66.05%

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Appendix B: Initial Regression Results

Variable 1 2 3 4 Pct. Cap on Defense -1.309 (-.68) Pct. Cap on Defense 2 .287 (.15) Pct. Payroll on Defense -9.728*** (-2.58) Pct Payroll on Defense 2 9.458** (2.32) Pct Def. Starters -11.393*** -11.072*** (-3.85) (-3.75) Pct Def. Starters 2 9.573*** 9.327*** (4.07) (3.96) Pct. Cap on Offense 4.698** (2.24) Pct. Cap on Offense 2 -5.048*** (-2.72) Pct. Payroll on Offense -5.531 (-1.30) Pct. Payroll on Offense 2 4.825 (1.21) Pct. Off. Starters -4.249* -2.508 (-1.91) (-1.15) Pct. Off. Starters 2 5.451*** 3.843** (2.90) (2.08) Coaching .0154*** .0157** .0126** .0139*** (2.80) (2.85) (2.41) (2.66) Playoffs Previous Year .355 .346*** .337*** .332 (6.23) (6.06) (.6.26) (6.16) Off. Injuries .033 .032 (.83) (.81) Def. Injuries .045 .042 (1.07) (1.00) Total Injuries -.104*** -.104*** -.090*** -.093*** (-3.58) (-3.59) (-3.42) (-3.54) Payroll Percent of Cap 1.440*** .990*** .915** .719*** (3.90) (4.24) (2.44) (3.09) More on Offense -.132 -.093 -.131 -.088 (-1.56) (-1.04) (-1.59) (-1.05) Std. Dev. Def. Payroll/Total 4.759 4.809 Payroll (1.52) (1.53) Home .337*** .335*** .377*** .376 (8.72) (8.66) (10.10) (10.07) Number of Observations 6030 6030 6802 6802 Pseudo R 2 Value .0487 .0500 .0562 .0547

Ness 42 Appendix C: 2008 Variable Data and Winning Percentage % Payroll Pct. Def. Std. Dev. Playoffs Pct Cap Pct Payroll Total Total Injuries * Total Injuries * At Coaching Def. Total on Spending Def. Payroll / Prev. Defense * Defense * Injuries * Pct. Payroll Pct. Def. Spending Team Cap Years Injuries Injuries Home Defense Starters Total Payroll Year Playoffs Prev. Playoffs Prev. At Cap Defense Starters Arizona 1 2 (median) (median) (median) 0.44276 0.676909942 0.038 0 0 0 2 0.885518652 1.353819884 Atlanta 0 1 (median) (median) (median) 0.46113 0.642487729 0.036 0 0 0 0 0.92226521 1.284975458 Baltimore 0 1 (median) (median) (median) 0.66041 0.577113972 0.037 0 0 0 0 1.320812733 1.154227944 Buffalo 1 9 (median) (median) (median) 0.5077 0.538841752 0.036 0 0 0 2 1.015399904 1.077683503 Carolina 1 7 (median) (median) (median) 0.43973 0.711546201 0.050 0 0 0 2 0.879455329 1.423092401 Chicago 1 5 (median) (median) (median) 0.59374 0.638440536 0.048 0 0 0 2 1.187473297 1.276881071 Cincinnati 0 6 (median) (median) (median) 0.47785 0.547852553 0.056 0 0 0 0 0.955695125 1.095705107 Cleveland 1 4 (median) (median) (median) 0.37113 0.652895514 0.045 0 0 0 2 0.74226339 1.305791028 Dallas 1 9 (median) (median) (median) 0.41714 0.626964543 0.048 1 0.518645 0.417137108 2 0.834274216 1.253929086 Denver 0 16 (median) (median) (median) 0.56589 0.546274318 0.045 0 0 0 0 1.131773298 1.092548635 Detroit 0 3 (median) (median) (median) 0.48131 0.502139412 0.027 0 0 0 0 0.962611366 1.004278824 Green Bay 0 3 (median) (median) (median) 0.54238 0.512984743 0.035 1 0.434388621 0.542384621 0 1.084769242 1.025969485 Houston 0 3 (median) (median) (median) 0.42241 0.589282515 0.035 0 0 0 0 0.84481194 1.178565031 Indianapolis 0 13 (median) (median) (median) 0.34723 0.294414635 0.046 1 0.273199828 0.347229095 0 0.69445819 0.588829269 Jacksonville 1 6 (median) (median) (median) 0.45785 0.593976391 0.036 1 0.478718448 0.457845083 2 0.915690166 1.187952782 Kansas City 0 8 (median) (median) (median) 0.52295 0.441698084 0.045 0 0 0 0 1.045901969 0.883396169 Miami 1 1 (median) (median) (median) 0.48527 0.495931156 0.033 0 0 0 2 0.970534077 0.991862312 Minnesota 1 3 (median) (median) (median) 0.55271 0.703058029 0.058 0 0 0 2 1.105417687 1.406116059 New England 0 14 (median) (median) (median) 0.37494 0.495387339 0.025 1 0.293175345 0.374943548 0 0.749887097 0.990774678 New Orleans 1 3 (median) (median) (median) 0.54228 0.594546243 0.042 0 0 0 2 1.084555053 1.189092486 New York Giants 1 13 (median) (median) (median) 0.39072 0.553842612 0.044 1 0.374338448 0.390720364 2 0.781440728 1.107685224 New York Jets 1 3 (median) (median) (median) 0.49143 0.731086916 0.049 0 0 0 2 0.982865184 1.462173833 Oakland 1 1.5 (median) (median) (median) 0.44859 0.7134993 0.056 0 0 0 2 0.897175762 1.4269986 Philadelphia 0 10 (median) (median) (median) 0.53555 0.475599432 0.055 0 0 0 0 1.07110983 0.951198864 Pittsburgh 1 2 (median) (median) (median) 0.38596 0.668594398 0.035 1 0.417799491 0.385905969 2 0.771811939 1.337188796 San Diego 1 11 (median) (median) (median) 0.50536 0.646956782 0.042 1 0.477160862 0.50536063 2 1.010721261 1.293913564 San Francisco 1 2.5 (median) (median) (median) 0.50244 0.599489337 0.045 0 0 0 2 1.004889176 1.198978674 Seattle 0 17 (median) (median) (median) 0.39977 0.730981565 0.047 1 0.351086552 0.399774299 0 0.799548598 1.46196313 St. Louis 1 5 (median) (median) (median) 0.34434 0.625464545 0.045 0 0 0 2 0.68867305 1.250929091 Tampa Bay 0 11 (median) (median) (median) 0.38223 0.586174978 0.032 1 0.336824776 0.38222848 0 0.764456961 1.172349957 Tennessee 1 15 (median) (median) (median) 0.44117 0.627228911 0.037 1 0.464564336 0.441167045 2 0.882334091 1.254457823 Washington 1 1 (median) (median) (median) 0.38390 0.500018013 0.044 1 0.366997103 0.383902284 2 0.767804568 1.000036026 Median 1 5 1 2 0 0.45949 0.594261317 0.044 0 0 0 2 0.918977688 1.188522634

Winning Percentage of Teams at the Salary Cap vs. Opponent At the Cap

At Cap vs. At Cap

0.75

0.6875

0.625 0.5625

0.5

0.4375

0.375 WinningPercentage 0.3125

0.25

e e e y ur jury Year ens nj n Hom f ens I I arters Neutral Away f. . De f St Off. Injury Def O Def on on ra tra tra xt Extra Def. InjuryE Ex Ex ore 1 1 M , , Extra Coaching 5% 5% More 5% Less oners ers art art St St on on

5% More 5% More Variables

Winning Percentage of Teams at the Salary Cap vs. Opponent Below the Cap

At Cap vs. Below Cap

0.75

0.6875

0.625

0.5625

0.5

0.4375 Winning Percentage Winning 0.375

0.3125

0.25 Neutral Home Aw ay Increase Increase One Extra One Extra Playoffs Playoffs Pct Pct Injury Injury, 5% Previous Previous Spending Spending Increase Year Year, 5% Def. 5% Def. 10% Def. Increase Starters Pct. Def. Payroll and Cap Variables

Winning Percentage of Teams Below the Salary Cap vs. Opponent At the Cap

Below Cap vs. At Cap

0.75

0.6875

0.625

0.5625

0.5

0.4375 Winning Percentage Winning 0.375

0.3125

0.25 Neutral Home Away Increase Increase One Extra Increase Increase One Extra Increase Pct Pct Injury Pct Pct Injury, Pct Spending Spending Spending Spending Make Spending Def. 5% Def. 10% Def. 5%, Def. Playoffs Def. One Extra Starters Starters Injury 5%, One 5% Extra Injury Variables

Winning Percentage of Teams Below the Salary Cap vs. Opponent Below the Cap

Below Cap vs. Below Cap

0.75 0.6875 0.625 0.5625 0.5 0.4375 0.375 0.3125 Winning Percentage Winning 0.25 0.1875 0.125

r y y y r % % % r tral me way jur 5 5% ju u A nju n .5 Ho I se In Ne f. f. I n ll 0 a Of De fe yro a a tr revious Year De P f. Payroll 1 , Extr x P l Defense 5% Coaching Yea E p f. ol % a Extra fs . De 5 r f Ca De ayr e y P s Ext v. lar e fen Playo D Sa . Pct De ll, se p ro Std a se re Ca a rease Std. Dev y Inc lar cre Inc Pct Pay In se a yroll, Sa e a cr P In s, ff Pct yo se la a P re Playoffs, Decrease Pct Payroll, Salary Cap Defense c In

Variables

Winning Percentage of Teams that Made the Playoffs vs. Playoff Teams

Playoffs Previous vs. Playoffs Previous

0.75

0.6875

0.625

0.5625

0.5

0.4375 WinningPercentage 0.375

0.3125

0.25 Neutral Home Aw ay Increase Pct Increase Pct At Cap Payroll Def. 5% Payroll Def. 10% Variables

Winning Percentage of Teams that Made the Playoffs vs. Non-Playoff Teams

Playoffs Previous vs. No Playoffs

0.75 0.6875 0.625 0.5625 0.5 0.4375 0.375 0.3125 WinningPercentage 0.25 Neutral Home Aw ay Extra One Extra One Extra One Extra One Extra At Cap Coaching Def. Injury, Def. Injury, Def. Injury, Def. Injury, Year Not At Cap At Cap Increase Increase Pct Pct Spending Spending Def. Def. Starters Starters 5%, Not At 5%,At Cap Cap Variables

Ness 46

Winning Percentage of Non-Playoff Teams vs. Playoff Teams

No Playoffs vs. Playoffs Previous

0.75 0.6875 0.625 0.5625 0.5 0.4375 0.375

0.3125 WinningPercentage 0.25 Neutral Home Aw ay Extra One Extra One Extra One Extra One Extra Coaching Def. Injury, Def. Injury, At Def. Injury, Def. Injury, Year Not At Cap Cap Increase Pct. Increase Pct. Spending Def. Spending Def. Starter 5%, Starter 5%, Not At Cap At Cap Variables

Winning Percentage of Non-Playoff Teams vs. Non-Playoff Teams

No Playoffs vs. No Playoffs

0.75

0.6875

0.625

0.5625

0.5

0.4375

0.375 Winning Percentage

0.3125

0.25 Neutral Home Aw ay Increase Pct Increase Pct Increase Pct Increase Pct Increase Pct Increase Pct Increase Pct Increase Pct Extra Payroll Payroll Payroll Payroll Payroll Def. Def. Def. Coaching Defense 5% Defense Defense Defense Defense Starters 5% Starters Starters Year 5%, One 5%, One 5%, One 5%, One 5%, One 5%, One Extra Off. Extra Off. Extra Def. Extra Def. Extra Off. Extra Def. Injury, Not Injury, At Injury, Not Injury, At Injury Injury At Cap Cap At Cap Cap Variables

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Appendix D: Implied Strategies by Team and Opponent

Team

Opponent

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References

Associated Press. “2009 Major League Baseball Salaries.” Retrieved September 5, 2009, from http://www.sportingnews.com/mlb/article/2009-04-09/2009-major- league-baseball-payrolls.

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Lackner, Al. “Salary Cap FAQ.” Askthecommish.com LLC. http://www.askthecommish.com/salarycap/faq.asp. Updated 19 January 2009.

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Data Sources

Rosters, Game, Seasonal, and Coaching Statistics:

Sports Reference LLC. www.pro-football.reference.com

USA Today Salary Database. Accessed through http://www.rodneyfort.com/PHSportsEcon/Common/OtherData/NFLSalaries/

Salary Cap: http://www.atlantafalcons.com/People/Fans/Salary_Cap_101/SCFeature.aspx (official website of an NFL team)

Naylor, David. “What Parity?” The Globe and Mail Oct. 30, 2009. Accessed through http://www.theglobeandmail.com/sports/what-parity/article1344720/

Injuries: http://www.jt-sw.com/football/pro/index.nsf/Historical?OpenPage

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