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 smallermarket 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 smallmarket 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 jtsw.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( X A β ) / (exp( X A β ) + exp( X B β ))
This equation can be rewritten as:
(( X − X ) β )
P(Team A) = 1 / (1 + e B A )
Both of these equations represent the probability that Team A will defeat Team B.
The variables XA and XB are not important individually; rather, it is the difference
between them that matters. XA and XB 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 offense1, 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.
Variable
Winning %
Winning % Against At Cap
Winning % Against Below
Cap
Winning % Against More on
Offense
Winning % Against More on
Defense
Playoffs Previous Year
Coaching
Std. Dev. Offense Spending
Std. Dev. Defensive
Spending
% Offense Spending on
Starters
% Defense Spending on
Starters
At Cap (>=.95
of Cap)
More on
Offense
More on
Defense
Below Cap
(<.95)
More on
Offense
More on
Defense
0.527380952
0.504596527
0.534970238
0.509339975
0.478
0.411842105
0.482
0.470954357
0.559201141
0.573012939
0.509057971
0.485981308
0.534552846
0.537748344
0.476830087
0.475258918
0.517241379
0.485714286
6.620833333
2,366,418.19
0.531409168
0.321189591
7.427710843
1,574,594.45
0.481121899
0.390566818
6.150662252
1,319,303.99
0.489019034
0.319381842
5.898840206
958,521.94
1,621,615.29
2,111,396.74
976,501.49
1,339,630.54
0.651442654
0.596375697
0.61868333
0.581789041
0.628833564
0.664445695
0.644115345
0.645990799
2417
1553
# of Entries
1680
1346
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
Ness 23
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.
Ness 24
Table 2. Conditional Logit Regression of Teams At the Salary Cap
Variable
1
2
3
4
Pct Payroll Defense
-.608
-.750
-.785
-.800
(-.94)
(-1.10)
(-1.14)
(-1.15)
Coaching
.0277*** .0275*** .0277*** .0221**
(2.90)
(2.86)
(2.88)
(2.25)
Def. Injuries
.102
.105
.111
.113
(1.38)
(1.42)
(1.49)
(1.51)
Total Injuries
-.187*** -.186*** -.195*** -.205***
(.3.53)
(-3.51)
(-3.67)
(-3.79)
Home
.293*** .302***
.297***
.306***
(4.25)
(4.30)
(4.22)
(4.28)
Pct. Def. Spending on
.373
.144
.663
Starters
(.66)
(.25)
(1.09)
Std. Dev. Def. Payroll/Total
8.85
8.24
Payroll
(1.24)
(1.13)
Playoffs Previous Year
.373***
(3.49)
Pct Cap Defense * Playoffs
Previous Year
Pct. Payroll Defense *
Playoffs Previous Year
Total Injuries * Pct. Payroll
Defense
Total Injuries * Pct Def.
Spending on Starters
Total Injuries * At Cap
Pseudo R2
.0344
.0348
.0369
.0475
Observations
1780
1780
1768
1758
Log Likelihood
-595.672 -595.451 -590.117 -580.324
5
-.0468
(-.04)
.0223**
(2.25)
.124
(1.64)
-.016
(-.07)
.306***
(4.28)
.628
(1.03)
7.53
(1.03)
-.344
(-.33)
.651
(.87)
.006
(.00)
-.417
(-.89)
6
.015
(.01)
.0206**
(2.08)
.078
(.99)
-.543*
(-1.75)
.320***
(4.44)
.553
(.91)
7.56
(1.03)
-.033
(-.03)
.234
(.31)
.242
(.18)
-.102
(-.21)
.659**
(2.45)
.0488
1758
-579.518
.0539
1758
-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
Ness 25
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
Pct Payroll Defense
-1.117* -1.363** -1.350*
-.995
(-1.74) (-2.10) (-1.86)
(-1.35)
Coaching
.0156* .0151* .0179*
.0136
(1.74)
(1.68)
(1.71)
(1.25)
Def. Injuries
-.044
-.035
.0207
.0337
(-.70)
(-.56)
(.30)
(.47)
Total Injuries
-.053
-.0477
-.0593
-.0480
(-1.25) (-1.13) (-1.25)
(-.98)
Home
.357*** .387*** .374***
.375***
(6.40)
(6.81)
(5.78)
(5.66)
Pct. Def. Spending on
1.764*** .860
.647
Starters
(3.34)
(1.40)
(1.03)
Std. Dev. Def. Payroll/Total
9.691**
9.895**
Payroll
(2.35)
(2.35)
Playoffs Previous Year
.361***
(3.66)
Pct Cap Defense * Playoffs
Previous Year
Pct. Payroll Defense *
Playoffs Previous Year
Total Injuries * At Cap
Total Injuries * Pct. Payroll
Defense
Total Injuries * Pct Def.
Spending on Starters
Pseudo R2
.0286
.0346
.0310
.0395
Observations
2722
2722
2126
2050
Log likelihood
-916.363 -910.704 -713.985
-682.434
5
-1.948
(-1.63)
.0162
(1.46)
.-269
(-.37)
-.388
(-1.61)
.375***
(5.63)
.537
(.85)
9.620**
(2.28)
-1.45
(-1.16)
2.165*
(1.79)
-.196
(-.13)
6
-1.996*
(-1.67)
.0145
(1.34)
.002
(.03)
-.728**
(-2.35)
.383***
(5.73)
.487
(.77)
9.535**
(2.25)
-1.44
(-1.15)
2.136*
(1.77)
-.192
(-.13)
.720
(1.42)
.919*
(1.76)
.445*
(1.76)
.0456
2050
-678.079
.0434
2050
-679.652
* Significant at 90% confidence level
** Significant at 95% confidence level
*** Significant at 99% confidence level
NOTE. – Standard errors are listed in parentheses.
Ness 26
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
Ness 27
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.
Ness 28
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.
Ness 29
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
Ness 30
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
Ness 31
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.
Ness 32
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
Ness 33
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.
Ness 34
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
Ness 35
“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
Ness 36
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
Ness 37
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
ecn3fg@virginia.edu.
Ness 38
Appendix A. Sample Salary Data
Team
Total Unit
Salary
1995 Defensive Unit Salary Statistics
Salary for
% of
Std. Dev.
Starters
Payroll
% of Cap
($37.1M)
% on
Starters
Arizona
Atlanta
Buffalo
Carolina
Chicago
Cincinnati
Cleveland
Dallas
Denver
Detroit
Green Bay
Houston
Indianapolis
Jacksonville
Kansas City
Miami
Minnesota
New England
New Orleans
New York
Giants
New York
Jets
Oakland
Philadelphia
Pittsburgh
San Diego
San Francisco
Seattle
St. Louis
Tampa Bay
Washington
$18,544,900.00
$18,434,900.00
$17,809,600.00
$14,984,500.00
$14,137,500.00
$13,567,100.00
$13,718,600.00
$14,741,800.00
$15,297,800.00
$14,382,800.00
$15,176,300.00
$13,498,000.00
$15,665,900.00
$13,354,500.00
$17,285,000.00
$14,904,500.00
$13,972,000.00
$14,100,800.00
$13,938,300.00
$836,491.63
$648,223.01
$797,552.35
$695,212.00
$447,325.02
$639,259.68
$473,690.18
$567,346.29
$594,079.11
$563,658.98
$938,862.33
$566,568.01
$690,405.00
$531,098.68
$788,993.12
$501,295.00
$532,566.93
$536,409.62
$574,645.63
$13,939,368.75
$12,161,818.75
$13,000,331.25
$11,101,506.25
$9,701,762.50
$8,637,718.75
$9,797,150.00
$8,714,862.50
$10,162,843.75
$10,787,987.50
$12,075,681.25
$9,124,787.50
$11,619,031.25
$9,097,256.25
$13,548,706.25
$10,771,512.50
$9,757,700.00
$9,350,993.75
$9,491,550.00
54.37%
50.95%
49.84%
49.41%
42.92%
39.39%
46.14%
42.01%
45.60%
40.07%
46.31%
41.51%
46.20%
44.75%
48.32%
42.20%
39.33%
42.40%
43.67%
49.99%
49.69%
48.00%
40.39%
38.11%
36.57%
36.98%
39.74%
41.23%
38.77%
40.91%
36.38%
42.23%
36.00%
46.59%
40.17%
37.66%
38.01%
37.57%
75.17%
65.97%
73.00%
74.09%
68.62%
63.67%
71.42%
59.12%
66.43%
75.01%
79.57%
67.60%
74.17%
68.12%
78.38%
72.27%
69.84%
66.32%
68.10%
$14,235,900.00
$433,416.98
$9,709,087.50
40.31%
38.37%
68.20%
$14,981,400.00
$14,628,700.00
$14,529,300.00
$16,868,900.00
$16,246,400.00
$13,268,000.00
$14,725,700.00
$16,694,400.00
$15,432,900.00
$16,345,100.00
$435,101.99
$445,334.91
$631,913.30
$764,210.16
$931,766.20
$475,961.09
$675,169.59
$641,592.92
$422,665.00
$730,622.00
$9,504,625.00
$9,509,731.25
$10,121,462.50
$10,588,093.75
$13,910,750.00
$9,845,812.50
$10,799,012.50
$11,844,456.25
$9,265,481.25
$12,833,425.00
48.06%
41.67%
41.50%
47.10%
46.26%
37.80%
40.73%
48.60%
44.17%
46.43%
40.38%
39.43%
39.16%
45.47%
43.79%
35.76%
39.69%
45.00%
41.60%
44.06%
63.44%
65.01%
69.66%
62.77%
85.62%
74.21%
73.33%
70.95%
60.04%
78.52%
Minimum
Maximum
Average
Std. Dev.
$13,268,000.00
$18,544,900.00
$15,182,383.33
$1,483,590.28
$422,665.00
$938,862.33
$617,047.89
$145,342.12
$8,637,718.75
$13,939,368.75
$10,692,483.54
$1,571,304.62
37.80%
54.37%
44.60%
3.95
35.76%
49.99%
40.92%
4.00
59.12%
85.62%
70.29%
6.01
Ness 39
1995 Offensive Unit Salary Statistics
Total Unit
Salary for
% of
Salary
Std. Dev.
Starters
Payroll
Team
Arizona
Atlanta
Buffalo
Carolina
Chicago
Cincinnati
Cleveland
Dallas
Denver
Detroit
Green Bay
Houston
Indianapolis
Jacksonville
Kansas City
Miami
Minnesota
New England
New Orleans
New York
Giants
New York Jets
Oakland
Philadelphia
Pittsburgh
San Diego
San Francisco
Seattle
St. Louis
Tampa Bay
Washington
Minimum
Maximum
Average
Std. Dev.
% of Cap
($37.1M)
% on
Starters
$14,137,800.00
$15,638,200.00
$15,838,300.00
$12,193,400.00
$15,613,700.00
$17,577,500.00
$14,841,600.00
$16,950,800.00
$17,566,100.00
$19,878,900.00
$14,492,900.00
$15,785,600.00
$17,024,700.00
$14,295,400.00
$15,919,300.00
$18,592,100.00
$19,847,200.00
$18,399,400.00
$16,424,100.00
$699,937.42
$608,531.44
$703,132.43
$455,939.47
$616,136.99
$867,022.24
$503,043.28
$819,267.61
$969,134.11
$938,395.71
$718,471.29
$557,880.56
$728,521.05
$544,481.98
$504,544.22
$863,254.44
$837,655.56
$896,865.41
$664,244.31
$10,460,718.75
$10,993,750.00
$10,503,018.75
$5,859,768.75
$9,185,856.25
$11,796,781.25
$8,879,037.50
$13,835,518.75
$13,324,493.75
$15,969,543.75
$10,502,806.25
$7,517,981.25
$10,671,818.75
$6,682,956.25
$9,543,112.50
$13,061,575.00
$13,403,887.50
$11,402,293.75
$12,007,331.25
41.45%
43.22%
44.33%
40.21%
47.41%
51.04%
49.92%
48.31%
52.36%
55.38%
44.23%
48.54%
50.21%
47.91%
44.50%
52.64%
55.87%
55.32%
51.46%
38.11%
42.15%
42.69%
32.87%
42.09%
47.38%
40.00%
45.69%
47.35%
53.58%
39.06%
42.55%
45.89%
38.53%
42.91%
50.11%
53.50%
49.59%
44.27%
73.99%
70.30%
66.31%
48.06%
58.83%
67.11%
59.83%
81.62%
75.85%
80.33%
72.47%
47.63%
62.68%
46.75%
59.95%
70.25%
67.54%
61.97%
73.11%
$19,385,200.00
$14,189,000.00
$17,287,800.00
$18,268,700.00
$17,791,900.00
$16,869,100.00
$20,370,900.00
$17,726,300.00
$16,863,500.00
$17,965,500.00
$15,978,100.00
$665,972.42
$587,915.25
$631,699.42
$801,115.98
$663,989.10
$617,486.46
$955,695.28
$845,556.26
$500,402.19
$735,134.42
$621,356.32
$13,442,956.25
$7,137,962.50
$11,627,612.50
$10,737,475.00
$11,287,875.00
$11,117,425.00
$13,554,087.50
$11,701,093.75
$10,251,112.50
$12,780,887.50
$7,509,175.00
54.89%
45.52%
49.25%
52.18%
49.68%
48.03%
58.04%
49.03%
49.09%
51.42%
45.39%
52.25%
38.25%
46.60%
49.24%
47.96%
45.47%
54.91%
47.78%
45.45%
48.42%
43.07%
69.35%
50.31%
67.26%
58.78%
63.44%
65.90%
66.54%
66.01%
60.79%
71.14%
47.00%
$12,193,400.00
$20,370,900.00
$16,790,433.33
$1,927,077.79
$455,939.47
$969,134.11
$704,092.75
$146,754.41
$5,859,768.75
$15,969,543.75
$10,891,663.75
$2,363,457.84
40.21%
58.04%
49.23%
4.39
32.87%
54.91%
45.26%
5.19
46.75%
81.62%
64.37%
9.43
Ness 40
Team
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Team
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Arizona Cardinals Defensive Unit Salary Statistics
Total Unit
Salary
Std. Dev.
% of Payroll
% of Cap
$18,544,900.00
$20,374,500.00
$20,013,100.00
$23,412,900.00
$26,753,200.00
$26,672,500.00
$20,800,709.00
$31,656,465.00
$29,041,612.00
$41,370,856.00
$30,073,665.00
$36,706,699.00
$42,956,057.00
$53,455,110.00
$836,491.63
$1,104,202.55
$1,059,757.17
$1,133,587.27
$1,167,755.07
$965,339.98
$661,353.28
$1,897,446.75
$1,186,393.24
$1,934,005.77
$1,547,531.31
$1,405,371.44
$1,547,697.22
$2,043,413.65
54.37%
54.61%
53.21%
46.14%
48.73%
45.51%
27.77%
47.27%
35.84%
52.39%
39.29%
34.73%
43.52%
43.78%
49.99%
49.97%
48.28%
44.69%
45.85%
42.90%
30.86%
44.52%
38.72%
52.51%
35.17%
38.84%
39.41%
46.08%
Arizona Cardinals Offensive Unit Salary Statistics
Total Unit
Salary
Std. Dev.
% of Payroll
% of Cap
$14,137,800.00
$16,214,700.00
$17,028,500.00
$26,617,000.00
$27,488,300.00
$31,103,600.00
$51,766,438.00
$34,392,075.00
$49,831,947.00
$35,948,289.00
$43,219,996.00
$66,423,733.00
$54,648,480.00
$67,240,400.00
$699,937.42
$707,346.74
$768,401.00
$992,442.46
$1,220,072.40
$1,401,145.49
$2,817,581.49
$1,410,248.75
$2,056,988.39
$1,782,582.35
$1,916,461.94
$3,410,061.21
$2,379,304.80
$3,572,429.95
41.45%
43.46%
45.27%
52.45%
50.07%
53.07%
69.12%
51.36%
61.49%
45.53%
56.47%
62.85%
55.37%
55.07%
38.11%
39.76%
41.08%
50.81%
47.11%
50.03%
76.80%
48.37%
66.44%
45.63%
50.55%
70.29%
50.14%
57.97%
% on
Starters
75.17%
84.34%
76.00%
53.76%
48.79%
59.95%
48.82%
55.48%
53.19%
66.02%
66.05%
69.61%
57.76%
68.46%
% on
Starters
73.99%
61.24%
65.07%
70.01%
59.31%
56.86%
70.01%
54.08%
58.69%
64.97%
65.25%
72.85%
59.87%
66.05%
Ness 41
Appendix B: Initial Regression Results
Variable
Pct. Cap on Defense
Pct. Cap on Defense2
1
-1.309
(-.68)
.287
(.15)
Pct. Payroll on Defense
Pct Payroll on Defense2
Pct Def. Starters
Pct Def. Starters2
-11.393***
(-3.85)
9.573***
(4.07)
2
3
-9.728***
(-2.58)
9.458**
(2.32)
-11.072***
(-3.75)
9.327***
(3.96)
Pct. Cap on Offense
4.698**
(2.24)
-5.048***
(-2.72)
Pct. Cap on Offense2
Pct. Payroll on Offense
-4.249*
(-1.91)
5.451***
(2.90)
.0126**
(2.41)
.337***
(.6.26)
.033
(.83)
-5.531
(-1.30)
4.825
(1.21)
-2.508
(-1.15)
3.843**
(2.08)
.0139***
(2.66)
.332
(6.16)
.032
(.81)
-.090***
(-3.42)
.915**
(2.44)
-.131
(-1.59)
-.093***
(-3.54)
.719***
(3.09)
-.088
(-1.05)
.377***
(10.10)
6802
.0562
.376
(10.07)
6802
.0547
Pct. Payroll on Offense2
Pct. Off. Starters
Pct. Off. Starters2
Coaching
Playoffs Previous Year
.0154***
(2.80)
.355
(6.23)
.0157**
(2.85)
.346***
(6.06)
.045
(1.07)
-.104***
(-3.58)
1.440***
(3.90)
-.132
(-1.56)
4.759
(1.52)
.337***
(8.72)
6030
.0487
.042
(1.00)
-.104***
(-3.59)
.990***
(4.24)
-.093
(-1.04)
4.809
(1.53)
.335***
(8.66)
6030
.0500
Off. Injuries
Def. Injuries
Total Injuries
Payroll Percent of Cap
More on Offense
Std. Dev. Def. Payroll/Total
Payroll
Home
Number of Observations
Pseudo R2 Value
4
Ness 42
Appendix C: 2008 Variable Data and Winning Percentage
Team
Arizona
Atlanta
Baltimore
Buffalo
Carolina
Chicago
Cincinnati
Cleveland
Dallas
Denver
Detroit
Green Bay
Houston
Indianapolis
Jacksonville
Kansas City
Miami
Minnesota
New England
New Orleans
New York Giants
New York Jets
Oakland
Philadelphia
Pittsburgh
San Diego
San Francisco
Seattle
St. Louis
Tampa Bay
Tennessee
Washington
Median
% Payroll Pct. Def.
Std. Dev. Playoffs
At Coaching Def. Total
on
Spending Def. Payroll / Prev.
Cap
Years Injuries Injuries Home Defense
Starters Total Payroll Year
1
2
0.038
0
(median) (median) (median) 0.44276 0.676909942
(median) (median) (median) 0.46113 0.642487729
0
1
0.036
0
(median) (median) (median) 0.66041 0.577113972
0
1
0.037
0
(median) (median) (median) 0.5077 0.538841752
1
9
0.036
0
(median) (median) (median) 0.43973 0.711546201
1
7
0.050
0
(median) (median) (median) 0.59374 0.638440536
1
5
0.048
0
(median) (median) (median) 0.47785 0.547852553
0
6
0.056
0
(median) (median) (median) 0.37113 0.652895514
1
4
0.045
0
(median) (median) (median) 0.41714 0.626964543
1
9
0.048
1
(median) (median) (median) 0.56589 0.546274318
0
16
0.045
0
(median) (median) (median) 0.48131 0.502139412
0
3
0.027
0
(median) (median) (median) 0.54238 0.512984743
0
3
0.035
1
(median) (median) (median) 0.42241 0.589282515
0
3
0.035
0
(median) (median) (median) 0.34723 0.294414635
0
13
0.046
1
(median) (median) (median) 0.45785 0.593976391
1
6
0.036
1
(median) (median) (median) 0.52295 0.441698084
0
8
0.045
0
(median) (median) (median) 0.48527 0.495931156
1
1
0.033
0
(median) (median) (median) 0.55271 0.703058029
1
3
0.058
0
(median) (median) (median) 0.37494 0.495387339
0
14
0.025
1
(median) (median) (median) 0.54228 0.594546243
1
3
0.042
0
(median) (median) (median) 0.39072 0.553842612
1
13
0.044
1
(median) (median) (median) 0.49143 0.731086916
1
3
0.049
0
1
1.5 (median) (median) (median) 0.44859 0.7134993
0.056
0
(median) (median) (median) 0.53555 0.475599432
0
10
0.055
0
(median) (median) (median) 0.38596 0.668594398
1
2
0.035
1
(median) (median) (median) 0.50536 0.646956782
1
11
0.042
1
(median) (median) (median) 0.50244 0.599489337
1
2.5
0.045
0
(median) (median) (median) 0.39977 0.730981565
0
17
0.047
1
(median) (median) (median) 0.34434 0.625464545
1
5
0.045
0
(median) (median) (median) 0.38223 0.586174978
0
11
0.032
1
(median) (median) (median) 0.44117 0.627228911
1
15
0.037
1
(median) (median) (median) 0.38390 0.500018013
1
1
0.044
1
1
5
1
2
0
0.45949 0.594261317
0.044
0
Pct Cap
Defense *
Playoffs Prev.
0
0
0
0
0
0
0
0
0.518645
0
0
0.434388621
0
0.273199828
0.478718448
0
0
0
0.293175345
0
0.374338448
0
0
0
0.417799491
0.477160862
0
0.351086552
0
0.336824776
0.464564336
0.366997103
0
Pct Payroll
Total Total Injuries * Total Injuries *
Defense *
Injuries * Pct. Payroll Pct. Def. Spending
Playoffs Prev. At Cap
Defense
Starters
0
2
0.885518652
1.353819884
0
0
0.92226521
1.284975458
0
0
1.320812733
1.154227944
0
2
1.015399904
1.077683503
0
2
0.879455329
1.423092401
0
2
1.187473297
1.276881071
0
0
0.955695125
1.095705107
0
2
0.74226339
1.305791028
0.417137108
2
0.834274216
1.253929086
0
0
1.131773298
1.092548635
0
0
0.962611366
1.004278824
0.542384621
0
1.084769242
1.025969485
0
0
0.84481194
1.178565031
0.347229095
0
0.69445819
0.588829269
0.457845083
2
0.915690166
1.187952782
0
0
1.045901969
0.883396169
0
2
0.970534077
0.991862312
0
2
1.105417687
1.406116059
0.374943548
0
0.749887097
0.990774678
0
2
1.084555053
1.189092486
0.390720364
2
0.781440728
1.107685224
0
2
0.982865184
1.462173833
0
2
0.897175762
1.4269986
0
0
1.07110983
0.951198864
0.385905969
2
0.771811939
1.337188796
0.50536063
2
1.010721261
1.293913564
0
2
1.004889176
1.198978674
0.399774299
0
0.799548598
1.46196313
0
2
0.68867305
1.250929091
0.38222848
0
0.764456961
1.172349957
0.441167045
2
0.882334091
1.254457823
0.383902284
2
0.767804568
1.000036026
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
0.5625
0.5
0.4375
0.375
Winning Percentage
0.625
0.3125
S
on
D
M
or
e
xt
ra
ta
r te
rs
In
ju
ry
ef
.
In
ju
ry
ff.
5%
E
S
ta
r te
rs
,1
on
S
5%
5%
M
or
e
on
M
or
e
5%
ta
r te
rs
,1
E
Le
ss
xt
ra
on
O
D
D
ef
ef
en
se
en
se
ea
r
Y
on
5%
Ex
tra
C
ra
Ex
t
M
or
e
oa
ch
in
g
O
ff.
ef
.
D
ra
Ex
t
In
ju
ry
In
ju
ry
ay
Aw
om
e
H
N
eu
tr a
l
0.25
Variables
Winning Percentage of Teams at the Salary Cap vs. Opponent Below the Cap
At Cap vs. Below Cap
0.75
0.6875
0.5625
0.5
0.4375
0.375
0.3125
0.25
Neutral
Home
Aw ay
Increase
Pct
Spending
Def. 5%
Increase
Pct
Spending
Def. 10%
Variables
One Extra One Extra
Injury
Injury, 5%
Increase
Def.
Starters
Playoffs
Previous
Year
Playoffs
Previous
Year, 5%
Increase
Pct. Def.
Payroll and
Cap
Winning Percentage
0.625
Winning Percentage of Teams Below the Salary Cap vs. Opponent At the Cap
Below Cap vs. At Cap
0.75
0.6875
0.5625
0.5
0.4375
Winning Percentage
0.625
0.375
0.3125
0.25
Neutral
Home
Away
Increase
Pct
Spending
Def. 5%
Increase
Pct
Spending
Def. 10%
One Extra
Injury
Increase
Pct
Spending
Def. 5%,
One Extra
Injury
Increase One Extra
Injury,
Pct
Make
Spending
Def.
Playoffs
Starters
5%, One
Extra Injury
Increase
Pct
Spending
Def.
Starters
5%
Variables
Winning Percentage of Teams Below the Salary Cap vs. Opponent Below the Cap
Below Cap vs. Below Cap
0.75
0.625
0.5625
0.5
0.4375
0.375
0.3125
0.25
0.1875
fs
Pr
e
vi
ou
s
Pc
Ye
y
tP
ar
C
ap
ay
ro
D
ll,
ef
en
S
al
se
ar
In
cr
y
5%
ea
C
ap
se
D
St
ef
d.
en
D
se
ev
In
5%
.
D
cr
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ea
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se
a
In
yr
St
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ol
d.
ea
l0
D
se
.5
ev
%
In
Pc
.
D
cr
tP
ef
ea
.P
ay
se
ro
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Pc
l l,
ro
tP
S
ll
al
1%
ay
ar
ro
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ll
C
D
ap
ef
D
en
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se
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se
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5%
,E
xt
ra
In
ju
ry
nj
ur
y
D
ef
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In
Ex
tr a
O
ff.
ra
se
re
a
fs
,D
ec
of
Pl
ay
Pl
ay
of
fs
,I
nc
re
as
e
P
ct
P
ay
ro
Pl
ay
of
ll,
Sa
la
r
ju
ry
r
Ye
a
Ex
t
Aw
ay
C
oa
ch
in
g
Ex
t ra
e
H
om
N
eu
tra
l
0.125
Variables
Winning Percentage
0.6875
Winning Percentage of Teams that Made the Playoffs vs. Playoff Teams
Playoffs Previous vs. Playoffs Previous
0.75
0.6875
0.5625
0.5
0.4375
Winning Percentage
0.625
0.375
0.3125
0.25
Neutral
Home
Aw ay
Increase Pct
Payroll Def. 5%
Increase Pct
Payroll Def. 10%
At Cap
Variables
Winning Percentage of Teams that Made the Playoffs vs. Non-Playoff Teams
0.75
0.6875
0.625
0.5625
0.5
0.4375
0.375
0.3125
0.25
Neutral
Home
Aw ay
Extra
Coaching
Year
One Extra One Extra One Extra One Extra
Def. Injury, Def. Injury, Def. Injury, Def. Injury,
Not At Cap
At Cap
Increase
Increase
Pct
Pct
Spending Spending
Def.
Def.
Starters
Starters
5%, Not At 5%,At Cap
Cap
Winning Percentage
Playoffs Previous vs. No Playoffs
At Cap
Variables
Ness 46
Winning Percentage of Non-Playoff Teams vs. Playoff Teams
No Playoffs vs. Playoffs Previous
0.6875
0.625
0.5625
0.5
0.4375
0.375
0.3125
Winning Percentage
0.75
0.25
Neutral
Home
Aw ay
Extra
Coaching
Year
One Extra
Def. Injury,
Not At Cap
One Extra
One Extra
One Extra
Def. Injury, At Def. Injury,
Def. Injury,
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
0.625
0.5625
0.5
0.4375
0.375
0.3125
0.25
Neutral
Home
Aw ay
Increase Pct Increase Pct Increase Pct Increase Pct Increase Pct Increase Pct Increase Pct Increase Pct
Payroll
Payroll
Def.
Def.
Def.
Payroll
Payroll
Payroll
Defense 5% Defense
Defense
Defense
Defense Starters 5% Starters
Starters
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
Extra
Coaching
Year
Variables
Ness 47
Winning Percentage
0.6875
Appendix D: Implied Strategies by Team and Opponent
Team
Opponent
Ness 48
References
Associated Press. “2009 Major League Baseball Salaries.” Retrieved September 5,
2009, from http://www.sportingnews.com/mlb/article/2009-04-09/2009-majorleague-baseball-payrolls.
Borghesi, Richard. “Allocation of scarce resources: Insight from the NFL salary cap.”
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Fort, Rodney. Personal Website. <www.rodneyfort.com>. Accessed 1 November 2009.
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Ness 49
Lackner, Al. “Salary Cap FAQ.” Askthecommish.com LLC.
http://www.askthecommish.com/salarycap/faq.asp. Updated 19 January 2009.
Larsen, Andrew, Aju J. Fenn, and Erin Leanne Spenner. “The Impact of Free Agency
and the Salary Cap on Competitive Balance in the National Football League.”
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Mason, Daniel S. (2004). Revenue Sharing and Agency Problems in Professional Team
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Mondello, Mike, and Joel Maxcy. “The impact of salary dispersion and performance
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Ness 50
Zuber, Richard A., John M. Gandar, and Benny D. Bowers. “Beating the Spread: Testing
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Ness 51
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
Ness 52