Florida State University Libraries
Electronic Theses, Treatises and Dissertations The Graduate School
2013 Effects of Time-off on Performance in the National Football League Jeremy J. Foreman
Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY
COLLEGE OF EDUCATION
EFFECTS OF TIME-OFF ON PERFORMANCE IN
THE NATIONAL FOOTBALL LEAGUE
By
JEREMY J. FOREMAN
A Thesis submitted to the Department of Sport Management in partial fulfillment of the requirements for the degree of Master of Science
Degree Awarded: Summer Semester, 2013
Jeremy J. Foreman defended this thesis on June 17, 2013.
The members of the supervisory committee were:
Ryan Rodenberg
Professor Directing Thesis
Joshua Newman
Committee Member
Yu Kyoum Kim
Committee Member
The Graduate School has verified and approved the above-named committee members, and certifies that the thesis has been approved in accordance with university requirements.
ii
TABLE OF CONTENTS
List of Tables v
List of Figures vii
Abstract x
CHAPTER ONE: INTRODUCTION 1 Scheduling Background 1 Controversy Surrounding Schedules 2 Brief History of NFL Bye Weeks 5 Purpose of Study 7 Significance of Study 7 Limitations 10 Layout of Thesis 11
CHAPTER TWO: LITERATURE REVIEW 12 Analysts’ Perceptions of Bye Weeks and Team Performance 13 Learning as a Function of Time 16 Respite as a Function of Time 19 Physiology, Performance, and Time 26 Summary of Previous Research Methods and Findings 30
CHAPTER THREE: METHODOLOGY 33 Model One: Bye Week Impact 34 Model Two: Time-Off Impact, Ceteris Paribus 35 Dichotomizing Model Two 37 Model Three: Optimal Bye Week for Uninterrupted Final Stretch 39
CHAPTER FOUR: RESULTS 42 Analysis of Model One: Bye Week Impact 42 Analysis of Model Two: Time-Off Impact, Ceteris Paribus 43 Analysis of Dichotomized Model Two 48 Analysis of Model Three: Optimal Bye Week for Uninterrupted Final Stretch 61
CHAPTER FIVE: DISCUSSION 66 Conclusions 66 Implications 75 Limitations 77 Future Research 80
iii
APPENDICES 85
A MODEL TWO 85
B REVISED MODEL TWO 87
C MODEL TWO FOR YOUNGER TEAMS 89
D MODEL TWO FOR OLDER TEAMS 91
E REVISED MODEL TWO FOR YOUNGER TEAMS 93
F REVISED MODEL TWO FOR OLDER TEAMS 95
G MODEL TWO FOR GOOD TEAMS 97
H MODEL TWO FOR BAD TEAMS 99
I REVISED MODEL TWO FOR GOOD TEAMS 101
J REVISED MODEL TWO FOR BAD TEAMS 103
K MODEL TWO FOR DIVISION GAMES 105
L MODEL TWO FOR NON-DIVISION GAMES 107
M REVISED MODEL TWO FOR DIVISION GAMES 109
N REVISED MODEL TWO FOR NON-DIVISION GAMES 111
O MODEL THREE 113
REFERENCES 115
BIOGRAPHICAL SKETCH 123
iv
LIST OF TABLES
4.1 Regression output for Model Two with DAYDIFSQ 45
4.2 Regression output for Model Two 45
4.3 Regression output for revised Model Two 46
4.4 Regression output for Model Two with younger teams 48
4.5 Regression output for revised Model Two with younger teams 49
4.6 Regression output for Model Two with older teams 50
4.7 Regression output for revised Model Two with older teams 51
4.8 Regression output for Model Two with good teams 52
4.9 Regression output for revised Model Two with good teams 52
4.10 Regression output for Model Two with bad teams 53
4.11 Regression output for revised Model Two with bad teams 54
4.12 Regression output for Model Two with division teams 55
4.13 Regression output for Model Two with non-division teams 56
4.14 Regression output for revised Model Two with division teams 56
4.15 Regression output for revised Model Two with non-division teams 57
4.16 Model Two with sample from Method One 61
4.17 Model Three regression output 62
4.18 Model Three multicollinearity output 63
A.1 Multicollinearity output for Model Two 86
B.1 Multicollinearity output for revised Model Two 88
C.1 Multicollinearity output for Model Two with only younger teams 90
v
D.1 Multicollinearity output for Model Two with only older teams 92
E.1 Multicollinearity output for revised Model Two with younger teams 94
F.1 Multicollinearity output for revised Model Two with older teams 96
G.1 Multicollinearity output for Model Two with only good teams 98
H.1 Multicollinearity output for Model Two with only bad teams 100
I.1 Multicollinearity output for revised Model Two with good teams 102
J.1 Multicollinearity output for revised Model Two with bad teams 104
K.1 Multicollinearity output for Model Two with only division games 106
L.1 Multicollinearity output for Model Two with only non-division games 108
M.1 Multicollinearity output for revised Model Two with division games 110
N.1 Multicollinearity output for revised Model Two with non-division games 112
vi
LIST OF FIGURES
4.1 Linearity of BYESQUAR 64
4.2 Linearity of BYESQUAR with trendlines 65
5.1 Sum of coefficients by bye week 73
A.1 Normality of residuals for Model Two 85
A.2 Homoscedasticity of residuals for Model Two 85
A.3 Linearity of regressors for Model Two 86
B.1 Normality of residuals for revised Model Two 87
B.2 Homoscedasticity of residuals for revised Model Two 87
B.3 Linearity of regressors for revised Model Two 88
C.1 Normality of residuals for Model Two with only younger teams 89
C.2 Homoscedasticity of residuals for Model Two with only younger teams 89
C.3 Linearity of regressors for Model Two with only younger teams 90
D.1 Normality of residuals for Model Two with only older teams 91
D.2 Homoscedasticity of residuals for Model Two with only older teams 91
D.3 Linearity of regressors for Model Two with only older teams 92
E.1 Normality of residuals for revised Model Two with younger teams 93
E.2 Homoscedasticity of residuals for revised Model Two with younger teams 93
E.3 Linearity of regressors for revised Model Two with younger teams 94
F.1 Normality of residuals for revised Model Two with older teams 95
F.2 Homoscedasticity of residuals for revised Model Two with older teams 95
F.3 Linearity of regressors for revised Model Two with older teams 96
G.1 Normality of residuals for Model Two with only good teams 97
vii
G.2 Homoscedasticity of residuals for Model Two with only good teams 97
G.3 Linearity of regressors for Model Two with only good teams 98
H.1 Normality of residuals for Model Two with only bad teams 99
H.2 Homoscedasticity of residuals for Model Two with only bad teams 99
H.3 Linearity of regressors for Model Two with only bad teams 100
I.1 Normality of residuals for revised Model Two with good teams 101
I.2 Homoscedasticity of residuals for revised Model Two with good teams 101
I.3 Linearity of regressors for revised Model Two with good teams 102
J.1 Normality of residuals for revised Model Two with bad teams 103
J.2 Homoscedasticity of residuals for revised Model Two with bad teams 103
J.3 Linearity of regressors for revised Model Two with bad teams 104
K.1 Normality of residuals for Model Two with only division games 105
K.2 Homoscedasticity of residuals for Model Two with only division games 105
K.3 Linearity of regressors for Model Two with only division games 106
L.1 Normality of residuals for Model Two with only non-division games 107
L.2 Homoscedasticity of residuals for Model Two with only non-division games 107
L.3 Linearity of regressors for Model Two with only non-division games 108
M.1 Normality of residuals for revised Model Two with division games 109
M.2 Homoscedasticity of residuals for revised Model Two of division games 109
M.3 Linearity of regressors for revised Model Two with division games 110
N.1 Normality of residuals for revised Model Two with non-division games 111
N.2 Homoscedasticity of residuals for revised Model Two with non-division games 111
N.3 Linearity of regressors for revised Model Two with non-division games 112
O.1 Model Three normality of residuals 113
O.2 Model Three homoscedasticity of residuals 113
viii
O.3 Model Three linearity of regressors 114
ix
ABSTRACT
Among National Football League (NFL) fans, coaches, and analysts, there are many different views on how time-off effects team performance. Differences in how time-off is allocated to teams has also become a source of controversy as debates continue regarding which teams received the least favorable schedules. This investigation was concerned with identifying how time-off prior to a game affects the final score, when is the best time to have a bye week, and why some teams may benefit more from time-off than other teams. Twenty-one seasons were examined using ordinary least squares regressions to determine that there is at least about a
.21 point advantage for each extra day of preparation time that a team receives prior to a game, relative to the time received by an opponent. This advantage is increased for older teams, less talented teams, and teams that are less familiar with their opponents. Unfamiliar opponents benefit from an additional day to prepare by about .38 points which accounts for approximately
2.6 points for a standard seven day bye week. Additionally, about 54.9 percent of teams defeat their opponents when coming off of a bye week by an average margin of victory of about 12.3 points compared to the approximately 8.7 points that non-bye week teams defeated bye week teams by on average.
x
CHAPTER ONE
INTRODUCTION
Scheduling Background
In recent years, the release of the National Football League (NFL) schedule has become
an increasingly popular event. In 2012, the NFL Network broadcasted a schedule release
program in a primetime television slot, at 7:00 P.M. Eastern standard time on Tuesday, April 17th
(Cimini, 2012; Rosenthal, 2012). In addition to the primetime program, the schedule release sparked multiple podcasts; opinion articles on major websites such as espn.go.com, nfl.com, and cbssports.com; and segments devoted to the topic on various television and radio programs such as SportsCenter, The Herd, and Mike and Mike about the schedule. In each of these podcasts, online articles, and national media broadcasts, the new NFL schedule has been debated by NFL analysts in multiple facets – especially the debates about how difficult each teams’ schedules are and how each team matches up with their opponents each week (Cimini, 2012; NFL’s Final
Week, 2012; Rosenthal, 2012; Show in review, 2012; Wilson, 2012). This suggests that teams’ schedules are a factor in team performance and game outcomes.
The opponents that each team plays, and whether they will play at home or away game, is determined prior to the release of the schedule. The information that is revealed by the schedule release is what day and time each team will play their predetermined opponents and which television network the games will be aired on (Cimini, 2012). The way that each team’s opponents are determined is primarily by what division they are in and partially by how they finished in their division the previous season. In the 16-game season, every team plays the other three teams in their division twice which yields 6 of the 16 games. Since there are four divisions
1
in both of the conferences in the NFL, every division plays one of the divisions in their same
conference every three years and one of the divisions in the other conference every four years.
With four teams in each division, playing one other division in each conference yields eight more games to play. The other two teams that make up a team’s opponents for the season are the other two teams in the same conference that ranked in the same place in their division (National
Football League [NFL], n.d.). For example, if a team came in third place in their division, they would play the other two teams in their conference that came in third place in their respective divisions that they were not already scheduled to play based on their division. NFL analysts often look at the opponents that a team will face and identify the strength of each teams’ schedules based on the opponents’ performance in the previous year. The more difficult the opponents are that a team plays, the stronger the schedule.
Controversy Surrounding Schedules
The strength of a schedule is frequently brought up in debates among NFL analysts (La
Canfora, 2012; Love, 2012a, 2012b). If a team has easier opponents, that team will have an
easier path to the postseason playoffs, and potentially an easier path to the Super Bowl
championship game. Conversely, if a team has to face more difficult opponents, that team will
be less likely to make the playoffs, and therefore, less likely to make it to the Super Bowl. The
fairness in the strength of schedule really lies in the fact that the schedule is predetermined. The
schedule is determined by a system, as opposed to a group who could conspire or a single person
who possesses a bias for or against a particular team.
Determining when a team will play each of its opponents, on the other hand, is not
accomplished by a system. A group of NFL employees, headed by Mr. Howard Katz, Senior
Vice President of Broadcasting and Media Operations, spend months examining the many
2
possible schedule combinations to try and determine which one pleases the most people and infuriates the least people. NFL teams submit requests to the NFL scheduling committee based on competitive advantages, religious observances, expected weather conditions, et cetera
(Battista, 2012). Whether this group actually does conspire against certain teams when deciding on a schedule would be difficult to determine; however, many fans, players, coaches, and analysts have voiced their concerns about getting the short end of the stick (Awholelottahaloti,
2012; Battista, 2012; Edreedfromtheu, 2012; Footman, 2012; La Canfora, 2012; Love, 2012a;
Rav'n, 2012; Ravenslifer, 2012). After being assigned a Thanksgiving night game in which his team would have to fly across the country to play, the San Francisco 49ers head coach Jim
Harbaugh was quoted as telling Katz, "Now that I’ve met you, I don’t hate you quite as much...That’s as good as you’re going to do" (as cited in Battista, 2012, para. 27). Many aspects play a role in the outcome of the schedule such as when the stadiums are available (especially for teams that share stadiums with other sports teams), the projected popularity of specific games (so that they may be televised nationally), trying to keep players’ schedules regular as they play in different time zones, and attempting to avoid conflicts with other entertainment events (Battista,
2012). It is a difficult task that may have no definitively correct outcome.
Timing of bye weeks is a major source of controversy (La Canfora, 2012; Love, 2012a,
2012b). Bye weeks are when a team does not have a game scheduled for that particular week and essentially gets the week off. It gives players a chance to get some rest and gives the team an extra week to prepare for their next opponent. Each team gets one bye week per season usually between weeks four and ten (NFL, n.d.). When asked about the 2012 NFL schedule and getting a week seven bye, Denver Broncos head coach John Fox said, "I've always preferred to have as close to the mid-season for a bye as possible and week seven is a pretty good turnout as
3
far as that timing goes" (as cited in Love, 2012a). When a bye week lands is important on its
own merit; however, it is also relative since teams have extra time to prepare during a bye. A
fair schedule, in terms of playing opponents returning from bye weeks, would either ensure that
no team played more than one team that was returning from a bye week or that each team only
returns from a bye week to play another team that is returning from a bye week. Based on the
schedules which have been created throughout the years since the bye week has been established,
one may think that the NFL does not have the luxury of composing a perfectly fair schedule
because disparities always exist between teams that have more time to prepare for opponents and
teams that have less time to prepare for opponents, respectively. For example, the 2012 regular
season schedule gave the Minnesota Vikings an additional 11.5 cumulative days throughout the
season to prepare for their opponents than their opponents received. Conversely, in that same
season, the Philadelphia Eagles faced their opponents with 25.2 fewer cumulative days to
prepare for their opponents. These numbers are not just due to bye weeks, but also largely a
result of games scheduled on Thursdays, Mondays, and occasionally even Saturdays (NFL, n.d.).
The majority of NFL games are played on Sundays with start times of either 1:00 P.M.
Eastern standard time or around 4:05 P.M. Eastern standard time. Sunday and Monday night
games are played from week one through week 16. Thursday games have been played in various
ways throughout the years. Thanksgiving day NFL games have been a tradition for many years;
however, in 2006, Thursday night games became a regular event with eight Thursday night
games being played that season. Since 2006, the amount of Thursday night games has steadily increased to 13 Thursday night games in 2012 (NFL, n.d.). All of these variations in schedules
could lead to a difference in preparation time for the next game of up to 11 days. In the 2012 schedule, the largest difference in preparation time occurred before the week 12 game between
4
the Minnesota Vikings and the Chicago Bears. Since the Vikings had a week 11 bye and the
Bears played on Monday night in week 11, there was about an 8.3 day difference in preparation
time that favored the Vikings (NFL).
Brief History of the NFL Bye Week
The bye week system that currently exists in the NFL began in 1990. Prior to 1990, 16
regular season games were played by each team over the course of 16 weeks, which means that
every team played one game every week. Beginning in 1990, the NFL adopted a 17 week
schedule, but the 16-game season remained. This change allowed each team to have a “bye”
week in which they did not have to play a regular season game for that particular week. This schedule alteration was embraced by team owners, NFL players, and NFL fans since it created more revenue for owners, a mid-season break for players, and a longer season for fans. Since the bye week proved to be so successful, the NFL attempted to lengthen the season even more in the
1993 season by implementing a two bye week regular season. This system generated discontent among all parties involved since television ratings began to plummet due to the fact that there were fewer games of interest to view each week. This occurred because during the 1993 season, there were only 28 teams and only two games available nationally on Sunday afternoon (before other media outlets such as DirecTV’s NFL Sunday Ticket were available.) With each team having two bye weeks per season, fewer options were available for watching interesting games.
The lack of interesting televised games caused football fans to be discontent, which aggravated the broadcast networks, and ultimately made the NFL dissatisfied with the two bye week system.
The two bye week regular season did not continue in the 1994 season and the NFL reverted back to the successful one bye week regular season (Simmons, 2010).
5
Between the 1994 and 2003 season, the NFL expanded from 28 teams to the 32 teams that exist today. In the 1994 and 1995 seasons, bye weeks spanned from week four through week 11. In the 1996 and 1997 seasons, bye weeks commenced in week three and continued through week ten. In the 1998 season, bye weeks still started in week three, but ended a week earlier, in week nine. Then in 1999, bye weeks existed every week except week one, and in the
2000 and 2001 seasons, there were no exceptions – at least one team had a bye week in each week of the regular season. From the 2002 season through the 2006 season, bye weeks began in week three and the final bye weeks were in week ten with the exception of the 2006 season when bye weeks were finished after week nine. From the 2007 season through the 2010 season, bye weeks occurred between weeks four and ten with the exception of the 2008 season when bye weeks started in the second week of the regular season. In the 2011 season, bye weeks spanned from week five through week 11 and in the 2012 season, bye weeks spanned from week four through week 11 (NFL, n.d.).
Another change to note that will be critical to this research is that beginning with the
2010 season, the NFL began trying to schedule more away games for teams coming off of a bye week. The league believes that the home field advantage will help negate the bye week advantage. Additionally, when making this change, the NFL also implemented a scheduling rule that limits the amount of road games against opponents coming off of bye weeks to a maximum of two games. Acknowledging that the schedules that the league creates are sometimes unfair to certain teams, the NFL has stated that they try to look at the scheduling inequity in recent history as to not give teams too much of a competitive disadvantage for multiple consecutive years
(McManus, 2012).
6
Purpose of Study
The purpose of this study is to identify whether or not there is a competitive advantage of
having more time to prepare for an opponent than the opponent has in the NFL. This study will
also attempt to quantify how much of an advantage is present in certain circumstances. For example, how much of an advantage does extra preparation time present teams that play each
other twice per year since they get to become very familiar with each other’s playing styles?
Another question that this study intends to address is how much of an impact on team
performance an early-season, mid-season, or late-season bye has? Could the impact depend on
the age of the team? NFL insider Jason La Canfora (2012) wrote an opinion article where he
said, "Pittsburgh, an older team, has a bye way back in Week 4 -- having to play all of that
cumulative football down the stretch will be a test" (para. 11).
Significance of Study
The results of this study could potentially have several implications. Kahn (2000)
showed numerous ways in which sports can be utilized to examine worker production. Entine
and Small (2008) found that in the National Basketball Association (NBA), “factors other than
the skill of the competing teams play critical roles in the outcome of games” and that rest is one of the factors that affects the outcome of a game (p. 7). If this is also true in the NFL, analysts will be able to use this information to further analyze strength of schedule and determine which teams really are performing better under the given circumstances, as they do when they are creating power rankings.
Many researchers from various disciplines also use sports to find out more information about sleep, body clocks, travel time, equality and disparity, determinants of success, et cetera
(Dubner, 2011; Entine & Small, 2008; Hall, Szymanski, & Zimbalist, 2002; Smith,
7
Guilleminault, & Efron, 1997; Steenland & Deddens, 1997). This research may be able to
contribute to these fields by bringing another piece of the puzzle together. A researcher examining team performance in any way could use the findings of this study to better estimate how much of a factor each variable plays. For example, if attempting to determine how much more successful a coach with one year of experience is compared to a rookie coach, one may want to know that in 2012 three out of the four rookie coaches had less cumulative time to prepare for their opponents than their opponents will had. On the other hand, three out of the four second-year coaches had more cumulative time to prepare for their opponents than their opponents had (ESPN, n.d.; NFL, n.d.). Not only would a researcher possibly want to know this, but they may be even more interested to know how much of an effect this may have.
This research also aims to assist team owners, managers, and coaches in determining
when they would like to play certain games, how they should prepare for games, and how
personnel should be evaluated. When requests for certain games to be played at specific dates
and times are submitted to the NFL scheduling committee, it would be helpful to know which
week would be optimal to have a bye for which teams. Currently, many people believe that
having a bye in the middle of the regular season is ideal for NFL teams (Awholelottahaloti,
2012; Edreedfromtheu, 2012; Footman, 2012; Love, 2012a; Rav'n, 2012; Ravenslifer, 2012).
What if it is not a ‘one size fits all’ situation? Could an older team perform better throughout the
season than a younger team based on when they have a bye week? This research intends to help
answer some of these questions and solve some of the dilemmas that members of the NFL face.
Additionally, Walberg & Tsai (1984) pointed out that “because human life is constrained by
time, activities should be allocated with great care and understanding” (p. 443). This research
8
seeks to provide more information on the optimal allocation of time for NFL teams, other sports organizations, and non-sports organizations.
This study could have implications beyond the world of sports as well. A bye week is
essentially a break from work, though different teams and coaches may choose to use the breaks in different ways. It could serve as a mental break, a physical break, both, or neither, depending on the situation, the individual players’ decisions, and the team philosophy. There are many studies and debates about vacation time and its impact on health, relationships, and performance
(Eden, 1990; Etzion et al., 1998; Etzion, 2003; Frankenhaeuser et al., 1989; Shirom, 1989;
Westman & Eden 1997; Westman & Etzion, 2001; Westman & Etzion, 2002). This research will contribute to the respite field of research by determining the effects that time-off has on performance in the complex world of the NFL by utilizing data that is directly related to
performance rather than perceptions of performance that were collected by survey and which are
usually used in respite studies (Eden, 1990; Etzion et al., 1998; Etzion, 2003; Westman & Eden
1997; Westman & Etzion, 2001; Westman & Etzion, 2002).
Since players and coaches typically do not use bye weeks purely for rest while forgetting
about football, it is important to address the possibility that they are using this additional time-off
to improve. The reality is that additional learning is taking place as a team prepares for their
next opponent (Henderson, 2012; Odum, 2013). This information could be helpful in
understanding the learning process. Are there diminishing returns to learning? At what point
have coaches and players learned all that they can about their opponent? Could this information
translate to giving vacation time to students in year-round school, where short breaks could
potentially improve the learning process? Though this research is not intended or designed to
answer all of these questions, insight from this research could provide assistance in future
9
research on these topics. Furthermore, research which has already been conducted in these areas could be beneficial to this study as well.
Sports are not immune to factors such as vacation time and accumulation of human
capital. Coaches and players need time to rest and increase their knowledge of their respective
occupations just as an accountant, a construction worker or an astronaut may need (49ers Public
Relations, 2012; Henderson, 2012; Love, 2012b; Odum, 2013). By studying the large quantity
of data that is available in the NFL, inferences can be made about other professions based on the findings. It is possible that job performance in the NFL may be similar to job performance in a
variety of other occupations and this research may have the potential to contribute to industries
outside of sports.
Limitations
The scope of this research does not allow for deciphering whether time-off was spent
learning, resting, or engaging in intense physical activity. Unless an interview or survey were to
be conducted with every team to see how their players and coaches allocate their time in their
respective bye weeks, it would be very difficult to determine whether they rested, studied,
exercised, or performed a combination of the these tasks. No surveys were conducted in this
research and the purpose of this research is not to determine how time-off is spent, but rather, the
impact of the time-off. With that being said, this study does not have the means to accurately
evaluate how time was allocated during each teams’ bye week.
Though a lack of surveying could be viewed as a limitation of this research, there are also
many reasons why surveying could hinder this research as well. Surveying consists of biases
throughout the process which include what questions are being asked, how the questions are
being asked and in what order, and how the perceptions and moods of the individuals filling out
10
the survey may differ. As Kahn (2000) pointed out, the sports industry can be a beneficial
industry to examine worker productivity because of the wealth of publicly available data. Purely
quantitative research based on factual numbers that are obtained through unbiased sources will
be beneficial for this study because the perceptions of performance are excluded and replaced
with the actual quantified performance in terms of teams’ scores. That is not to say that I do not
have my own biases or that this thesis is free of bias, but the numbers used to analyze the data are not based on anybody’s perceptions or biases, but based on what actually occurred. This is what makes sports studies so useful – the transparency in factors such as wages and job
performance. So, even though a lack of surveying may be seen as a limitation, it is also a benefit
in this sort of research.
Layout of Thesis
The remainder of this thesis is organized in the following format: in Chapter Two, I will
address previous research pertaining to the relationships between time and learning, respite and
performance, time and recuperation, and similar research and evidence that has been found in the
NBA; in Chapter Three, I will address the methodology that will be used in this study, describe
the models being used, offer my hypotheses for the model, and the reasoning behind the use of
the chosen methodology; in Chapter Four, I will explain the key results of the research findings
and interpretations of those findings; and in Chapter Five, I will summarize the strengths,
weaknesses, and results of the research, as well as provide insight on future research possibilities.
11
CHAPTER TWO
LITERATURE REVIEW
Much research has been conducted in the areas of learning, respite, and physiological aspects of sports (Berger, 1962; Billat, Sirvent, Py, Koralsztein, & Mercier, 2003; Cardinale &
Bosco, 2003; Costill, 1986; Eden, 1990; Etzion et al., 1998; Etzion, 2003; Fleck & Kraemer,
1987; Fox, 1979, 1984; Fox & Matthews, 1974; Frankenhaeuser et al.,1989; Fredrick &
Walberg, 1980; Kember, Ng, Tse, Wong, Pomfret, 1996; Hooper, MacKinnon, & Hanrahan,
1997; Kereszty, 1971; Kuipers & Keizer, 1988; Mellerowicz & Barron, 1971; Michaels &
Miethe, 1989; Noakes, 1986; Plant, Ericsson, Hill, Asberg, 2005; Rau & Durand, 2000; Ryan,
Burke, Falsetti, Frederick, & Brown, 1983; Shirom, 1989; Talag, 1973; Westman & Eden 1997;
Westman & Etzion, 2001; Westman & Etzion, 2002). However, there has been relatively little research conducted in the area of learning as a function of time, and virtually no research has been published regarding learning as a function of respite or learning during time-off in sports, or more specifically, in the NFL. Similar statements can be made about research in respite and physiological recuperation. Some research examining the effects of rest between games and travel time on game performance has been conducted for the NBA (Entine & Small, 2008;
Steenland & Deddens, 1997). There have also been studies examining performance and time such as proper training regiments for various sports and the optimal time of day to perform which used the NFL to examine circadian rhythms (Dubner, 2011; Smith et al., 1997). Each of these studies will assist in further understanding the knowledge that currently exists in the areas of learning, respite, and recuperation time and determining the proper steps to take in this
12
research which will examine the role that additional time between games plays and when that time is taken on the outcome of games.
Analysts’ Perceptions of Bye Weeks and Team Performance
Various non-academic sports analysts have provided information regarding bye weeks
and American football team performance (Barnwell, 2012; Bretherton, 2009; Everson, 2010;
Lange, 2012; Love, 2012a, 2012b; Neupauer, 2011). George Bretherton (2009) of The Fifth
Down, a New York Times NFL blog, stated that two reasons why NFL teams should benefit
from additional time-off are due to recuperation and coaching adjustments. Bretherton also
found that, since 1990, the record for teams playing after a bye week is 309-276-1, a 52.7
winning percentage. Bretherton characterizes the advantage of a bye week as being no more
than a modest advantage. Though his examination yields insight into the impact that a bye week
may have, it has many flaws. The most obvious flaw may be the fact that he does not exclude
observations in which both teams playing each other are coming off of bye weeks. This suggests
that maybe the 52.7 winning percentage is closer to 50 percent than it should be (because of the
fact that when two teams play each other, one will likely win and one will likely lose, creating a
50 percent winning percentage.) Randy Lange (2012) examined these same games but reduced
his sample size and removed games in which two bye week teams competed against each other.
Lange found that since 2002, teams coming off of bye weeks have a win-loss record of 162-128,
a 55.9 winning percentage. He states that this winning percentage indicates that the bye week
does present an advantage, but not much of an advantage.
On the other hand, there are also people who have examined bye weeks and found them
to actually hinder a team. Darren Everson (2010) wrote an article for The Wall Street Journal in
which he described his findings for bye weeks in six of the major Bowl Championship Series
13
(BCS) college football conferences. Since 2002, the Big 12 has won 52 percent of their games
after a bye week, the Pacific 12 (PAC-12) and the Southeastern Conference (SEC) have won half
of their games after a bye week, the Atlantic Coast Conference (ACC) has won 47.7 percent of their games after a bye week, the Big East has won 45.3 percent of their games after a bye week, and the Big Ten has only won 34.7 percent of their games after a bye week. All six of these conferences combine for a total winning percentage of 48 percent for games after bye weeks.
But, perhaps, student athletes differ from professional athletes in the way they use or are affected by time-off. It is possible that something may occur such as students focus more on school and less on future opponents on a week off.
Special circumstances may also exist in the NFL that cause bye weeks to be less effective due to how time-off is spent. David Neupauer (2011) compared the first seven weeks of the
2011 season to all of the previous seasons since the 2000 season. He found that the winning percentage of teams coming off of bye weeks was about 54.2 percent between from 2000 through 2010, but dropped to 25 percent in the first seven weeks of the 2011 season. After plotting the 11 seasons of observations against a normal bell curve, he found that the 2011 season was so rare, that it was over four standard deviations below the mean winning percentage for teams coming off of bye weeks. Neupauer attributes the steep decline to the new collective bargaining agreement (CBA) that was passed just prior to the 2011 season and states that players must be given at least four consecutive days off, to include Saturday and Sunday. Neupauer; however, acknowledges that his sample size for the season was small and that there were still plenty of games to be played after bye weeks which could increase the winning percentage.
Bill Barnwell, a staff writer for Grantland, examined and wrote an article about whether or not the timing of a bye week presented a competitive advantage. Barnwell (2012) used data
14
from the 1994 through 1998 seasons as well as 2002 through 2011 seasons and found that teams
with bye weeks in weeks three, four, seven, and ten had cumulative winning percentages above
50 and teams with bye weeks in weeks five, six, eight, and nine had cumulative winning
percentages below 50. He also found an inverse relationship between bye weeks and winning
percentages with a correlation coefficient of -.5, indicating that the later a team has a bye week,
the more likely that are to have a lower winning percentage. Barnwell does admit to being
skeptical of these results due to having a small sample size of only 57 observations. Over this
span of fourteen seasons, Barnwell also looked for a relationship between later bye weeks and
Super Bowl victories. He found that having a late bye week had no effect on winning a Super
Bowl and noted that “no single week had more than three of the 14 champs, and Week 7 and
Week 10 laid claim to that crown. Every single "regular" bye week has produced at least one champ over that time frame” (para. 6). Barnwell then looked at how teams with late byes perform in the final five games of the regular season. He found that teams with bye weeks in weeks three and four had winning percentages above 50 percent in the final five games of the regular season, whereas teams with bye weeks in weeks nine and ten had winning percentages below 50 percent. All of Barnwell’s findings thus far have opposed what intuition would suggest about time off, as well as the popular beliefs of sports fans and analysts. Finally, Barnwell looked at teams playing before a bye week as well as teams playing after a bye week and findings were aligned with what most fans’ and analysts’ intuition would suggest. Teams playing before a bye week have won about 50.5 percent of their games in this fourteen season timespan, and teams playing after a bye week have won almost 55 percent of their games in the same period.
15
Though the aforementioned non-academic sources provide helpful information in understanding how bye weeks affect performance, there are some clear flaws with this research.
This research typically has not gone through a formal process of scrutiny that would have made the research more profound and useful. If the research had been conducted in an academic environment, the research would likely have accounted for other variables and held them constant while analyzing the bye week effects.
Learning as a Function of Time
In the NFL, there are multiple ways to study opponents and to study to enhance one’s own performance. Elite NFL athletes are described by analysts, columnists, and commentators as having many different characteristics which often include arriving early to practice and team meetings, being among the last to leave practices and meetings, and chronically examining game film (Arthur, 2012; Frank 2012). Likewise, those who show up late to or dismiss themselves early from organized team functions are often assumed to not be living up to their full potential
(Frank, 2012; Lombardi, 2011). Research conducted in academic settings has shown that, in general, there is a positive relationship between independent study time and academic performance as well as time in the classroom and academic performance (Fredrick & Walberg,
1980; Kember, Ng, Tse, Wong, Pomfret, 1996; Michaels & Miethe, 1989; Plant, Ericsson, Hill,
Asberg, 2005; Rau & Durand, 2000). However, the positive relationship between study time and academic performance may not always hold true and at some point, diminishing returns may occur over time in the learning process (Fox, 1979; Fredrick & Walberg, 1980; Metcalfe, 2011;
Nelson & Leonesio, 1988; Walberg & Tsai, 1984).
Although such things as ballet, music, chess, science, and writing performance cannot be
measured so precisely, they appear to show diminishing returns relative to time: good or
16
even excellent performance by the usual standards may only require a half to an hour a
day of concentrated effort; but national rankings or one's best may require, among other
things, three to eight hours of instruction and practice daily. (Pushing past some point, of
course, may produce not only diminishing but negative returns.) (Fredrick & Walberg,
1980, p. 191)
Walberg and Tsai (1984) also stated that there are crucial opportunity costs associated with study time that could result in less than desirable academic performance. For example, a student may spend so much time studying that they forget to eat or refuse to sleep an adequate amount of time which could result in a worse academic performance due to an increase in study time. The same could be said of an NFL player who is attempting to perfect a single aspect of his performance while the rest of his skills diminish at a more rapid rate than the rate at which new skills are being acquired. Both of these are examples of opportunity costs which students as well as NFL athletes could relate to since football players can also work so hard toward a goal that they fail to take proper care of their bodies or students can attempt to improve one aspect of their lives while other aspects more rapidly deteriorate.
In a study conducted by Nelson and Leonesio (1988), self-paced studying practices were examined and multiple conclusions were reached. Among those conclusions, a few may be relevant when examining the impact of time-off on team performance in the NFL. In the study, participants were given various items to master which could have consisted of general information questions or word pairs to memorize. The participants were required to master each item in which they were presented. Even though they were allotted an unlimited amount of time to study and master every item, the participants decided to quit studying prior to mastering the required items. Lack of mastery has been noted previously in research and continues to be
17
studied (Le Ny, Denhiere & Le Taillanter, 1972). This single conclusion reached by Nelson and
Leonesio has two implications on the impact of time-off on team performance in the NFL. First of all, if unconstrained by time, there will be a certain point when people decide on their own to stop using time to study a particular item. This means that there is a point in time when nobody is studying a given item and allotted time can be limited without constraining anybody. Whether this point in time occurs within a weeks’ time or extends beyond a year is currently unknown; however, there is evidence that indicates a point in time when this occurs does exist. Second, this research conclusion indicates that, in the NFL, a team can study an opponent or their own performance for a given amount of time and will choose to terminate studying prior to fully mastering their knowledge of the opponent or their own performance.
Another conclusion that was drawn from this Nelson and Leonesio (1988) study was that
“large increases in self-paced study time can yield little or no increase in the subsequent likelihood of recall” (p. 676). This concept is known as the labor-in-vain effect which simply means that “people may spend a great deal of time selectively working on the most difficult items, but this extra time and effort is without payoff” (Metcalfe, 2011, p. 260). When the study was dichotomized into a speed-focused learning group and an accuracy-focused learning group,
Nelson and Leonesio (1988) found that the “extra amount of self-paced study time in the accuracy group yielded only 1% or 2% more recall for each extra second of study time” (p. 685).
Related to the idea of diminishing returns, this specific example indicates that there is not only a point when everybody is finished studying the given items, but also a point that occurs prior to terminating study when extra time yields nearly negligible returns. Similar to the ideas presented in the previous paragraph, this conclusion means that there is likely a point in time when the bulk of knowledge is obtained that could prove useful for performing well in the following game. For
18
example, a team could be virtually as prepared to play their opponent, from a learning
standpoint, after three days of studying compared to a week or two of studying. Or perhaps the
time period which contains the majority of the knowledge that can be learned to perform well in
the following game is one week, two weeks, a month or a year. At the moment, this information
is not currently available, but knowing that such a time period exists is important to
understanding how time-off, which is often used as study time, affects performance in the NFL.
Respite as a Function of Time
Westman and Eden (1997) stated that “a respite from work may be a day off, a weekend, a vacation, or some other form of absence from the work setting when the everyday pressures of the job are absent” (p. 516). For an NFL player, off-seasons, bye weeks, and even an extra day off between games could be considered respite. By analyzing research that has been conducted by various experts in the field of respite, additional knowledge may be accumulated regarding respite in the NFL. These experts have analyzed both the effects of respite on job performance and satisfaction, as well as how time affects respite, which will assist in our understanding of respite in the NFL.
Respite has been studied and determined to have numerous beneficial effects on people that transcend the line between work and life (Eden, 1990; Etzion et al., 1998; Etzion, 2003;
Frankenhaeuser et al., 1989; Shirom, 1989; Westman & Eden 1997; Westman & Etzion, 2001;
Westman & Etzion, 2002). Shirom (1989) argued that practitioners prescribe respite to remedy burnout since the most important element of burnout is exhaustion. Respite offers people a chance to rejuvenate their energies and improve their overall well-being (as cited in Westman &
Etzion, 2002, p. 585). The study conducted by Westman and Etzion (2001) examined blue collar workers and revealed that vacation decreases job stress, burnout, and absenteeism and increases
19
employees’ perceived performance. These studies confirm the generally accepted notion that
respite is beneficial for one’s well-being but also provide evidence that benefits may also be seen
by employers as work performance and quality of life is improved by an employee’s temporary
absence.
The benefits of respite are well documented; however, the exact amount of time-off that is needed to reap the benefits of respite has yet to be determined (Eden, 1990; Etzion et al., 1998;
Etzion, 2003; Frankenhaeuser et al., 1989; Shirom, 1989; Westman & Eden 1997; Westman &
Etzion, 2001; Westman & Etzion, 2002). Since respite is assumed to be a remedy for burnout which is caused by exhaustion, it would make sense that the amount of respite necessary for recovery could be linked to the amount of exhaustion an employee has accumulated. Following this rationale, one may assume that an unlimited amount of respite could likely remedy any amount of exhaustion that has been accumulated in the workplace and be able to completely replenish one’s well-being. In terms of replenishing the well-being of employees, and therefore temporarily disregarding the work performance benefits of respite, the question of ‘Is more time- off better?’ must be answered. Steenland and Deddens (1997) studied the effect of time-off between games in the NBA and found consistent results over the eight seasons examined (from
1987-1995) indicating that “both home and visiting team benefited significantly from having more than 1 day between games (1.1 point improvement for the home team, 1.6 point improvement for the visitor team)” (p. 368). Steenland and Deddens (1997) research indicates that there are indeed benefits that can be observed in athletic competitions from having more than a single day between games.
Kelly (2006) conducted a similar study on the NBA and came to the following conclusions:
20
Winning percentages of teams are reduced when they are involved in back-to-back
games. This was explained by teams having less opportunity for rest and preparation,
especially in the case of the second game. The playing of back-to-back games on the
road brings additional physical and psychological demands on players and coaches and
further reduces success rates. Five years of regular season data from the 1999-2000 to
the 2003-2004 seasons found that teams playing back-to-back games on the road won
both games at a rate of only 18.04%, significantly below a normally distributed
probability rate of 25% for winning both games. The chances of losing both of the games
are greater than those for winning both games. The expected normal probability for
losing both road games is 25%, but in a back-to-back setting the observed losing
percentage rises to 41.35%. (as cited in Kelly, 2008, p. 2)
Kelly’s research found that there is a lower likelihood of winning an athletic competition similar to professional football when less time is allotted between games. The actual percentages that he gives may be somewhat misleading though, given that Kelly does not account for the home-court advantage that exists aside from the portion captured by rest and travel. Previous studies on home-court advantage in the NBA have stated that there is at least a 60 percent advantage for the home team. Given that statistic, the expected normal probability of losing both road games would be at least 36 percent (as opposed to 25 percent), compared to the 41.35 percent that Kelly observed (Courneya & Carron, 1992; Entine & Small, 2008; Gandar et al., 2001; Jones, 2007;
Schwartz & Barsky, 1977; Trandel & Maxcy, 2011). Nevertheless, the fact still remains that as time between games decreases, so does athletic performance. Kelly (2006) cites the sources of higher loss probabilities from increased time constraints as being less time for preparation and
21
rest, which he refers to as physical and psychological demands that are experienced by both
players and coaches (as cited in Kelly, 2008).
It is unrealistic to assume an unlimited amount of time between games, so determining the upper boundary of time to not be constrained by time between games is important. This is especially important in sports since practice is always needed and players have to worry about skills declining or not ‘staying sharp’ enough to perform at their best ability (Odum, 2013). As was the case in the learning literature, there could also be diminishing returns to performance relative to time-off. This could be caused by the factors mentioned above, such as the inability to ‘stay sharp.’ In the case of the NBA, Steenland and Deddens (1997) study revealed that “the beneficial effect tended to peak with 3 days between games for both home and visiting teams, declining after ≥4 days between games” (p. 368). Steenland and Deddens (1997) came to the
conclusion that “the tailing off of improvement with more rest is presumably due to players
starting to lose ‘sharpness’ with too many days off" (p. 369).
Previous studies on respite outside of the sports industry have sought to estimate how
long it takes for the benefits of vacation time to wear off (Etzion, 2003; Westman & Eden, 1997;
Westman & Etzion, 2001). Westman and Eden (1997) found that burnout levels returned to their
pre-vacation levels by the third week after returning from vacation. Of the blue-collar workers
studied by Westman and Etzion (2001), the researchers came to the conclusion that stress,
burnout, and performance had returned to pre-vacation levels one month after returning from
vacation. Etzion (2003) also found that stress returned to pre-vacation levels in the course of a
month, but burnout remained lower than pre-vacation levels beyond one month. From each of
these findings, it can be estimated that the overall effects of time-off may last between about
22
three weeks to over one month. Furthermore, these findings could also extend to the sports
industry and lend some additional insight into how time-off affects performance.
Of the research conducted in the area of respite, there are certain types of studies that
may have more characteristics of respite relevant to the NFL than other studies. These studies
examine working under different circumstances which provide a break from the regular, often
monotonous, daily grind that many employees are exposed to. In the NFL, this break could be
comparable to an extended period when no regular season games are being played (assuming at
least temporary job security, such as after the 53-man roster has been finalized, though every
game is an evaluation that could result in a player being cut from the team), playing in a certain
location that appeals to a player where they do not often get the opportunity to play, or even
playing for an NFL team following a career outside of the sports industry (for example, working
as an insurance agent, selling cellular telephones in the mall, or any other occupation that does
not provide professional athlete level training prior to being employed by the NFL). Etzion et al.
(1998) conducted a study on the effects of reserve military service as respite. Acknowledging
that active military service is not a traditional form of respite, such as vacation time or a leisurely
weekend, Etzion et al. (1998) examined the idea that a change of pace and scenery from the everyday workplace may be a key factor that influences the positive effects of respite. They found that the active military service did serve as a form of respite with benefits that included the
alleviation of burnout and reduced levels of strain as compared to the reservists’ civilian counterparts who remained on the job. Although a decrease was noticed in levels of burnout and strain, they did not decrease to the lowest levels possible. This study proved that even though the respite was not a time of leisure, positive effects still occurred similar to those that would
have occurred if the employee had taken a vacation.
23
Westman and Etzion (2002) conducted a study that also examined working under different circumstances, but this study was about short overseas business trips. These trips have many of the same attributes as the reservists’ active military service, which include a change in employees’ environments and working instead of focusing on leisure. Westman and Etzion found that, similar to the findings of Etzion et al. (1998), these short overseas business trips also have beneficial effects similar to the effects that result from a vacation. In terms of the NFL, even though the player may be working to stay physically and mentally ready for a regular season game, off-seasons, bye weeks, or unusual playing locations may result in a more rejuvenated, motivated, and dedicated player. On the other hand, as noted by DeFrank,
Konopaske, and Ivancevitch (2000), working under unfamiliar conditions or taking on work during a vacation could also cause increased levels of anxiety, frustration, and stress.
There are hardships that are inherent to diverging from routine, particularly in traveling for business purposes. In the NFL, business traveling is inevitable because at least ten games per year are away games and training camps are often located far from the city in which the team is based. There are often more than ten away games for teams that make the playoffs or play an additional home game in an unusual location such as Toronto or London. Fisher and Cooper
(1990) suggest that workers who travel demonstrate distress because of the frequent changes in their daily routine to which they have to adjust. NFL analyst and former NFL coach Steve
Mariucci described weeks 12 through fourteen of the Houston Texans 2012 schedule as having a rare three consecutive road games in which they play on three different days of the week:
Thursday, Sunday, and Monday in weeks 12, thirteen, and fourteen, respectively. Mariucci further claimed that the Texans “got hosed” in the schedule making process because three consecutive road games on three different days of the week “throw your schedule out of whack”
24
(Love, 2012b). Mariucci stated the importance of these schedule irregularities when he explained what coaches look for when the schedule is released. “You want to know when…is my bye or when is my Thursday night game, my short weeks, my long weeks” (Eisen, 2012).
To demonstrate the negative effects that travel can have, Liese, Mundt, Dell, Nagy, and
Demure (1997) found that business travelers were three times more likely to file medical claims than their non-traveling counterparts. After Westman and Etzion (2002) explained their results, they offered the following conclusion to the contradictory findings in the previous literature:
Contrary to some studies which have found that business trips impair psychological
health (Liese et al., 1997; DeFrank et al., 2000), we found that they have an ameliorative
effect. These seemingly contradictory findings call for the identification of mediating
variables. One promising mediating variable is the person–occupation fit, which could
explain why some people suffer from business trips while others thrive on them.” (p.
590).
Clearly, as intuition would suggest and previous research has shown, business travel does have its hardships (Liese et al., 1997; DeFrank et al., 2000). Many questions on this topic related to the NFL are still unanswered. Though it may be just as important to understand the impacts of traveling on NFL athletes as it is on non-sport industry employees, in terms of performance, game outcomes, and competitive advantages, if every team has to travel for approximately half of their scheduled games, is traveling a relevant issue? Some teams, due to their location, division, or schedule, may have to travel further distances than others, so does that play a role?
Are some teams or players better at handling the hardships of traveling? Is age a factor? These unanswered questions are questions that must be addressed when considering how respite affects performance, especially since nearly every NFL game requires at least one team to travel.
25
Studies of employees new to an organization could assist in determining the effects of
traveling on players of different ages or experience levels. Nelson and Quick (1991) found that
recurring opportunities to temporarily leave the new work space for business purposes may result
in new employees being able to decrease some of their psychological distress. Though it may be
routine for veterans in the organization, the newcomers may have less routine to break and fewer
social attachments that allow them to benefit more from traveling. Additionally, new
experiences can be exciting, rejuvenating, and motivating all on their own, whereas veterans may
be more likely to have a more accustomed or complacent mentality.
Physiology, Performance, and Time
Understanding basic ideas in sports physiology can be useful in understanding how time
affects athletic performance. Fatigue, muscular recuperation, and other physiological factors
play a role in how well the body functions with respect to time. Numerous studies have been
conducted in the field of sports physiology and there is a lot that is known about how athletes
should train and perform as well as what their bodies go through as they do train and perform
(Berger, 1962; Billat, Sirvent, Py, Koralsztein, & Mercier, 2003; Cardinale & Bosco, 2003;
Costill, 1986; Fleck & Kraemer, 1987; Fox, 1979, 1984; Fox & Matthews, 1974; Hooper, 1997;
Kereszty, 1971; Kuipers & Keizer, 1988; Mellerowicz & Barron, 1971; Noakes, 1986; Ryan et
al., 1983; Talag, 1973). There is also a lot that is unknown (Billat, Sirvent, Py, Koralsztein, &
Mercier, 2003; Cardinale & Bosco, 2003; Fox, 1979, 1984). Since all bodies are different and
are controlled by brains that are even more diverse, studies in sport physiology are not always perfect. Psychological factors affect how the body functions and can differ from athlete to athlete as well as coach to coach (Fleck & Kraemer, 1987; Fox, 1979, 1984; Hooper, 1997;
Kereszty, 1971; Kuipers & Keizer, 1988; Mellerowicz & Barron, 1971).
26
Staleness in sports is something that little is known about and may be caused by psychological factors (Fleck & Kraemer, 1987; Fox, 1979, 1984; Hooper, 1997; Kereszty, 1971;
Kuipers & Keizer, 1988; Mellerowicz & Barron, 1971). Nobody knows for sure exactly what staleness is, or why it occurs, but “it is probably related to or caused by chronic fatigue” (Fox,
1979, p. 303). Hooper et al. (1997) conducted a study on how moods may indicate staleness and recovery among elite swimmers. The researchers characterized an athlete as being stale if the athlete failed to improve performance and was excessively fatigued. Hooper et al. (1997) found that the moods of the athletes “were significantly correlated with training intensity but not with training volume” (p. 1). Some of the psychological factors that may cause staleness are boredom, depression, or lack of interest (Fox, 1979). It could also be that the psychological factors cause the physical factors of staleness, or conversely, the physical factors may cause the psychological factors. Many researchers have found that symptoms such as irritability, emotional instability, increased injury susceptibility, and irregular sleeping patterns may occur as a result of staleness (Mellerowicz & Barron, 1971; Ryan et al., 1983). According to Kereszty
(1971), stale athletes “seem to recover more slowly and may feel exhausted for several hours after a workout” and may also encounter fatigue in times of rest (as cited by Kuipers & Keizer,
1988, p. 82). Perhaps the most noticeable and impactful symptom of staleness is decreased performance (Costill, 1986; Fox, 1979, 1984; Hooper, 1997; Mellerowicz & Barron, 1971;
Noakes, 1986; Ryan et al., 1983). The severe fatigue that results in staleness could be a result of overtraining, indefinite use of a single training program, engaging in multiple training regimens simultaneously, or a lack of periodization (Fleck & Kraemer, 1987; Kuipers & Keizer, 1988).
The factors attributed to staleness have been covered, which most likely consist of fatigue and various psychological factors; however, proper physical recuperation is always necessary for
27
athletes, no matter their mental state or the training regimen. Overtraining, which was mentioned in the previous paragraph, is defined by Kuipers and Keizer (1988) as “an imbalance between training and recovery” (p. 79). This gives a very simple definition to a very complex
idea. How much recovery time is needed with respect to training time? Does it matter what sort
of training is being conducted or how strenuous it is aerobically or anaerobically? Fox and
Matthews (1974) analyzed ratios of work to relief time and found that when training for sports
such as football, a one to three ratio of work to relief is most beneficial, whereas in more aerobic
sports, the ratio is closer to one to one. Fox (1984) also examined optimal days per week to
work out for various sports and the optimal duration of the training programs. Training
programs tailored for anaerobic sports, such as football, should incorporate three days per week
of training over a span of between eight to ten weeks. Athletic trainers are aware of how to develop optimal training schedules, and on a week-by-week basis, they typically utilize the aforementioned three days per week. The problem is that the NFL regular season is 17 weeks
long without accounting for preseason or playoffs which is much longer than ten weeks. It is
also important to notice how the regular season has expanded over the years to now having a 17
week regular season and more playoff games. If the season continues to expand, for example, to
the proposed nineteen week regular season, the quality of athletic performances may be
negatively affected due to the extended training programs that would occur and the increased
likelihood of overtraining, staleness, or injury. Fox (1984) also stated that lengthy endurance-
based activities, such as marathons, may require several days of recovery; however, for activities
which are short in duration but high in intensity, such as sprinting or possibly weightlifting, a
recovery period of around an hour could be sufficient. An activity such as football, especially
depending upon the position being played, would fall somewhere in between this spectrum.
28
As observed in the field of learning and respite, physical recuperation also has the properties of diminishing returns (Berger, 1962; Fox et al., 1975; Nelson & Leonesio, 1988;
Steenland & Deddens, 1997; Talag, 1973). These diminishing returns come in a couple forms
(Berger, 1962; Fox et al., 1975; Talag, 1973). First of all, diminishing returns to maximal aerobic power occur as the duration of the training period is extended (Fox et al., 1975). Though not a large effect, there is a slight difference in how the returns diminish relative to duration among different training frequencies. For example, for the first seven weeks of a training program, a four day per week training program will result in more aerobic power than a two day per week program, but by the thirteenth week, the latter program will be yielding better results due to the greater diminishing returns of the former program. The two day per week program also experiences diminishing returns throughout the thirteen weeks, especially between weeks seven and thirteen when the improvement in maximal aerobic power is fairly stagnant (Fox et al.). Diminishing returns also occur in other ways when examining workouts. Some of these instances are when repetitions in a weightlifting set increase, the strength gained from each subsequent repetition decreases; or when the number of days following an exercise increases, the amount of muscle soreness experienced from each subsequent day decreases relative to the previous day (Berger, 1962; Talag, 1973). These concepts of diminishing returns in sports physiology are important to understand when examining how time-off affects performance in the
NFL because they provide knowledge about whether the quality of the athletic performance should taper off or not. If athletic performance does deteriorate over time, these concepts may assist in determining when the quality of performance begins to deteriorate, and possibly, the rate at which it deteriorates.
29
Summary of Previous Research
This chapter has cited experts in the NFL, NBA, field of learning, field of respite, and
field of physiology. Each of these experts’ contributions in their respective fields will be utilized in analyzing how time-off affects performance in the NFL. For example, as previously mentioned, NFL coach John Fox believes that it is optimal to have a bye week in the middle of the regular season, such as the seventh week of the regular season (Love, 2012a). Whether a mid-season bye is optimal for all teams or just for some teams has yet to be formally researched.
The consensus in the learning research community is that more time to study is often
better; however, there may be diminishing returns (Fredrick & Walberg, 1980; Nelson &
Leonesio, 1988; Walberg & Tsai, 1984). Some learning researchers believe that there is a labor-
in-vain effect which indicates that maybe extra preparation time does not matter too much
(Metcalfe, 2011; Nelson & Leonesio, 1988). Steenland and Deddens (1997) who conducted research on the NBA found that some time off between games definitely benefitted NBA athletes but maybe too much extra preparation time causes players and coaches to lose sharpness. Kelly
(2006) found that less time for rest and preparation decreased the likelihood of winning in the
NBA.
Respite researchers have contributed to this topic in many ways. They have found that there are definitely individual benefits to respite, but benefits to companies or teams are more difficult to examine (Eden, 1990; Etzion, Eden, & Lapidot, 1998; Etzion, 2003; Frankenhaeuser et al., 1989; Shirom, 1989; Westman & Eden, 1997; Westman & Etzion, 2001; Westman &
Etzion, 2002). They have analyzed how long respite takes to wear off and found that many of the benefits last no longer than a month (Etzion, 2003; Westman & Eden, 1997; Westman &
Etzion, 2001). Respite researchers have also examined respite in terms of working under
30
different conditions, similar to the respite that NFL players receive (Etzion et al., 1998; Westman
& Etzion, 2001). The benefits of respite under these conditions exist; however, they are not as pronounced as respite received when on a leisurely break from work where no work is expected.
Some respite researchers, such as DeFrank et al. (2000), have determined that working under unfamiliar conditions or taking on work during a vacation could be very detrimental. Some respite researchers have acknowledged that there is a difference in how certain people handle unfamiliar working conditions and hypothesize that age, experience, or possibly even family situation may be a factor in how people adapt to their unfamiliar environments (Nelson & Quick,
1991; Westman & Etzion, 2002). In the NFL, it is possible that the older players who are more accustomed to NFL life may do better when traveling, though probably not over the course of many consecutive games. Younger athletes typically have more testosterone which aids in faster recovery (Jones, 1993; Kujawa & Jones, 1990; Kujawa, Kinderman, & Jones, 1989). NFL analyst Jason La Canfora said that older teams with early bye weeks will really be challenged when having to play a lot of consecutive games without a break (La Canfora, 2012).
Former NFL coach and current NFL analyst Steve Mariucci cited schedule irregularities such as playing multiple consecutive road games or playing on three different nights in a row as being possible problematic situations (Love, 2012b). Sport physiologists have confirmed through research that schedule irregularities may increase the chances of athletes becoming stale.
Liese et al. (1997) found that business travelers are three times more likely to file medical claims. Sport physiologists have also found that the optimal training duration should last no longer than eight to ten weeks and that, like learning and respite, there are diminishing returns in physical training as well (Fox 1979, 1984; Fox et al., 1975).
31
There are many possibilities of how time-off could affect the NFL based on the theories
and research presented by the experts who have been cited in this chapter. I will take the
information that they have presented and apply it in a quantitative study of how time-off affects performance in the NFL and try to obtain a better understanding of, not only what happens in the
NFL, but what may occur in other industries as well. Depending on the results of this study, the ideas from the experts will also be useful when drawing conclusions about the findings of this research.
32
CHAPTER THREE
METHODOLOGY
The quantitative research in this thesis will focus on three questions: (a) how much of an advantage exists for a team with more time-off than their opponent?, (b) what factors impact how much of an effect time-off has?, and (c) which week of the regular season is the optimal week to have a bye and what factors affect the optimal bye week? To answer these questions, secondary data will be used and analyzed that covers the time frame that commences with the 1990 season and ends with the 2012 season, but excludes the 1993 and 2001. The rationale behind selecting these 21 seasons is because this time frame encompasses all of the NFL seasons in which the modern bye week has been utilized, but not more than one bye week per team per season. Data will be obtained primarily from the official website of the NFL (http://www.nfl.com/) which provides information on the final score of each game; each teams’ win-loss records; and how successful each team has been in producing or preventing passing, rushing, and return yards.
Data regarding the players’ ages and the game start times and dates will be obtained through
Football @ JT-SW.com (http://www.jt-sw.com/), a website that maintains credible football data and has been used in publications found in Journal of Economics and Business, The International
Journal of the History of Sport, and Journal of Quantitative Analysis in Sports (Borghesi, 2008;
Brown, 2005; Govan, Langville, and Meyer, 2009). Where information is not available from the
Football @ JT-SW.com website, such as game start times prior to 1995, it will be obtained through the website Pro-Football-Reference.com which has been cited in the Journal of Sports
Economics, Journal of Quantitative Analysis in Sports, and Managerial and Decision Economics,
33
among others (Berri & Bradbury, 2010; Goff & Wisley, 2006; Rosenfeld, Fisher, & Adler, 2010;
Schuckers, 2011).
Model One: Bye Week Summary
The first method that I will use to examine how time-off affects performance will be structured in a similar way to the studies conducted by Smith et al. (1997) and Dubner (2011).
These two studies examined the effects of circadian rhythms by analyzing the performance of west coast NFL teams playing night games on the road against east coast teams. Smith et al.
(1997) simply examined the win-loss records of west coast teams in these scenarios and found that from the 1970 season through the 1994 season, west coast teams won 63.5% of their away games against east coast teams. When west coast teams won, on average, they won by about
14.7 points, whereas the east coast teams won by, on average, about nine points per game.
Dubner (2011) replicated the study utilizing more recent data and found more profound results.
Using this same method, I will seek to determine how much more likely a team coming off of a bye week is to winning a game against a team who has not had a bye week. I will compile a list of all of the games that were played between teams in which one team was coming off of a bye week and the other team was not. Then I will add up all of the wins and losses that the bye week teams accumulated to establish a winning percentage. Then I will dichotomize my compiled list by bye team wins and bye team losses to further examine the average amount of points that bye week teams won by and non-bye week teams won by in these particular games. This simple examination will help detect the presence of a bye week advantage on the most basic level.
Smith et al. (1997) acknowledged that their methods may be flawed due to factors such as the ability of the west coast teams compared to that of the east coast teams.
34
Model Two: Time-Off Impact, Ceteris Paribus
Model Two will seek to determine how much more of an advantage is present for teams
with additional time-off relative to their opponent, holding the ability of the opposing teams
constant. This will present a few strengths that Model One fails to account for such as
accounting for team abilities and analyzing relative days off between teams rather than just
whether the teams are coming off of bye weeks or not. In order to account for other variables,
such as home field advantage or team ability, I will use ordinary least-squares (OLS) regressions
to obtain the best linear unbiased estimations for examining the effect of time-off on
performance given the assumptions that the error term distribution has a mean of zero and is
normally distributed, the error term is uncorrelated with the independent variables, the error term
observations are uncorrelated with each other, the error term has a constant variance, and no
independent variable is a perfect linear function of another independent variable. Furthermore,
these assumptions will be tested and depicted in the form of graphs following the regression
analyses.
The data will consist of observations beginning with the second week of the regular season and will conclude with the 16th week of the regular season. The first week will not be included in the data set because there was no previous meaningful game, which means that the amount of time between the present game and the most recent meaningful game of a particular regular season will not be attainable. The final game of the regular season will not be included in the data set because there is an incentive to rest elite players or intentionally lose to secure a better draft selection. I will use a dependent variable of score differences (SCOREDIF) in favor of the home team, which would mean that if the home team beat the away team by seven points, the number associated with that observation would be seven, but if the away team beat the home
35
team by seven, the number associated with that observation would be negative seven. Similar studies by Gandar, Zuber, O’Brien, and Russo (1988); Sauer, Brajer, Ferris, and Marr (1988); and Zuber, Gandar, and Bowers (1985) used a dependent variable of score differences between the home and away team have also used OLS for examining gambling market efficiency and this is the same dependent variable used in other similar studies (Boulier, Stekler, & Amundson,
2006; Entine & Small, 2008; Steenland & Deddens, 1997; Wagner, 1987).
With the SCOREDIF dependent variable, I will use nine independent variables. Prior studies which have examined NFL game outcomes have used independent variables that are used to explain team strengths such as passing yards, rushing yards, and return yards (Sauer et al.,
1988; Wagner, 1987; Watnik & Levine, 2001; Zuber et al., 1985). To best account for the ability of the teams over the course of a season, the season totals will be used, but averaged to put the variables in ‘per game’ quantities which are easier to grasp as was done by Sauer et al. (1988).
For example, if a team has 40 passing touchdowns in a season, it is easier to understand that they average 2.5 passing touchdowns per game. The first eight independent variables will be (1) the difference between the home team’s passing yards per game and the away team’s passing yards allowed per game (HOMEPASS), (2) the difference between the away team’s passing yards per game and the home team’s passing yards allowed per game (AWAYPASS), (3) the difference between the home team’s rushing yards per game and the away team’s rushing yards allowed per game (HOMERUSH), (4) the difference between the away team’s rushing yards per game and the home team’s rushing yards allowed per game (AWAYRUSH), (5) the difference between the home team’s kick return yards per game and the away team’s kick return yards allowed per game
(HOMEKRET), (6) the difference between the away team’s kick return yards per game and the home team’s kick return yards allowed per game (AWAYKRET), (7) the difference between the
36
home team’s punt return yards per game and the away team’s punt return yards allowed per
game (HOMEPRET), and (8) the difference between the away team’s punt return yards per game
and the home team’s punt return yards allowed per game (AWAYPRET). Since the home team scoring would result in a higher difference in score, in the home team’s favor, I hypothesize that the variables HOMEPASS, HOMERUSH, HOMEKRET, and HOMEPRET will be positively correlated with SCOREDIF and AWAYPASS, AWAYRUSH, AWAYKRET, and AWAYPRET will be negatively correlated with SCOREDIF. The final independent variable will be the difference between the home team’s days off prior to the game and the away team’s days off prior to the game (DAYSDIFF). A similar variable has been used when analyzing rest in the
NBA which accounted for whole days off between games; however, DAYSDIFF will also include fractions of days (Entine & Small, 2008; Steenland & Deddens, 1997). I hypothesize that, due to learning, respite effects, and physical recuperation, DAYSDIFF will be positively correlated with SCOREDIF since both calculations are made by subtracting the away statistic from the home statistic.
Dichotomizing Model Two
In order to obtain an in-depth assessment of how time-off affects game outcomes, it will
be necessary to determine how the age, quality, and familiarity of teams factor into the
relationship between time-off and game outcomes. If age were an independent variable in Model
Two, it would only yield information about how much age effects winning with other variables
held constant. What I want to know is if older teams benefit more or less from time-off than
younger teams, with other variables held constant. The same questions could be made with the
other two factors: team quality and familiarity. Based upon previous literature on the
37
aforementioned subjects, I predict that time-off will have a more profound effect on older teams,
better teams, and less familiar teams.
To test these hypotheses, I will dichotomize Model Two on three separate occasions.
First, I will dichotomize Model Two by average team age. The oldest 16 teams will be identified
as older teams and the youngest 16 teams will be identified as younger teams. One regression
will consist of games played between older teams and the other regression will consist of games
played between younger teams. This dichotomized model will yield results that indicate whether
or not older or younger teams perform better after relatively more time-off than their opponents.
I hypothesize that the regression among the older teams will yield more significant results in
terms of t-statistics than the observations collected for the younger teams. This hypothesis
comes from the idea that older teams will use the time-off more adequately to recuperate
physically, as well as use their football wisdom which has accumulated over their many years in
the league to study their opponent.
Then, I will reunite all of the observations again and separate them into two different regressions. One regression will consist of observations where good teams play against good opponents and another regression where bad teams play against bad opponents. For this examination, a team will be categorized as a good team if its ‘points for’-to-‘points against’ ratio is greater than or equal to one or a bad team if its ‘points for’-to-‘points against’ ratio is less than one. The results will indicate whether or not good teams are better at preparing for opponents
than bad teams when given extra time to prepare. I predict that the regression with the good
teams will not only have a higher correlation coefficient for DAYSDIFF, but the results will also
be more significant due to the idea that better teams will likely have better coaches and players
who are skilled at studying and physically preparing for opponents.
38
Again, I will reunite the observations so that I may dichotomize Model Two again. This time, I will extract the observations from Model Two in which the teams are playing division opponents. Since division opponents play one another twice every season, this will help examine the effect that familiarity with the opponent has on team performance with respect to time-off. I hypothesize that the significance of DAYSDIFF for division opponents will be less than that of non-division opponents because teams that are more familiar with each other will likely benefit less from additional time-off relative to teams that are not familiar with each other.
Model Three: Optimal Bye Week for Uninterrupted Final Stretch
The third and final model that I will use to examine scheduling and bye week effects in
this thesis will again utilize OLS regression, but this time with the dependent variable being the
team’s winning percentage in the uninterrupted final stretch of the regular season (STRETCH).
For example, in the 2012 season, the last week of byes was week 11, so the uninterrupted final
stretch of the regular season would be the team’s winning percentage for the final five games of the regular season which span from week 12 to week 16. This dependent variable is similar the
dependent variables in studies by Chatterjee, Campbell, and Wiseman (1994) and Hall,
Szymanski, and Zimbalist (2002). Prior studies that used winning percentages as a dependent variable and this model is that the prior studies were concerned with examining the effects of independent variables such as player salaries, whereas this model is interested in examining bye weeks – a topic which has not appeared in many academic journals. As in Model Two, week 17
is being excluded from the winning percentage that composes STRETCH because of teams’ tendencies to decrease efforts for the purposes of resting elite players prior to playoff games or other similar competitive strategies that incentivize less than maximal effort. Due to the nature of this dependent variable, the data set will be restricted to the 17 NFL seasons of the years 1992,
39
1994-1998, and 2002-2012 seasons because the final bye weeks in 1990 and 1991 were in week
14 leaving only two weeks to examine wins and losses as a dependent variable, the 1993 season
had two bye weeks, and the 1999-2001 seasons did not have multiple weeks without byes at the
end of the regular season. The independent variables that will be used in this regression will be
(1) the teams’ percentage of games at home (HOMEPCT), (2) the percentage of games in the
uninterrupted final stretch of the regular season in which teams have relative preparation time
advantages of at least nineteen hours (TIMEADV), (3) the percentage of games in the
uninterrupted final stretch of the regular season in which teams have relative preparation time
disadvantages of at least nineteen hours (TIMEDIS), (4) the teams’ winning percentage up until
the uninterrupted final stretch of the regular season (WPEARLY), (5) the percentage of opponent
teams that have a higher WPEARLY than the observed team (OPEARLY), (6) the teams’
assigned bye weeks (BYEWEEK), and (7) the squared values of the bye weeks assigned to the
teams (BYESQUAR). Intuition suggests that when teams (a) play more home games teams, (b)
have more time to prepare for opponents, and (c) are more successful than their opponents, the
more likely they will be to beat their opponents. Therefore, I hypothesize that HOMEPCT,
TIMEADV, and WPEARLY will be positively correlated with STRETCH; and TIMEDIS and
OPEARLY will be negatively correlated with STRETCH. The key variables of interest in this model will be BYEWEEK and BYESQUAR. The reason for including both a BYEWEEK and a
BYESQUAR variable is to test for a parabolic relationship with STRETCH. As identified in the literature review, it is believed that a mid-season bye week is optimal, so these two variables will help identify whether or not this belief actually exists in the data. With that being said, I
hypothesize that BYEWEEK will have a positive relationship with STRETCH and BYESQUAR
will have a negative relationship with STRETCH. These positive and negative relationships
40
would indicate that the optimal bye week does not exist at the extremes (either early in the season or late in the season), but somewhere in the middle.
41
CHAPTER FOUR
RESULTS
Analysis of Model One: Bye Week Summary
Model One examined teams coming off of bye weeks versus opponents that were not
coming off of bye weeks. I hypothesized that the percentage of wins for teams coming off of bye weeks would be higher than that of their opponents that were not coming off of bye weeks.
Additionally, I hypothesized that the teams coming off of bye weeks would not only win more
often, but by larger margins when they did win in comparison to their opponents that were not coming off of bye weeks. The 21 NFL seasons that were examined in Model One yielded 475 observations. In these 475 observations, teams coming off of bye weeks defeated teams that were not coming off bye weeks on 261 occasions for a winning percentage of about 54.9 percent.
When the team that was coming off of a bye won the game, the average margin of victory was approximately 12.3 points.
Teams that were not coming off of bye weeks defeated their opponents that were coming off of bye weeks 213 times out of 475 for a winning percentage of about 44.8 percent. When the teams that were not coming off of bye weeks defeated their opponents, they won by an average margin of victory of about 8.7 points. The difference between the average margin of victory of the team coming off of a bye week and their opponent that did not get a bye week prior to the game observed is about 3.6 points greater for the team coming off of a bye week. In these observations, one game resulted in a tie which combines with the 261 wins and 213 losses from teams coming off of bye weeks for a total of 475 observations.
42
Analysis of Model Two: Time-Off Impact, Ceteris Paribus
Model Two examined the same 21 NFL seasons as Model One, but utilized ordinary least
squares regression to hold other variables constant in order to better examine the impact of time- off prior to a football game. Eight of the nine variables were used to account for the ability of
each team in terms of yardage gained and allowed by each team in the categories of passing,
rushing, kick returning, and punt returning. The ninth variable of the model was DAYSDIF
which accounted for the amount of time that the home team had to prepare less the amount of
time the away team had to prepare for the game in terms of days. The dependent variable was
SCOREDIF which was the amount of points scored by the home team less the amount of points
scored by the away team in the particular game being observed. I hypothesized that the variables
HOMEPASS, HOMERUSH, HOMEKRET, and HOMEPRET will be positively correlated with
SCOREDIF and AWAYPASS, AWAYRUSH, AWAYKRET, and AWAYPRET will be
negatively correlated with SCOREDIF.
The results of the regression indicate that each of the variables were significant at the
95% confidence level except HOMERUSH and AWAYRUSH. The constant, which was also
significant at the 95% confidence level, may have served as somewhat of a representation of a
home field advantage due to the fact that the dependent variable is the home team’s score less the
away team’s score and the constant is the portion of the score difference that occurs without any
of the variables that were accounted for. Only three of the eight performance variables had
coefficients that went the hypothesized direction with HOMEPASS and HOMERUSH being
positively correlated with SCOREDIF and AWAYPASS being negatively correlated with
SCOREDIF. Also, the constant was positively correlated with SCOREDIF which helps confirm
the idea that the constant may represent a home field advantage.
43
The variable of interest in this model, DAYSDIF, was significant at a 95% confidence level with a t-statistic of about 2.46. The coefficient associated with the DAYSDIF variable, which was positive as predicted, was about .211. This coefficient indicates that for each additional day that a team has to prepare for its opponent, the team with more time to prepare will score about .211 more points than their opponent. For a team who has a bye week prior to a game and is playing an opponent without a bye week, an advantage of about seven more days to prepare may be present which would account for a score difference of about 1.5 points with the aforementioned variables that are accounted for in this regression held constant.
To evaluate the linearity of the DAYSDIF variable, an additional variable was added to the model which was the squared value of DAYSDIF (DAYDIFSQ). This variable was used to examine if there was a parabolic relationship between the number of additional days a team had off prior to a game relative to their opponent and SCOREDIF. The results of this analysis, which reveal that the newly added DAYDIFSQ variable is insignificant at the 95% confidence level with a t-statistic of about -1.03. Additionally, the DAYDIFSQ variable was not highly correlated with any of the nine other variables in this regression which suggests that the significance of
DAYDIFSQ was not diminished due to multicollinearity. Furthermore, even if the DAYDIFSQ variable was significant, the total effect of the two variables of interest, DAYSDIF and
DAYDIFSQ, peaked at about 7.7 days of additional time-off for a team relative to an opponent, as shown in Table 4.1. Of the 4522 observations, there are only 11 occurrences of difference in time-off between teams of 7.7 or more days which equates to less than one-fourth of a percent of the observations. The low t-statistic for DAYDIFSQ, the fact that DAYDIFSQ is not highly correlated with the other variables in this regression, and the total effect of the two variables of
44
interest in this regression peaking at around 7.7 days suggest that DAYDIFSQ is not a necessary
variable in this model.
Table 4.1: Regression output for Model Two with DAYDIFSQ
Days DAYSDIF DAYDIFSQ Total 1 0.219 -0.014 0.205 2 0.438 -0.057 0.381 3 0.657 -0.128 0.529 4 0.875 -0.227 0.648 5 1.094 -0.355 0.740 6 1.313 -0.511 0.802 7 1.532 -0.695 0.837 7.7 1.685 -0.841 0.844 8 1.751 -0.908 0.843
Model Two utilized 4522 observations of games played since 1990. The overall predictive ability of this model is very weak with an R-squared of about .079. If these variables
Table 4.2: Regression output for Model Two
Variable Coefficient Standard error t-statistic HOMEPASS 0.035 0.006 6.32 AWAYPASS -0.033 0.005 -6.07 HOMERUSH 0.006 0.009 0.66 AWAYRUSH 0.008 0.009 0.89 HOMEKRET -0.104 0.010 -10.38 AWAYKRET 0.108 0.010 10.54 HOMEPRET -0.048 0.022 -2.13 AWAYPRET 0.069 0.022 3.10 DAYSDIF 0.211 0.086 2.46 constant 2.602 0.210 12.40 Note: R-squared is about .079
only account for about eight percent of the variation in SCOREDIF, then there is likely to be
additional variables that could assist in better predicting SCOREDIF. Since the performance
45
variables in this model are composed of differences between two separate performance variables they can be split from eight variables into 16. Kick return variables can be difficult to predict whether they will be positively or negatively correlated with SCOREDIF due to the facts that it is better for a team to gain more yards; however, a team only returns more than one kick per game if their opponent is scoring points. With the problems associated with kick returns, Model
Two may improve if the kick return variables are excluded. Additionally, the average punt return yardage gained per game by a team is about 21 yards which is about one-tenth of the average pass yardage gained per game by a team and less than one-fifth of the average rush yardage gained per game by a team. Considering that passing and rushing yards account for the majority of yards gained in a game and punt return yards account for about five percent of yards gained per game, excluding all return variables, as done by Sauer et al. (1988) and Zuber et al.
(1985), may improve the simplicity and accuracy of the model.
When the eight performance variables are split into 16 variables and then the punt and kick return variables are excluded for a total of eight performance variables, plus the DAYSDIF variable, the R-squared of the model increases to about .224 which is not strong, but is much
Table 4.3: Regression output for revised Model Two
Variable Coefficient Standard error t-statistic OFFPASS 0.087 0.006 14.94 OFFRUSH 0.131 0.010 13.05 DEFPASS -0.066 0.008 -7.96 DEFRUSH -0.115 0.011 -10.82 OFFPASSAWAY -0.079 0.006 -13.76 OFFRUSHAWAY -0.100 0.010 -9.97 DEFPASSAWAY 0.053 0.008 6.43 DEFRUSHAWAY 0.118 0.011 11.07 DAYSDIF 0.258 0.079 3.28 constant -0.085 3.427 -0.02 Note: R-squared is about .224
46
improved from the model with combined performance variables. Table 4.3 shows the regression results of the revised model where OFFPASS is the amount of passing yards gained by the home team, OFFRUSH is the amount of rushing yards gained by the home team, DEFPASS is the amount of passing yards allowed by the home team, DEFRUSH is the amount of rushing yards allowed by the home team, OFFPASSAWAY is the amount of passing yards gained by the away team, OFFRUSHAWAY is the amount of rushing yards gained by the away team,
DEFPASSAWAY is the amount of passing yards allowed by the away team, and
DEFRUSHAWAY is the amount of rushing yards allowed by the away team. Each of these quantities is the average per game quantity of the season. With this revised model, the t-statistic of the DAYSDIF variable also increases to about 3.28 with a coefficient of about .258 which would account for about 1.8 points per week of extra preparation time. Each of the nine variables in this model is significant and the coefficients go the directions hypothesized. Once again, to test whether there is a parabolic relationship between the difference in time-off between games and SCOREDIF, the DAYDIFSQ variable was added to this revised regression. The results of the regression that pertain to the DAYDIFSQ variable in this model were similar to those of the original model with the combined performance variables, but this time with a lower t-statistic and a total effect of the two variables of interest that does not peak until after two weeks of additional time-off.
After running the regressions for Model Two, I tested the assumptions of the normality of the residuals, homoscedasticity of the residuals, multicollinearity among the independent variables, and linearity of the independent variables. The table and graphs did not indicate any clear violation of the OLS assumptions and can be found in Appendix A. The assumption tests
47
for the revised model with the split performance variables can be found in Appendix B of this
thesis.
Analysis of Dichotomized Model Two
I dichotomized Model Two by separating the observations on three separate occasions to
determine if team age, team quality, or familiarity would increase or decrease the significance of the DAYSDIF variable. I hypothesized that the regression with the observations from the older teams would yield more significant results in terms of t-statistics than the observations collected from the younger teams. This hypothesis came from the idea that older teams might use the time-off more adequately to physically recuperate as well as use their football wisdom which has accumulated over their many years in the league to study their opponent. The split between young teams and old teams occurred around the age of 28.2 years old for the average age of the team’s starting players.
There were 1135 observations used for the regression among younger teams with the youngest average age of a team’s starting players being about 24.1 years old. In this regression,
Table 4.4: Regression output for Model Two with younger teams
Variable Coefficient Standard error t-statistic HOMEPASS 0.046 0.011 4.12 AWAYPASS -0.038 0.011 -3.32 HOMERUSH -0.020 0.018 -1.11 AWAYRUSH -0.005 0.018 -0.30 HOMEKRET -0.093 0.020 -4.58 AWAYKRET 0.133 0.021 6.36 HOMEPRET -0.005 0.045 -0.12 AWAYPRET -0.038 0.046 -0.84 DAYSDIF 0.172 0.167 1.03 constant 2.681 0.443 6.06 Note: R-squared is about .101
48
the coefficients related to the HOMERUSH, HOMEKRET, HOMEPRET, and AWAYKRET
variables did not go the direction hypothesized. Additionally, the HOMERUSH, AWAYPRET,
HOMEPRET, AWAYRUSH, and DAYSDIF variables were insignificant at the 95% confidence
level. The R-squared of this regression was about .101, accounting for only about 10.1 percent of the variation in the SCOREDIF dependent variable. After splitting up the performance variables of the younger team observations into a revised model, as was done in the analysis of
Model Two, about 22.6 percent of the variation in the dependent variable was explained. In this revised model that was limited to observations of younger teams, all of the variables went the directions hypothesized and every variables except DAYSDIF was significant at the 95%
Table 4.5: Regression output for revised Model Two with younger teams
Variable Coefficient Standard error t-statistic OFFPASS 0.081 0.011 7.23 OFFRUSH 0.075 0.020 3.67 DEFPASS -0.071 0.018 -4.04 DEFRUSH -0.130 0.021 -6.26 OFFPASSAWAY -0.084 0.011 -7.51 OFFRUSHAWAY -0.125 0.020 -6.19 DEFPASSAWAY 0.054 0.017 3.11 DEFRUSHAWAY 0.127 0.020 6.21 DAYSDIF 0.178 0.155 1.15 constant 12.983 6.713 1.93 Note: R-squared is about .226
confidence level. The table and graphs for the OLS assumption tests for the original model with observations limited to younger teams can be found in Appendix C and the table and graphs for the revised model can be found in Appendix D.
The regression that was ran for the older teams used 1125 observations with the oldest average age of a team’s starting players being about 31.9 years old. In this regression, only the
49
return variables of HOMEKRET, HOMEPRET, AWAYKRET, and AWAYPRET did not go the
direction hypothesized. Also, the variables HOMERUSH, HOMEPRET, AWAYRUSH,
AWAYPRET, AWAYPASS, and DAYSDIF were insignificant at the 95% confidence level.
The R-squared of this regression was about .064, but rose to about .221 in the revised model.
Table 4.6: Regression output for Model Two with older teams
Variable Coefficient Standard error t-statistic HOMEPASS 0.037 0.011 3.35 AWAYPASS -0.021 0.011 -1.89 HOMERUSH 0.015 0.017 0.91 AWAYRUSH -0.006 0.017 -0.34 HOMEKRET -0.107 0.020 -5.39 AWAYKRET 0.081 0.020 4.04 HOMEPRET -0.061 0.045 -1.37 AWAYPRET 0.059 0.045 1.33 DAYSDIF 0.263 0.173 1.52 constant 2.823 0.438 6.45 Note: R-squared is about .064
Furthermore, in the revised model, all of the variables went the direction hypothesized and they were all significant at the 95% confidence level. The table and graphs for the OLS assumption tests for the original model with observations limited to older teams can be found in Appendix E and the table and graphs for the revised model can be found in Appendix F.
To address the question that initially inspired the dichotomization of the data into two regressions: one of older teams and one of younger teams, the DAYSDIF variable in the regression with the older teams had a higher t-statistic than the DAYSDIF variable in the regression with the younger teams. With the original variables, the t-statistic of the DAYSDIF variable for the regression with the older teams was about 1.52 which was greater than that of the regression with the younger teams which was about 1.03. After splitting the performance
50
Table 4.7: Regression output for revised Model Two with older teams
Variable Coefficient Standard error t-statistic OFFPASS 0.093 0.012 7.69 OFFRUSH 0.153 0.020 7.78 DEFPASS -0.063 0.016 -3.87 DEFRUSH -0.080 0.022 -3.71 OFFPASSAWAY -0.061 0.012 -5.10 OFFRUSHAWAY -0.096 0.020 -4.89 DEFPASSAWAY 0.041 0.016 2.53 DEFRUSHAWAY 0.118 0.022 5.45 DAYSDIF 0.351 0.158 2.22 constant -9.861 6.999 -1.41 Note: R-squared is about .221
variables and using the revised model, the regression with the older team observations had a
DAYSDIF variable with a t-statistic of about 2.22, whereas the regression with the younger team had a DAYSDIF variable with a t-statistic of about 1.15. These regressions confirmed my hypothesis that the DAYSDIF t-statistic would be higher for the older teams than the younger teams; however, the DAYSDIF variable in the original models was not sufficient to be deemed significant at the 95% confidence level. On the other hand, the revised model that was limited to observations from only older teams exhibited a significant DAYSDIF variable at the 95% confidence level that had a coefficient of about .351.
The hypothesis in Chapter Three was that the regression with the good teams would not only have a higher coefficient for the DAYSDIF variable, but the t-statistic would also be greater than that of the bad teams due to the idea that better teams will likely have better coaches and players who are skilled at studying and physically preparing for opponents. After dichotomizing the data into one data set with teams that had more points scored than allowed, referred to as good teams, and another with more points allowed than scored, referred to as bad teams, I ran the regression for the good teams which consisted of 2304 observations. Most of the coefficients for
51
Table 4.8: Regression output for Model Two with good teams
Variable Coefficient Standard error t-statistic HOMEPASS -0.010 0.008 -1.33 AWAYPASS -0.049 0.007 -6.75 HOMERUSH -0.018 0.012 -1.53 AWAYRUSH -0.037 0.012 -3.12 HOMEKRET -0.032 0.014 -2.29 AWAYKRET 0.100 0.013 7.48 HOMEPRET -0.058 0.029 -1.96 AWAYPRET 0.026 0.031 0.83 DAYSDIF 0.180 0.115 1.56 constant 8.255 0.330 25.03 Note: R-squared is about .065
the variables did not go the direction hypothesized and less than half of the variables were significant at the 95% confidence level (even though HOMEPRET appears to be significant in
Table 4.8, the t-statistic was rounded and the actual value is closer to -1.957). The R-squared for this regression was about .065 and increased to about .13 after splitting up the performance variables and excluding the return variables for the revised model. The revised model had all of the variable coefficients going the direction hypothesized all of the variables except DAYSDIF
Table 4.9: Regression output for revised Model Two with good teams
Variable Coefficient Standard error t-statistic OFFPASS 0.056 0.009 6.31 OFFRUSH 0.094 0.015 6.27 DEFPASS -0.033 0.012 -2.83 DEFRUSH -0.048 0.017 -2.76 OFFPASSAWAY -0.080 0.008 -9.92 OFFRUSHAWAY -0.090 0.014 -6.51 DEFPASSAWAY 0.062 0.012 5.39 DEFRUSHAWAY 0.113 0.015 7.70 DAYSDIF 0.196 0.111 1.76 constant -3.154 4.778 -0.66 Note: R-squared is about .130
52
were significant at the 95% confidence level. The table and graphs for the OLS assumption tests for the original model with observations limited to good teams can be found in Appendix G and the table and graphs for the revised model can be found in Appendix H.
The regression composed of bad teams had 2218 observations. In this regression, the variables HOMERUSH, HOMEKRET, HOMEPRET, and AWAYKRET did not go the direction hypothesized. The variables HOMEPASS and AWAYPRET were the only insignificant variables at the 95% confidence level in this regression. The R-squared of this regression was
Table 4.10: Regression output for Model Two with bad teams
Variable Coefficient Standard error t-statistic HOMEPASS 0.005 0.008 0.59 AWAYPASS -0.049 0.007 -6.72 HOMERUSH -0.059 0.012 -4.93 AWAYRUSH -0.039 0.012 -3.39 HOMEKRET -0.066 0.013 -4.94 AWAYKRET 0.055 0.014 3.93 HOMEPRET -0.067 0.030 -2.23 AWAYPRET -0.030 0.028 -1.04 DAYSDIF 0.334 0.112 2.97 constant -3.374 0.330 -10.24 Note: R-squared is about .073
about .073 and increased to about .148 after splitting the performance variables and excluding the return variables. In the revised model, all of the variables’ coefficients went the direction hypothesized and each of the variables was significant at the 95% confidence level. The table and graphs for the OLS assumption tests for the original model with observations limited to bad teams can be found in Appendix I and the table and graphs for the revised model can be found in
Appendix J.
53
The DAYSDIF variable had both a higher t-statistic and a higher coefficient in the regression with the observations from the bad teams than the regression with the observations from the good teams. With the original variables, the DAYSDIF t-statistic for the regression with the bad teams was about 2.97 compared to about 1.56 for the regression with the good teams. Additionally, the coefficient associated with DAYSDIF for the regression with the observations from the bad teams was about .334, but about .18 for the regression with the observations from the good teams. After splitting up the performance variables and excluding
Table 4.11: Regression output for revised Model Two with bad teams
Variable Coefficient Standard error t-statistic OFFPASS 0.044 0.009 4.83 OFFRUSH 0.055 0.016 3.50 DEFPASS -0.039 0.012 -3.12 DEFRUSH -0.069 0.015 -4.59 OFFPASSAWAY -0.077 0.008 -9.73 OFFRUSHAWAY -0.113 0.014 -8.04 DEFPASSAWAY 0.046 0.012 3.98 DEFRUSHAWAY 0.122 0.015 8.21 DAYSDIF 0.344 0.108 3.20 constant 5.147 4.804 1.07 Note: R-squared is about .148
the return variables, the t-statistic of the DAYSDIF variable for the regression of the bad teams’
observations was about 3.2 with a coefficient of about .344. After splitting up the performance
variables in the regression of the good teams’ observations, the t-statistic of the DAYSDIF variable increased to about 1.76 with a coefficient of about .196. Each of these regressions indicates that the hypotheses from Chapter Three for the good and bad teams were unconfirmed.
The hypothesis from Chapter Three that the t-statistic of the DAYSDIFF variable for
division opponents would be less than that of non-division opponents because teams that are
54
more familiar with each other would likely benefit less from additional time-off relative to teams
that may not be as familiar with each other. The regression consisting solely of division games
had 1896 observations. In this regression, the AWAYRUSH and all of the kick and punt return
variables did not go the direction hypothesized. Also in this regression, the DAYSDIF variable,
both rushing variables, and both punt return variables were insignificant at the 95% confidence
Table 4.12: Regression output for Model Two with division teams
Variable Coefficient Standard error t-statistic HOMEPASS 0.028 0.009 3.10 AWAYPASS -0.044 0.009 -5.05 HOMERUSH 0.024 0.013 1.81 AWAYRUSH 0.011 0.013 0.84 HOMEKRET -0.118 0.016 -7.58 AWAYKRET 0.107 0.016 6.85 HOMEPRET -0.047 0.035 -1.33 AWAYPRET 0.057 0.035 1.61 DAYSDIF 0.043 0.140 0.30 Constant 2.150 0.319 6.74 Note: R-squared is about .092
level. The R-squared of this regression was about .092, but increased to about .239 after splitting the performance variables and excluding the return variables. In the revised model, each of the variables went the direction hypothesized and all of the performance variables were significant at the 95% confidence level. The table and graphs for the OLS assumption tests for the original model with observations limited to division games can be found in Appendix K and the table and graphs for the revised model can be found in Appendix L.
In the regression with the non-division opponents, there were 2626 observations which is about 38.5 percent more observations than the regression with the observations solely from division opponents. In this regression with only non-division opponents, both of the rushing
55
Table 4.13: Regression output for Model Two with non-division teams
Variable Coefficient Standard error t-statistic HOMEPASS 0.039 0.007 5.46 AWAYPASS -0.027 0.007 -3.80 HOMERUSH -0.007 0.011 -0.61 AWAYRUSH 0.005 0.011 0.46 HOMEKRET -0.096 0.013 -7.26 AWAYKRET 0.107 0.014 7.93 HOMEPRET -0.047 0.029 -1.62 AWAYPRET 0.077 0.029 2.68 DAYSDIF 0.311 0.109 2.86 Constant 2.926 0.278 10.52 Note: R-squared is about .074
variables and all of the return variables did not go the direction hypothesized. Furthermore, the
HOMEPRET variable and both of the rushing variables were insignificant. The R-squared of this regression was about .074, but increased to about .219 for the revised model. In the revised model, each of the variables went the direction hypothesized and all of the variables were significant at the 95% confidence level. The table and graphs for the OLS assumption tests for the original model with observations limited to non-division games can be found in Appendix M
Table 4.14: Regression output for revised Model Two with division teams
Variable Coefficient Standard error t-statistic OFFPASS 0.074 0.009 8.16 OFFRUSH 0.150 0.015 9.86 DEFPASS -0.043 0.013 -3.26 DEFRUSH -0.128 0.016 -7.93 OFFPASSAWAY -0.087 0.009 -9.88 OFFRUSHAWAY -0.104 0.015 -6.79 DEFPASSAWAY 0.054 0.013 4.17 DEFRUSHAWAY 0.099 0.016 6.09 DAYSDIF 0.084 0.128 0.65 Constant 0.614 5.217 0.12 Note: R-squared is about .239
56
and the table and graphs for the revised model can be found in Appendix N.
The DAYSDIF t-statistic in both the original and revised regressions was higher for the regressions for the non-division opponents than the division opponents. The DAYSDIF t- statistic for the original regression with the observations of the division games was about .3 with a coefficient of about .043, but increased to a t-statistic of about .65 with a coefficient of about
.084 in the revised regression. The DAYSDIF t-statistic for the original regression with the
observations of the non-division games was about 2.86 with a coefficient of about .311, but
increased to a t-statistic of about 3.68 with a coefficient of about .368 in the revised model.
Table 4.15: Regression output for revised Model Two with non-division teams
Variable Coefficient Standard error t-statistic OFFPASS 0.094 0.008 12.47 OFFRUSH 0.117 0.013 8.81 DEFPASS -0.082 0.011 -7.59 DEFRUSH -0.106 0.014 -7.52 OFFPASSAWAY -0.075 0.008 -9.95 OFFRUSHAWAY -0.096 0.013 -7.26 DEFPASSAWAY 0.054 0.011 4.98 DEFRUSHAWAY 0.132 0.014 9.39 DAYSDIF 0.368 0.100 3.68 Constant -0.517 4.548 -0.11 Note: R-squared is about .219
These regressions confirmed my hypothesis that the DAYSDIF variable of the non-division games would have a higher t-statistic than that of the division games. Though my hypothesis has been confirmed and the t-statistic of the DAYSDIF variable is much larger for the non-division games than that of the division games, it must be noted that there are also about 38.5 percent more observations for the regression consisting of non-division games.
57
In the original and unrevised Model Two, examining both the dichotomized data sets as well as the full set of 4522 observations, 5 of the 42 passing, rushing, and punt return variables were statistically significant at the 95% confidence level but the coefficients associated with the variables went against intuition by either having a negative coefficient when intuition suggests that it should be positive or vice versa. On the other hand, 13 of the 42 aforementioned variables were significant and had coefficients that went the directions hypothesized and the remaining 24 variables were statistically insignificant at the 95% confidence level. Many researchers believe that a considerable gap exists between statistical significance and economic or practical significance which is often a result of large sample sizes and disregarding the size and direction of the coefficients (Miller & Rodgers, 2008; Woolridge, 2009; Ziliak & McCloskey, 2008).
With large sample sizes, parameters can be estimated very precisely: Standard errors are
often quite small relative to the coefficient estimates, which usually results in statistical
significance. Some researchers insist on using smaller significance levels as the sample
size increases, partly as a way to offset the fact that standard errors are getting smaller.
For example, if we feel comfortable with a 5% level when n is a few hundred, we might
use the 1% level when n is a few thousand. Using a smaller significance level means that
economic and statistical significance are more likely to coincide, but there are no
guarantees. (Woolridge, 2009, p. 136)
In an attempt to remedy this potential problem of artificially inflated statistical significance, the variables in the revised model, which were all going the directions hypothesized, were examined to see if they can meet the criteria for a 99% confidence level and to see how high of a confidence level the variables could meet. In the revised Model Two with all 4522 observations, all of the variables meet the criteria for statistical significance at the
58
99.9% confidence level except for DAYSDIF which meets the criteria for statistical significance
at the 99.8% confidence level. The regression with the younger teams had variables that all
exceeded the statistical significance level at the 99.9% confidence level except for
DEFPASSAWAY which was statistically significant at the 99.8% confidence level and
DAYSDIF which was statistically insignificant at the 95% confidence level. The regression with
the older teams had variables that all exceeded the 99.9% confidence level except for
DEFPASSAWAY which was statistically significant at the 98% confidence level and DAYSDIF
which was statistically significant at the 95% confidence level. The regression with the good
teams had variables that all exceeded the statistical significance level at the 99.9% confidence
level except for DEFPASS and DEFRUSH which were both statistically significant at the 99%
confidence level, and DAYSDIF which was statistically insignificant at the 95% confidence
level. The regression with the bad teams had variables that were all statistically significant at the
99.9% confidence level except for DEFPASS and DAYSDIF which were both statistically significant at the 99.8% confidence level. The regression with division games had variables that were all statistically significant at the 99.9% confidence level except for DEFPASS which was statistically significant at the 99.8% confidence level and DAYSDIF which was statistically insignificant at the 95% confidence level. The regression with non-division games had variables that were all statistically significant at the 99.9% confidence level. The variable of interest,
DAYSDIF, was statistically significant at the 99.8% confidence level or higher for the full regression of 4522 observations, the regression limited to bad teams, and the regression limited to non-division games.
Another way to examine the practical significance of the variables in Model Two is by examining the size and direction of the coefficients (Berri & Schmidt, 2010; Miller & Rodgers,
59
2008; Woolridge, 2009; Ziliak & McCloskey, 2008). In both the initial and the revised Model
Two, including the regressions of the dichotomized data sets, all of the DAYSDIF coefficients were positively correlated with the dependent variable which indicates that the more time between games a team has, relative to their opponents, the better the team will perform. For division opponents, the DAYSDIF coefficient indicates that for each additional day between games that a team has compared to their opponents, there exists an advantage of no more than one-tenth of a point, which equates to no more than six-tenths of a point per week of additional time between games. This information indicates that the DAYSDIF variable is insignificant in practical terms as well as statistical terms in division games. In the revised models, the
DAYSDIF variable for all of the 4522 observations as well as the regressions limited to old teams, bad teams, and non-division games have coefficients of over one-fifth of a point per additional day between games which could account for between 1.8 points and 2.6 points for an additional week of extra preparation time between games. The size and direction of these coefficients indicate that the DAYSDIF variable in these cases is likely to be practically significant as well as statistically significant.
Another way to alleviate the problems of the potential gap between statistical significance and practical significance due to a large data set would simply be to utilize a smaller sample size.
To accomplish this, the 475 observations that were used in Method One will be used to analyze the revised Model Two. The output of the regression is displayed in Table 4.16 on the following page. With this data set of about one-tenth of the observations from Model Two with the full
4522 observations, the DAYSDIF variable is statistically significant at the 99% confidence level and with a coefficient of about one-fourth of a point per additional day between games relative to a team’s opponent, appears to be practically significant as well.
60
Table 4.16: Model Two with sample from Method One
Variable Coefficient Standard error t-statistic OFFPASS 0.081 0.017 4.77 OFFRUSH 0.163 0.029 5.57 DEFPASS -0.095 0.024 -3.91 DEFRUSH -0.114 0.032 -3.59 OFFPASSAWAY -0.090 0.017 -5.17 OFFRUSHAWAY -0.052 0.029 -1.80 DEFPASSAWAY 0.078 0.026 3.06 DEFRUSHAWAY 0.094 0.033 2.87 DAYSDIF 0.245 0.084 2.92 constant -2.797 10.350 -0.27 Note: R-squared is about .259
Analysis of Model Three: Optimal Bye Week for Uninterrupted Final Stretch
Model Three examined the final uninterrupted stretch of each NFL team throughout 17
seasons with bye weeks spanning from week one through week 11. These criteria allowed for a
regression to be ran with 531 observations. The hypothesis from Chapter Three was that the
variables HOMEPCT, TIMEADV, and WPEARLY would be positively correlated with
STRETCH; and TIMEDIS and OPEARLY would be negatively correlated with STRETCH.
After running the regression, TIMEDIS did not go the direction hypothesized and each of the aforementioned variables in this paragraph was insignificant except for OPEARLY and
WPEARLY.
Also included in this regression were the variables BYEWEEK and BYESQUAR. I hypothesized that BYEWEEK would have a positive relationship with STRETCH and
BYESQUAR would have a negative relationship with STRETCH. These positive and negative relationships would indicate that the optimal bye week does not exist at the extremes (either early in the season or late in the season), but somewhere in the middle. The regression indicated
61
that what was occurring was actually the opposite of my hypotheses: BYEWEEK was negatively
related to STRETCH and BYESQUAR was positively related to stretch suggesting that early or
late bye weeks are better than midseason bye weeks. The t-statistic associated with the
BYEWEEK variable was about -1.49 and the t-statistic associated with the BYESQUAR
variable was about 1.5. The low t-statistics associated with the two bye week variables render
the two variables insignificant at the 95% confidence level. The R-squared of the model was
about .218 which credits the model for explaining about 21.8 percent of the variation in the
STRETCH variable.
After running the regressions for Model Three, I tested the assumptions of the normality
of the residuals, homoscedasticity of the residuals, multicollinearity, and linearity of the model.
The regression output for Model Three is displayed below. Of the OLS assumptions tested, the
Table 4.17: Model Three regression output
Variable Coefficient Standard error t-statistic HOMEPCT 0.126 0.087 1.45 TIMEADV 0.018 0.072 0.24 TIMEDIS 0.025 0.074 0.33 WPEARLY 0.510 0.046 10.99 OPEARLY -0.644 0.127 -5.07 BYEWEEK -0.038 0.026 -1.49 BYESQUAR 0.003 0.002 1.50 constant 0.601 0.111 5.41 Note: R-squared is about .218
only concerns arose from the correlation between the BYEWEEK and BYESQUAR variables and the nonlinearity of the BYESQUAR variable.
62
The variance inflation factor (VIF) assesses the degree of collinearity observed in a model. The high variance inflation factors among the BYESQUAR and BYEWEEK variables exhibited in Model Three as shown by Table 4.3 indicate that the two variables may have a
Table 4.18: Model Three multicollinearity output
Variable VIF 1/VIF BYESQUAR 33.21 0.030 BYEWEEK 32.98 0.030 TIMEADV 1.06 0.946 OPEARLY 1.03 0.971 HOMEPCT 1.03 0.974 TIMEDIS 1.02 0.982 WPEARLY 1.01 0.987 Note: Mean VIF is 10.19
strong linear relationship. To examine this relationship further, the Pearson correlation
coefficient of the BYESQUAR and BYEWEEK variables is about .985 which yields further
evidence of these two variables being highly correlated. Since there is not a perfect linear relationship between BYESQUAR and BYEWEEK, OLS can still be the best linear unbiased
estimator. The issues that are related to a multicollinearity problem are that the two variables
become too difficult to measure independently and the significance of the variables diminishes.
Thus, true multicollinearity problems are characterized by low t-statistics and artificially inflated
R-squared values. To analyze these problems, I removed BYESQUAR from Model Three and
found that the R-squared of the model reduced from about .218 to about .215 while the t-statistic
of BYEWEEK went from about -1.49 to about -.08. Then, I added BYESQUAR back into
Model Three and removed BYEWEEK. By doing this, the R-squared of the model reduced to
about .215 and the t-statistic of the BYESQUAR variable decreased from about 1.5 to about .18.
Though both variables are insignificant, the results of the regression with both BYEWEEK and
63
BYESQUAR variables present an important aspect of the relationship between STRETCH and a given bye week which is that there is a parabolic relationship between a team’s bye week and the
STRETCH variable as exhibited by the negative and positive coefficients of BYEWEEK and
BYESQUAR, respectively.
The other concern presented by testing the OLS assumptions is that BYESQUAR may not have a very linear relationship with the dependent variable. Though the scatterplot in Figure
4.1 does not show any clear signs of nonlinearity, Figure 4.2 includes the linear trendline of the residuals as well as a nonlinear trendline for the residuals to identify deviations from linearity more precisely. Figure 4.2 shows a clearly parabolic trendline; however, this trendline does not drastically deviate from the linear trendline, even at its most extreme points. The fact that
BYESQUAR exhibits nonlinearity indicates that the strength of the relationship between the
BYESQUAR variable and STRETCH, the dependent variable, is being underestimated by Model
Figure 4.1: Linearity of BYESQUAR
64
Figure 4.2: Linearity of BYESQUAR with trendlines
Three. The table and graphs used to test the remainder of the OLS assumptions can be found in
Appendix O of this thesis.
65
CHAPTER FIVE
DISCUSSION
Conclusions
The purpose of the research conducted in this thesis was to examine the effect that time- off has on team performance in the NFL. To draw conclusions on this topic, I used multiple models to include Models Two and Three as well as a variety of modified versions of Model
Two which were all presented in Chapter Three. The unmodified version of Model Two which utilized 4522 observations to examine the effect of time-off on performance indicated that the overall effect of a single extra day off relative to the amount of time that a team’s opponent receives results in over one-fifth of a point in the score difference when controlling for the eight original performance variables that were proposed and composed of the differences between home and away team passing, rushing, kick returning, and punt returning yards gained and allowed. Though the variable used to analyze time-off was significant at the 95% confidence level, the overall predictive ability of the model considering all of the variables was weak and there were some complications with the kick return variable since teams benefit from yards per return; however, the more kicks a team returns suggests that the team’s opponents are scoring more points.
To help alleviate the problems of Model Two that make the predictive ability of the dependent variable low, I separated the performance variables which were composed of two other performance variables and excluded the return variables, as described in Chapter Four, to create a revised model. This model improved the predictive capabilities markedly and was also
66
able to better address the return yards dilemma while keeping the model simple with only nine
variables. The results of this revised model showed that each additional day off relative to an
opponent could increase the score difference by about .258 points in favor of the team with more
time-off.
Bretherton (2009) stated that playing after a bye week presented an advantage that was
“modest at best” (para. 3). Lange (2012) stated that the bye week does help, “but not a lot”
(para. 5). Considering that the average margin of victory in the 21 seasons examined in this thesis is about 11.69, a bye week could account for over 15 percent of the average margin of victory. Comparatively, Entine and Small (2008) estimated that about 10.5 percent of the home court advantage was a result of additional rest allowed for by scheduling in the NBA.
Furthermore, almost one-fourth of the games from the data set in this thesis were decided by three or fewer points which indicates that a bye week could account for at least about half of the margin of victory for this large portion of close games. The evidence presented in this thesis refutes the claims of Bretherton and Lange who indicated that there is not much of an advantage, when, in fact, the advantage accounts for about half a field goal, or over 15 percent of the average margin of victory in the NFL.
Everson (2010) found that in certain BCS college football conferences, bye weeks may be a disadvantage. Though none of the research in this thesis suggests that a bye week is ever a disadvantage, the fact that the regressions that limited observations to younger teams had such low coefficients and insignificant t-statistics for the DAYSDIF variable may suggest that the age of the team has an effect on how teams perform after time-off. Additionally, Everson reported that a few conferences do win at least half of their games after bye weeks which may suggest that another factor to consider could be team location, or perhaps even hometown of players which
67
may all be linked to how teams in certain conferences perform after bye weeks. Or the
difference between this thesis and the statistics reported by Everson is the fact that this thesis studied professional athletes whereas Everson studied college students. Though this thesis did not study college football teams, the findings in this thesis
In any industry or setting, it seems obvious that one would need more time to study something with which they are less familiar. The research conducted in this thesis indicates that the NFL is likely not immune to this concept since time-off differences in non-division games is more significant than time-off differences in division games. Additionally, the time-off coefficient is much larger for non-division games than it is for division games as well as the full sample with the 4522 observations. The original model that was limited to non-division games had a coefficient for DAYSDIF of about .311 and the revised model’s DAYSDIF coefficient is about .368 which means that in a non-division game, a bye week could result in a score difference being altered by about 2.6 points in favor of the team with a bye when playing an opponent without a bye. Of the 2626 non-division games observed in this sample, about 3.8 percent of the games had opponents facing each other with differences in days between games of more than seven days which would result in a change in points of the score difference that is almost the value of a field goal. The differences in coefficients and t-statistics between the division games and non-division games seem to indicate that familiarity with an opponent plays a role in how beneficial additional preparation time can be. Both coaches and players study their opponents prior to games and perhaps each team within a division knows their opponents well enough that they do not need much study time or that the study time spent on familiar opponents may not be as valuable due to diminishing returns or the labor-in-vain effect (Fredrick &
Walberg, 1980; Metcalfe, 2011; Nelson & Leonesio, 1988; Walberg & Tsai, 1984).
68
There was no evidence to confirm the idea the hypothesis that was stated in Chapter
Three that good teams perform relatively better than bad teams after receiving extra time between games. The data indicates that bad teams benefit much more from extra time-off than
good teams do. In fact, it appears that additional time-off for good teams may not have an
impact on team performance at all. Perhaps this is because good teams that are trying to prepare
for the playoffs use additional time off to rest injured or key players to prepare for the
postseason, or maybe they are even strategizing for postseason opponents. On the other hand,
bad teams are more likely to be winning every game that they can in the regular season and
coaches, injured players, and key players are probably more concerned with winning their next
regular season game since they may not have playoff aspirations. The impact of an extra day off
for a team which, on average, allows more points than it scores could benefit by about .344
points which would add up to about 2.4 points for an extra week of preparation time. It could
also be that the better players and coaches have already benefitted all that they can within their
regularly allotted time-off, whereas less talented players and coaches may need additional time to
study opponents or physically prepare for a game. This is similar to the research that suggests
that there are diminishing returns to knowledge consumption as well as a labor-in-vain effect in
accumulating human capital (Fredrick & Walberg, 1980; Metcalfe, 2011; Nelson & Leonesio,
1988; Walberg & Tsai, 1984).
The research conducted in this thesis indicates that additional time-off between games is
more advantageous for older teams than younger teams. The results of the time-off variable for
younger teams was insignificant; however, the time-off variable for older teams was significant
with a coefficient of about .351 which means that with an extra week off, an older team may have an advantage of about 2.5 points. When considering why some studies have shown that
69
working away from the regular work setting, similar to working during a bye week, benefits
some personnel but harms other personnel, Westman and Etzion (2002) thought that factors such
as marital status or previous work experiences could be the difference. Since marital status and
age are likely correlated, perhaps marital status is a reason for the differences exhibited in how time-off effects performance. Additionally, younger players may not have learned how to optimally utilize the extra time-off between games. The difference between older and younger teams being affected by additional time-off could also be the result of younger athletes typically having more testosterone than older athletes which could aid in faster recoveries from injuries
(Jones, 1993; Kujawa & Jones, 1990; Kujawa, Kinderman, & Jones, 1989). Since younger athletes may not need additional time to heal, time-off before a game could be less of a factor in their performance on the day of the game; however, additional time-off to heal may be a contributing factor to the performance of older athletes.
Model Three examined which week of the regular season is the optimal week to have a bye. Model Three only had 531 observations over a span of 17 years. Furthermore, the variables that were being used to examine the effect of the bye week were highly correlated; however, neither variable was useful alone. The fact that the variables were highly correlated reduced the
t-statistics of the BYEWEEK and BYESQUAR variables which were about -1.49 and 1.5,
respectively. Additionally, the lack of observations was also a likely cause of reduced t-statistics
for these variables.
Since the t-statistics of -1.49 and 1.5 are insignificant at the 95% confidence level, there is no clear indication that an early-, mid-, or late-season bye week is more advantageous for performing in the final uninterrupted stretch of the regular season. The current popular belief is that a mid-season bye is most advantageous for succeeding in the regular season
70
(Awholelottahaloti, 2012; Edreedfromtheu, 2012; Footman, 2012; Love, 2012a; Rav’n, 2012;
Ravenslifer, 2012). Though insignificant, the coefficients exhibited in Model Three indicate that
reality may be contrary to popular belief. Since the coefficient associated with the bye week variable is negative and the coefficient associated with the squared value of the bye week is positive, the optimal bye week is more likely to be either early or late in the regular season, based on the 531 observations used in Model Three. On page 73, Figure 5.1 shows the values of the sum of the BYEWEEK and BYESQUAR coefficients at each bye week examined in Model
Three. The points on the graph characterized by triangles are from the entire 531 observation sample.
Barnwell (2012) used a linear test to examine the relationship between bye weeks and a final five game stretch of the regular season. He found that it was slightly more advantageous to have an early bye week as opposed to a late bye week, as exhibited by a correlation coefficient.
If the results from Model Three were significant, this model would partially support Barnwell’s findings; however, it would also indicate that there is also a relative advantage for teams with later bye weeks.
If mid-season byes are the least optimal byes, this could be due to the fact that the effects of time-off wear off after approximately three weeks to one month (Etzion, 2003; Westman &
Eden, 1997; Westman & Etzion, 2001). For example, if bye weeks extend through week 10 (as is most common), then the final uninterrupted stretch of the regular season would consist of the seven games between weeks 11 through 17. The statistical analysis conducted in this thesis indicate that there is an advantage when playing teams after a bye week, but perhaps there is also advantages to playing a week after a bye and the benefits of the time-off could linger for three weeks to one month as they do in other industries (Etzion, 2003; Westman & Eden, 1997;
71
Westman & Etzion, 2001). This would mean that a team with a bye in week six or seven could lose any benefits that they received from their bye week when the uninterrupted final stretch of the regular season commences in week 11. This could assist in explaining why there is a disadvantage for teams with mid-season byes; however, it does not assist in explaining relative advantages in early- and late-season bye weeks.
The result of the mid-season bye week disadvantage could also be due to the fact that players may be more prone to staleness when given a mid-season bye. Severe fatigue which may result in staleness could be caused by overtraining or the indefinite use of a single training regimen (Fleck & Kraemer, 1987; Kuipers & Keizer, 1988). Fox (1984) found that training over a span of between eight to ten weeks is optimal for anaerobic sports, such as football. If bye weeks typically commence around week three or four and cease around week 10 or 11, then coaches and trainers can make the necessary adjustments in the training programs around the time of these bye weeks. On the other hand, if a team has a mid-season bye week, they may believe that their training program is a success and will not be inclined to make any changes around the time of the mid-season bye week.
The timing of bye weeks may also depend on the composition of the players on the team.
When the data for Model Three is split between younger teams (that have an average age of starting players of below 28 years old) and older teams (that have an average age of starting players of 28 years old and older), it seems that the performance of older teams may be more sensitive to the timing of bye weeks than that of younger teams. There were 265 observations used for the younger teams which consisted of teams that had an average age among the starting players of below 28 years old. There were 266 observations used for the older teams which consisted of teams that had an average age among the starting players of 28 years old and above.
72
Figure 5.1 below shows the values of the sum of the BYEWEEK and BYESQUAR coefficients
at each bye week examined in Model Three for younger teams, older teams, and all teams. The
sum of the coefficients indicates about how many percentage points teams may be losing when
assigned a particular bye week. Though insignificant, the evidence that suggests that older teams
may be more sensitive to the timing of bye weeks aligns with the beliefs of NFL analysts (La
Bye Week 0 -0.02 1 2 3 4 5 6 7 8 9101112 -0.04 -0.06 -0.08 Younger -0.1 Older -0.12 Total -0.14 Sum ofSum Coefficients -0.16 -0.18 -0.2
Figure 5.1: Sum of coefficients by bye week
Canfora, 2012). The cause of older teams being more sensitive to the timing of bye weeks may be because younger athletes typically have more testosterone than older athletes which could aid in faster recoveries from injuries (Jones, 1993; Kujawa & Jones, 1990; Kujawa, Kinderman, &
Jones, 1989). When examining why some studies indicate that short overseas business trips serve as a form of respite while other studies see business trips as harmful for employees,
Westman and Etzion (2002) cited factors such as marital status or previous work experiences as possible variables that could affect the results of the studies. Since there is likely a correlation between marital status, work experience, and age, these factors suggested by Westman and
73
Etzion (2002) may be a cause for the possible increased sensitivity of bye week timing among older teams.
If early- and late- season bye weeks are optimal and mid-season bye weeks are a disadvantage for teams, are there any teams that have been consistently getting early- and late- season byes or any teams that have been consistently getting mid-season byes? After examining the average of each team’s sum of coefficients from the BYEWEEK and BYESQUAR variables, it turns out that the five franchises that have had the most advantageous bye weeks throughout the 21 seasons examined in this thesis were the New Orleans Saints, Cincinnati Bengals, Chicago
Bears, Baltimore Ravens (formerly Cleveland Browns), and Tennessee Titans (formerly Houston
Oilers). The five franchises that have had the least advantageous bye weeks in this time span were the St. Louis Rams (formerly Los Angeles Rams), Atlanta Falcons, Washington Redskins,
Tampa Bay Buccaneers, and Indianapolis Colts. The mean value of the yearly average of coefficient sums for all 32 franchises examined was about -.049 with a standard deviation of about .016. The only franchise with a yearly average of coefficient sums for the BYEWEEK and
BYESQUAR variables that was beyond two standard deviations from the mean was the New
Orleans Saints with only having 3 out of 21 seasons with bye weeks between weeks five and nine.
After examining when each team gets assigned certain bye weeks, there seemed to be a trend of early- and late-season bye weeks being assigned to the previous seasons’ Super Bowl teams. To look further into this, I compared the mean value of the yearly average of coefficient sums for all franchises examined, which was about -.049, with that of the previous seasons’
Super Bowl teams. The previous seasons’ Super Bowl teams had a mean value of about -.033 for the sum of coefficients for the variables BYEWEEK and BYESQUAR for the 21 seasons
74
observed in this thesis. This value would be the sixth highest, above 27 other franchises if included in the list of average coefficient sums for the 32 NFL franchises. Examining this even further, the Super Bowl losers of the season had an average coefficient sum of about -.022 for the
BYEWEEK and BYESQUAR variables indicating that, on average, the losers of the previous seasons’ Super Bowl may receive more advantageous bye weeks than every team except for the
New Orleans Saints. Since the t-statistics of Model Three’s BYEWEEK and BYESQUAR variables were insignificant, these occurrences may be happening at random. The NFL claims that they look at the schedules of previous seasons to attempt to avoid competitive disadvantages as a result of scheduling (McManus, 2012).
Implications
The findings in this thesis could have many implications. The implications may be for the league, NFL analysts, coaches, and franchise executives and managers. The information provided in this thesis could assist the NFL in creating schedules and teams in evaluating personnel. A few instances when the information in this thesis may have been able to contribute some insight into how time-off effects team performance are examined in the following paragraphs.
In the 2011 season, the Super Bowl champion New York Giants may not have even made
the playoffs if it was not for a three point victory over the Miami Dolphins in week eight. Prior
to the week eight game, the New York Giants had seven more days to prepare for the game than
the Miami Dolphins had. The results of Model Two with the 4522 observations indicates that
the advantage that the New York Giants had may have altered the final score difference by about
1.8 points. However, since this was a non-division game, the results from Model Two with just
non-division game observations indicates that the additional time-off given the New York Giants
75
may have altered the final score difference by about 2.6 points. The New York Giants may have
also benefited from being a bad team in this game against the Miami Dolphins. In the 2011
season, the New York Giants scored fewer points against their opponents throughout the season
than they allowed to be scored on them. On the other hand, the Miami Dolphins had scored
more points than their opponents throughout the season than they allowed. When the
observations in Model Two were dichotomized by good and bad teams, the results indicated that
bad teams benefit more from additional time-off than good teams do.
In 2010, Head Coach Mike Singletary of the San Francisco 49ers may have saved his job by advancing to the playoffs after winning a division title if they would have had more preparation time and been able to defeat the Carolina Panthers in week seven. In this matchup, the Carolina Panthers had defeated the San Francisco 49ers by three points. The Carolina
Panthers had over seven more days to prepare for the game than the San Francisco 49ers did which, according to the results of Model Two for non-division opponents, the final score difference may have been altered by about 2.6 points. Similar to when the New York Giants faced the Miami Dolphins in 2011, the Carolina Panthers may have benefited from being a bad team in this game since they allowed more points in the 2010 season than they had scored against their opponents. Had Mike Singletary had won this game, he would have taken the San
Francisco 49ers to their first postseason since the 2002 season and would have likely have been able to remain the head coach of the San Francisco 49ers.
Though the BYEWEEK and BYESQUAR variables in Model Three which were used to measure how the timing of bye weeks impacts the final uninterrupted stretch of the regular season were insignificant, the results of the regression still have implications. The findings indicate that there is no clear advantage to having a mid-season bye week; however, Model
76
Three does offer insight for future research to be conducted in this area. Teams may also choose to use the insignificant information when submitting requests to the NFL scheduling committee.
Teams may also choose to decide on how important bye weeks are to their teams based on factors such as age, NFL experience, or marital status. The league may also choose to use the information presented when attempting to decrease instances of competitive disadvantages due
to scheduling.
All of the information that has been presented in this thesis in regards to time-off between games and optimal bye weeks can be used to decrease the scheduling inequity in the NFL. If this information was combined with other information that takes into account factors such as travel distance, home field advantage, consecutive road games, and other possible scheduling inequity elements, a metric could be developed that yields an analytic quantification of the advantage or disadvantage that exists in each team’s schedule. With this sort of schedule evaluation tool, the inequity in scheduling that exists between teams could be minimized to enhance the overall competitiveness of each team in the league.
Limitations
As noted in Chapter One, one of the limitations faced in this thesis could be the fact that
no interviewing, surveying, or direct observations were conducted in this research. Insight about how coaches, trainers, and players operate during periods of time-off could prove to be useful when examining the impact of time-off on performance and why some teams are more successful
than others following extended periods of time-off. The fact that qualitative data was not used in
this study also helps protect against other limitations such as biases and other differences in
interpretations that are present during interviews and surveys. In addition to the limitation of not
having gathered qualitative data, other limitations were exposed during the process of conducting
77
this research such as having a limited data set, my lack of foresight prior to conducting the research, and other statistical limitations.
The limited data set comes into play in multiple stages of this thesis. The full version of
Model Two used a data set of 4522 observations and even when those observations were dichotomized, no dichotomized data set had fewer than 1125 observations which was sufficient for providing a significant DAYSDIF variable. However, Model Three was restricted to only
531 observations due to the fact that the model covered 17 seasons of approximately 30 teams per season, depending on the season. Since bye weeks have only been consistently used in the
NFL since 1990 and the NFL seasons of 1990, 1991, 1993, 1999, 2000, and 2001 were omitted from this model because they either had two bye weeks per team or the bye weeks extended too far into the season to gauge its impact on the uninterrupted final stretch of the regular season, there is no option for extending the data set for Model Three except for waiting for more NFL seasons to pass. Furthermore, if factors such as the newest CBA are contributing to changes in how time-off effects performance, as suggested by Neupauer (2011), then more than two years of data is needed to address these questions.
As I was conducting this study, a few things occurred to me which could have improved this research. First of all, the fact that kick return yards are not always beneficial played a role in the outcome of the research presented in this thesis. I attempted to control for this fact as much as possible by combining all returning yards so that the impact would be more of a result of the talent of the special teams personnel; however, the fact that the average kick return yards per game is about four times the quantity of the average punt return yards per game causes the kick return yards to outweigh the punt return yards. A possible solution to account for this problem would be to divide the return yards by the number of returns.
78
Another issue that may have limited this study is the fact that each NFL season is
different and gameplay in the NFL seems to evolve in a way that is not captured by the models.
For example, 3000 passing yards in the 2012 season is different from 3000 passing yards in the
1990 season. Not only have players and coaching strategies evolved to create changes such as
the aforementioned example, but officiating has changed as well. Pass interference
interpretations have changed throughout the time span accounted for in this thesis, as have
different rules that have been created or eliminated such as the wedge formation that was used
for kickoff returns. Since each NFL season is different the results of the models presented in this
thesis may be compromised to a degree.
Though a large data set that included thousands of observations was useful in obtaining
precise results, that same large data set may have also artificially inflated the statistical
significance of the variables in Model Two. To bring a more of a sense of practical significance
into the Model Two variables, the variables were tested to see if they were statistically
significant at confidence levels of at least 99%. Then, the size and direction of the coefficients
of the variables in Model Two were examined and appear to be significant in a practical sense.
Finally, I ran the Model Two regression that consisted of 4522 observations with a data set that
was approximately one-tenth of that size and still found statistically significant results. Since
practical significance is more of an abstract idea that requires judgment rather than blindly
following t-statistics and p-values, the practical significance of the variables within this thesis
may still be challenged even though they seem to be practically significant based on the three
previously mentioned tests.
79
Future Research
To utilize this research and build upon it, there are many directions that future research
could go. The first and most obvious would be to correct the deficiencies cited in this thesis.
This can be accomplished by conducting interviews, conducting surveys, or directly observing
how teams use time-off. This information could also assist in determining issues such as
whether studying has a greater or lesser impact on performance than physically recuperating or
training. Surveying, interviewing, and observing could also prompt future research on
individuals within the team to examine how time-off affects the performance of individual
players and what the differences are in how each individual prepares. Deficiencies in this thesis
could also be corrected by dividing return yards into per return quantities. To account for
performance variables that evolve throughout NFL seasons, these variables can be standardized
to reflect performance given a certain season.
Team familiarity was analyzed in this thesis which yields information about learning and human capital accumulation. To extend these ideas further, it may be useful to examine situations when the next opponent is unknown? For example, during the NBA playoffs, when a team has won a series but is still waiting to find out who they will play (since days can differ in the NBA and a series can go to seven games), does the extra time-off benefit the team as much as when the next opponent they will face is already announced? Studying time-off in the NBA postseason could be beneficial to begin examining the impact on team performance that studying and learning has in team sports. Another direction that could be taken to examine studying and learning in team sports and further the research in this thesis is by examining any effects of how a team performs after a bye week when playing an easier opponent followed by a difficult opponent. This sort of study could yield insight into whether or not teams focus on one game at
80
a time or if during a bye week they may be looking forward toward their next two opponents, particularly if the likelihood of succeeding against the first opponent following a bye is high and
the likelihood of succeeding against the second opponent following a bye is lower.
The NBA, as well as Major League Baseball (MLB), could also be examined since they
have all-star breaks between basketball and baseball games. These breaks could be examined to
see if teams and players benefit from these breaks when they are not participating or if they lose
sharpness as suggested by Steenland and Deddens (1997). The results could also lend insight on
whether or not professional athletes are susceptible to the same diminishing returns to
performance that are brought on by respite in other industries (Etzion, 2003; Westman & Eden,
1997; Westman & Etzion, 2001). These ideas could be further examined by analyzing data that
shows the effect of how many weeks have gone by since a team’s last bye week on game
performance. Additionally, information gathered on this topic could be used to inform elite
players and team managers and executives on the effects of allowing players to compete in
international competitions.
Now that the research in this thesis has examined the effects of time-off on success in the
regular season, this research can be furthered by examining the impact of time-off on postseason
performance. Research in this area could address purely postseason matters such as how
postseason bye weeks impact performance, how the effects of postseason bye weeks may have
changed throughout the history of postseason bye weeks, or what effects the bye week prior to
the Super Bowl may have. Research could also address how time-off and scheduling inequity
affects postseason berths and postseason success. The cumulative differences in time-off relative
to a team’s opponents may also be a contributing factor as mentioned in the anecdotal evidence
presented about how the 2012 Philadelphia Eagles went from an eight win team to a four win
81
team and the 2012 Minnesota Vikings went from a three win team to a 10 win team after
receiving schedules with the least and most cumulative time-off relative to their opponents,
respectively.
After the effects of time-off on performance have been thoroughly examined and optimal
schedules for time-off are determined, researchers can begin studying and searching for evidence
of scheduling trends. These trends could help identify if there is or has ever been any bias in
scheduling that has not been previously identified. Trends may uncover preferential treatment
given to certain markets or owners. More importantly, researchers would be able to assist in
identifying ways to eliminate biases in the scheduling process and reduce scheduling inequity.
Researchers would be able to explore options for distributing bye weeks, whether it be a random
process, something that is earned, or something that is allocated in reverse order to the worst
teams first similar to the draft.
Another direction that researchers could go to further the research conducted in this study would be to analyze the trends of coaches who are fired and determine how much of a factor scheduling inequity could be in the decision making process of whether to retain personnel or invest in new personnel. Perhaps there is a mentality in the NFL that a coach should be able to win regardless of circumstances such as scheduling inequity. In order to successfully extend the research in this thesis toward the direction of linking possible erroneous personnel to scheduling inequity, this future research would be particularly useful after determining how time-off effects the postseason, the optimal time-off within schedules, and if cumulative time-off relative to opponents is a factor.
Other factors could also contribute to scheduling inequity that relate to time-off. For example, is time-off less valuable when a team has to spend more time traveling greater
82
distances than playing a home game? Examining whether age is a factor in traveling as suggested by Westman and Etzion (2002) could also help further the research conducted in this thesis. Future studies related to scheduling inequity could also examine the likelihood of winning a second, third, or fourth consecutive road game and compare those likelihoods to the likelihood of winning a second, third, or fourth consecutive home game? Furthermore, future research could examine whether teams that spend more time traveling or play more consecutive away games are more susceptible to injury which would be similar to occurrences in other industries (Leise et al., 1997). Perhaps older teams experience more injuries related to travel greater distances or competing in consecutive away games. Could playing on different days of the week such as Monday, Saturday, or Thursday affect injuries or team performance as suggested by NFL analyst and former head coach Steve Mariucci (Love, 2012b)? What about playing games at different times than a team is accustomed to? Or does regularity not matter and only body clocks (Dubner, 2011; Smith et al., 1997)? There are many directions that future research can take in reference to scheduling inequity that could benefit from the research conducted in this thesis.
Entine and Small (2008) found that a portion of the home court advantage experienced in the NBA can be attributed to additional rest granted to the home team due to scheduling. It is possible that a similar situation could be occurring in the NFL. Future research could examine how much of an effect, if any, time-off could have on home field advantage in the NFL. The
NFL could be attempting to increase revenue at the stadiums through ticket and merchandise sales by creating a home field advantage and an environment in which nearby fans of the local team want to spend money.
83
The statistical evidence in this thesis could indicate that time-off and bye weeks are more of an advantage than a disadvantage. Everson (2010) reported that most college football conferences having losing records for games following bye weeks; however, there are a few conferences that do win at least half of their games after bye weeks. This information suggests that there may be another factor to consider such as team location, or perhaps even hometown of players, which may be linked to how teams in certain conferences perform after bye weeks.
Everson also did not hold other factors constant, like team ability, in his statistical analysis of performance after bye weeks which could be another cause for the discrepancy between the research in this thesis and his study. Another difference between this thesis and the statistics reported by Everson (2010) is the fact that this thesis studied professional athletes whereas
Everson (2010) studied college students, which may be a reason for the differences and certainly warrants further investigation.
The research conducted in this thesis could also be used to further analyze how time-off affects different groups outside of sports, in other sports, or even other football leagues.
Extending this research beyond the NFL and examining how time-off affects older or veteran employees in comparison to younger or newer employees or high performers in comparison to below average performers in other industries could provide valuable insight into how different people may benefit from differences in time-off. Additionally, study how time-off affects athletes in other sports such as golf or other leagues such as the Arena Football League (AFL) which have different demographics and characteristics could provide more information on how different demographics can benefit from and use time-off as well as how different sports leagues should operate at each level of competition in order to receive optimal results from their athletes.
84
APPENDIX A MODEL TWO
The following graphs and table were used to test the OLS assumptions of Model Two using Stata.
Figure A.1: Normality of residuals for Model Two
Figure A.2: Homoscedasticity of residuals for Model Two
85
Figure A.3: Linearity of regressors for Model Two
Table A.1: Multicollinearity output for Model Two
Variable VIF 1/VIF HOMERUSH 1.24 0.806 AWAYRUSH 1.24 0.809 AWAYPASS 1.12 0.897 HOMEPASS 1.12 0.897 HOMEPRET 1.11 0.904 AWAYPRET 1.09 0.914 HOMEKRET 1.07 0.938 AWAYKRET 1.06 0.940 DAYSDIF 1.00 0.999 Note: Mean VIF is 1.12
86
APPENDIX B REVISED MODEL TWO
The following graphs and tables show the regression output and OLS assumptions of
Model Two using Stata after splitting the performance variables and excluding the return variables.
Figure B.1: Normality of residuals for revised Model Two
Figure B.2: Homoscedasticity of residuals for revised Model Two
87
Figure B.3: Linearity of regressors for revised Model Two
Table B.1: Multicollinearity output for revised Model Two
Variable VIF 1/VIF OFFPASS2 1.21 0.823 OFFPASS2AWAY 1.21 0.824 OFFRUSH2 1.18 0.849 OFFRUSH2AWAY 1.18 0.850 DEFPASS2AWAY 1.16 0.858 DEFPASS2 1.16 0.859 DEFRUSH2AWAY 1.16 0.862 DEFRUSH2 1.15 0.867 DAYSDIF 1.00 0.999 Note: Mean VIF is 1.16
88
APPENDIX C MODEL TWO FOR YOUNGER TEAMS
The following graphs and tables show the regression output and OLS assumptions of
Model Two using Stata and a limited data set of only younger teams.
Figure C.1: Normality of residuals for Model Two with only younger teams
Figure C.2: Homoscedasticity of residuals for Model Two with only younger teams
89
Figure C.3: Linearity of regressors for Model Two with only younger teams
Table C.1: Multicollinearity output for Model Two with only younger teams
Variable VIF 1/VIF AWAYRUSH 1.35 0.739 HOMERUSH 1.32 0.756 AWAYPASS 1.20 0.835 HOMEPASS 1.18 0.848 HOMEPRET 1.17 0.857 AWAYPRET 1.14 0.875 HOMEKRET 1.10 0.912 AWAYKRET 1.09 0.915 DAYSDIF 1.01 0.991 Note: Mean VIF is 1.17
90
APPENDIX D MODELEL TWO FOR OLDER TEAMS
The following graphs andnd tables show the regression output and OLS assussumptions of
Model Two using Stata and a limimited data set of only older teams.
Figure D.1: Normalitality of residuals for Model Two with only olderr teamste
Figure D.2: Homoscedasasticity of residuals for Model Two with only oldelder teams
91
Figure D.3: Linearityity of regressors for Model Two with only olderr teamste
Table D.1: Multicollillinearity output for Model Two with only olderr teamste
Variable VIF 1/VIF HOMERUSH 1.22 0.818 AWAYRUSH 1.20 0.831 AWAYPASS 1.09 0.919 HOMEPASS 1.09 0.921 AWAYKRET 1.09 0.921 AWAYPRET 1.08 0.927 HOMEKRET 1.08 0.929 HOMEPRET 1.07 0.931 DAYSDIF 1.00 0.997 Note: Mean VIF is 1.10
92
APPENDIX E REVISED MODEL TWO FOR YOUNGER TEAMS
The following graphs and tables show the regression output and OLS assumptions of revised Model Two using Stata and a limited data set of only younger teams.
Figure E.1: Normality of residuals for revised Model Two with younger teams
Figure E.2: Homoscedasticity of residuals for revised Model Two with younger teams
93
Figure E.3: Linearity of regressors for revised Model Two with younger teams
Table E.1: Multicollinearity output for revised Model Two with younger teams
Variable VIF 1/VIF OFFPASS2AWAY 1.25 0.798 OFFPASS2 1.22 0.822 OFFRUSH2AWAY 1.20 0.832 DEFPASS2 1.19 0.841 OFFRUSH2 1.18 0.847 DEFPASS2AWAY 1.18 0.849 DEFRUSH2AWAY 1.16 0.860 DEFRUSH2 1.11 0.905 DAYSDIF 1.01 0.992 Note: Mean VIF is 1.17
94
APPENDIX F REVISED MOODEL TWO FOR OLDER TEAMMS
The following graphs andnd tables show the regression output and OLS assussumptions of revised Model Two using Stata anand a limited data set of only older teams.
Figure F.1: Normalityity of residuals for revised Model Two with olderer teamst
Figure F.2: Homoscedastisticity of residuals for revised Model Two with olderold teams
95
Figure F.3: Linearityy oof regressors for revised Model Two with olderer teamst
Table F.1: Multicollinelinearity output for revised Model Two with olderer teams
VarVariable VIF 1/VIF OFFOFFPASS2AWAY 1.24 0.808 OFFOFFPASS2 1.22 0.821 DEFDEFPASS2 1.21 0.826 DEFDEFPASS2AWAY 1.20 0.831 DEFDEFRUSH2 1.20 0.833 OFFOFFRUSH2AWAY 1.19 0.838 DEFDEFRUSH2AWAY 1.19 0.839 OFFOFFRUSH2 1.16 0.859 DAYDAYSDIF 1.01 0.994 NotNote: Mean VIF is 1.18
96
APPENDIX G MODELEL TWO FOR GOOD TEAMS
The following graphs andnd tables show the regression output and OLS assussumptions of
Model Two using Stata and a limimited data set of only good teams.
Figure G.1: Normalitality of residuals for Model Two with only good teamste
Figure G.2: Homoscedasasticity of residuals for Model Two with only gooood teams
97
Figure G.3: Linearityity of regressors for Model Two with only good teamste
Table G.1: Multicollillinearity output for Model Two with only good teamste
Variable VIF 1/VIF HOMERUSH 1.26 0.793 HOMEPASS 1.16 0.859 AWAYRUSH 1.16 0.861 AWAYPASS 1.12 0.890 HOMEPRET 1.11 0.898 AWAYKRET 1.07 0.933 AWAYPRET 1.06 0.940 HOMEKRET 1.01 0.987 DAYSDIF 1.00 0.998 Note: Mean VIF is 1.11
98
APPENDIX H MODEDEL TWO FOR BAD TEAMS
The following graphs andnd tables show the regression output and OLS assussumptions of
Model Two using Stata and a limimited data set of only bad teams.
Figure H.1: Normaliality of residuals for Model Two with only bad teamstea
Figure H.2: Homoscedadasticity of residuals for Model Two with only bad teams
99
Figure H.3: Linearitrity of regressors for Model Two with only bad teamstea
Table H.1: Multicollollinearity output for Model Two with only bad teamstea
Variable VIF 1/VIF AWAYRUSH 1.17 0.858 HOMERUSH 1.16 0.863 AWAYPASS 1.14 0.878 HOMEPASS 1.11 0.903 AWAYKRET 1.09 0.917 HOMEPRET 1.09 0.922 AWAYPRET 1.06 0.944 HOMEKRET 1.03 0.966 DAYSDIF 1.00 0.997 Note: Mean VIF is 1.09
100
APPENDIX I REVISED MOMODEL TWO FOR GOOD TEAMMS
The following graphs andnd tables show the regression output and OLS assussumptions of revised Model Two using Stata anand a limited data set of only good teams.
Figure I.1: Normalityity of residuals for revised Model Two with goodd teamst
Figure I.2: Homoscedasticsticity of residuals for revised Model Two with goodgo teams
101
Figure I.3: Linearityy oof regressors for revised Model Two with goodd teamst
Table I.1: Multicollineinearity output for revised Model Two with goodd teamst
VarVariable VIF 1/VIF OFFOFFPASS2 1.51 0.664 OFFOFFRUSH2 1.29 0.775 DEFDEFPASS2 1.26 0.792 OFFOFFPASS2AWAY 1.20 0.831 OFFOFFRUSH2AWAY 1.17 0.857 DEFDEFPASS2AWAY 1.16 0.861 DEFDEFRUSH2AWAY 1.16 0.861 DEFDEFRUSH2 1.06 0.943 DAYDAYSDIF 1.00 0.999 NotNote: Mean VIF is 1.20
102
APPENDIX J REVISED MMODEL TWO FOR BAD TEAMSS
The following graphs andnd tables show the regression output and OLS assussumptions of revised Model Two using Stata anand a limited data set of only bad teams.
Figure J.1: Normalitylity of residuals for revised Model Two with bad teamste
Figure J.2: Homoscedastiasticity of residuals for revised Model Two with badba teams
103
Figure J.3: Linearityty of regressors for revised Model Two with bad teamste
Table J.1: Multicollinllinearity output for revised Model Two with badd teamste
VarVariable VIF 1/VIF DEFDEFPASS2 1.25 0.801 OFFOFFPASS2 1.24 0.804 OFFOFFPASS2AWAY 1.22 0.817 OFFOFFRUSH2AWAY 1.19 0.843 DEFDEFPASS2AWAY 1.17 0.855 DEFDEFRUSH2AWAY 1.16 0.865 OFFOFFRUSH2 1.14 0.874 DEFDEFRUSH2 1.07 0.935 DAYDAYSDIF 1.00 0.999 NotNote: Mean VIF is 1.16
104
APPENDIX K MODELL TTWO FOR DIVISION GAMES
The following graphs andnd tables show the regression output and OLS assussumptions of
Model Two using Stata and a limimited data set of only division games.
Figure K.1: Normalityity of residuals for Model Two with only divisionn gamesg
Figure K.2: Homoscedasticsticity of residuals for Model Two with only divisiision games
105
Figure K.3: Linearityy oof regressors for Model Two with only divisionn gamesg
Table K.1: Multicollinelinearity output for Model Two with only divisionn games
Variable VIF 1/VIF HOMERUSH 1.26 0.791 AWAYRUSH 1.26 0.792 HOMEPRET 1.13 0.881 AWAYPRET 1.13 0.883 AWAYPASS 1.13 0.888 HOMEPASS 1.12 0.896 AWAYKRET 1.06 0.939 HOMEKRET 1.06 0.941 DAYSDIF 1.00 0.998 Note: Mean VIF is 1.13
106
APPENDIX L MODEL TWWO FOR NON-DIVISION GAMESES
The following graphs andnd tables show the regression output and OLS assussumptions of
Model Two using Stata and a limimited data set of only non-division games.
Figure L.1: Normality of residuals for Model Two with only non-divisiosion games
Figure L.2: Homoscedasticitcity of residuals for Model Two with only non-divisiondiv games
107
Figure L.3: Linearity off rregressors for Model Two with only non-divisiosion games
Table L.1: Multicollinearearity output for Model Two with only non-divisiosion games
Variable VIF 1/VIF HOMERUSH 1.23 0.812 AWAYRUSH 1.22 0.817 HOMEPASS 1.12 0.892 AWAYPASS 1.11 0.899 HOMEPRET 1.09 0.915 AWAYPRET 1.08 0.930 AWAYKRET 1.07 0.933 HOMEKRET 1.07 0.934 DAYSDIF 1.00 0.998 Note: Mean VIF is 1.11
108
APPENDIX M REVISED MODODEL TWO FOR DIVISION GAMMES
The following graphs andnd tables show the regression output and OLS assussumptions of revised Model Two using Stata anand a limited data set of only division games.
Figure M.1: Normalityy oof residuals for revised Model Two with divisionion games
Figure M.2: Homoscedasticiticity of residuals for revised Model Two with diviivision games
109
Figure M.3: Linearity of regressors for revised Model Two with divisionion games
Table M.1: Multicollineanearity output for revised Model Two with divisionion games
VarVariable VIF 1/VIF OFFOFFPASS2 1.24 0.806 OFFOFFPASS2AWAY 1.23 0.810 DEFDEFPASS2AWAY 1.23 0.815 DEFDEFPASS2 1.21 0.825 OFFOFFRUSH2AWAY 1.19 0.843 OFFOFFRUSH2 1.18 0.847 DEFDEFRUSH2 1.18 0.849 DEFDEFRUSH2AWAY 1.17 0.852 DAYDAYSDIF 1.00 0.997 NotNote: Mean VIF is 1.18
110
APPENDIX N REVISED MODEEL TWO FOR NON-DIVISION GAMESGA
The following graphs andnd tables show the regression output and OLS assussumptions of revised Model Two using Stata anand a limited data set of only non-division gameses.
Figure N.1: Normality off rresiduals for revised Model Two with non-divisiision games
Figure N.2: Homoscedasticityity of residuals for revised Model Two with non-divisiondi games
111
Figure N.3: Linearity of reregressors for revised Model Two with non-divisiision games
Table N.1: Multicollinearitarity output for revised Model Two with non-divisvision games
VarVariable VIF 1/VIF OFFOFFPASS2AWAY 1.21 0.829 OFFOFFPASS2 1.21 0.830 OFFOFFRUSH2 1.18 0.846 OFFOFFRUSH2AWAY 1.17 0.853 DEFDEFRUSH2AWAY 1.15 0.866 DEFDEFRUSH2 1.14 0.875 DEFDEFPASS2 1.14 0.876 DEFDEFPASS2AWAY 1.14 0.879 DAYDAYSDIF 1.00 0.997 NotNote: Mean VIF is 1.15
112
APPENDIX O MODEL THREE
The following graphs were used to test the OLS assumptions of Model Three using Stata.
Figure O.1: Model Three normality of residuals
Figure O.2: Model Three homoscedasticity of residuals
113
Figure O.3: Model Three Linearity of regressors
114
REFERENCES
49ers Public Relations. (2012, December 31). Coach’s notebook: Dec. 31. Retrieved February 5, 2013 from http://www.49ers.com/news/article-2/Coachs-Notebook-Dec-31/2ecb23ec- cd90-48db-9e26-6690966681c8
Arthur, K. (2012, April 17). 2012 NFL draft: When it comes to prospects, I'm just trying to find a balance. Field Gulls. Retrieved May 14, 2012 from http://www.fieldgulls.com/2012/4/17/2955089/2012-nfl-draft-when-it-comes-to- prospects-im-just-trying-to-find-a
Awholelottahaloti (2012, August 16). Early bye week in 11 straight seasons? [Msg 2]. Message posted to http://boards.baltimoreravens.com/topic/47977-early-bye-week-in-11-straight- seasons/
Barnwell, B. (2012, November 7). Is this real: Is the late bye week a competitive advantage? [Blog post]. Grantland. Retrieved November 8, 2012 from http://www.grantland.com/blog/the-triangle/post/_/id/42166/is-this-real-is-the-late-bye- week-a-competitive-advantage
Battista, J. (2012, April 19). The art and science of scheduling meet in the N.F.L. office. New York Times. Retrieved May 14, 2012 from http://www.nytimes.com/2012/04/20/sports/nfl-schedule-makers-try-their-best-to-please- everybody.html?pagewanted=all&_r=0
Berger, R. A. (1962). Effects of varied weight training programs on strength. Research Quarterly, 33, 168-181.
Berri, D. J., & Bradbury, J. C. (2010). Working in the land of the metricians. Journal of Sports Economics, 11, 29-47.
Berri, D. J., & Schmidt, M. B. (2010). Stumbling on wins: Two economists expose the pitfalls on the road to victory in professional sports. Princeton, NJ: Financial Times Press.
Billat, V. L., Sirvent, P., Py, G., Koralsztein J. P., & Mercier, J. (2003). The concept of maximal lactate steady state: A bridge between biochemistry, physiology and sport science. Sports Medicine, 33, 407-426.
Borghesi, R. (2008). Allocation of scarce resources: Insight from the NFL salary cap. Journal of Economics and Business, 60, 536-550.
Boulier, B. L., Stekler, H. O., & Amundson, S. (2006). Testing the efficiency of the National Football League betting market. Applied Economics, 38, 279-284.
115
Bretherton, G. (2009, October 13). Playing after a bye week: An advantage or overrated? [Blog post]. New York Times. Retrieved November 8, 2012 from http://fifthdown.blogs.nytimes.com/2009/10/13/playing-after-a-bye-week-an-advantage- or-overrated/
Brown, S. E. (2005). Exceptionalist America: American sports fans' reaction to internationalization. The International Journal of the History of Sport, 22, 1106-1135.
Cardinale, M., & Bosco, C. (2003). The use of vibration as an exercise intervention. Exercise and Sport Sciences Reviews, 31, 3-7.
Chatterjee, S., Campbell, M. R., & Wiseman, F. (1994). Take that jam! An analysis of winning percentage for NBA teams. Managerial and Decision Economics, 15, 521-535.
Cimini, R. (2012, April 17). Get ready, schedule released Tuesday [Blog post]. Retrieved February 5, 2013 from http://espn.go.com/blog/new-york/jets/post/_/id/11887/get-ready- schedule-released-tuesday
Cooper, C. L., & Payne, R. (Eds.). (1978). Stress at Work. Chichester, England: Wiley.
Costill, D. L. (1986). Inside running. Basics of Sports Physiology. Carmel, IN: Benchmark Press.
Courneya, K. S., & Carron, A. V. (1992). The home advantage in sport competitions: a literature review. Journal of Sport & Exercise Psychology, 14, 13 - 27.
DeFrank, R. S., Konopaske, R., & Ivancevitch, J. M. (2000). Executive travel stress: Perils of the road warrior. Academy of Management Executive, 14, 58–71.
Dubner, S. J. (2012, April 20). Freakonomics. In Football freakonomics: How do players’ body clocks affect their performance? Retrieved July 20, 2012 from http://www.freakonomics.com/2012/04/20/football-freakonomics-how-do-players-body- clocks-affect-their-performance/
Eden, D. (1990). Acute and chronic job stress, strain, and vacation relief. Organizational Behavior and Human Decision Processes, 45, 175–193.
Edreedfromtheu (2012, August 16). Early bye week in 11 straight seasons? [Msg 14]. Message posted to http://boards.baltimoreravens.com/topic/47977-early-bye-week-in-11-straight- seasons/
Eisen, R. (Host). (2012, April 17). Rich Eisen Podcast [Audio podcast]. Retrieved from http://richeisen.nfl.com/
Entine, O. A., & Small, D. S. (2008) The role of rest in the NBA home-court advantage. Journal of Quantitative Analysis in Sports, 4, 1-9.
116
ESPN. (n.d.). NFL coaches. Retrieved February 5, 2013 from http://espn.go.com/nfl/coaches Etzion, D., Eden, D., & Lapidot, Y. (1998). Relief from job stressors and burnout: Reserve service as a respite. Journal of Applied Psychology, 83, 577–585.
Etzion, D. (2003). Annual vacation: Duration and relief from job stress and burnout. Anxiety, Stress & Coping: An International Journal, 16, 213-226.
Everson, D. (2010, October 14). The myth of the bye-week advantage. The Wall Street Journal. Retrieved November 8, 2012 from http://online.wsj.com/article/SB10001424052748703673604575550133637891028.html
Fisher, S., & Cooper, C. (1990). On the move. New York, NY: Wiley.
Fleck, S. J., & Kraemer, W. J. (1987). Designing resistance training programs. Champaign, IL: Human Kinetics.
Footman DCXLV (2012, August 16). Early bye week in 11 straight seasons? [Msg 3]. Message posted to http://boards.baltimoreravens.com/topic/47977-early-bye-week-in-11-straight- seasons/
Fox, E. L., & Mathews, D. K. (1974). The interval training: conditioning for sports and general fitness. Philadelphia, PA: W.B. Saunders.
Fox, E. L., Bartels, R. L., Billings, C. E., O’Brien, R., Bason, R., & Mathews, D. K. (1975). Frequency and duration of interval training programs and changes in aerobic power. Journal of Applied Physiology, 38, 481-484.
Fox, E. L. (1979). Sports Physiology. Philadelphia, PA: W.B. Saunders.
Fox, E. L. (1984). Sports Physiology (2nd ed.). Philadelphia, PA: W.B. Saunders.
Frank, R. (June 6, 2012). Comcast sportsnet philly. Vick’s work ethic inspiring teammates. Retrieved June 10, 2012 from http://phillyburbs.csnphilly.com/06/06/12/Vicks-work- ethic-inspiring-teammates/phillyburbs_landing_eagles.html?blockID=720488
Frankenhaeuser, M., Lundberg, U., Fredrikson, M., Melin, B., Tuomisto, M., Myrstern, A., Hedman, M., Bergman-Losman, B., & Willin, L. (1989). Stress on and off the job as related to sex and occupational status in white-collar workers. Journal of Organizational Behavior, 10, 321–346.
Fredrick, W. C., & Walberg, H. J. (1980). Learning as a function of time. The Journal of Educational Research, 73, 183-194.
Gandar, J., Zuber, R., O'Brien, T., & Russo, B. (1988). Testing rationality in the point spread betting market. The Journal of Finance, 43, 995-1008.
117
Gandar, J. M., Zuber, R. A., & Lamb, R. (2001). The home field advantage revisited: A search for the bias in other sports betting markets. Journal of Economics and Business, 53, 439- 453.
Goff, B. L., & Wisley, T. O. (2006). Is there a managerial life cycle? Evidence from the NFL. Managerial and Decision Economics, 27, 563-572.
Govan, A. Y., Langville, A. N., & Meyer, C. D. (2009). Offense-Defense Approach to Ranking Team Sports. Journal of Quantitative Analysis in Sports, 5, 1-17.
Hall, S., Szymanski, S., & Zimbalist, A. S. (2002). Testing causality between team performance and payroll. Journal of Sports Economics, 3, 149-168.
Henderson, B. (2012, November 19). Bye weeks still full of football for Pete Carroll. Retrieved February 5, 2013 from http://mynorthwest.com/422/2132795/Bye-week-still-full-of- football-for-Pete-Carroll
Hooper, S. L., MacKinnon, L. T., & Hanrahan, S. (1997). Mood states as an indication of staleness and recovery. International Journal of Sport Psychology, 28, 1-12.
Jones, K. J. (1993). Recovery from facial paralysis following crush injury of the facial nerve in hamsters: differential effects of gender and androgen exposure. Experimental neurology, 121, 133-138.
Jones, M. B. (2007). Home advantage in the NBA as a game-long process. Journal of Quantitative Analysis in Sport, 3, 1-13.
Kahn, L. M. (2000). The Sports Business as a Labor Market Laboratory. The Journal of Economic Perspectives, 14, 75-94.
Kelly, Y. J. (2006). “Competitive Balance and Scheduling of Back-to-Back Games in the NBA”. Unpublished paper.
Kelly, Y. J. (2008). (Working Paper). Cost Reduction, Competitive Balance, and the Scheduling of Back-to-Back Games in the NBA. IASE/NAASE Working Paper Series, Paper No. 08-10.
Kelly, Y. J. (2010). The myth of scheduling bias with back-to-back games in the NBA. Journal of Sports Economics, 11, 100-105.
Kember, D., Ng, S., Tse, H., Wong, E. T. T., & Pomfret, M. (1996). An examination of the interrelationship between workload, study time, learning approaches and academic outcomes. Studies in Higher Education, 21, 347-358.
Kereszty, A. (1971). Overtraining. In L. Larson (Ed.), Encyclopedia of sport sciences and medicine (pp. 218-222). New York, NY: Macmillan.
118
Kuipers, H., & Keizer, H. A. (1988). Overtraining in elite athletes: Review and directions for the future. Sports Medicine, 6, 79-92.
Kujawa, K. A., & Jones, K. J. (1990). Testosterone-induced acceleration of recovery from facial paralysis in male hamsters: temporal requirements of hormone exposure. Physiology & behavior, 48, 765-768.
Kujawa, K. A., Kinderman, N. B., & Jones, K. J. (1989). Testosterone-induced acceleration of recovery from facial paralysis following crush axotomy of the facial nerve in male hamsters. Experimental neurology, 105, 80-85.
La Canfora, J. (April 17, 2012). National Football League. Packers, Patriots looking super after NFL schedule release. Retrieved May 14, 2012 from http://www.nfl.com/news/story/09000d5d82861043/article/packers-patriots-looking- super-after-nfl-schedule-release
Lange, R. (2012, October 23). Some numbers on bye weeks, Folk in the crunch [Blog post]. Official Site of the New York Jets. Retrieved November 8, 2012 from http://blog.newyorkjets.com/2012/10/23/some-numbers-on-bye-weeks-folk-in-the- crunch/
Le Ny, J. F., Denhiere, G., & Le Taillanter, D. (1972). Regulation of study-time and interstimulus similarity in self-paced learning conditions. Acta Psychologica, 36, 280- 289.
Liese, B., Mundt, K. A., Dell, L. D., Nagy, L., & Demure, B. (1997). Medical insurance claims associated with international business travel. Occupational and Environmental Medicine, 54, 499–503.
Lombardi, M. (October 21, 2011). National Football League. Misguided belief leads Vikings to turn to rookie Ponder. Retrieved May 14, 2012 from http://www.nfl.com/news/story/09000d5d823542cd/article/misguided-belief-leads- vikings-to-turn-to-rookie-ponder
Love, J. (Director). (2012a). Broncos coach John Fox talks 2012 NFL schedule [Television series episode]. In E. Weinberger (Coordinating producer), NFL total access.
Love, J. (Director). (2012b). Who got hosed? [Television series episode]. In E. Weinberger (Coordinating producer), NFL total access.
Mellerowicz, H. & Barron, D. K. (1971). Overtraining. In L. Larson (Ed.), Encyclopedia of sport sciences and medicine (pp. 1310-1312). New York, NY: Macmillan.
Metcalfe, J. (2011). Desirable difficulties and studying in the region of proximal learning. In A. S. Benjamin (Ed.), Successful remembering and successful forgetting: A Festschrift in honor of Robert A. Bjork (pp. 259-276). New York, NY: Psychology Press.
119
Michaels, J. W., & Miethe, T. D. (1989). Applying theories of deviance to academic cheating. Social Science Quarterly, 70, 872-885.
Miller, J. E., & Rodgers, Y. (2008). Economic importance and statistical significance: guidelines for communicating empirical research. Feminist Economics, 14, 117-149.
National Football League. (n.d.). Schedules. Retrieved February 5, 2013 from http://www.nfl.com/schedules
Nelson, T. O., & Leonesio, R. J. (1988). Allocation of self-paced study time and the “labor-in- vain effect.” Journal of Experimental Psychology: Learning, Memory, & Cognition, 14, 676-686.
Nelson, D., & Quick, J. (1991). Social support and newcomer adjustment in organizations: Attachment theory at work? Journal of Organizational Behavior, 12, 543–554.
Neupauer, D. (2011, October 30). Numbers game: Bye week blues. The Official Site of NFL Films. Retrieved November 8, 2012 from http://nflfilms.nfl.com/2011/10/30/numbers- game-bye-week-blues/
NFL’s final week only division games. (2012, April 20). Retrieved February 5, 2013 from http://sports.espn.go.com/nfl/news/story?id=5117858
Noakes, T. (1986). Love of running. Cape Town, South Africa: Oxford University Press.
Odum, C. (2013, January 2). NFL playoffs: Bye weeks not always a good thing. Retrieved February 5, 2013 from http://www.kjonline.com/sports/bye-weeks-not-always-a-good- thing_2013-01-01.html
Plant, E. A., Ericsson, K. A., Hill, L., Asberg, K. (2005). Why study time does not predict grade point average across college students: Implications of deliberate practice for academic performance. Contemporary Educational Psychology, 30, 96-116.
Rau, W., & Durand, A. (2000). The academic ethic and college grades: Does hard work help students to ‘make the grade’? Sociology of Education, 73, 19-38.
Rav'n Maniac (2012, August 16). Early bye week in 11 straight seasons? [Msg 7]. Message posted to http://boards.baltimoreravens.com/topic/47977-early-bye-week-in-11-straight- seasons/
Ravenslifer (2012, August 16). Early bye week in 11 straight seasons? [Msg 8]. Message posted to http://boards.baltimoreravens.com/topic/47977-early-bye-week-in-11-straight-seasons/
Rosenfeld, J. W., Fisher, J. I., Adler, D., & Morris, C. (2010). Predicting Overtime with the Pythagorean Formula. Journal of Quantitative Analysis in Sports. Online publication. doi: 10.2202/1559-0410.1244.
120
Rosenthal, G. (August 17, 2012). National Football League. Welcome to schedule release day. Retrieved February 5, 2013 from http://www.nfl.com/news/story/09000d5d8285e112/article/welcome-to-schedule-release- day-at-the-nfl
Ryan A. J., Burke, E. R., Falsetti, H. L., Frederick, E. C., & Brown, R. L. (1983). Overtraining of athletes: A round table. Physician and Sports Medicine, 11, 93-110.
Sauer, R. D., Brajer, V., Ferris, S. P., & Marr, M. W. (1988). Hold your bets: another look at efficiency of the gambling market for national football league games. Journal of Political Economy, 96, 206-213.
Schuckers, M. (2011). An Alternative to the NFL Draft Pick Value Chart Based upon Player Performance. Journal of Quantitative Analysis in Sports. Online publication. doi: 10.2202/1559-0410.1329.
Schwartz, B., & Barsky, S. F. (1977) The home advantage. Social Forces, 55, 641-661.
Shirom, A. (1989). Burnout in work organizations. In L. Cooper & I. Robertson (Eds.), International review of industrial and organizational psychology (pp. 25–48). New York, NY: Wiley.
Show in review. (2012, April 18). Retrieved February 5, 2012 from http://espn.go.com/espnradio/show/_/showId/theherd/postId/7828007/show-review
Simmons, B. (2010). Breaking down the NFL’s bye week. ESPN. Retrieved May 14, 2012 from http://m.espn.go.com/wireless/story?storyId=5794972&wjb=&pg=1&lang=ES
Smith, R. S., Guilleminault, C., Efron, B. (1997). Circadian rhythms and enhanced athletic performance in the National Football League. Sleep, 20, 362-365.
Steenland, K., & Deddens, J. A. (1997). Effect of travel and rest on performance of professional basketball players. Sleep, 20, 366-369.
Talag, T. S. (1973). Residual muscular soreness as influenced by concentric, eccentric, and static contractions. Research Quarterly, 44, 458-469.
Trandel, G. A., & Maxcy, J. G. (2011). Adjusting winning-percentage standard deviations and a measure of competitive balance for home advantage. Journal of Quantitative Analysis in Sports, 7, 1-12.
Uyar, B., & Surdam, D. (2012). Searching for on-field parity: Evidence from the National Football League scheduling during 1991-2006. Journal of Sports Economics. Advance online publication. doi: 10.1177/1527002512438901.
121
Wagner, G. O. (1987). College and professional football scores: A multiple regression analysis. The American Economist, 31, 33-37.
Walberg, H. J., & Tsai, S. (1984). Reading achievement and diminishing returns to time. Journal of Educational Psychology, 76, 442-451.
Watnik, N., & Levine, R. A. (2001). NFL Y2K PCA. Journal of Statistics Education, 9, 1-12.
Westman, M., & Eden, D. (1997). Effects of respite from work on burnout: Vacation relief and fade-out. Journal of Applied Psychology, 82, 516–527.
Westman, M., & Etzion, D. (2001). The impact of vacation and job stress on burnout and absenteeism. Psychology and Health, 16, 595–606.
Westman, M., & Etzion, D. (2002). The Impact of Short Overseas Business Trips on Job Stress and Burnout. Applied Psychology: An International Review, 51, 582–592.
Wilson, R. (2012, April 17). CBS sports. 2012 NFL schedule released [Blog post]. Retrieved February 5, 2012 from http://www.cbssports.com/nfl/blog/eye-on- football/18628037/2012-nfl-schedule-released
Woolridge, J. M. (2009). Introductory econometrics: A modern approach. Mason, OH: South- Western Cengage Learning.
Ziliak, S. T., & McCloskey, D. N. (2008). The cult of statistical significance: How the standard error costs us jobs, justice, and lives. Ann Arbor, MI: University of Michigan Press.
Zuber, R. A., Gandar, J. M., Bowers, B. D. (1985). Beating the spread: testing the efficiency of the gambling market for National Football League Games. Journal of Political Economy, 93, 800-806.
122
BIOGRAPHICAL SKETCH
Jeremy J. Foreman was born in Redding, California in 1985. At 17 years old, he enlisted in the United States Marine Corps where he worked as a finance non-commissioned officer. In
2007, at the age of 21, he got married to Vanessa Herrera in Las Vegas, Nevada. Upon separating from the Marine Corps in 2007, he temporarily worked as an insurance agent prior to reenlisting in the Air Force Reserve and enrolling at California State Polytechnic University,
Pomona as a full-time student. At California State Polytechnic University, Pomona, he majored in Economics, minored in Nonviolence Studies, tutored for all undergraduate courses in economics, and took a graduate course in microeconomics. In 2010, at 24 years old, his wife gave birth to his son in West Covina, California. After receiving his Bachelor of Science degree in economics in 2011, he pursued graduate studies at Florida State University where he was a teaching assistant for macroeconomics and health economics and instructed multiple physical education courses. In 2012, he separated from the Air Force Reserve to enlist in the Coast Guard
Reserve. In 2013, he plans to receive his Master of Science degree in sport management upon completion of this thesis.
123