Biased impartiality among National Hockey League referees.
Lopez, Michael J. ; Snyder, Kevin
Introduction
Fans, coaches, and players often complain that referees make
decisions based on factors other than what occurred on the playing
surface. Although support for match fixing is scant, spectators
frequently accuse officials of bias against their team. In reality, the
bias usually rests with the irate fans or participants, while referees
are loath to discuss the matter. However, anecdotal evidence from
referees suggests that they are aware of how games are being called and
work to balance infractions. Adding to the debate on make-up calls is
former NHL senior referee, Kerry Fraser, who stated in 2011,
When a referee realizes he made a call in error, the most difficult
thing to overcome is "human nature"--the natural tendency to
attempt to fix it or make it right with an even-up call. The referee
wants to be fair and recognizes something he did just wasn't fair.
Fraser went on to say, "It occurs in all jobs and all walks of
life. It can be enhanced when under pressure."
Combined with fan reactions, these quotes suggest the possibility
of temporary bias existing in the officiating of a sporting game. As the
individuals charged with enforcing the rules of the game and policing
player behaviors, referees are in place as an impartial party to
maintain order and ensure a safe, fair outcome. However, officials are
also faced with numerous pressures of their own including from
spectators in the building (Boyko, Boyko, & Boyko, 2007; Buraimo,
Forrest, & Simmons, 2009; Moskowitz & Wertheim, 2011; Nevil,
Balmer, & Williams, 2002; Scoppa, 2008; Sutter & Kochera, 2004),
from their peers, and from the league offices that determine their
employment. Significant financial ramifications also ride on perceptions
of a fairly called game. Balancing these pressures and maintaining
strong working relationships with each group is a high wire act,
delicately walked by referees each game. Given these expectations, how
do referees maintain the integrity of the game while balancing numerous
influences? Also, when would a referee be most likely to exhibit
temporary bias to further the broader goal of the integrity of the
match?
Although several scholars have explored officiating bias under
different conditions (Boyko et al., 2007; Moskowitz & Wertheim,
2011; Mongeon & Mittelhammer, 2011), few studies have considered
that biases may change throughout the course of a game. By looking at
games and seasons in their totality, previous research has assumed that
biases are consistent throughout an entire contest. Further, this
assumption fails to allow for variation in referee behavior based on
game conditions or other situational factors. These assumptions have led
researchers to conclude that home or popular teams are always more
likely to receive a favorable call from an official (Moskowitz &
Wertheim, 2011; Price, Remer, & Stone, 2012). However, this paper
highlights how referees subconsciously shift their bias as the game
progresses based on the flow of the game. The model developed here
illustrates when referees have incentives to call penalties on each
team. By using a sample of National Hockey League (NHL) data, this
research answers the questions of when referees allow for
"make-up" calls within a game.
The paper starts by reviewing background information on the
National Hockey League (NHL) and the role of referees. Second, areas
where "biased impartiality" may occur within the sport of
hockey are examined, followed by a review of literature on player
actions. A description of the sample used in this study follows, along
with our analysis. This paper concludes with a discussion of the
results, limitations of our work, and avenues for future research.
Background
The National Hockey League
Based on revenues, the National Hockey League is the fourth largest
professional sporting league in North America. The NHL consists of 30
teams with 23 located in the United States and 7 in Canada. Revenues for
the 2012 season are estimated at $3.2 billion, representing a 50%
increase over the past 7 years (Staples, 2012). As with most other
professional sport leagues, a disproportionate share of these revenues
are earned in the postseason (Leeds & von Allmen, 2004; Robst,
VanGilder, Berri, & Vance, 2011). However, differing from the NFL,
NBA, and MLB, the NHL's primary source of revenue is ticket sales.
The variability of this revenue stream creates greater incentives for
the NHL to create close games, perhaps even favoring home teams, with
high levels of outcome uncertainty across games and seasons (Coates
& Humphreys, 2012; Fort, 2011; Staudohar, 2005). In playoff games,
these incentives are enhanced due to a larger audience following through
numerous media outlets.
The primary responsibility of hockey officials (two referees and
two linesmen) is to monitor the play of the teams, watching for
violations and penalties as a way of providing legitimacy to the
contest. The referees are the only ones charged with calling penalties,
though they can consult with the linesmen when necessary. Violations,
such as offsides or icing, are mostly clear cut with little judgment
necessary to determine where the puck was in relation to an offensive
player. However, there is significant discretion in awarding penalties
given the rule book's latitude in defining undesirable behavior.
Typical penalties include stick violations of slashing, hooking, or
high-sticking, as well as physical infringements such as boarding,
roughing, interference, elbowing, and fighting. Additionally, teams are
assessed a penalty for having too many players on the ice and delaying
the game, though these are easier to identify and called with near
uniformity. When a penalty is called, the offending team loses a player
on the ice for the shorter of 2 minutes or until the other team scores.
More severe penalties can be 5 minutes or disqualification from the
game. Losing a player is a significant disadvantage. In the 2011-12
season, teams scored on 17.0% of their opportunities with an extra
skater, and 20.9% of all goals were scored via a power play
(www.nhl.com). In a game where winning teams typically score between
three and four goals, penalties can play a significant role in
determining the outcome.
In an attempt to call a fair game, referees may possess an
unconscious bias towards evening up penalty calls. Subconsciously
influenced by a desire to avoid directly favoring one team, officials
may also inadvertently demonstrate bias by ignoring borderline acts that
could be deemed in violation of a rule. This slight shift in standard
occurs due to the degree of interpretation in the role and is not
indicative of illicit actions from a referee.
The practice of evening up calls can have both positive and
negative impacts on the game. One clear advantage for spectators is the
likelihood of a close, competitive game. Exciting, unpredictable
finishes make for good television and entertainment. However, the
negative impacts of evening up calls outweigh the positive benefits.
When violations are ignored or inconsistently called, participants
struggle to regulate their actions to the desired behaviors. As a
result, greater incentives exist for retaliation and dangerous play.
Additionally, inconsistent officiating has the potential to undermine
the public's confidence in the fairness of the game and the
independence of the referees.
Other models of referee behavior
Although there may be many reasons for home advantage (Koyama &
Reade, 2008), recent academic work has identified officials'
behavior as an explanation for the greater success of home teams (Boyko
et al, 2007; Pettersson-Lidbom & Priks, 2009; Leard & Doyle,
2010). Appealing to an implicit desire to appease the partisan crowd
leads to a bias in the distribution of calls favoring the home team.
Impacts of this behavior are illustrated in the effect of crowd noise
(Nevill, Balmer, & Williams, 2002), added time in soccer matches
(Sutter & Kochera, 2004) and games played in empty stadia
(Pettersson-Lidbom & Priks, 2009). These studies have found
favoritism effects for an aggregate group of officials, as well as
individual referees. Other scholars link biases and behaviors of
referees in response to crowd behaviors (Scoppa, 2008; Garicano,
Palacios-Huerta, & Prendergast, 2005; Nevill et al, 2002; Boyko et
al, 2006). Buraimo et al. (2009) represents an exception within the
literature to the assumption of consistent biases favoring the home
team, finding evidence instead of make-up calls in European football
leagues. Ultimately, home teams win approximately 55% of games, a
difference of 5% from the expected mean of 50% if all games were played
at a neutral site. This bias has been connected to favorable home team
calls and is consistent across numerous sports, including baseball,
football, basketball, hockey, soccer, and the Olympic Games (Moskowitz
& Wertheim, 2011; Nevill et al., 2002).
Models of player behavior
Penalty and goal outcomes depend upon both referee and player
behaviors. Numerous studies have been conducted to assess the impact of
player aggression on the outcome of games (Buraimo et al., 2009; Jewell,
2009; Widmeyer & Birch, 1984; Widmeyer & McGuire, 1997). In each
instance, as in our model, aggression is viewed as actions beyond the
boundary of ordinarily accepted activities required in the sport and is
punished through the incursion of a penalty or foul.
As a context for understanding aggression and officiating, European
soccer has been used to explain how referees manage yellow and red cards
issued for aggressive fouls (Buraimo et al., 2009). Beyond the referee
bias towards home teams found in several similar studies, players modify
their behavior and become more aggressive when behind in a match
(Buraimo et al., 2009). Aggressive actions by players may be the result
of a tactical shift or frustration in how the game has progressed.
Players may be more likely to commit a foul when the game is likely to
be lost and the opportunity cost of disqualification is low (Jewell,
2009). However, when referees are added, hockey players are not deterred
from committing penalties but more penalties are observed due to greater
enforcement efforts (Heckelman & Yates, 2003). The combination of
these studies suggests that players' actions are consistent with
the team's strategy and have little variance in relation to referee
behaviors.
Aggression is also studied as a strategy to increase the likelihood
of success. Through an examination of hockey results, Widmeyer and Birch
(1984) examine the impact of first period penalties on future
performance. Although counterintuitive, committing penalties in the
beginning of a game may help increase the chances of a victory through
intimidation of the opponent (Widmeyer & Birch, 1984). Aggression
may be more prevalent with familiarity of the opponent as penalties
increase between frequent rivals seeking to carry the intimidation
advantage over to multiple games (Widmeyer & McGuire, 1997).
Building on prior frameworks of referee bias and player aggression,
our paper continues in pursuit of referee tendencies to balance penalty
calls. Whereas prior research has sought a bias towards specific teams
(Price et al., 2012), we model the behavior of referees with each team
treated equally in search of a balance of penalty calls. The following
section outlines how data was collected to answer these questions. The
paper continues by displaying the results and discussing the conclusions
drawn based on the incentives of hockey referees.
Theory and Calculation
The nature of hockey officiating creates a desirable laboratory for
examining referee behavior. In a given game, hockey referees assign an
average of fewer than 10 total penalties. This number is lower than
other sports, as basketball referees may assign 25-30 fouls per game and
football officials spot 12-15 violations. The greater ease of tracking
referee behavior, combined with the greater ability to affect the
outcome (due to the severity of the punishment and the closeness of
games), provides a strong data set for empirically testing the
referee's issuance of penalties.
Our interest lies in measuring NHL referee behavior in both playoff
and regular season games. To account for the disproportionate amount of
revenue earned by the NHL in the playoffs (Leeds & von Allmen, 2004;
Robst et al., 2011), the sample includes all playoff games from
2006-2012 (n=599) and a randomly selected group of regular season games
(n=450) from the same seasons. The websites www.nhl.com and www.espn.com
were used for data collection.
Of primary interest is the number of power-play creating penalties
per period. A period based analysis of penalty counts is selected for
three reasons. First, we are concerned with the balancing of all penalty
calls, including those warranted and those that may be questionable.
Perceptions of fairness move beyond debatable calls that go each way,
and referees recognize that the totality of the game must be managed
sufficiently, not in constant response to a mistaken call. Second, with
two intermissions, officials have two opportunities to reflect upon how
the game has progressed. While this may not necessarily dictate how
referees call games, the breaks provide for analysis over a larger
period of time than the previous play-by-play data. Penalties are
awarded as the play dictates and referees are likely to be unable and
unwilling to alternate power play opportunities. Finally, penalty calls
need not be evened up with the same type of penalty. While other studies
of aggression measure the type of foul committed, balancing penalty
calls need not match a slashing call with a similar slash by an
opponent. In collecting data, matching minors or matching fighting
penalties are excluded as these do not give one side an advantage and
frequently involve lower degrees of judgment.
Our hypothesis is that teams with more penalties called on them
early in the game will receive fewer penalties later in the game, both
in terms of expected penalties compared to the opposition and the
frequency of playing future periods with more penalties. The dependent
variables for our analysis are second and third period penalty counts,
for each model respectively.
Each model uses a unique set of independent variables. For modeling
second period outcomes, information on penalties and score at the
conclusion of the first period was used. This includes a variable for
absolute goal differential (Tied, 1 goal, 2 goals, 3+ goals), if the
team is ahead (Yes/No), and the teams' penalty differential
entering the period. For modeling third period data, we use score and
penalty statistics from the end of the second period. Postseason fixed
effects also include indicators for the 7th game of a series (Yes/No) or
if the game was played in the Stanley Cup Finals (Yes/No). For regular
season models, a binary variable for attendance (High/Low) is determined
by the arena drawing at least 95% of its capacity for a particular game.
This variable is excluded from the playoff models due to all playoff
games being sold out. Additional fixed effects are included for team and
opponent in both populations to adjust for the tendency of certain teams
to give or receive higher or lower penalty counts. Each model is fit on
the penalty data from all teams, and, as in Buraimo et al. (2009), fits
are also estimated separately for home and away teams.
Penalties and score are recorded and tracked by period for the home
and road team, and an indicator for referee pairing is included. We
compare mean penalties per period given location, goal differential, and
penalty differential at the start of the period. Goal differential is
defined as the difference in the number of goals each team had scored
when the period began. A team's penalty differential is defined as
the difference between the number of power-play inducing penalties
previously called on that team and their opponent. For example, a
second-period penalty differential of three indicates that a team was
called for three more penalties than the opposition in first period.
Also, the frequency of finishing the second and third periods with
higher penalties, given previous penalty differentials, is calculated.
While previous work on penalties per period is scarce, Alan Ryder
(2004) suggested hockey outcomes can be approximated by a Poisson
distribution. A count variable falls under the Poisson distribution if
the observation time is fixed and the events operate independently and
at a constant rate over time. In hockey, penalties can be called at all
moments of a game, and the per-period length among both our populations
is 20 minutes. A Pearson [chi square] test for over- or underdispersion
can identify whether a data set appears to be drawn from a Poisson
distribution, and is used with our penalties per period information.
A generalized linear mixed effects model for Poisson data
(McCulloch & Neuhaus, 2001) is used for four dependent variables,
second and third period penalties in both the regular season and the
postseason. For periods showing over- or underdispersion, the variance
parameter of the Poisson fit is adjusted using a quasi-likelihood fit
(Wedderburn, 1974). In all models, we use random intercepts for each
referee pairing to account for the fact that the same set of referees
preside over multiple NHL games together. With 147 unique referee pairs
in our data, and because we are not interested in the specific behavior
of individual referees, this term is not considered as a fixed effect.
Results
Penalty Calls by Period
Mean 2nd and 3rd period penalties per team are shown in Table 1. In
postseason games, teams with a higher number of first period penalties
finished the second period with fewer penalties nearly twice as often as
the team with fewer first period penalties (46% vs. 26%, with the
remaining 28% an equal number of 2nd period penalties). This difference
is larger for the home team (50% vs. 21%), teams participating in the
Stanley Cup Finals (51% vs. 20%), and teams participating in postseason
Game 7 (58% vs. 5%).
Teams with more first period penalties in regular season games also
finished the second period with fewer penalties more often than their
opponents (43% vs. 29%). This difference was slightly higher in the
games reaching our 95% attendance cutoff (48% vs. 25%).
Figure 1 shows the effect of an unequal end of first-period penalty
differential on mean second period penalties per team. The strongest
effect is shown in postseason Game 7s, where teams whistled for more
first period penalties receive an average of 0.75 fewer second period
penalties.
The ratios of the mean and variance of second period penalties in
the postseason and regular season are 0.86 and 0.77, respectively,
suggesting Poisson models be adjusted for underdispersion using a
quasi-likelihood fit. The ratio of the mean and the variances of third
period penalties are 1.09 and 1.02, close enough to 1, as judged by a
lack of significance in the Pearson test for dispersion, to fit using a
traditional likelihood approach. The random intercept for referee
pairing is significant in all models, as judged by a likelihood ratio
test.
[FIGURE 1 OMITTED]
Effect estimates from our mixed effect models of second and third
period penalty counts, from the postseason and regular season groups,
are shown in Tables 2-5 alongside their standard errors. First period
penalty differential is a significant predictor for both home (rate
ratio 0.94, 95% CI 0.90--0.98) and away (Rate Ratio 0.91, 95% CI
0.87--0.94) second period postseason penalties (Table 2). In a Poisson
regression with explanatory variable X, a rate ratio is estimated by
[e.sup.[beta]], where [beta] is the coefficient on X. In this case, X
represents the first period penalty differential, and our estimate
suggests that for each increase of 1 in the end of first period penalty
differential between a home team and its opponent, that team will be
whistled for 6% fewer second period penalties. The effect estimate for
series round (Stanley Cup Finals vs. other) is borderline significant
(p<0.10), suggesting referees may call fewer penalties when stakes
are increased.
Table 3 presents shows estimates from our fit of third period
postseason penalties. Teams with more cumulative penalties than their
opponents entering the third period of postseason games are called for
fewer infractions than their opponents, with this effect slightly
stronger for home teams (RR 0.95, 95% CI 0.92-0.99) than away teams (RR
0.97, 95% CI 0.93-1.01). Effect estimates for the absolute goal
differential terms are large and statistically significant, suggesting
games entering the period with a larger absolute score differential
result in a significantly higher number of penalties than games tied at
the beginning of the period. This is consistent with prior research
indicating that fouls of aggression are more common when the opportunity
cost of winning the match is lower (Jewell, 2009).
Tables 4 and 5 show model estimates for regular season second and
third period penalties, respectively. First period penalty differential
is a strong predictor of second period penalties for the home team (RR
0.91, 95% CI 0.87-0.96) and a moderate predictor for the away team (RR
0.94, 95% CI 0.88-1.00). For third period regular season penalties, a
larger penalty differential at the beginning of the period results in a
significantly fewer number of calls on the home team (RR 0.95, 95% CI
0.91-0.99) but not for the away team (RR 0.99, 95% CI 0.95-1.04).
In all models, a fixed effect for whether or not the team is
playing with the lead entering the period is not a significant
predictor, and regular season penalty counts are not noticeably affected
by whether or not the game reached the 95% attendance cutoff.
Control Checks
Most penalties are called as a result of a player being put in a
defensive position; therefore, different proxies for aggressive behavior
were attempted to control for changes in player behavior. One proxy we
considered was shots on goal. Aggressive teams may register more
offensive possessions and draw more penalties. However, these same teams
may receive more penalties in the act of acquiring the puck to begin
with, thus negating the likelihood of gaining and advantage through more
time on offense. Inclusion of shots per period failed to improve our
models or modify the effect of penalty differential, suggesting that an
attacking offense does not correlate strongly with penalty outcomes.
While player behaviors do change throughout the game, the most
likely changes are tactical in nature. Losing teams may adjust which
lines receive more ice time and allow more ice time for strong offensive
players. However, this is likely counterbalanced by the leading
team's tactical shift of issuing more ice time to strong defenders
who are less likely to commit a penalty. This change in tactics, seen
through player behavior, reduces the risk that the results are due to
player, rather than referee, behaviors. These findings are consistent
with prior research on aggression and NHL referee actions (Heckelman
& Yates, 2003).
One potential issue with our design is that players and teams may
use a less aggressive style of play if they have already received a
larger number of penalty calls. In soccer and basketball, for example,
league rules enforce additional penalties to repeat in-game offenders
and their teams that might force competitors to adjust their style of
play. However, other than the penalty itself, hockey rules do not place
additional punishment on players or teams for higher frequencies of
penalty calls, except in the rare case that a player receives multiple
game misconduct penalties for severe infractions. As a result, because
they are allowed to continue aggressive behavior throughout the contest,
it seems plausible that hockey players are less likely to adjust their
aggressiveness compared to athletes in other sports. In our data, the
weak correlation between one team's first and second period
penalties (-0.03 for postseason, -0.05 for regular season), and a
team's cumulative first and second period penalties with their
third period penalties (0.00 for postseason, 0.03 for regular season)
suggest that team's do not noticeably change their aggressiveness
relative to previous infractions.
While Buraimo et al. (2009) used relative goal differential as a
predictor of soccer infractions using in-game data, absolute goal
differential was used in our models. As shown in Table 1, there does not
appear to be a consistent growth of penalty frequency by relative goal
differential. In fact, penalty counts appear to vary only with respect
to how far the score deviates from a tie game at the beginning of the
period. To check this claim, we estimated all of our models using
relative goal differential and compared these fits to the ones provided
in Tables 2-5 using the Akaike Information Criterion statistic.
Inclusion of absolute goal differential, instead of relative goal
differential, yielded roughly equivalent or much stronger fit statistics
in our models.
Prior research has also suggested that large markets or popular
teams may receive preferential treatment by officials (Price et al.,
2012). To account for this, we examined the difference in penalty
distribution based on presence in hockey's "Original
Six," which includes the teams from Boston, Toronto, Chicago,
Montreal, Detroit, and the New York Rangers. Inclusion of this variable
did not result in a significant improvement to the model.
Finally, to assess a possible association between regular and
postseason penalty behavior, we examined the correlation between regular
and postseason penalty rank, judged by the ranking of postseason
qualifiers in penalties per game. No strong positive correlations
between the rankings were found, and in some years, negative
correlations were found, suggesting style of play is dictated by mostly
by opponents and game strategies that change for the playoffs. In total,
these control checks provide some assurance that other factors, such as
player behaviors, have not unduly influenced the results.
Discussion
Our findings make several key contributions within the literature
on referee behaviors. First, by removing the assumption that referees
are continually biased towards home teams, we find that the penalty
frequency is determined by penalty differential and score of the game.
Second, this model recognizes the psychological desire for fairness
inherent in the role of a referee. The model incorporates how bias is
implemented and situational factors where one team is more likely to
receive a power play. Third, this model is built upon the recognition
that referees play a significant role in preserving the integrity of a
sporting league, along with the associated financial returns. Finally,
this research builds on the work of Buraimo et al. (2009) and Price et
al. (2012) by illustrating how officials institute bias in a different
sport. Our model demonstrates how and when preferences for fairness as
equality are implemented into the sport of hockey. In total, these
contributions better our understanding of the human element involved in
refereeing.
The hypothesis of make-up calls among NHL referees is enhanced by
looking at penalty calls in postseason overtime. In professional hockey,
games ending regulation in a tie move to the sudden death format, in
which the game ends after the first goal is scored. In 25 of the 134
postseason overtime games since 2006, at least two total penalties were
called. In 19 of the contests with multiple penalties (76%), the second
power play was awarded to the team that was called for the first
penalty. We would expect the second power play to be awarded to the
opposite team 50% of the time. However, this sample proportion is
significantly different from 0.5, as judged using a 1-sample z-test for
proportions (p <0.01). Thus, in the most intense moments of the most
important games, the tendency for a reversal of penalties appears to be
the strongest.
In our data set, for both regular and postseason and in both second
and third periods, teams with more penalties entering the period were
called for fewer infractions. The effect of penalty differential was
relatively similar comparing regular and postseason play, with stronger
effects evident for the home team. Our findings complement the recent
work of Mongeon and Mittelhammer (2011), which used continuous flow to
suggest that referees use make-up calls to keep games close in the
regular season. While play-by-play data may reveal within-period changes
in behavior, discretizing by period offers the advantage in that at the
end of each period, team personnel is mostly reset. As a result, a
reversal in a penalty call is less likely to be effected by the changes
in on-ice personnel that occur with each result of a power play.
To consider the possibility that the effect of penalty differential
is modified by one of our other fixed effects, we also tested the
significance of two-way interaction terms between each fixed effect and
penalty differential entering the period. The only two marginally
significant interaction terms linked Game 7 status with penalty
differential for second period postseason data (Table 6), and games
reaching our attendance cutoff with penalty differential in our second
period regular season model (Table 7). Combined with Figure 1, the
estimates in Table 7 provide moderate evidence that the effect of prior
penalty differential is largest when games are played in front of larger
crowds. While we used a binary cutoff of 95% attendance to indicate
games that were more highly attended, the p-value for our interaction
term between penalty differential and our attendance variable was at
least moderately significant (p < 0.10) using all integer cutoffs
between 90 and 99%.
While this analysis is able to illustrate situations where one team
is more likely to be called for a penalty, the impact on the overall
outcome of the game is mostly undetermined. In our sample, we looked at
the effect of prior penalty differential on the likelihood of each team
winning the game. Because teams with more penalties earlier in games are
receiving more power play opportunities later in games, it is plausible
that such teams are more likely to win these contests. This extends the
work of Widmeyer and Birch (1984) by providing a rationale for their
observation that aggressive teams early in games are more likely to win.
Among postseason games tied at the end of the first period, the
team with more first period penalties was significantly more likely to
win the contest (OR 1.20, 95% CI, 1.07-1.33) than the team with fewer
first period penalties. In postseason games tied after the second
period, we found moderate evidence that the team with higher cumulative
first and second period penalties was more likely to win the game (OR
1.13, 95% CI 1.00-1.28). No significant evidence of an increased
likelihood of winning existed in regular season games for either period.
Conclusion
Our analysis identifies how referees may issue "even-up"
calls over the course of a professional hockey game to achieve
perceptions of balance and fairness. In-game analysis finds significant
evidence that referees exhibit a form of "biased impartiality"
when a team has a negative penalty differential, and there is support
that this effect is strongest in games when the referees are under the
most pressure. Results also suggest this tendency may be stronger for
the home team.
However, there are a number of limitations to the model of
officiating. In using only hockey in the sample, the same types of
behaviors may not be found in other sports or other industries. The
linkage between game situation and referee behavior may not be as
prevalent in other settings. Idiosyncratic characteristics unique to
hockey may also fail to carry over to other samples. Additionally, the
data in this study is limited based on categorization by period, rather
than as a continuous flow during the game. Further research that tracks
penalty calls by time rather than period may provide further
illumination into the actions of referees. Finally, all infractions
(roughing, boarding, interference, etc.) were counted the same in this
analysis. Referees may penalize specific behaviors with greater
regularity when attempting to even up calls. Research into these details
may provide additional enlightenment into how referees achieve their
biased impartiality.
Beyond the additions mentioned above, future studies building on
this work are numerous. Exploring other sports or professions could
provide new insight into areas of biased impartiality. While this study
only consists of games, a longitudinal study of the NHL could map
different changes in league and referee incentives towards developing
the game on and off the ice. Extensions of this study may also include
how consumers respond to changes in refereeing behavior.
In conclusion, the model derived from this research illustrates how
NHL referees even up penalty calls to increase perceptions of fairness.
The effect of these calls is to balance scoring opportunities and
ultimately, the number of games won or lost by each team. This study is
unique in its approach of examining how bias may evolve through the
course of a game. In contrast to studies concerned with only the final
outcome, this isolation of bias effect provides greater insight into
referee behaviors and motivations. Although long debated by spectators,
players, and coaches, empirical evidence supports the idea that referees
even up penalty calls in the spirit of equal opportunity and financial
incentive.
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Michael J. Lopez [1] and Kevin Snyder [2]
[1] Brown University
[2] Southern New Hampshire University
Michael J. Lopez is a PhD candidate in the Department of
Biostatistics in the Brown University School of Public Health. His
research interests include the application of statistical methods to
identify trends and responses to incentives in sport.
Kevin Snyder is an assistant professor of sport management at
Southern New Hampshire University. His interests include sport
management and business strategy in the innovation and knowledge
services.
Table 1: Mean (SE) Penalties per Period
2nd period
Postseason Regular
season
Team Home 1.44 (0.05) 1.44 (0.05)
Away 1.70 (0.05) 1.52 (0.05)
Penalty Fewer penalties 1.80 (0.06) 1.71 (0.06)
differential Even penalties 1.63 (0.06) 1.35 (0.06)
at start of More penalties 1.46 (0.06) 1.37 (0.06)
period
Goal Down 3+ goals 2.43 (0.32) 1.64 (0.27)
differential Down 2 goals 1.57 (0.11) 1.36 (0.12)
at start of Down 1 goal 1.59 (0.07) 1.44 (0.08)
period Tied 1.53 (0.06) 1.49 (0.06)
Ahead 1 goal 1.70 (0.07) 1.40 (0.08)
Ahead 2 goals 1.60 (0.13) 1.68 (0.12)
Ahead 3+ goals 2.20 (0.27) 1.88 (0.21)
3rd period
Postseason Regular
season
Team 1.27 (0.05) 1.17 (0.05)
1.42 (0.05) 1.29 (0.05)
Penalty 1.44 (0.05) 1.31 (0.05)
differential 1.26 (0.07) 1.07 (0.07)
at start of 1.30 (0.06) 1.19 (0.06)
period
Goal 1.99 (0.18) 1.54 (0.15)
differential 1.54 (0.12) 1.18 (0.11)
at start of 1.20 (0.08) 1.20 (0.08)
period 1.07 (0.06) 1.04 (0.07)
1.26 (0.07) 1.29 (0.07)
1.53 (0.10) 1.09 (0.09)
1.73 (0.14) 1.48 (0.14)
Table 2: Estimates (SE) from Generalized Linear Mixed Model (GLMM)
of log(2nd Period Penalties) from Postseason Games
Model
Overall Home teams
(n = 1198) (n = 599)
Intercept 0.974 (0.100) ** 0.879 (0.142) **
Penalty differential -0.075 (0.014) ** -0.062 (0.022) **
after P1
Ahead (yes vs. no) 0.009 (0.051) 0.014 (0.078)
Score differential 0.059 (0.054) 0.057 (0.084)
(1 vs. tied) after P1
Score differential 0.062 (0.070) -0.009 (0.107)
(2 vs. tied) after P1
Score differential 0.362 (0.092) ** 0.247 (0.143) *
(3+ vs. tied) after P1
Cup finals (yes vs. no) -0.172 (0.092) * -0.225 (0.133) *
Game 7 (yes vs. no) -0.183 (0.112) -0.332 (0.180) *
Home team (yes vs. no) -0.121 (0.040) ** NA
Away teams
(n = 599)
Intercept 0.921 (0.130) **
Penalty differential -0.097 (0.020) **
after P1
Ahead (yes vs. no) 0.004 (0.071)
Score differential 0.054 (0.072)
(1 vs. tied) after P1
Score differential 0.138 (0.093)
(2 vs. tied) after P1
Score differential 0.461 (0.120) *
(3+ vs. tied) after P1
Cup finals (yes vs. no) -0.112 (0.116)
Game 7 (yes vs. no) -0.064 (0.139)
Home team (yes vs. no) NA
Note: All models include random effects for referee pairing and
adjustments for team and opponent. Score differential represents
the absolute value of the difference in the score between the two
teams at the beginning of the period, with a tie game used as
the reference category.
** p < 0.01
* p < 0.10
Table 3: Estimates (SE) from Generalized Linear Mixed Model
(GLMM) of log(3rd Period Penalties) from Postseason Games
Model
Overall Home teams
(n = 1198) (n = 599)
Intercept 0.630 (0.130) ** 0.405 (0.178) **
Penalty differential -0.041 (0.013) ** -0.053 (0.019) **
after P2
Ahead (yes vs. no) -0.051 (0.056) -0.043 (0.079)
Score differential 0.123 (0.071) * 0.203 (0.102) *
(1 vs. tied) after P2
Score differential 0.347 (0.079) ** 0.350 (0.114) **
(2 vs. tied) after P2
Score differential 0.528 (0.080) ** 0.554 (0.116) **
(3+ vs. tied) after P2
Cup finals (yes vs. no) -0.140 (0.113) -0.277 (0.157) *
Game 7 (yes vs. no) -0.161 (0.132) -0.074 (0.183)
Home team (yes vs. no) -0.135 (0.050) ** NA
Away teams
(n = 599)
Intercept 0.686 (0.175) **
Penalty differential -0.032 (0.019) *
after P2
Ahead (yes vs. no) -0.022 (0.082)
Score differential 0.099 (0.101)
(1 vs. tied) after P2
Score differential 0.369 (0.110) **
(2 vs. tied) after P2
Score differential 0.545 (0.111) **
(3+ vs. tied) after P2
Cup finals (yes vs. no) -0.035 (0.151)
Game 7 (yes vs. no) -0.205 (0.191)
Home team (yes vs. no) NA
Note: All models include random effects for referee pairing
and adjustments for team and opponent.
** p < 0.01
* p < 0.10
Table 4: Estimates (SE) from Generalized Linear Mixed Model (GLMM)
of log(2nd Period Penalties) from Regular Season Games
Model
Overall Home teams
(n = 900) (n = 450)
Intercept 0.426 (0.059) ** 0.269 (0.190)
Penalty differential after P1-0.075 (0.018) ** -0.092 (0.026) **
Ahead (yes vs. no) -0.077 (0.051) -0.075 (0.073)
Score differential -0.049 (0.056) -0.046 (0.081)
(1 vs. tied) after P1
Score differential 0.020 (0.073) 0.029 (0.106)
(2 vs. tied) after P1
Score differential 0.172 (0.104)* -0.003 (0.164)
(3+ vs. tied) after P1
Attendance > 95% 0.037 (0.052) 0.122 (0.101)
Home team (Yes vs. No) -0.055 (0.049) NA
Away teams
(n = 450)
Intercept 0.600 (0.200) **
Penalty differential after -0.060 (0.031) *
Ahead (yes vs. no) -0.053 (0.089)
Score differential -0.059 (0.084)
(1 vs. tied) after P1
Score differential -0.028 (0.118)
(2 vs. tied) after P1
Score differential 0.298 (0.153) *
(3+ vs. tied) after P1
Attendance > 95% -0.023 (0.084)
Home team (Yes vs. No) NA
Note: All models include random effects for referee pairing
and adjustments for team and opponent.
** p< 0.01
* p < 0.10
Table 5: Estimates (SE) from Generalized Linear Mixed Model
(GLMM) of log(3nd Period Penalties) from Regular Season
Games
Model
Overall Home teams
(n = 900) (n = 450)
Intercept -0.008 (0.174) -0.220 (0.233)
Penalty differential -0.035 (0.015) * -0.053 (0.020) **
after P2
Ahead (yes vs. no) 0.006 (0.063) 0.104 (0.092)
Score differential 0.151 (0.088) * 0.054 (0.122)
(1 vs. tied) after P2
Score differential 0.044 (0.098) -0.035 (0.139)
(2 vs. tied) after P2
Score differential 0.357 (0.098) ** 0.309 (0.139) *
(3+ vs. tied) after P2
Attendance > 95% -0.035 (0.066) -0.040 (0.109)
Home team (yes vs. no) -0.099 (0.057) * NA
Away teams
(n = 450)
Intercept 0.094 (0.260)
Penalty differential -0.010 (0.023)
after P2
Ahead (yes vs. no) -0.041 (0.17)
Score differential 0.243 (0.131)
(1 vs. tied) after P2
Score differential 0.081 (0.141)
(2 vs. tied) after P2
Score differential 0.370 (0.149) *
(3+ vs. tied) after P2
Attendance > 95% 0.007 (0.098)
Home team (yes vs. no) NA
Note: All models include random effects for referee pairing
and adjustments for team and opponent.
** p < 0.01
* p< 0.10
Table 6: Estimates (SE) from Generalized Linear Mixed Model
(GLMM) of log(2nd Period Penalties) from Postseason Games, Including
Interaction Term
Model
Overall Home teams
(n = 1198) (n = 599)
Intercept 0.979 (0.100) ** 0.879 (0.142) **
Penalty differential -0.070 (0.015) ** -0.062 (0.022) **
after P1
Ahead (yes vs. no) 0.009 (0.051) 0.014 (0.078)
Score differential 0.058 (0.054) 0.057 (0.084)
(1 vs. tied) after P1
Score differential 0.062 (0.070) -0.009 (0.107)
(2 vs. tied) after P1
Score differential 0.361 (0.092) ** 0.247 (0.143) *
(3+ vs. tied) after P1
Cup Finals (yes vs. no) -0.169 (0.092) * -0.225 (0.133) *
Game 7 (yes vs. no) -0.210 (0.112) * -0.331 (0.181) *
Home team (yes vs. no) -0.120 (0.040) ** NA
Penalty differential -0.139 (0.082) * 0.007 (0.140)
after P1 * game7
Away teams
(n =599)
Intercept 0.953 (0.131) **
Penalty differential -0.097 (0.020) **
after P1
Ahead (yes vs. no) 0.010 (0.071)
Score differential 0.044 (0.072)
(1 vs. tied) after P1
Score differential 0.130 (0.093)
(2 vs. tied) after P1
Score differential 0.451 (0.120) **
(3+ vs. tied) after P1
Cup Finals (yes vs. no) -0.099 (0.116)
Game 7 (yes vs. no) -0.113 (0.145)
Home team (yes vs. no) NA
Penalty differential -0.241 (0.106) *
after P1 *game7
Note: All models include random effects for referee pairing and
adjustments for team and opponent. Score differential represents
the absolute value of the difference in the
score between the two teams at the beginning of the period,
with a tie game used as the reference category.
** p < 0.01
* p< 0.10
Table 7: Estimates (SE) from Generalized Linear Mixed Model
(GLMM) of log(2nd Period Penalties) from Regular Season Games,
Including Interaction Term
Model
Overall Home teams
(n = 900) (n = 450)
Intercept 0.409 (0.147) ** 0.278 (0.202)
Penalty differential -0.021 (0.030) -0.025 (0.046)
after P1
Ahead (yes vs. no) -0.078 (0.052) -0.077 (0.073)
Score differential -0.055 (0.057) -0.070 (0.082)
(1 vs. tied) after P1
Score differential 0.003 (0.074) 0.018 (0.106)
(2 vs. tied) after P1
Score differential 0.149 (0.106) -0.051 (0.166)
(3+ vs. tied) after P1
Attendance > 95% 0.036 (0.056) 0.134 (0.102)
Home team (yes vs. no) -0.062 (0.050) NA
Penalty differential after -0.089 (0.037) * -0.104 (0.056) *
P1 * attendance > 95%
Away teams
(n = 450)
Intercept 0.441 (0.210) *
Penalty differential 0.026 (0.038) *
after P1
Ahead (yes vs. no) -0.057 (0.089)
Score differential -0.046 (0.083)
(1 vs. tied) after P1
Score differential -0.031 (0.113)
(2 vs. tied) after P1
Score differential 0.327 (0.156) *
(3+ vs. tied) after P1
Attendance > 95% -0.035 (0.084)
Home team (yes vs. no) NA
Penalty differential after -0.130 (0.052) *
P1 * attendance > 95%
Note: All models include random effects for referee pairing
and adjustments for team, season, and opponent.
** p < 0.01
* p < 0.10
