The Effects of Minimum Salaries on Career Length: Evidence from the National Football
League
Johnny Ducking
Assistant Professor of Economics
Department of Economics
North Carolina A&T State University
jcduckin@ncat.edu
and
Christopher Bollinger
Gatton Professor of Economics
Department of Economics
University of Kentucky
crboll@uky.edu
Abstract
We use National Football League (NFL) data to analyze the impact of minimum salaries on an
employee’s career length. The NFL has a salary structure in which the minimum salary a player
can receive increases with the player’s years of experience. Salary schedules similar to the
NFL’s exist in public education, federal government agencies, the Episcopalian church, and
unionized industries. NFL data allows us to control for a player’s productivity. We find
statistically significant evidence that minimum salaries shorten career length when they require
teams to increase a player’s base salary or total compensation from year t to year t+1.
Introduction
An extensive amount of research has examined the impact of race on career length in
professional sports (Jibou, 1988; Hoang and Rascher, 1999; Groothuis and Hill, 2004; Groothuis
and Hill, 2008; Ducking, Groothuis, and Hill, 2013b). The findings in this literature on exit
discrimination are mixed on whether race impacts career length. Jibou (1988) and Hoang
Rascher (1999) and find evidence of exit discrimination. Groothuis and Hill (2004 and 2008)
and Ducking, Groothuis, and Hill (2013b) do not find evidence of exit discrimination. Ducking,
Groothuis, and Hill (2013a) conduct one of the first studies to analyze the impact of minimum
salaries on career length. They use National Basketball Association (NBA) data and do not find
strong evidence that the presence of minimum salaries shorten careers.
A significant body of research has also examined the impact of minimum wages on
employment (Brown, Gilroy, and Kohen, 1982; Card, 1992a&b; Card and Krueger, 1994;
Dickens, Machin, and Manning, 1999) and on the earnings distribution (Behrman, Sickles, and
Taubman, 1983; Dickens et al., 1999; Johnson and Browning, 1983; Katz and Krueger, 1992;
Neumark, Schweitzer, and Wascher, 2004). The findings in this research have generally been
that the minimum wage reduces employment among low skill workers, and teens in particular,
while the overall effects on the income distribution are small but tend to redistribute income
downward. However, the literature is far from complete agreement on any of these findings.
A compensation structure similar to the minimum wage is a minimum salary, such as that
found in the National Football League (NFL) which we study here.
The minimum salary is a
price floor on the salary a player can earn for an entire year of work. The minimum wage is
difficult to study since it is, in general, uniform across all workers, and does not change
significantly very often. The minimum salary schedule in the NFL, by contrast, depends upon
years of service (see table 1) and hence varies exogenously over the player's career. However,
like the minimum wage, a significant portion of players (workers) in the NFL earn salaries well
above the minimum. This allows measurement of employment effects of the minimum salary
that have broader implications. Perhaps more importantly, the quality of individual productivity
data in professional sports aids in identifying the value of the marginal product of workers
(players), a key component for a complete analysis of any labor market. Finally, the NFL
provides an interesting labor market structure because the cap on the "active roster" and because
1
of the clear entry of new workers each year. These components make the labor market structure
a unique laboratory to study how firms react to the minimum wage structure (Kahn, 2000). Fort
and Quirk (1995) demonstrate that professional sports firms appear to behave as profit
maximizing firms. While the results here apply in a specific case, the implications aid in a
broader understanding of the impact of price floors in labor markets, and other markets in
general.
Professional football is not the only place where minimum salaries are seen. Minimum
salary schedules are often employed to protect older workers. One obvious place is within the
federal government: the "GS" scale covers employees from low skill up through professionals
such as Ph.D. economists. A number of union contracts also specify effectively a minimum
salary schedule which is tied to experience and restricts hours worked. Other schedules of this
type can be found in state governments and religious organizations. A major difference between
most of these settings and the NFL, is that in most of the other settings involving minimum
salary schedules, workers cannot be easily dismissed.
The fact that rosters are constantly
shifting, allows us to examine how these rising schedules affect career length, the margin on
which the NFL can most obviously respond to these salaries. Understanding this response sheds
light on the impact of minimums in many settings.
We estimate hazard models for career length using players who appeared on the 53 man
roster as a rookie during any season from 2000 through 2008. We focus on players in three
defensive positions (defensive backs, defensive lineman and linebackers) and three offensive
positions (running backs, tight ends and wide receivers). Separate models are estimated for the
defensive and offensive players, but the results on the measure of the impact of the minimum
salary schedule are surprisingly similar. We find that the minimum salary schedule has
statistically significant impacts on career length, shortening an effected player's career by as
much as .43 of a season for every $10,000 increase in the minimum salary. Since typical
increases are in the range of $50,000 to $100,000, careers are shortened by as much as 3 or 4
seasons.
National Football League Labor Market Structure
Each NFL firm has a roster constraint of 53 players during the regular season.
Observationally, most teams maintain a 53 man roster throughout the season, indicating that this
2
is a binding constraint. The impact of the minimum salary schedule is necessarily on which
specific players the team maintains on its roster. Table 1 presents the minimum salary schedule
during the study period measured in real terms. In general, players with more experience have a
higher minimum, and that minimum increases from year to year. However the increases are not
uniform due to changes in inflation as well as negotiations. Increasing the price of a player as his
level of experience increases provide NFL teams with the incentive to substitute less
experienced, and less expensive players for more experienced expensive players. This incentive
exists as long as the younger, inexperienced players are more profitable than the older,
experienced players. Therefore, the NFL’s minimum salary schedule can reduce career length
through this incentive. We formally model this here.
A number of previous studies of professional sports leagues have made the assumption
that teams maximize profits (Hamlen Jr., 2007; Fort and Quirk, 1995; Scully, 1974; Vrooman,
1995). We also assume that NFL teams maximize profits. The revenue generated by player i is
equal to the value of the marginal product from employing player i, VMPi. VMPi is also the
maximum amount a team is willing to pay player i. In a perfectly competitive industry an
employee’s salary is equal to the value of his marginal product. In the NFL, employers may
have monopsony power because players chosen in the NFL draft can sign contracts only with the
team that drafts them.
Draft picks in the NFL are initially assigned in a manner that the teams with the lowest
winning percentages have the earlier picks in each of the seven rounds. The maximum length for
a rookie contract is 6 years for players chosen in the first half of the first round of the NFL draft,
5 years for players chosen in the second half of the first round of the NFL draft, and 4 years for
players chosen in the second through seventh rounds of the NFL draft. Each round of the NFL
draft typically has 32 selections, one selection for each team. Any undrafted free agents with 3
years of experience or less can only negotiate with their initial team when their contracts expire
if the initial team offers them a 1 year contract. It should be noted that most of these contracts
are not guaranteed, and some players with less experience can be cut from the team at little or no
cost to the firm.
There is evidence that player salaries are close to the value of their marginal products in
spite of the fact that teams have some monopsony power (MacDonald and Reynolds, 1994;
Rosen and Sanderson, 2000; Krautmann, Von Allmen, and Berri, 2009). The salary paid to
3
player i, Si, is an amount that is negotiated between the player and the team (Conlin and
Emerson, 2003). In the absence of a minimum salary, the negotiated salary will fall between the
players outside wage, Oi, and his value of marginal product to the firm: Oi ≤ Si ≤ VMPi. When a
player faces a mandated minimum salary, MMSi, at each level of experience, the player’s
negotiated salary is less than or equal to the value of marginal product and greater than or equal
to his mandated minimum salary, MMSi ≤ Si ≤ VMPi. Profits per player are the difference
between the player’s VMP and the total amount of compensation paid to the player. The total
compensation paid to the player includes the salary plus any bonuses. For simplicity, we define
profits per player as the difference between the value of a player’s marginal product and the
salary paid to the player, VMPi – Si. Even though profits per player are VMP minus the player’s
total compensation, VMP – S captures the impact of minimum salaries. Teams employ the 53
players for which the sum of profits per player is the largest. Therefore, each team’s total profits
are a function of profits per player,
(1) profits = f(VMP1 – S1,VMP2 – S2, …,VMP53 – S53)
Even though the value of a player’s marginal product may depend on the productivities of the
other players employed by the team, team management has an idea of a player’s value of
marginal product given various combinations of players. Management ultimately chooses the
combination of players in a manner that maximizes profits.
This implies that the profits for the
marginal, 54th player, are less than the profits for any other player.
The minimum salary schedule may shorten the career length of players by causing the
profits per player from hiring player i to fall below the profits per player from hiring player 54,
the marginal player. Player 54 is the individual with the largest profits per player not previously
employed by the team. 1 If this occurs, the team is going to dismiss player i and hire player j.
Player i’s career length is shortened if no other team employs player i. Therefore, when VMPi –
MMSi < VMP54 – S54, player i’s career length may be shortened. Again, in the absence of the
minimum schedule, the salary paid by the firm could be negotiated lower, and the player could
be retained. This mechanism also shows that the NFL’s salary structure artificially increases the
1
The position of player j may depend on the position of player i. If the team is looking for a replacement player to perform
player i’s duties, the position of player j would be one of the positions capable of replacing player i’s duties on the field.
Depending on player i’s role on the team, there may be one of many positions capable of replacing player i’s duties. If the team
does not need a player to perform player i’s specific duties, the team will simply employ the player with the highest profits per
player who was not previously employed by the team.
4
minimum cost of an input for teams whether there is a corresponding increase in the value of the
player or not.
When the career length of a player is shortened total employment at the firm and in the
industry remains the same but the experience distribution of those employed is likely to change,
as the marginal player is likely to be younger and hence facing a lower minimum salary. This
salary structure is mainly expected to impact a marginal or average player because the value of
marginal product for a star player is significantly larger than the highest mandated minimum
salary. If a player’s salary is equal to or close to the mandated minimum salary, an additional
year of experience could cause the player to lose his job due to the mechanism described above.
The minimum salary schedule is also expected to reduce efficiency by eliminating a set of
outcomes that could be mutually beneficial for both teams and players.
Empirical Model
In order to analyze the impact of the NFL’s salary structure on a player’s career length,
we estimate hazard models of career length using data from the NFL. The hazard model
estimates the impact of minimum salaries and other relevant explanatory variables on the length
of time a player spends in the NFL. Specifically we estimate a Weibull proportional hazard
model for defensive positions and offensive positions. The baseline hazard is denoted by h0(t),
time is denoted by t, the set of covariates is denoted by xj, and the Weibull proportional hazard
model is denoted by h(t|xj). The parameter p describes the direct effect of time, net of other
explanatory variables, in Weibull distributions. If p>1, the hazard increases over time, while if
p<1, the hazard decreases over time. In sports, the hazard increases over time (p>1) because the
hazard of ending a career is large and growing year by year, based on aging. Formally, we
estimate
(2) h(t|xj) = ptp – 1exp(β0 + xjβx),
where t is the number of seasons played, and the xj vector measures individual and team
characteristics.
The Weibull distribution allows for flexibility in the baseline hazard and is an appropriate
choice as long as the baseline hazard is monotonically increasing or decreasing. The
proportional hazard model allows both time-varying and time invariant covariates to have a
proportional impact on the baseline hazard. There are many other possible functional forms, but
5
the estimates from hazard models are not sensitive to these alternatives as long as there are no
policy spikes, times at which many failures occur, such as 52 weeks of unemployment or the date
of reauthorization of welfare benefits. See Manton, Singer, and Woodbury (1992). There are no
such fixed policy times in sports careers.
Data
We use NFL data on defensive backs, defensive linemen, linebackers, running backs, tight
ends, and wide receivers from 2000 to 2008. We create two samples using these six positions, a
sample for defensive positions and a sample for offensive positions.
We chose these six
positional groups for two reasons: performance statistics that can be used to measure their
productivity are readily available and there are typically at least 3 players that play these
positions for each team during the course of a football game. The first reason is important
because the availability of performance statistics allow us to control for a player’s productivity.
The second reason is important because choosing positions where there is typically less than 3
players playing in a game will result in an extremely small sample size.
We exclude
quarterbacks, punters, and kickers because typically only one player plays these positions during
the course of a football season.
We exclude offensive linemen because they do not have any
performance measures to control for productivity.
Productivity, team, salary, and demographic information are used as control variables in
this analysis. We obtain data on player performance and demographic information from the NFL
official website (www.nfl.com/players). We use the minimum salary schedule to determine a
player’s mandated minimum salary. We obtain salary data on a player’s base salary, signing
bonus,
and
other
bonuses
from
the
USA
Today’s
NFL
salary
database
(content.usatoday.com/sportsdata/football/nfl/salaries/team). We used the CPI with 2009 as the
base year in order to adjust for inflation.
Players are not included in the sample for the following reasons: 1) their career started
before the year 2000; 2) they play for more than one team in a season; 3) they have a missing or
skipped season from the NFL’s official website or the USA Today’s NFL salary database, and 4)
the total salary is less than the minimum salary in the USA Today’s NFL salary database
indicating that the player only played a partial season.
6
In both the offensive and defensive models, we include games played and games started.
These and all other player performance variables are time varying, and measured at the season
level. Games played measures how often, overall, the player is used on the field by the team.
This captures an intensity margin of productivity. Those players who are considered starters, and
hence start the game, are typically considered the highest performing players. While these are
crude proxies, they accurately measure the team's perception of the value of the player.
Defensive player productivity is measured by tackles, sacks, passes defended,
interceptions, and forced fumbles. Tackles are defined as the total number of times a player
tackles an opponent during a season. Sacks are defined as the total number of times a player
tackles the opposing quarterback behind the line of scrimmage during a season. Passes defended
and interceptions measure the total number of times a player breaks up a pass or catches a pass
thrown by the opposing quarterback. Forced fumbles are defined as the total number of times a
defensive player causes an offensive player to lose the football. Tackles, sacks, passes defended,
interceptions, and forced fumbles are expected to have a positive impact on career length
because they measure the impact of the player’s ability to help his team stop their opponent from
scoring.
Offensive player productivity is measured by touches, yards, touchdowns, fumbles, and
fumbles lost. Touches are defined as the sum of a player’s rushing attempts and receptions, that
is when the player possesses the ball and as such accounts for the number of opportunities a
player has to gain yards. Touches are expected to have a negative impact on career length
because holding yards (and other measures) constant, an additional touch is simply another
opportunity for a player to get injured. Yards are defined as the sum of a player’s rushing and
receiving yards. Yards are expected to have a positive impact on career length because they
measure the impact of the player’s ability to help the team get closer to a scoring opportunity.
Touchdowns are defined as the sum of a player’s rushing and receiving touchdowns.
Touchdowns are expected to have a positive impact on career length because they measure the
impact of the player’s ability to help the team score points. Fumbles represents the number of
times a player has possession of the football and loses possession while fumbles lost measures
those fumbles where the opposing team recovers possession. Fumbles and fumbles lost are
expected to have a negative impact on career length because they represent either an opportunity
for the opposing team to gain possession, or an actual loss of possession.
7
In addition to direct performance measures, we include demographic variables believed
to be associated with performance. Height, weight and age are all measured during the first
season the player enters professional football. Weight is expected to have a positive impact on
player career length, while age is expected to have a negative impact. Height is ambiguous as it
can be beneficial due to improved visibility on the field, but may increase injuries for a variety of
reasons.
We also include overall team performance to account for interactions with other
players. The win percentage and playoff appearance variables measure overall success of the
team.
The explanatory variables of interest in this analysis are measures of the salary minimum
on the individual player.
We calculate this in two different ways: mandatory raise and
mandatory income increase. Mandatory raise is defined as the base salary increase a team must
give to a player from year t to year t+1 in order for the player to earn the minimum salary for
year t+1. For those players whose year t salary is above the year t+1 minimum, a value of zero
is entered because they do not require a raise.
Mandatory income increase is defined as the total increase in income a player must
receive from year t to year t+1 in order for the player to earn the minimum salary for year t+1.
The difference between these two measures is that a player requires a mandatory raise when his
base salary is less than the next year’s minimum salary but a player requires a mandatory income
increase when his total salary (base salary plus bonuses) is less than the next year’s minimum
salary. We also create two indicator variables, mandatory raise indicator and mandatory income
increase indicator, which are coded as one when a player has to receive a mandatory raise or
mandatory income increase.
The defensive sample contains 653 players and 2,347 player years. Defensive backs
represent 42.7% of the defensive players while defensive linemen represent 29.6% of the
defensive players.
Linebackers represent the remaining 27.7% of the defensive players.
Defensive backs have slightly shorter careers than other defensive positions and hence represent
only 40.5% of the defensive player years, while linemen and linebackers represent 31.1% and
28.4% of the defensive player years respectively.
The offensive sample contains 418 players and 1,368 player years in the offensive
positions sample. Running backs and wide receivers represent 39.7% and 41.4% of the offensive
players respectively. Tight ends account for only 18.9% of the offensive sample.
8
Running
backs have slightly shorter careers than other offensive players and represent only 38.5% of the
offensive player years. Tight ends have slightly longer careers and represent 20.5% of the player
years, while wide receivers represent 41.0% of player years.
Table 2 presents player year averages for both samples. Because these are player year
averages, they tend to over-represent players who have longer careers. Of particular note are the
variables measuring mandatory raises and mandatory income increases. A mandatory raise is
required by 69.2% of the defensive sample and 70.0% of the offensive sample. A mandatory
income increase is required by 34.6% of the defensive sample and 37.4% of the offensive
sample. Defensive players, on average, have 13.0 games played, 7.3 games started, 41.2 tackles,
1.3 sacks, 3.0 passes defended, 0.7 interceptions, and 0.6 forced fumbles. Offensive players, on
average, have 12.2 games played, 5.5 games started, 54.2 touches, 391.3 yards, 2.5 touchdowns,
0.8 fumbles, and 0.5 fumbles lost.
Table 3 presents the distribution of how the minimum salary schedule effects mandatory
raises and mandatory income increases through the distribution of seasons played. A large
number of star players require a mandatory raise because they receive a large amount of their
income in bonuses.
Only a few star players require a mandatory income increase.
Both
mandatory raises and mandatory income increases are concentrated among players with less
experience. There is one interesting notch occurring at seven years of experience. Referring
back to table 1, we note that beginning at 7 years of experience, the minimum is the same
through season 9, but represents a relatively large increase over season 6. This accounts for the
higher percent of increases at season 7, and the nearly zero necessary increases after that.
Survival Estimates
We present four basic models for both samples. Two models (labeled (1) and (3) in the
tables) use the indicator for mandatory raise and mandatory income increase respectively as the
variable of interest, while models (2) and (4) use the monetary values of mandatory raise and
mandatory income increase. Tables 4 and 5 display the Weibull regression results for the
defensive and offensive positions. Mandatory raise indicator, mandatory raise in $10,000s,
mandatory income increase indicator, and mandatory income increase in $10,000s are all
negative and statistically significant for the defensive and offensive positions. This provides
evidence that minimum salaries shorten career length for both the defensive and offensive
9
positions. Indeed, since the coefficients in the Weibull Regression reported in tables 4 and 5 are
the marginal effects on the average career length, the implication is that players who are
impacted by the salary minimum have a career length between 2.5 and 3.5 seasons shorter than
those with similar characteristics who are not impacted by the salary minimum.
The largest impact is seen in models 3 and 4 where the actual increase in income is
measured, accounting for any bonuses the team may have paid the player in previous seasons.
Bonuses often shift the risk associated with uncertain future performance to the player. Players
with high incentive bonuses who are typically earning those bonuses are less likely to be the
marginal player and hence the salary increase, while potentially changing the risk profile, may
not be indicative of a marginal player. The set of players requiring an income increase is smaller
than the set requiring a salary increase.
Typically, when an income increase is required, the
income and salary are identical. For this reason, we argue that models 3 and 4 better capture the
implications of the minimum salary structure.
Overall, we prefer model 4 (or 2) using the measure of income (or salary) increase needed.
It should be noted, however, that when the model is evaluated at average values of income (or
salary) increase, the impact on number of seasons played is quite comparable with the simple
indicator measure. Hence, the simple indictor still serves a purpose as a summary measure of
average impact on players. In examining the impact on specific types of players, as we do
below, the more detailed measures of model 4 are preferred. Specifications for each of the six
positions were estimated separately, but the results were similar.
While not the focus of this study, the coefficients on other variables are reasonably
sensible. Those that are statistically significant match general expectations. For example, more
tackles and more sacks as a defensive player increase career length, while being older decreases
career length.
Many of the coefficients, while sensible in sign are not statistically significant.
Joint tests of performance measures indicate statistical significance of at least some of these
variables.
Conclusions
This paper uses NFL data to measure the impact of minimum salaries on career length.
In a parametric model, based on the Weibull distribution, variables measuring the required salary
and income increases are negative and statistically significant for both the defensive and
10
offensive positions. We find strong evidence that minimum salaries have a negative impact on
career length.
These results have important implications for other industries because whenever
minimum salaries force a worker’s pay to be higher than their value to the firm, the worker’s
career length is expected to be shortened regardless of industrial structure, gender, or magnitude
of minimum salaries. However, the magnitude of the minimum salaries in the NFL is far greater
than the magnitude of the minimum salaries in most other industries. The market structure in the
NFL differs from most other market structures that employ minimum salary schedules. The NFL
only employs males but other industries with minimum salary schedules employ both males and
females. In spite of all of these differences between the NFL and any other industry that utilizes
a minimum salary schedule, we argue that career lengths will be shortened any time the
employer has the ability to dismiss or fire workers and the salary structure forces the firm to pay
the worker more than the value of the worker to the firm. Therefore, any industry that has a
minimum salary schedule in place should be aware that this salary structure has the ability to
shorten the career length of an employee when it forces the employer to pay the employee more
than the employee’s value to the firm.
11
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13
Tables
Table 1: Minimum Salaries by Credited Seasons in 2009 Dollars
Credited Seasons
Year
0
1
2
3
4
5 or 6
2000 240,451 342,611 446,018 479,656 514,540 548,178
2001 253,180 360,994 471,230 506,361 542,702 577,833
2002 268,320 357,760 447,201 536,641 626,081 626,081
2003 262,341 349,789 437,236 524,683 617,960 617,960
2004 261,215 346,394 431,573 516,751 607,609 607,609
2005 252,655 335,042 417,430 499,817 593,190 593,190
2006 292,647 372,460 452,273 532,086 622,540 622,540
2007 294,890 372,492 450,095 527,698 615,647 615,647
2008 293,951 368,684 443,417 518,150 602,848 602,848
2009 310,000 385,000 460,000 535,000 620,000 620,000
14
7-9
548,178
577,833
775,148
763,705
749,573
730,502
755,562
744,985
727,403
745,000
10 plus
548,178
577,833
894,401
880,301
863,145
840,352
861,979
848,455
827,047
845,000
Table 2: Summary Statistics
Variable
Time Invariant
Seasons Played
Age at Rookie Year
Weight at Rookie Year
Height (inches) at Rookie Year
Defensive Back
Defensive Lineman
Linebacker
Tight End
Wide Receiver
Running Back
Time Varying
Mandatory Raise Indicator
Mandatory Raise (in 10000s)
Mandatory Income Increase
Indicator
Mandatory Income Increase
(in 10000s)
Games Played
Games Started
Win Percentage
Playoff Appearance
Tackles
Sacks
Passes Defended
Interceptions
Forced Fumbles
Total Touches
Total Yards
Touchdowns
Fumbles
Fumbles Lost
Defensive Positions
Mean
Median
n= 653
3.59
3
22.6
23
238.3
235
73.4
73
0.437
0
0.296
0
0.277
0
na
na
na
na
na
na
n = 2347
0.692
1
5.641
7.379
0.346
0
Offensive Positions
Mean
Median
n =418
3.27
3
22.7
23
220.4
217
72.9
73
na
na
na
na
na
na
0.189
0
0.414
0
0.397
0
n = 1368
0.7
1
5.834
7.383
0.374
0
2.477
0
2.847
0
13.049
7.305
0.509
0.385
41.196
1.293
2.985
0.728
0.637
na
na
na
na
na
15
6
0.5
0
35
0
2
0
0
na
na
na
na
na
12.186
5.471
0.496
0.363
na
na
na
na
na
54.21
391.273
2.461
0.841
0.474
14
3
0.5
0
na
na
na
na
na
25
243
1
0
0
15
Table 3: Percentage of Players Requiring a Mandatory Raise or Mandatory Income
Increase
Defensive Sample
Offensive Sample
Mandatory
Mandatory
Mandatory
Income
Number
Mandatory Income
Number of
Raise
Increase
of
Raise
Increase
Season
Players
Required
Required
Players
Required
Required
1
653
94.5%
32.8%
418
93.1%
40.4%
2
504
94.6%
60.1%
284
94.4%
60.6%
3
392
84.9%
56.1%
213
83.1%
58.7%
4
291
41.6%
19.6%
151
45.0%
22.5%
5
201
12.9%
2.0%
118
10.2%
1.7%
6
150
16.0%
3.3%
88
15.9%
1.1%
7
93
25.8%
7.5%
57
36.8%
14.0%
8
44
4.5%
2.3%
29
17.2%
0.0%
9
19
0.0%
0.0%
10
30.0%
10.0%
Total
2347
69.2%
34.6%
1368
70.0%
37.4%
16
Table 4: Weibull Regression Results for Defensive Positions (n=2347)
Variables
(1)
(2)
(3)
(4)
Mandatory Raise Indicator
-2.773***
(0.001)
Mandatory Raise (in 10000s)
-0.305***
(0.000)
Mandatory Income Increase
-3.427***
Indicator
(0.000)
Mandatory Income Increase
-0.451***
(in 10000s)
(0.000)
Games Played
0.299***
0.286***
0.307***
0.296***
(0.000)
(0.000)
(0.000)
(0.000)
Games Started
-0.173
-0.167
-0.203
-0.191
(0.145)
(0.153)
(0.113)
(0.125)
Tackles
0.144***
0.144***
0.158***
0.153***
(0.001)
(0.000)
(0.001)
(0.000)
Sacks
2.113***
2.172***
2.243***
2.361***
(0.001)
(0.001)
(0.001)
(0.001)
Passes Defended
0.779***
0.759***
0.770***
0.753***
(0.000)
(0.000)
(0.001)
(0.001)
Interceptions
0.427
0.402
0.533
0.555
(0.482)
(0.503)
(0.409)
(0.394)
Forced Fumbles
-0.208
-0.261
-0.162
-0.216
(0.740)
(0.668)
(0.811)
(0.741)
Win Percentage
0.074***
0.073***
0.085***
0.086***
(0.001)
(0.001)
(0.001)
(0.000)
Playoff Appearance
-0.929
-0.976
-1.164
-1.21
(0.248)
(0.224)
(0.175)
(0.156)
Age at Beginning of Career
-0.975***
-0.986***
-0.981***
-0.965***
(0.000)
(0.000)
(0.000)
(0.000)
Height (in inches)
-0.046
-0.027
-0.032
-0.021
(0.805)
(0.886)
(0.868)
(0.914)
Weight
0.092***
0.091***
0.093***
0.097***
(0.000)
(0.000)
(0.000)
(0.000)
Defensive Back
3.293***
3.294***
3.282***
3.491***
(0.003)
(0.003)
(0.004)
(0.003)
Defensive Linemen
-3.711***
-3.720***
-3.720***
-4.067***
(0.004)
(0.004)
(0.005)
(0.002)
Marginal Effects are reported. P-values are in parentheses. Significance Level: ***1%, **5%,
*10%.
17
Table 5: Weibull Regression Results for Offensive Positions (n=1368)
Variables
(1)
(2)
(3)
(4)
Mandatory Raise Indicator
-2.587***
(0.004)
Mandatory Raise (in 10000s)
-0.290***
(0.000)
Mandatory Income Increase
-2.686***
Indicator
(0.000)
Mandatory Income Increase
-0.291***
(in 10000s)
(0.001)
Games Played
0.342***
0.343***
0.362***
0.358***
(0.000)
(0.000)
(0.000)
(0.000)
Games Started
0.212
0.201
0.217
0.221
(0.104)
(0.116)
(0.120)
(0.111)
Touches
-0.069***
-0.067***
-0.071***
-0.071***
(0.007)
(0.008)
(0.009)
(0.009)
Yards
0.018***
0.018***
0.019***
0.019***
(0.003)
(0.003)
(0.003)
(0.003)
Touchdowns
0.132
0.128
0.171
0.155
(0.649)
(0.653)
(0.583)
(0.621)
Fumbles
0.066
0.041
-0.015
0.049
(0.913)
(0.945)
(0.982)
(0.940)
Fumbles Lost
0.266
0.324
0.343
0.320
(0.767)
(0.713)
(0.716)
(0.732)
Win Percentage
0.044**
0.043**
0.038*
0.038*
(0.029)
(0.034)
(0.081)
(0.080)
Playoff Appearance
-1.027
-0.963
-0.853
-0.807
(0.213)
(0.243)
(0.340)
(0.367)
Age at Beginning of Career
-1.150***
-1.155***
-1.070***
-1.117***
(0.000)
(0.000)
(0.000)
(0.000)
Height (in inches)
-0.267
-0.251
-0.263
-0.238
(0.130)
(0.143)
(0.152)
(0.190)
Weight
0.063**
0.058**
0.062**
0.060**
(0.011)
(0.016)
(0.016)
(0.019)
Tight End
-0.058
0.001
-0.045
-0.197
(0.953)
(0.999)
(0.966)
(0.850)
Wide Receiver
1.175
1.092
1.148
0.966
(0.247)
(0.276)
(0.285)
(0.364)
Marginal Effects are reported. P-values are in parentheses. Significance Level: ***1%, **5%,
*10%.
18