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A relationship between temperature and aggression in NFL football penalties
Curtis Craig , Randy W. Overbeek , Miles V. Condon , Shannon B. Rinaldo
PII: S2095-2546(15)00002-2
DOI: 10.1016/j.jshs.2015.01.001
Reference: JSHS 161
To appear in:
Journal of Sport and Health Science
Please cite this article as: Craig C, Overbeek RW, Condon MV, Rinaldo SB, A relationship between
temperature and aggression in NFL football penalties, Journal of Sport and Health Science (2015), doi:
10.1016/j.jshs.2015.01.001.
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Running head: TEMPERATURE AND AGGRESSION IN FOOTBALL 1
Original article
A relationship between temperature and aggression in NFL football penalties
Curtis Craig
a
, Randy W Overbeek
a
, Miles V Condon
b
, Shannon B Rinaldo
b
a
Department of Psychology, Texas Tech University, Lubbock, Texas 79401, USA
b
Department of Marketing, Texas Tech University, Lubbock, Texas 79401, USA
Corresponding author: Curtis Craig
E-mail address: curtis.craig@ttu.edu
Running head: Temperature and aggression in football
Received 28 February 2014; revised 12 June 2014; accepted 17 September 2014
Abstract
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Purpose: Increased ambient temperature has been implicated in increased physical aggression,
which has important practical consequences. The present study investigates this established
relationship between aggressive behavior and ambient temperature in the highly aggressive
context of professional football in the national football league (NFL).
Methods: Using a publicly available dataset, authors conducted multiple hierarchical regression
analyses on game-level data (2326 games).
Results: The analysis revealed that temperature positively predicted aggressive penalties in
football, and that this relationship was significant for teams playing at home but not for visiting
teams.
Conclusion: These results indicate that even in the aggressive context of football, warmer
weather contributes to increased violence. Further, the presence of the heat-aggression
relationship for the home team suggests that the characteristics of interacting groups may
influence whether heat would have an adverse effect on the outcome of those interactions.
Keywords: Aggression; American football; Intergroup; Sports; Temperature;
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1. Introduction
Weather is an environmental characteristic that influences affect and cognition. In fact,
researchers have shown that ambient temperature is the primary factor in this relationship.
1
The
experience of warm spring weather is associated with increased positive affect and broadened
cognition, while hotter summer weather is associated with decreased positive affect and
frustration and winter weather associated with more depressive symptoms. A consequence of
decreased positive affect in hot weather is an increase in aggressive acts of violence.
2-4
Anderson
and colleagues
3
investigated rates of violent crime and property crime in the United States over a
45-year period and demonstrated more violent assaults with temperature increases, after
controlling for population and age.
Several models have been explored in the literature to explain the relationship between
temperature and aggression. The predominant model is General Aggression Model,
5-7
which
suggests there are combinations of inputs that impact the internal states of the individual (e.g.,
anger), such as environmental/situational factors and personal tendencies (e.g., poor self-
control). These inputs then influence decision making processes that determine whether a
behavioral outcome is aggressive. In this model, ambient temperature is an environmental input
biasing both affect (e.g., irritation) and mental schemas toward aggression.
The importance of the heat-aggression relationship becomes more concerning, given the
recognition of climate change and the possible impact of increased average global temperature
on human interaction, with growing evidence linking warmer temperatures to intergroup conflict
frequency.
8
Also, given the continued growth of the human population
9
and the known
relationship between population growth, conflict, and warfare,
10
an understanding of the
characteristics such as heat that affect the nature of human violence is essential. An overview of
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potential effects of increasing global temperature on human society reveals several broad
categories of negative consequence, including but not limited to increasing civil unrest, higher
individual irritation, and an increasing tendency to perceive aggression in others.
11
Given the concern of increased intergroup conflict due to population increase and
increased global temperatures, heat and aggression would be important to study in an intergroup
context. Previous research on intergroup emotions and aggression have found that the primary
predictor between individual endorsement of offensive actions towards outgroups is the
perceived strength of the ingroup (e.g., size), although this relationship is mediated by reported
experience of anger.
12
The rationale for this relationship is unclear, but it may be due to a rapid
calculation that intergroup competition between members of social species makes necessary. As
an example of this, ingroup chimpanzees are significantly more likely to act aggressive toward
an outgroup intruder when the ingroup has the numerical advantage.
13
Given that heat
contributes to negative affective states such as anger, which mediates the ingroup strength and
offensive action relationship, one could anticipate that the heat-aggression relationship is more
pronounced for contexts where one group has more perceived support than the other group.
1.1. Sports, heat, and aggression
Researchers have extended the investigation of temperature and aggression to team
sports, as they provide a unique and well-defined natural experiment. Highly competitive games
involve precarious social relationships; therefore, ambient temperature is likely to influence
behavioral outcomes during games. In baseball, as temperature increases, so does the number of
batters struck by a pitch. Reifman et al.
14
suggest that rising temperatures result in aggressive
tendencies in players, leading to intentional aggressive throws by pitchers. Further research in
baseball demonstrated that in even hotter conditions, if teammates have been struck by the
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opposing team’s pitcher, pitchers are more likely to retaliate by hitting the batter with the ball,
particularly with increasing number of teammates struck.
15
1.2. Present study
The national football league (NFL) football season is ideal for examining the heat-
aggression phenomenon, as football is played in the colder fall, winter, and spring seasons,
allowing for a wide range of available temperatures to explore the heat-aggression relationship.
The variability in location is also important as weather turns cool in northern states earlier and
temperatures are elevated longer in southern states.
More importantly, NFL football is a contact sport, which may be considered especially
aggressive, as evidenced by the increased risk of traumatic brain injury
16,17
and cognitive
dysfunction
18
following participation. Therefore, examining data from football games allows
consideration and analysis of the effect of ambient temperature on aggression in a heightened
aggression setting, and allows investigation of whether high ambient temperature retains its
influence to increase aggressive acts. Though football may be considered aggressive in general,
combative penalties (e.g., unnecessary roughness) can distinguish between hostile (or affective)
aggression, which may be sensitive to temperature, and instrumental or purposeful aggression.
The context of football allows for an investigation into the relationship between heat,
physical aggression, and intergroup dynamics. Given the aforementioned findings on increased
ingroup support contributing to aggressive action, football teams playing at home (high ingroup
support) are more likely to commit acts of aggression against the opposing team, particularly
under conditions of high ambient temperature as heat contributes to negative affective states such
as anger. Furthermore, heat is more likely to contribute to aggression by influencing the internal
state of home team players, who are more apt to experience territoriality and pressure because
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they perform on their own turf and before the home crowd.
19
The present study investigates the
issue by using football as the context to first verify whether the heat-aggression relationship
exists, and then determine whether the relationship holds true for both home teams and away
teams.
There is also some debate on whether the relationship between temperature and
aggression is linear or non-linear.
20-22
There is some evidence that the relationship is curvilinear
when the ability to escape both heat and social contact is taken into account. However, re-
analyses of these data have primarily found a linear relationship, particularly during periods of
high violence risk,
23
which suggests that in the high physical context of NFL football a linear
relationship should be present between temperature and aggressive penalties.
The finding of increased aggression in higher temperatures would have significant
implications for other aggression contexts where the ambient temperature varies. These contexts
can include other aggressive sports such as rugby, but of more concern are those situations where
lives are at stake, such as mass protests and warfare. Therefore, we predict that a significant
linear relationship between temperature and aggressive penalties will be found, despite the
already aggressive context of the sport, and that this relationship will hold true for home teams
but not visiting teams due to the perceived ingroup support of home teams.
2. Methods
To explore the temperature and aggression relationship in football, the authors obtained
publicly available, secondary data from the website Armchair Analysis.
24
It contained game-
level data for all games in the NFL seasons 2000-2011. Variables included but were not limited
to information on game-day temperature, points by home team and away team, number and type
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of penalties. Each game functioned as an independent unit of analysis, generating data for the
variables of interest.
2.1. Game characteristics and measures
Two thousand three-hundred and twenty six games included all required measures and
were analyzed after excluding one game as an outlier due to an excessive number of penalties.
The descriptive statistics are presented in Table 1. The average temperature per game was 58.27
, ranging from -1 to 109 . As the temperature information is particularly important, mean
temperature is 59.01 (SD = 16.43) with a median of 61, temperature skewness is -0.390 (SD =
0.046), and kurtosis is -0.163 (SD = 0.093), The 10th percentile is 36, 25th percentile is 48, 50th
percentile is 61, 75th percentile is 70, and 90th percentile is 80. Considering the games with
temperature data, 173 of them were below freezing and 97 above 85 . Humidity was included
as a control variable, because high humidity is uncomfortable
25
and discomfort is thought to be
related to negative affect.
4
The humidity considered here is relative humidity, the percentage of
water vapor (partial pressure/saturated pressure) present at a given temperature. Average point
spread between teams was included as a control variable. Scores from the home and visitor teams
were aggregated to provide a total points score for each game. Penalties such as taunting, face
masks, unnecessary roughness, and unsportsmanlike conduct were coded as aggressive. All other
penalties are coded as non-aggressive. Besides total non-aggressive and total aggressive
penalties, aggressive penalty counts were measured separately for both the home teams and the
away teams. In order to verify whether team level tendencies would significantly affect the
following analyses, a simple ANOVA found that there was a significant effect of teams on
visitor aggressive penalties (F(31, 3155) = 2.141, p < 0.001) and on home aggressive penalties
(F(31, 3155) = 2.044, p = 0.001). However, including temperature as a covariate, the interaction
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between team and temperature is not significant for visitors (F(31, 2723) = 873, p = 0.668) or
home (F(31, 2723) = 0.907, p = 0.583). This implies that temperature effects do not interact with
specific team predilections. Other potential control variables such as the southern culture of
honor
26
were excluded from the analysis as substantive prior research
27-29
has found that
particular variable confounded with temperature, as the southern regions of the U.S. tend to be
hotter than other regions.
3. Results
Multiple simultaneous regression analyses were performed to determine if temperature
predicted the amount of aggressive penalties (1) overall, (2) for the home team, and (3) for the
visiting team. Corresponding logistic regressions were also performed alongside the standard
ordinary least squares regression analyses, and while not reported here, the results were highly
similar. The correlation matrix is presented in Table 2. The results indicate that for overall
aggressive penalties: non-aggressive penalties and total game points accounted for a significant
amount of the variance (R
2
= 0.037, F (5, 2320) = 17.877, p < 0.001). Total game points, non-
aggressive (technical) penalties, and ambient temperature were all significantly associated with
more aggressive penalties, but point spread and humidity were not (Table 3). Controlling for the
other variables, temperature significantly predicted aggressive penalties (β = 0.055, p = 0.008). A
follow-up analysis also found that temperature significantly predicts non-aggressive penalties (β
= 0.158, p < 0.001), when controlling for total game points, point spread, and humidity.
Total game points, non-aggressive penalties, visitor aggressive penalties, and ambient
temperature were all significantly associated with more home aggressive penalties, but point
spread and humidity were not (Table 4). Controlling for the other variables, temperature
significantly predicted home aggressive penalties (β = 0.060, p = 0.004).
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Total game points, non-aggressive penalties, and home aggressive penalties were all
significantly associated with more visitor aggressive penalties, but point spread, humidity, and
temperature were not (Table 5). Controlling for the other variables, temperature did not
significantly predict visitor aggressive penalties (β = 0.013, p = 0.546). Given that a heat effect
was found for home aggressive penalties and not for visitor aggressive penalties, a repeated
measures ANOVA was conducted with aggressive penalties as the dependent variable, team
(visitor vs. home) as the repeated measures factor, and temperature, total points, point spread,
humidity, and non-aggressive penalties as covariates. However, there was no significant
interaction between temperature and the team repeated measures factor (F(1, 2320) = 2.194, p =
0.193).
Visitor team aggressive penalties correlates with home team aggressive penalties (r(2324)
= 0.165, p < 0.001). To determine if temperature influences reciprocal aggression or retaliatory
behavior in football as it does in baseball,
14
two regressions were conducted. Controlling for total
game points, point spread, non-aggressive penalties, humidity, home aggressive penalties, and
temperature, the interaction between home aggressive penalties and temperature was not a
significant predictor of visitor aggressive penalties (β = -0.010, t(2318) = -0.515, p = 0.607).
The equivalent analysis, controlling for the same variables, found that the interaction between
visitor aggressive penalties and temperature was not a significant predictor of home aggressive
penalties (β = 0.003, t(2318) = 0.133, p = 0.895). This suggests that temperature does not
influence the proneness towards reciprocal aggression in football, at least as measured by
aggressive penalties.
To determine whether the relationship between temperature and aggressive penalties was
linear or non-linear in nature, the standardized temperature values (z-scores) were squared and
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cubed into temperature squared (Temperature
2
) and temperature cubed (Temperature
3
). Game
points, point spread, non-aggressive penalties, and humidity were entered as control variables.
The model was significant (R
2
= 0.039, F(7, 2318) = 13.419, p < 0.001). Temperature was
significant, primarily the linear temperature term (β = 0.087, p = 0.009, Table 6 and Fig. 1 ) and
secondarily by the quadratic term (β = -0.049, p = 0.047).
4. Discussion
The goal of this study was to examine whether a linear relationship exists between
temperature and aggression in the context of football, an intensely physical contact sport. To do
so, we operationalized aggression by classifying certain penalties as aggressive, and then
determined whether this relationship held true for both home and away teams.
The present study provides an extension of the previous research in baseball by
employing a broader range of available temperatures, and by testing the heat-aggression
hypothesis in the context of already substantial aggression inherent in the game. The initial
analysis found that temperature had a significant effect on aggressive penalties, coinciding with
the previous work demonstrating the relationship between temperature and criminal acts,
3
as well
as between temperature and aggression in baseball.
14,15
This significant relationship persisted
when controlling for total team points, humidity, point spread, and other types of penalties. The
relationship was positive, indicating that more aggressive penalties occurred as the temperature
increased, even in the more aggressive social context of football. Temperature also positively
predicted non-aggressive penalties, consistent with human performance research literature
demonstrating higher rates of errors in complex perceptual-motor tasks during high
temperatures.
30,31
Aggressive penalties remained significant after controlling for non-aggressive
penalties, implying the two penalty types are distinct.
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The pattern of results changed when aggressive penalties were analyzed separately
between home and visiting teams. The relationship was significant for aggressive penalties
committed by the home team, but not for those committed by the visiting team. These diverging
results imply that the social context also has a role to play in whether temperature will lead to
increased aggression. In the context of football, playing in front of supportive fans may garner a
sense of high ingroup support, which leads to increased acts of aggression towards opposing
teams, and allows temperature to play a significant role in being overly aggressive towards the
visiting team. This finding has relevance for other domains in which intergroup interactions
occur, particularly between dominant groups and weaker groups. For example, developmental
research considering peer group effects on bullying have supported the relationship of social
groups on aggression when studying adolescent bullying.
32,33
However, the interpretation of
these results should be taken cautiously as the expected interaction was not significant, perhaps
due to power issues and few games being played at exceptionally high temperatures (more than
85 ℉).
The total amount of variance explained was significant when entering in both linear and
non-linear terms simultaneously, with both the linear and non-linear term β coefficients
significantly predicting aggressive penalties. The variance accounted for was similar to those
reported by the previously discussed baseball studies.
14
This, along with the higher value of the β
weight for the linear term relative to the non-linear term, suggests that aggressive penalties are
more frequently performed in hot weather. Researchers have argued a primarily linear heat-
aggression relationship, with hotter temperatures leading to more aggression and cooler
temperatures leading to less aggression.
20
Although there is some dispute on whether there is a
linear or curvilinear relationship between temperature and aggression,
22
the weight of the
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evidence is for a linear relationship once proper methodological approaches are utilized,
23
and
the present study generally supports a linear relationship.
4.1. Limitations
A few limitations arise in the present analysis. Given that the identification of penalties
requires the subjective judgment of refereeing officials, an analysis would not be comprehensive
without considering and controlling for their involvement. However, the present dataset lacks
any data on referees. A future study would be helpful in delineating the influence of referees, as
perhaps irritated or hot referees may be prone to call penalties, particularly those labeled here as
aggressive. As a corollary, the size of the crowd may influence both the group dynamics and the
referees’ judgments. Heat and irritation increases the perception of aggression in others.
29
A
related limitation is that there is only one measure of aggression in the present study, which
could be bolstered by other measures not available in the present data, such as type and
frequency of injuries.
Also, the present study is not immune to the problem of restriction of range, which is an
issue in temperature-aggression research. When looking at large datasets with the primary
interest being effects at the tails of the distribution sample, the bulk of the sample tends to
gravitate around the mean (normal curve) and this tends to outweigh patterns occurring at the
extremes of the distribution in analyses.
21
Given that extremely high temperatures are uncommon
and moderate temperatures are more common, this leads to less information to utilize when
considering these extremes. Also, modern football stadiums are usually built to be cool and air-
conditioned, further restricting the range of temperature data points in the present study.
Somewhat related to the range limitation, the second limitation notes that although the
analysis suggested the relationship between temperature and aggressive penalties in football to
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be linear, close consideration of Fig. 1 would show a small dip in temperatures somewhat
consistent with a curvilinear relationship as the significant non-linear term indicates, implying
that the current data should be interpreted cautiously. The reason may be that while irritability
increases at extremely high temperatures, heat stress and fatigue also increase with high physical
activity, leading to reduced ability to commit aggressive physical acts in the context of an
intensely athletic game such as football. This explanation is drawn from research studying
environmental effects as heat on industrial work and construction,
34
as well as reasonable
speculation in the heat hypothesis literature that significant physical activity contributing to
violence is unlikely in temperature outside the normal range.
35
5. Conclusion
High temperature leads to increased aggression, and this relationship appears in many
areas of life. This study generalizes this relationship to the sport of football, and suggests that the
temperature and aggression relationship is linear. Furthermore, the relationship appears to be
affected by social context, with only home team aggression being affected by high heat, which
has implications for intergroup conflict. Future research should consider other social contexts
that may be relevant to see if these results generalize, and also determine how heat influences
aggressive acts even in situations of high conflict, such as civil disputes, protests, and warfare
11
.
Acknowledgment
The authors wish to thank Dennis Erny and the team at Armchair Analysis for
maintaining their database and being willing to share sports data for academic research.
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Table 1
Descriptive statistics of the analyzed game level data (n = 2326).
Measure
Min Max Mean SD
Temperature ()
-1 109 58.274 16.967
Humidity (%)
0 100 58.795 20.019
Game points
3 106 41.892 14.215
Point spread
0 24 5.373 3.396
Aggressive penalties
0 9 2.074 1.629
Aggessive penalties for visiting team
0 6 1.045 1.076
Aggressive penalties for home team
0 6 1.030 1.058
Non-aggressive penalties
2 32 12.178 4.308
Non-aggressive penalties for visiting team
0 20 6.319 2.933
Non-aggressive penalties for home team
0 18 5.859 2.729
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Table 2
Correlation matrix of the analyzed game level variables (n = 2326)
1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
1. Temperature
—
2. Humidty -0.131**
—
3. Game points -0.017 0
.000
—
4. Point spread -0.091** -0
.031
0.001
—
5. Aggressive penalties 0.071** -0.01
2
0.082**
-0
.027
—
6. Aggressive penalties for
visiting team 0.035 -0
.004
0.056**
-0
.026
0.768**
—
7. Aggressive penalties for home
team 0.074** -0
.015
0.069**
-0
.015
0.758** 0.165**
—
8. Non-aggressive penalties 0.099** -0
.019
0.027
-0
.038
0.166** 0.134**
0.120**
—
9. Non-aggressive penalties for
visiting team 0.061** -0
.014
0.010
-0
.027
0.123** 0.094**
0.094**
0.780**
—
10. Non-aggressive penalties for
home team 0.091** -0
.015
0.032
-0
.030
0.130** 0.110**
0.089**
0.740**
0.157**
—
*p < 0.05; **p < 0 .01.
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Running head: TEMPERATURE AND AGGRESSION IN FOOTBALL 20
Table 3
Regression on overall aggressive penalties.
Measure
B B SE β t p
(Constant)
0.714 0.220
—
3.243 0.001
Game points
0.009 0.002 0.078 3.847 < 0.001
Point spread
-0.008 0.010 -0.016 -0.790 0.430
Non-aggressive penalties
0.060 0.008 0.158 7.715 < 0.001
Humidity
0.000 0.002 -0.002 -0.110 0.912
Temperature
0.005 0.002 0.055 2.665 0.008
Note: R
2
= 0.037, F(5, 2320) = 17.877, p < 0.001.
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Table 4
Regression predicting aggressive penalties for the home team.
Measure
B B SE β t p
(Constant)
0.220 0.143
—
1.542 0.123
Game points
0.004 0.002 0.059 2.896 0.004
Point spread
-0.001 0.006 -0.003 -0.134 0.893
Non-aggressive penalties
0.023 0.005 0.093 4.510 < 0.001
Opponent aggressive
penalties
0.144 0.020 0.147 7.151 < 0.001
Humidity
0.000 0.001 -0.005 -0.235 0.814
Temperature
0.004 0.001 0.060 2.890 0.004
Note: R
2
= 0.044, F(6, 2319) = 17.752, p < 0.001.
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Table 4
Regression predicting aggressive penalties for the visiting team.
Measure
B B SE β t p
(Constant)
0.389 0.145
—
2.680 0.007
Game points
0.003 0.002 0.043 2.124 0.034
Point spread
-0.006 0.006 -0.018 -0.893 0.372
Non-aggressive penalties
0.028 0.005 0.113 5.487 < 0.001
Opponent aggressive penalties
0.150 0.021 0.147 7.151 < 0.001
Humidity
0.000 0.001 0.002 0.089 0.929
Temperature
0.001 0.001 0.013 0.604 0.546
Note: R
2
= 0.043, F(6, 2319) = 17.203, p < 0.001.
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Running head: TEMPERATURE AND AGGRESSION IN FOOTBALL 23
Table 6
Regression analysis comparing linear vs. non-linear temperatures.
Measure
B B SE β t p
(Constant)
1.116 0.186
—
5.995 < 0.001
Game points
0.009 0.002 0.078 3.821 < 0.001
Point spread
-0.008 0.010 -0.017 -0.831 0.406
Non-aggressive penalties
0.058 0.008 0.155 7.519 < 0.001
Humidity
-0.001 0.002 -0.006 -0.298 0.766
Temperature
0.008 0.003 0.087 2.602 0.009
Temperature
2
0.000 0.000 -0.049 -1.988 0.047
Temperature
3
0.000 0.000 -0.058 -1.579 0.114
Note: R
2
= 0.039, F(7, 2318) = 13.419, p < 0.001.
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Running head: TEMPERATURE AND AGGRESSION IN FOOTBALL 24
Fig. 1. Average aggressive penalties by temperature. Solid line represents actual average
penalties, the dotted line represents predicted average penalties by temperature. Error bars
represent SE of the mean.
