Determinants of stoppage time awarded to teams in the English premier league.
Watanabe, Nicholas M. ; Wicker, Pamela ; Reuter, James C. 等
Introduction
The final match of the 2014 UEFA Champions League showed that
stoppage time is important in football (soccer) matches: Real Madrid was
awarded five minutes of stoppage time when it was one goal behind at the
end of the second half. Sergio Ramos scored the equalizer in the third
minute of the stoppage time so that Real Madrid forced two 15-minute
overtime periods during which they finally won the match (Spiegel,
2014). Also, the 1999 UEFA Champions League final between FC Bayern
Munich and Manchester United was decided in stoppage time: FC Bayern
Munich entered stoppage time with a one-goal lead, but Manchester United
scored two goals within three minutes of stoppage time and, thus, won
the Champions League (Fussball-Woche, 2013). Moreover, the championship
of the 2011-2012 season in the English Premier League (EPL) was decided
in stoppage time: Manchester City scored two goals in the first and
third minute of the stoppage time and beat Manchester United in both the
match and the standings. Both teams had 89 points, but the goal
difference was in favor of Manchester City (Express, 2012). The
championship of the 2000-2001 season of the German Football Bundesliga
was also determined in stoppage time on the last match day: FC Bayern
Munich scored the equalizer in the fourth minute of the stoppage time
against Hamburg and was, thus, one point ahead of FC Schalke 04 (TZ,
2012). Thus, the stoppage time awarded to teams is not only critical in
knock-out matches, but also in national championship races.
The goals scored in stoppage time (when they are decisive for the
match outcome) can affect a team's standing in the table, which, in
turn, affects the qualification for European competitions (UEFA
Champions League, UEFA Europa League), whether teams are relegated to
the lower division, and, ultimately, the revenues of clubs. There are
sometimes only a few points difference between qualifying and
non-qualifying teams, and between teams that are relegated to the lower
division and teams that manage to stay in the league. While qualifying
for the UEFA Champions League and the UEFA Europa League is associated
with significant increases in revenues in the following season, being
relegated to the lower division leads to significant financial losses.
For example, in the 2012-2013 UEFA Champions League a total of 904.6
million EUR was distributed to clubs with 8.6 million EUR being awarded
to every team that qualified for the group stage (UEFA, 2013a). In the
same season, a total of 209 million EUR was distributed in the UEFA
Europa League with every team that qualified for the group stage earning
1.3 million EUR (UEFA, 2013b). For teams being relegated, the loss of
television revenues is particularly significant. For example, in the EPL
every club can expect to earn approximately 40 million GBP in broadcast
income, while clubs in the Championship (second division) only generate
3 million GBP in television revenues (Switzer, 2011). Thus, the costs of
not qualifying for the international UEFA competitions and the
respective costs of relegation are substantial.
Since the stoppage time awarded to teams can be critical to teams
and may affect their revenues, the purpose of this study is to examine
the factors that determine the amount of stoppage time a team is awarded
at the referee's discretion. That is, a referee in a professional
football match is the final arbiter over when the whistle will be blown
to signal the end of a match. While previous research has already
examined the determinants of stoppage time in professional football, no
distinction was made between incidents (e.g., goals, substitutions,
fouls, red cards, yellow cards) during regulation time in the second
half and during stoppage time. Additionally, this research employs a new
variable to measure the number of seconds matches were stopped for
treatment of injuries. The empirical setting is the EPL where data for
this research was collected by examining every single event that
occurred in the second half of each match of the 2012-2013 and the
2013-2014 seasons. The findings from the models indicate some
inconsistencies in stoppage time given since only fouls in stoppage have
a significant positive effect, but not fouls in the second half. Also,
referees awarded more stoppage time for incidents in stoppage time than
in regulation. The number of seconds lost for injuries during the second
half were not fully mirrored in the stoppage time. This study
contributes to the body of research on referee bias by considering a
wider range of influencing factors in modeling stoppage time
determinants.
Literature Review
This research focuses on the concept of stoppage time (Sutter &
Kocher, 2004), often also described as injury time (Garicano,
Palacios-Huerta, & Prendergast, 2005; Rocha, Sanches, Souza, &
da Silva, 2013; Scoppa, 2008). Following the Laws of the Game (FIFA,
2014), stoppage time is defined by the allowance made in either period
for all time lost through substitutions, assessment of injury to
players, removal of injured players from the field of play for
treatment, wasting time, and any other cause. Yet, it is emphasized that
an "allowance is only made when these delays are excessive"
(FIFA, 2014, p. 104). The fourth official indicates the minimum of
additional time (in minutes) that should be added after each half. This
is considered by the referee who can increase this time but not reduce
it. No rules of thumb are provided for certain stoppages--the concrete
"allowance for time lost is at the discretion of the referee"
(FIFA, 2014, p. 29) indicating the subjective component of stoppage time
and a potential for referee bias. The Laws of the Game are also used by
the EPL (2015).
Referee bias has been the subject of a plethora of research
articles in a wide array of academic fields. Within sport economics,
referee bias has been studied in a variety of contexts including
professional football (Buraimo, Forrest, & Simmons, 2010; Dawson,
Dobson, Goddard, & Wilson, 2007; Page & Page, 2010), baseball
(Mills, 2013), hockey (Mongeon & Longley, 2013), American football
(Allen, 2002), and basketball (Price & Wolfers, 2010; Rodenberg
& Lim, 2009). For the case of football, research has primarily
examined the English Premier League (Boyko, Boyko, & Boyko, 2007;
Buraimo et al., 2010; Johnston, 2008; Reilly & Witt, 2013) and the
German Bundesliga (Buraimo et al., 2010; Dohmen, 2008; Riedl, Strauss,
Heuer, & Rubner, 2015; Sutter & Kocher, 2004). Beyond
professional team sports, research has also looked at referee bias in
sports that are subjectively judged like figure skating (Findlay &
Ste-Marie, 2004; Zitzewitz, 2006), boxing (Balmer, Nevill, & Lane,
2005), and gymnastics (Balmer, Nevill, & Williams, 2003). The latter
studies are also considered in this review because they inform the
present research.
In football, referee bias was mainly measured by the number of
yellow or red cards, or fouls called (e.g., Boyko et al., 2007; Dawson
& Dobson, 2010; Dawson et al., 2010; Reilly & Witt, 2013). Only
a few studies examined stoppage time (e.g., Dohmen, 2008; Garicano et
al., 2005; Riedl et al., 2015; Rocha et al., 2013; Scoppa, 2008; Sutter
& Kocher, 2004). Stoppage time can be critical given the number of
decisive goals that are scored in stoppage time. The factors influencing
stoppage time included the number of substitutions, penalties, yellow
and red cards, crowd composition, score difference, and whether the
stadium has a track and field track (e.g., Garicano et al.2005; Riedl et
al., 2015; Rocha et al., 2013; Scoppa, 2008; Sutter & Kocher, 2004).
Only Scoppa (2008) included the number of goals scored, while only
Dohmen (2008) considered the number of fouls and treatments for
injuries. Yet, the latter only considered the total number of fouls in
the game because separate information for each half was not available.
Also, Dohmen (2008) considered only the number of treatments and not the
actual number of seconds needed for treating injuries. Moreover, no
study could be identified that distinguished between incidents (e.g.,
goals, substitutions, cards) during regulation of the second half and
during stoppage time. These aspects are taken into account in this
study.
The majority of studies provided evidence of a referee bias in
football (e.g., Boyko et al., 2007; Dawson & Dobson, 2010) with a
few exceptions (Johnston, 2008). Given that this study's focus is
on stoppage time, this review of determinants also concentrates on the
determinants of stoppage time. First, the score difference is critical
for the awarded stoppage time, specifically for home teams; research
shows that the home team is favored because it is awarded significantly
more stoppage time in close matches where it is behind (Dohmen, 2008;
Garicano et al., 2005; Riedl et al., 2015; Rocha et al., 2013; Scoppa,
2008). In this context, the social pressure by the crowd was examined.
The crowd composition, crowd size, and the crowd's proximity to the
field (depending on the presence of a track and field track) were found
to affect the quality of refereeing (Dohmen, 2008; Garicano et al.,
2005; Scoppa, 2008).
Second, most previous studies documented a positive effect of the
number of yellow and red cards on stoppage time (Dohmen, 2008; Riedl et
al., 2015; Rocha et al., 2013; Scoppa, 2008; Sutter & Kocher, 2004),
while only the number of yellow cards was significant in another study
(Garicano et al., 2005). The number of player substitutions was mainly
found to have no significant impact on stoppage time (Dohmen, 2008;
Garicano et al., 2005; Rocha et al., 2013) with the exception of two
studies where a positive effect was documented (Scoppa, 2008; Riedl et
al., 2015). Moreover, the number of penalties and goals scored had no
significant effect on stoppage time (Scoppa, 2008). The number of fouls
had a negative effect in previous research, while the number of injury
treatments had no significant effect (Dohmen, 2008). This finding is
surprising since injury treatments typically result from fouls and are
explicitly mentioned as one factor that should be accounted for in the
definition of stoppage time (FIFA, 2014).
Research on referee bias in professional football can be informed
by studies in other sports that are subjectively judged like figure
skating (Campbell & Galbraith, 1996; Findlay & Ste-Marie, 2004;
Zitzewitz, 2006). These studies provided evidence of a nationalistic
bias (or synonymously, compatriot-judge effect), meaning that skaters of
the same nationality as the judge received significantly higher scores
(Campbell & Galbraith, 1996; Zitzewitz, 2006). Similarly, Dawson and
Dobson (2010) examined the behavior of referees in European cup football
matches and found support for a nationality bias. Research on referee
bias in figure skating also documented a reputation bias, meaning that
skaters known by the judges received higher rankings and higher
technical merit marks compared with unknown skaters (Findlay &
Ste-Marie, 2004). In their study, reputation was conceptualized as
simply knowing the skater. Mills (2013) applied the idea of reputation
to baseball players, although he called it status. He found support for
a status-based bias when examining referee behavior in baseball.
Data and Empirical Strategy
Data Collection
Data for this research was collected on multiple Internet-based
sites, including the official site of the Premier League. Match specific
data, including stoppage time given, the number of fouls, yellow cards,
red cards, substitutions, goals scored, injuries, and the total time
play was stopped for injuries in the second half and the stoppage time
were all collected from PremierLeague.com match trackers. The
PremierLeague.com match trackers are scrolling slide shows on the
Premier League website that are updated during the run of play for each
match in the league. In this, more than 600 individual match tracker
slideshows were analyzed to collect data (in the form of every event
that occurred in a second half) for every Premier League match between
August 2012 and May 2014. These match trackers are web-based programs
that allow individuals from anywhere in the world to follow every
Premier League match in real-time, with all incidents in the match
updated with the exact time they happened. Furthermore, the match
tracker slideshows are available through the Premier League official
website at all times, allowing access to data and information from all
matches from the past several years. The club, squad, referee, and
manager specific data for each match in the study were collected through
the football-lineup.com website that contains data from almost every
professional football league. Finally, the betting odds data were
gathered from football-data.co.uk, where betting data from the Bet365
bookmaker website are summarized. In all, the data collected from two
seasons produced 634 observations after matches with goal differentials
higher than two were removed from the dataset. Thus, this study focuses
on close matches in accordance with previous research (Dohmen, 2008;
Garicano et al., 2005).
Measures and Variables
In line with previous research (Dohmen, 2008; Riedl et al., 2015;
Rocha et al., 2013), the dependent variable is stoppage time seconds,
which represents the exact number of seconds that the match was allowed
to continue (StoppageGiven) after 90 minutes. As aforementioned,
previous research has employed a variety of independent variables to
control for factors that may have influenced the amount of stoppage time
given by a referee. The first two variables employed are the number of
goals scored in the regulation period of the second half (ranging from
the beginning of halftime to the 90th minute; RegulationGoals) and the
number of goals scored in the stoppage time (StoppageGoals). Likewise,
fouls, number of substitutions, and injuries in the secondhalf of a
match are also incidents where the run of play can come to a stop. For
this research, the number of times players were fouled in the 45 minutes
of the second half (RegulationFouls), substituted (RegulationSubs),
given red cards (RegulationRed), and given yellow cards
(RegulationYellow) was collected for every match. Additionally,
variables were also collected for fouls (StoppageFouls), substitutions
(StoppageSubs), red cards (StoppageRed), and yellow cards
(StoppageYellow) during stoppage time. Moreover, the number of injuries
(Injuries) that required a stoppage of play as well as the number of
total seconds in which play was delayed for injuries (InjurySeconds) was
retrieved for every match. The InjurySeconds variable is a step forward
in the analysis of the amount of stoppage time given at the end of
matches, as this is the first paper to actually take into account the
amount of time a match is delayed by individuals receiving treatment for
injuries. This group of match variables was collected for only the
second half of matches, as stoppage time in the second half of a match
should be reflective of events that occur during the 45 minutes of play.
On the contrary, Dohmen (2008) was only able to obtain data for the
number of fouls during the entire match.
To control for a potential nationalistic bias that may exist among
Premier League referees, this study considered the nationalities of all
referees, managers, and squad members who participated in the league
during the 2012-2013 and 2013-2014 seasons. Notably, all the referees in
the Premier League were born in England, and thus prevented the need to
construct a variable to control for referee nationality. Dummy variables
were created to measure whether a manager for a club was from England or
another country, with a 1 indicating the manager was English, and a 0
indicating they were from a country outside of England. A separate
variable was constructed for the home (HomeManagerEng) and the away team
(AwayManagerEng). For the squads, the total number of foreign players
for each club was divided by the total number of players on the entire
squad to produce a percentage of English players for each squad. This
percentage of English players measure was constructed for both home and
away teams. Metrics were created calculating the percentage of English
players on a squad among the group of players had made at least 10
appearances in league matches for the club. The percentage for away team
English players was then subtracted from the home team (EngPctDiff) to
measure the difference in the ratio of English players on a squad.
Recent studies into referee bias have also included measures to try
and capture aspects of a match that reflect the importance of the match
to fans. Importance of a match has been measured through dummy variables
(Rocha et al., 2013) or through the use of uncertainty of outcome
measures. Uncertainty of outcome is hypothesized to reflect the
importance of matches to fans, by indicating the probability of one of
the teams winning the match (Rottenberg, 1956). In this, a match with a
high uncertainty would be of high interest because of it being hard to
predict the outcome. Buraimo et al. (2010) employed betting odds for
professional football matches in Germany and England, while others have
used differences in quality between the two teams in a match (Page &
Page, 2010). This research employs betting odds data similar to Buraimo
et al. (2010), with the difference being that this research collected
data from the Bet365 bookmaker website. Thus, the first variable in this
research is the BookmakerDiff, which measures the difference in
bookmaker odds for each team in a match to win. This measure is
calculated by simply subtracting the odds of the away team winning from
the odds of the home team winning. The values produced by the
BookmakerDiffmeasure can range between negative and positive numbers,
with negative numbers indicating that the home team was the favorite for
the match, and positive numbers indicating the away team was the
favorite.
Previous research examining referee bias has considered different
measures of team strength or quality like measures of uncertainty of
outcome (Buraimo et al., 2010), relative league position (Reilly &
Witt, 2013), or the average quality of the two clubs involved in a match
(Page & Page, 2010). As stated earlier, there may be a reputation
bias with better performing teams being favored by referees. Within this
research, the measure used is FiveYearRank, which is the average
position in the league tables for the team over the previous five years.
A five-year period was chosen because reputation has to be established
over time. In this, a team in the Premier League would be ranked between
1 through 20, as there are 20 teams in the league. Because of promotion
and relegation, the 24 teams that were in the Football Championship were
considered to be ranked 21 through 44, and the 24 teams in the Football
League One (the third tier of English football) were ranked 45 through
68. Within this dataset, several teams actually moved through two or
three tiers of professional football in England over the previous five
years, and thus the metrics reflect the average positions of these teams
to capture the expected historical performance of the clubs.
To control for the specific performance and experience of referees
two sets of variables were constructed. The first variable was a simple
measure of the number of years of experience that a referee had in the
Premier League as the main official of matches (TopFlightExp). To
capture additional individual differences that may possibly exist
between officials, a dummy variable for each referee was constructed to
measure their existence as the official in charge of a match.
Team-specific variables were also included to measure the presence of
each club within the match, and to denote whether these clubs were the
home team or the away team.
The attendance at each match is also included within this study. A
large number of studies on referee bias have employed the attendance
variable to control for the size of the crowd (Pettersson-Lidbom &
Priks, 2010). Theories of the effect of the number of fans in attendance
range from the social pressure placed on referees from large fan bases
to the potential that the environment of a large match may create
difficulties in making accurate and unbiased decisions (Buraimo et al.,
2013; Dawson & Dobson, 2010; Johnston, 2008; Pettersson-Lidbom &
Priks, 2010; Reilly & Witt, 2013). Like more recent studies have
done, this study transforms the attendance data into its natural
logarithm (LnAttend). A variable (Derby) was also included in the model
to take into account derby matches within the Premier League that are of
high importance. An example of a Derby would be the match between
Tottenham Hotspur and Arsenal, which is dubbed the "North London
Derby," and is considered an important match for both squads.
Because of the contentious nature of these matches, it is appropriate to
control for their presence, as referees may be specifically assigned
because of their ability to officiate a high-profile match.
A final key variable included within this research is the ScoreDiff
variable, which is calculated by subtracting the number of goals the
away team had at the 90th minute of each match from the number of goals
the home team had in the same time frame. This variable is of importance
because it controls for the relative match position of the home team
compared to the away team. A positive number for the differential
indicates that the home team is winning, and the literature indicates
that a referee who is biased would give less stoppage time in that
match, so that the home team would have less time they would need to
defend. Likewise, a home team that was losing in a match could expect to
receive more time if there is referee bias, as they would need as much
time as possible to try and score a goal to either tie or win a match
(Garicano et al., 2005). The listed variables can also be viewed in
Table 1, alongside descriptions of what each variable measures. Tables 2
and 3 present the summary statistics of the variables employed in this
research.
Statistical Model
Previous studies examining referee bias have used OLS models
(Dohmen, 2008; Scoppa, 2008; Sutter & Kocher, 2004), as well as
ordered Probit models (Buraimo et al., 2013; Dawson & Dobson, 2010).
Studies investigating referee decisions to give penalties or red/yellow
cards have primarily employed univariate or bivariate ordered probit
models in order to analyze the determinants that may influence the
decision to award penalties or give cards in a match. OLS regression
models have been primarily used in the examination of referee bias to
consider the number of minutes (Sutter & Kocher, 2004) or seconds
(Dohmen, 2008) given in the stoppage time period at the end of a match
by a referee. For the purpose of this research, the dependent variable
to measure the amount of time given at the end of the match is in
seconds, and, thus, a regression approach is fitting.
This research distinguishes between two models that differ in terms
of sample size: Models 1 and 2 are composed of all Premier League
matches in which the score differential was two goals or less at the
90th minute mark. The difference between Model 1 and 2 comes in the form
of injuries, which are measured in Model 1 through the total number of
injuries in the second half, while Model 2 measures the number of
seconds the match was delayed in the second half for injuries. Likewise,
Models 3 and 4 are composed of all Premier League matches that had a
differential in the number of goals scored at one or were tied at the
90th minute mark. Similar to Models 1 and 2, Models 3 and 4 differ in
the measurement of injuries through either the number of total injuries
or the number of seconds a match was delayed for treatment of injuries.
In this, Models 1 and 2 have 634 observations, while Models 3 and 4 have
478 observations. While the dataset employed for each model was
different in the number of observations, the variables remain consistent
among all of the models in this research.
Further considering the panel dataset within this research, it is
important to determine what type of regression should be run to produce
the best estimators possible. Because of the nature of panel data, the
data were tested within the STATA statistical software package in order
to determine the use of fixed or random effects within the models. The
Hausman test did not return a significant value, indicating no
significant differences between using fixed or random effects models
(Wooldridge, 2002). Considering that the previous literature examining
referee bias has employed regression models with fixed effects to
examine data of a similar nature (Buraimo et al., 2010; Dohmen, 2008),
this research likewise follows a similar method. Thus, a fixed effects
regression was run to estimate results from the dataset. The models for
this research take the form of the following equation:
[StoppageGiven.sub.it] = [theta] +
[[beta].sub.1][RegulationGoals.sub.it] +
[[beta].sub.2][StoppageGoals.sub.it] +
[[beta].sub.3][RegulationSubs.sub.it] +
[[beta].sub.4][StoppageSubs.sub.it] +
[[beta].sub.5][RegulationFouls.sub.it] +
[[beta].sub.6][StoppageFouls.sub.it] + [[beta].sub.7][Injuries.sub.it] +
[[beta].sub.8][RegulationRed.sub.it] +
[[beta].sub.9][StoppageRed.sub.it] +
[[beta].sub.10][RegulationYellow.sub.it] +
[[beta].sub.11][StoppageYellow.sub.it] +
[[beta].sub.12][EngPctDiff.sub.it] +
[[beta].sub.13][HomeManagerEng.sub.it] +
[[beta].sub.14][AwayManagerEng.sub.it] +
[[beta].sub.15][BookmakerDiff.sub.it] +
[[beta].sub.16][TopFlightExp.sub.it] +
[[beta].sub.17][FiveYearRank.sub.it] + [[beta].sub.18][LnAttend.sub.it]
+ [[beta].sub.19][Derby.sub.it] + [[beta].sub.20][ScoreDiff.sub.it] +
[[beta].sub.21]Home [Team Effects.sub.it] + [[beta].sub.22]Away Team
[Effects.sub.it] + [[beta].sub.23][Referee Effects.sub.it] +
[[micro].sub.it] (1)
Results and Discussion
Four regression models were run employing the above equation. They
are summarized in Tables 4 and 5. The difference in the two models is
the method of measuring injuries, as well as the aforementioned
difference in the goal differential of the match being a condition for
inclusion. The first model explained about 50.1% of the variation in the
dependent variable while the rest of the models explained 59.5% (Model
2), 37.2% (Model 3), and 50.4% (Model 4).
The number of goals scored both in the regulation period of the
second half and the stoppage time had a positive and significant effect
on stoppage time. In prior studies, the effect of goals was
insignificant (Scoppa, 2008). For all models, the goal variables were
significant at the 1% level, indicating that referees do give more
stoppage time for goals during a match. Notably, the coefficient of
goals in stoppage time was around two times greater than the one for
second-half goals in the models. This may indicate that while referees
gave more time for any goal scored, scoring in stoppage time tended to
have the referee give a significantly greater amount of time. In this
sense, it would seem that referees may be more willing to add additional
time to a match when a goal is scored in the stoppage time period,
especially in the case of this dataset, where all the games are
relatively close in regards to score differential. It is, thus, that
goals may not be equal in the eyes of a referee dependent on when the
goal is scored.
Substitutions and injuries each had positive and significant
coefficients in all models, while only fouls in stoppage time have a
positive and significant effect in all four models. First, considering
substitutions, it was found that the more substitutions that took place
in the second half, the more stoppage time a referee gave. Additionally,
referees tended to give more stoppage time for substitutions in stoppage
time than in the regulation 45 minutes of the second half. The
difference in results for fouls may indicate that fouls are not a very
good predictor of the amount of stoppage time if they occur during the
regulation time of the second half. Because fouls occur during the run
of play, and often do not take very much time away from the game,
referees may overlook fouls, or only add on a minimal amount of time
when they do occur. However, the results indicate that when the fouls
happened in stoppage time, referees did add on significantly more
stoppage time. Considering the amount of time that actually passes
during a foul and the time to get the ball stopped and play started
again, it would seem that the amount of time given per foul is not truly
reflective of lost time in a match. While it could be argued that this
is part of the run of play, the results indicate that a good strategy by
a team trying to preserve a lead would be to foul opponents during
regulation time in the second half in order to waste more time. It is
worth noting that some teams may adopt this tactic to try and disrupt
the flow of play during matches. Thus, the question remains as to
whether a referee is giving a correct amount of time to recoup time
wasted by teams. However, this strategy does not hold up for stoppage
time, as fouling during this time period was linked with significantly
more time given by the referee. Likewise, substitutions during the first
45 minutes of the second half had a minimal effect on the amount of
stoppage time given, with a single substitution only adding about seven
to eight seconds of stoppage time.
The number of injuries that occurred in a match had a significant
and positive effect on the amount of stoppage time given, with around 33
to 34 seconds of time added on for each injury that required a stoppage
in play. The number of injury seconds was also positive and significant,
with about 0.6 seconds of stoppage time added for every second play was
stopped for an injury in the second half. Thus, the stoppage time does
not fully mirror the total number of seconds lost due to injuries. The
average amount of time for injury treatment in a match was approximately
50 seconds, which would produce on average about 30 seconds of stoppage
time. Both of these findings are contrary to the study of Dohmen (2008),
who found no significant effect of the number of injury treatments on
the length of second-half stoppage time in close games of the German
Football Bundesliga. Surprisingly, treatments had the anticipated
positive and significant effect on first-half stoppage time in his
study, but the coefficients were relatively small, indicating that
referees awarded approximately one second of stoppage time for every
treatment. Since his research focused on the influence of social forces,
no further discussion of these effects was provided (Dohmen, 2008).
The number of yellow cards both in regulation and in stoppage time
significantly add to stoppage time awarded at the end of a match. Yet,
more seconds are awarded in stoppage time than in regulation. Regarding
red cards, only those in the second half significantly affect stoppage
time; those given in stoppage time have no significant effect (with the
exception of Model 2). The positive effects of the number of cards
during the second half on stoppage time are in accordance with previous
research (Dohmen, 2008; Riedl et al., 2015; Rocha et al., 2013; Scoppa,
2008).
Tests for nationality bias among referees indicated that there was
not any evidence of any such behavior in Models 1, 2 and 3. The
difference in the percentage of home and away squads that were English
were insignificant in examining matches with a goal differential of two
or less, as were the variables measuring whether home and/or away
managers were English. However, Model 4 found the percent difference in
English nationality of squads to be negative and significant. This means
that when away teams had a higher percentage of English players in
matches with a one-goal differential, there was significantly more
stoppage time added to the match. In this, the results of Models 1, 2,
and 3 differ from the work of Dawson and Dobson (2010), but Model 4 is
similar in finding that there was evidence of referee bias in decision
making when nationality was factored in. It is likely that there may be
more nationality bias evident in decisions like calling fouls (Price
& Wolfers, 2010) or giving cards than in simply adding time at the
end of a match.
The measures of team quality and uncertainty of outcome were
insignificant in both models. First, in regards to team quality, the
five-year measure of average table position for a club was not
significant, and results did not change when other time variations of
the measure such as three-year-average were substituted. Thus, there is
no indication of a reputation bias in this study. Additionally, the
difference in bookmaker odds for home and away team winning was
insignificant in all models. These results indicate that Premier League
referees were not biased in regards to the historical quality of the
teams in the match, nor by the win probability for the teams in each
match. The findings in regards to bookmaker odds is in contrast to the
work of Buraimo et al. (2010), who found that there were significant
relations between odds of winning and referee decisions in a match. The
differences that exist between these studies could be because of the
nature of the decisions that were examined. As with the differences
between this research and other prior studies, the findings could differ
because there may be inherently more biased decision making in giving
red cards and not in giving stoppage time at the end of a match.
The attendance variable was insignificant in all models. Various
models were tested using both the natural logarithm of attendance, as
well as attendance in its natural form. In all cases, there was no
relation between the number of attendees at a match and the stoppage
time given. Prior research has found mixed effects in regards to
attendance having a significant impact on the decision making of
referees in regards to giving red cards and penalties (Dawson &
Dobson, 2010; Pettersson-Lidbom & Priks, 2010; Reilly & Witt,
2013). This study finds results similar to that produced by Reilly and
Witt (2013), who also documented that attendance did not affect referee
decision making. It is noted within the literature, that teams playing
in larger stadiums may have an effect on the referees because of social
pressures placed on them (PetterssonLidbom & Priks, 2010). However,
this study found no such evidence of social pressure or crowd size
affecting referee decisions. Additionally, the Derby variable was also
insignificant in all models, indicating that even those matches with
higher social pressure because of the rivalry between the teams involved
in the match did not affect the amount of stoppage time given by a
referee.
The measure of referee experience was also found to be
insignificant within this research. Referee experience has previously
been measured by dummy variables for elite referees (Dawson &
Dobson, 2010). Within the literature, it is the case that many studies
have not used variables to measure the quality of referees who were in
charge of matches, with most studies employing no effects or just
referee specific effects (e.g., Downward & Jones, 2007; Johnston,
2008; Page & Page, 2010). In the case of this study, the years of
Premier League experience were included to control for the quality of
referees. However, for many referees, there is often a period of many
years of work in lower leagues and as assistant officials before they
are given the chance to be the main official in the Premier League.
Thus, it could potentially be the case that those who are granted
entrance to the Premier League are already at a high level from so many
years of experience that they do not differ greatly in regards to
stoppage time given at the end of a match. Additionally, it could be the
case that as more leagues have become cognizant of referee issues, that
the Premier League has monitored and instructed referees very carefully
in regards to the amount of stoppage time given. Thus, there could be
less influence of experience on the amount of stoppage time that
referees give at the end of matches.
The variable ScoreDiff measuring the difference in goals scored
between the home team and away team was insignificant in all four
models. These results indicate that there is no presence of bias among
referees giving more time to either home or away teams during Premier
League matches. Several permutations of score differential variables, as
well as dummy variables for match conditions such as home team leading,
were run in other regressions, and generally returned similar results as
the ones presented in this research. Thus, the present study could not
support the home team advantage evident in previous research (Dohmen,
2008; Garicano et al., 2005; Riedl et al., 2015; Rocha et al., 2013;
Scoppa, 2008). It is likely that the score differential turns
insignificant when controlling for a variety of other determinants of
stoppage time.
The results of the team and referee effects were generally
insignificant in both models with the exception of two variables. First,
in Model 1, when the Premier League club Everton was away, they were
found to receive significantly less time at the 10% level. It was found
that when controlling for other factors, Everton received almost 30
seconds less stoppage time when they were away than any other club. In
Models 1 and 2, the other team effects were all insignificant, but
referee Kevin Friend was found to be positive and significant in regards
to time given at the 1% level. These findings indicate that in matches
that had a score differential of two or less, Friend gave about 48
seconds more stoppage time as compared to his colleagues. In Models 3
and 4 examining matches with a goal differential of one or less, none of
the team- or referee-specific effects were significant. Overall the
results from all models point towards a better understanding of factors
that influence the amount of stoppage time given at the end of a match
by a referee.
Conclusion
This study examined the determinants of stoppage time at the end of
the second half in close matches of the 2012-2013 and 2013-2014 of the
EPL. It adds to the body of research on referee bias in professional
football by including more factors than previous research. Specifically,
this study distinguished between incidents (e.g., red and yellow cards,
substitutions) in regulation and in stoppage time. It also considers
factors like the number of goals scored, fouls, and injuries that have
only been included separately in a few studies (Dohmen, 2008; Scoppa,
2008). The exact number of injury seconds is also considered, which has
been neglected in previous research.
The key findings of this research are that the number of goals,
substitutions, and yellow cards both in the regulation time in the
second half and in stoppage time have a significant positive effect on
stoppage time. Only fouls in stoppage time significantly add to stoppage
time; fouls in the regulation time in the second half do not. On the
contrary, red cards during regulation significantly add to stoppage
time, but not red cards in stoppage time. The number of injuries during
the second half has a significant positive effect on stoppage time. Yet,
the findings indicate that only approximately 60% of the injury time is
mirrored in stoppage time. Also, referees awarded more stoppage time
seconds for incidents (goals, substitutions, fouls, yellow cards) in
stoppage time than in regulation. The latter results reveal some
inconsistencies in the amount of stoppage time awarded by referees in
the EPL.
The findings help to understand how referees award stoppage time at
the end of a match in regards to various events that can occur during
the run of play. Given the importance of a result, a team could
potentially lose points in the standings because of the stoppage time
given, which could have direct impacts in regards to their position in
the table. Considering the ending of the 2012-2013 Premier League
season, Tottenham Hotspur ended up one point in the table behind
fourth-place Arsenal. The difference of a single point in this case
meant the difference between qualifying for UEFA Champions League and
the UEFA Europa League. In this, the difference in revenues between the
two competitions could be in the tens of millions of Euros based on
performance in those competitions. Thus, a single point in the table
could be determined by the amount of stoppage time given at the end of
the match, and has important consequences for the revenue and future of
many professional football clubs, especially in leagues that employ
promotion and relegation. Therefore, it is vital for the Premier League
to monitor and ensure that referees do not exhibit bias in making
decisions such as deciding the amount of stoppage time to give.
This study provides important implications for the monitoring and
evaluation of referees in the Premier League. To date, the evaluation
process employed by the league has been rather secretive, with a numeric
rating given to referees after each match. However, this data has not
been made available to the public, thus making it more difficult to
understand how referees are truly managed by the league. Thus, a more
transparent system could potentially be beneficial in the monitoring and
evaluation process. Such information could also be used in future
studies. It would also be interesting to examine how the stoppage time
given at the end of the first half affects the stoppage time at the end
of the second half. Currently, information about the first half stoppage
time is not available from the Premier League. Another direction for
future research would be the extension of the present research design to
other leagues.
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Nicholas M. Watanabe (1), Pamela Wicker (2), and James C. Reuter
(1)
(1) University of Missouri
(2) German Sport University Cologne
Nicholas M. Watanabe, PhD, is an assistant teaching professor in
the Department of Parks, Recreation and Tourism's sport management
emphasis. His research interests include sport management and sport
economics.
Pamela Wicker, PhD, is a senior lecturer in the Department of Sport
Economics and Sport Management. Her main research interests include
sport economics, sport finance, and sport management.
James C. Reuter is a graduate of the Department of Parks,
Recreation and Tourism. His research interests include sport management
and economics.
Table 1. Overview of Variables
Variable Description
StoppageGiven Time given at the end of regulation
(in seconds)
RegulationGoals Goals scored during the 45 minutes of second
half regulation time
StoppageGoals Goals scored during the stoppage time given
at the end of a match
RegulationSubs Number of substitutions during second half
regulation time
StoppageSubs Number of substitutions during stoppage time
in the second half
RegulationFouls Number of fouls during second half regulation
time
StoppageFouls Number of fouls during stoppage time in the
second half
Injuries Number of injuries in the second half of a
match
InjurySeconds Total number of seconds that play was stopped
for injuries in the second half
RegulationRed Number of red cards during second half
regulation time
StoppageRed Number of red cards during second half
stoppage time
RegulationYellow Number of yellow cards during second half
regulation time
StoppageYellow Number of yellow cards in second half
stoppage time
EngPctDiff Percent of home team squad members from
England minus the percent of away team squad
members from England
HomeManagerEng Dummy variable measuring if the home team
manager is English (1 = yes)
AwayManagerEng Dummy variable measuring if the away team
manager is English (1 = yes)
BookmakerDiff Difference in win probability between the
home and away team
TopFlightExp Number of years of experience for the referee
in the Premier League as a main official
FiveYearRank Average position of a club over the previous
five years
LnAttend Natural log of attendance at the match
Derby Dummy variable measuring derby matches
between rival opponents.
ScoreDiff Home team goals scored in 90 minutes minus
away team goals scored in 90 minutes
Table 2. Summary Statistics for Model 1 and 2 (Games with a
Two-Goal Differential or Less after 90 Minutes)
Model 1 & 2-634 Observations
Variables Mean Std. Dev. Min Max
StoppageGiven 267 70.47 125 762
RegulationGoals 1.241 1.134 0 5
StoppageGoals 0.1151 0.3244 0 2
RegulationSubs 4.027 1.050 1 6
StoppageSubs 0.1987 0.4443 0 3
RegulationFouls 10.68 3.345 2 21
StoppageFouls 1.046 0.9717 0 5
Injuries 0.8438 0.8812 0 5
InjurySeconds 48.68 59.88 0 348
RegulationRed 0.0757 0.2821 0 2
StoppageRed 0.0158 0.1247 0 1
RegulationYellow 1.792 1.342 0 7
StoppageYellow 0.3297 0.5950 0 5
EngPctDiff 0.0015 0.1502 -0.3626 0.3595
HomeManagerEng 0.2224 0.4162 0 1
AwayManagerEng 0.3233 0.4681 0 1
BookmakerDiff -2.091 5.133 -27.87 9.64
TopFlightExp 6.722 3.903 0 13
FiveYearRank 14.74 10.25 1.400 40.4
LnAttend 10.42 0.3555 9.644 11.23
Derby 0.0442 0.2056 0 1
ScoreDiff 0.1893 1.188 -2 2
Table 3. Summary Statistics for Model 3 and 4 (Games with a
One-Goal Differential or Less after 90 Minutes)
Model 3 & 4--478 Observations
Variables Mean Std. Dev. Min Max
StoppageGiven 275 72.72 126 762
RegulationGoals 1.134 1.110 0 5
StoppageGoals 0.1046 0.3131 0 2
RegulationSubs 3.994 1.049 1 6
StoppageSubs 0.2134 0.4538 0 3
RegulationFouls 10.83 3.324 2 21
StoppageFouls 1.098 0.9803 0 5
Injuries 0.8703 0.9018 0 5
InjurySeconds 49.68 60.69 0 348
RegulationRed 0.0837 0.2990 0 2
StoppageRed 0.0146 0.1203 0 1
RegulationYellow 1.866 1.342 0 6
StoppageYellow 0.3828 0.6260 0 5
EngPctDiff 0.0004 0.1499 -0.3595 0.3595
HomeManagerEng 0.2155 0.4116 0 1
AwayManagerEng 0.3159 0.4654 0 1
BookmakerDiff -1.800 4.737 -27.87 8.6
TopFlightExp 6.690 3.895 0 13
FiveYearRank 15.04 10.10 1.4 40.4
LnAttend 10.40 0.3501 9.644 11.23
Derby 0.0544 0.2270 0 1
ScoreDiff 0.0921 0.7770 -1 1
Table 4. Regression Results for Games with a Two-Goal
Differential or Less after 90 Minutes; Dependent Variable:
Stoppage Time Given
Model 1 Model 2
Variable Coeff. P > Coeff. P >
[absolute [absolute
value value
of t] of t]
RegulationGoals 11.02 0.000 10.29 0.000
StoppageGoals 29.15 0.000 29.53 0.000
RegulationSubs 7.836 0.001 7.310 0.000
StoppageSubs 34.39 0.000 32.86 0.000
RegulationFouls -0.7795 0.288 -0.1806 0.787
StoppageFouls 13.26 0.000 10.29 0.000
Injuries 33.24 0.000 -- --
InjurySeconds -- -- 0.6221 0.000
RegulationRed 28.08 0.000 29.06 0.000
StoppageRed 21.15 0.241 28.67 0.080
RegulationYellow 7.868 0.000 8.360 0.000
StoppageYellow 17.27 0.000 17.04 0.000
EngPctDiff -22.92 0.241 -28.45 0.109
HomeManagerEng -10.91 0.278 -8.370 0.360
AwayManagerEng 0.7141 0.885 1.036 0.817
BookmakerDiff -0.0602 0.925 -0.0262 0.964
TopFlightExp -0.3697 0.527 -0.2899 0.585
FiveYearRank 0.7735 0.663 1.064 0.510
LnAttend 28.63 0.552 10.62 0.808
Derby -1.136 0.919 1.216 0.905
ScoreDiff -1.659 0.429 -1.618 0.396
Home Team Fixed Effects Included Included
Away Team Fixed Effects Included Included
Referee Fixed Effects Included Included
Constant -148 -0.300 29.04 0.060
[R.sup.2] 0.5007 0.5948
Table 5. Regression Results for Games with a One-Goal
Differential or Less after 90 Minutes; Dependent Variable:
Stoppage Time Given
Model 3 Model 4
Variable Coeff. P > Coeff. P >
[absolute [absolute
value of value of
t] t]
RegulationGoals 14.18 0.000 13.25 0.000
StoppageGoals 27.86 0.002 30.52 0.000
RegulationSubs 8.329 0.002 7.828 0.002
StoppageSubs 34.53 0.000 32.73 0.000
RegulationFouls -0.9902 0.259 -0.1218 0.877
StoppageFouls 14.24 0.000 12.14 0.000
Injuries 34.54 0.000 --- ---
InjurySeconds --- --- 0.6531 0.000
RegulationRed 26.12 0.004 28.07 0.001
StoppageRed 10.48 0.645 20.01 0.328
RegulationYellow 7.819 0.000 8.478 0.000
StoppageYellow 15.95 0.001 15.64 0.000
EngPctDiff -32.01 0.169 -39.87 0.057
HomeManagerEng -9.882 0.420 -8.990 0.414
AwayManagerEng 1.303 0.826 1.845 0.729
BookmakerDiff -0.4303 0.581 -0.3173 0.651
TopFlightExp -0.3802 0.591 -0.3861 0.545
FiveYearRank 1.377 0.504 1.314 0.479
LnAttend 71.61 0.197 50.10 0.316
Derby -7.446 0.547 -5.051 0.650
ScoreDiff -1.699 0.646 -0.8944 0.788
Home Team Fixed Effects Included Included
Away Team Fixed Effects Included Included
Referee Fixed Effects Included Included
Constant -603 0.297 -387 0.458
[R.sup.2] 0.3719 0.5040
