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\title{Harbingers of foul play: A field study of gain/loss frames and regulatory fit in the NFL}

\author{
Evan Polman\thanks{University of Wisconsin-Madison,
4255 Grainger Hall, 975 University Ave., Madison WI 53706,
Email: evan.polman@wisc.edu. ORCID 0000-0001-6317-2107.}
\and
Lyn M. Van Swol\thanks{University of Wisconsin-Madison.
ORCID 0000-0002-2484-748X.}
\and
Paul R. Hoban\thanks{University of Wisconsin-Madison.
ORCID 0000-0002-9868-6674.}
}

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\newcommand{\jhead}{Judgment and Decision Making, Vol.~15, No.~3}
\newcommand{\jdate}{May 2020}
\pagestyle{myheadings} \markright{\protect\small \href{\jref}{\jhead}, \jdate \hfill Frames, focus, fit, foul play, football \qquad}
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\href{\jref}{\jhead}, \jdate, pp.\ 353-370
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{\small \href{\jref}{\jhead}, \jdate, pp.\ 353--370}
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\begin{onecolabstract}
%\end{latexonly}
Do people cheat more when they have something to gain, or when they have
something to lose? The answer to this question isn’t straightforward, as
research is mixed when it comes to understanding how unethical people will
be when they might acquire something good versus avoid something bad. To
wit, research has found that people cheat more in a loss (vs.\ gain) frame,
yet research on regulatory focus has found that people cheat more in a
promotion focus (where the focus is on acquiring gains) than in a
prevention focus (where the focus is on avoiding losses). Through a
large-scale field study containing 332,239 observations including 27,350
transgressions, we address the contradictory results of gain/loss frames
and regulatory focus on committing unethical behavior in a context that
contains a high risk of detecting unethical behavior (NFL football games).
Our results replicated the separate effects of more cheating in a loss
frame, and more cheating in a promotion focus. Furthermore, our data
revealed a heretofore undocumented crossover interaction, in
accordance with regulatory fit, which could disentangle past results:
Specifically, we found promotion focus is associated with more cheating in
a loss (vs.\ gain) frame, whereas prevention focus is associated with more
cheating in a gain (vs.\ loss) frame. In gridiron football, this translates
to offensive players fouling more when their team is losing (vs.\ winning)
and defensive players fouling more when their team is winning (vs.
losing).

\smallskip
\noindent
Keywords: unethical behavior, cheating, gain/loss frames, regulatory fit, field studies, football
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]
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{\renewcommand{\thefootnote}{}

\footnotetext{

Copyright: \copyright\ 2020.
The authors license this article under the terms of the
\href{http://creativecommons.org/licenses/by/3.0/}{Creative Commons
  Attribution 3.0 License.}
}}

\saythanks

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\section{Introduction}

Accumulating research has found that gain and loss frames affect unethical
and selfish behavior, with the overall conclusion that a loss frame
appears to foster more unethical, deceptive behavior than a gain frame
(Brewer \& Kramer, 1986; Cameron \& Miller, 2009; Grolleau, Kocher \&
Sutan, 2016; Kern \& Chugh, 2009; Neale \& Bazerman, 1985; Pettit, Doyle,
Lount Jr. \& To, 2016; Robben et al., 1990; Schindler \& Pfattheicher,
2017). For example, one study found that people cheated more on their
taxes when facing a balance due (loss) than a refund (gain; Robben et al.,
1990). In a similar vein, another study found that participants playing a
game in an experiment cheated more when their performance was tied to
losing status than gaining status (Pettit et al., 2016). Barring the fact
that losing money (or status) is obviously different from gaining it,
research on gain/loss frames typically examines cases that \textit{ceteris
paribus} contain the same prospect, yet that prospect takes on a different
meaning when it is framed as a gain or as a loss (for a review, see
Kühberger, 1998). Take for example the decision to acquire a business by
unethical means: Study participants were more likely to engage in
corporate eavesdropping when they had a 75\% chance of losing the
acquisition than when they had a 25\% chance of gaining the acquisition
(Kern \& Chugh, 2009). Why does loss framing provoke this unethical
behavior? Decades of research have found that people are more risk-seeking
in a loss frame, and more risk-averse in a gain frame (Kahneman \&
Tversky, 1984) – and unethical behavior is generally viewed as a risky
choice (Gino \& Margolis, 2011).

That said, nearly all of the studies that have tested the effects of
gain/loss frames on unethical behavior have examined behavior in
situations in which there is virtually no implied possibility of detecting
unethical behavior. In fact, most studies are designed in such a way to
precisely make participants feel as though detection is outright
impossible. For example, participants are asked to shred materials that
might evidence their unethical behavior (Gino, Ayal \& Ariely, 2009); or
researchers use aggregate measures of dishonesty, such as the
dice-under-a-cup task, which preclude measuring whether an individual
cheats, but can detect dishonesty at the group-level (Fischbacher \&
Föllmi-Heusi, 2013). In past studies, with few exceptions (e.g., Robben et
al., 1990), there is very little risk of getting caught should a
participant decide to cheat, steal, etc. Thus, while theoretically, risk
should explain the relationship between gain/loss frames and unethical
behavior, risk of getting caught has not been highly salient in previous
research. 

Another caveat of past research is that it has tended to focus on unethical
behaviors that have a solely self-serving advantage for the individual.
However, a wide range of anecdotal evidence and recent reports suggest
that individuals pursue unethical behavior with an ardor that goes beyond
mere \textit{self}{}-serving behavior. For example, among police, it is
not uncommon for members to “plead the fifth” and remain silent to fellow
members’ transgressions. Likewise, in business and politics, unethical
behavior may manifest in cronyism or nepotism; and often this behavior is
enacted for the benefit of others (Padgett \& Morris, 2005). For instance,
when accountants misrepresent an organization’s performance, it is
sometimes for its shareholders’ or clients’ benefit (Deis \& Giroux,
1992). Likewise, in academia, it is perhaps not uncommon for dissertation
advisors to gush about their students on the job market in recommendation
letters, although their students may not merit such cajolery.

These examples suggest that unethical behavior is more nuanced than a
matter of self-serving motives (Hildreth, Gino \& Bazerman, 2016; Levine
\& Schweitzer, 2015). However, researchers have generally treated
unethical behavior as self-interested behavior, leaving us largely
uninformed about unethical behavior that is motivated to help others in
addition to the self.

In this regard, we carried out the following large-scale field study to
test what effect frames will have on unethical behavior when the risk of
detection is relatively high – choosing as our context one that contains
not solely a high level of risk detection, but also, punishment for
unethical behavior (when it is detected). Specifically, we examined 2,917
games across eleven seasons in the National Football League (NFL) of the U.S.
Furnishing our measure of unethical behavior, we tabulated every instance
a penalty was called against a player, and we coded whether that player’s
team was currently winning (in a gain frame) or losing (in a loss frame).
In this vein, we can measure whether unethical behavior (in the form of
breaking the rules) is more likely when an alleged wrongdoer’s team is
winning or losing, in a context where the risk of detection is relatively
high and the transgression can benefit others and the self.

Besides testing the effect of gain and loss frames on misbehavior, our
context enables something more. In football, there is an offense and a
defense – and the players’ motives on each are not unlike the goals of
regulatory focus (Higgins, 1998). The offense tries to score points, akin
to a promotion focus (where the focus is on acquiring gains); and the
defense tries to avoid points from being scored, akin to a prevention
focus (where the focus is on avoiding losses). More than just a
superfluous operationalization, regulatory focus has itself been shown to
affect unethical behavior – with results that are at odds with the
findings in the literature on gain/loss frames. For example, Gino and
Margolis (2011) found more cheating among participants primed with a
promotion focus than a prevention focus, despite the former being
associated with gains and the latter with losses. Likewise, Solgos (2015)
found that a promotion focus leads to more cheating than a prevention
focus, in particular because a promotion focus is associated with an
eagerness for taking chances to attain a positive outcome, whereas a
prevention focus is associated with caution and vigilance, which inhibit
the temptation for cheating.

In fact, despite that most research has found that loss frames foster
unethical behavior, some research on gain/loss frames has found a
different pattern. For instance, despite the opening example describing
that participants are more likely to cheat during a game to avert losing
status than to gain status (Pettit et al., 2016), other research has found
the opposite, whereby unethical behavior was found to be higher among
study participants aiming to ascend in status than warding off a loss in
status (Vriend, Jordan \& Janssen, 2016). In additional support for the
role of gain frames provoking unethical behavior, the main reason for
cheating among college students is “to get ahead” (Simkin \& McLeod, 2009,
p.\ 447); likewise quoted for bankers who confess to making illegal trades
(Tenbrunsel \& Thomas, 2015, p.\ 4).

Research on goal pursuit is also consistent with this idea that gain frames
motivate more unethical behavior than loss frames: Research has shown that
people who have yet to meet their goals are more likely to engage in
unethical behaviors, precisely to attain their goals (Ordóñez, Schweitzer,
Galinsky \& Bazerman, 2009; Schweitzer, Ordóñez \& Douma, 2004). In this
vein, research has concluded that the more people are focused on
individual gains, the more they are willing to deceive or cheat
(Schweitzer, DeChurch \& Gibson, 2005). In further support, research has
found that participants who surpassed someone else’s task performance were
more likely to behave dishonestly in the dice-under-a-cup task, in part
because beating another person led participants to feel more entitled to
rewards (Schurr \& Ritov, 2016). Relatedly, winning a lottery has also
been found to increase dishonest behavior, compared with losing a lottery
(Siniver \& Yaniv, 2018); and along these lines, research has also found
that positive affect increases people’s dishonest behavior (Vincent,
Emich \& Goncalo, 2013).

Thus the answer to the question, do people cheat more when they have
something to gain, or when they have something to lose, is ambiguous
considering the mixed findings in the separate literatures on gain/loss
frames and regulatory focus. To reconcile the findings, we investigated
both gain and loss frames and crossed each with both types of regulatory
focus to explore their separate and (heretofore untested) interactive
effects on misbehavior, in a context that contains a high risk of
detecting misbehavior. In particular we examined behavior that is
committed with the purpose of helping oneself and one’s organization
(team) to achieve its goals.

Given the substantial value and broad theoretical importance of unethical
behavior, our work can be seen as an attempt to illuminate novel
methodological and theoretical aspects of the connection between gain/loss
frames, regulatory focus, and unethical behavior as well as
a replication attempt of past work. In particular, while theoretically and
separately, gain/loss frames and regulatory focus should affect people’s
propensity for unethical behavior, it is typical for both frames and
regulatory focus to co-exist: Someone can be in a gain frame or a loss
frame, and simultaneously have a promotion focus or a prevention focus.
This raises the question of how frames and regulatory focus work in tandem
to affect unethical behavior. From an empirical and theoretical
standpoint, it is noteworthy that no research has yet investigated how
these two effects work jointly on influencing unethical behavior, despite
the fact that both make predictions about individuals’ unethical behavior.
We undertake this important theoretical task. 

In a nutshell, we propose that gain/loss frames and regulatory focus work
together to modulate unethical behavior in a way that corresponds to
regulatory fit (Higgins, 2000). When promotion focus is paired with a gain
frame, or when prevention focus is paired with a loss frame, people
experience regulatory fit – “feeling right” about what they are doing –
compared to when promotion focus is paired with a loss frame, or when
prevention focus is paired with a gain frame. Generally, when people
experience regulatory fit and “feel right,” they feel more engaged, such
that when there is a mismatch between gain/loss frame and regulatory
focus, promotion focused people feel dejected in a loss frame, and
prevention focused people feel quiescent in a gain frame (Idson, Liberman
\& Higgins, 2000). Germane to the current research, the “feel right”
feeling that characterizes regulatory fit produces an experience that
one’s current behavior is moral or correct (Camacho, Higgins \& Luger,
2003). That is, more than just a pleasant feeling, regulatory fit is
considered a feeling tied to “the use of means that are socially accepted
or agreed on or match general moral principles” (p.\ 499). In other words,
regulatory fit is tied to ethical behavior, which is often defined as
behavior that is consistent with generally accepted norms of moral
behavior (Treviño, Weaver \& Reynolds, 2006).

It is thus theoretically plausible that regulatory \textit{mis}fit could
provoke unethical behavior. Several lines of research hint at this idea.
In one study, Spiegel, Grant{}-Pillow, and Higgins (2004) found that
participants who experienced regulatory fit were more likely to hand in an
assignment on time, suggesting that among participants who experience
regulatory misfit, students were less concerned about breaking the rules
and missing the deadline. In other research, participants experiencing
regulatory misfit judged both decisions and their organization’s
procedures as less fair than participants experiencing regulatory fit
(Camacho et al., 2003; Roczniewska, Retowski \& Higgins, 2018); and along
these lines, research has shown that a sense of unfairness motivates
unethical behavior (Skarlicki \& Folger, 1997). 

On balance, then, the evidence for gain/loss frames on unethical behavior
is quite mixed. Some studies have found that loss frames foster unethical
behavior, and some have found the opposite pattern – that gain frames
foster unethical behavior. Quite possibly, one reason for these mixed
findings is regulatory fit. In particular, when people experience
regulatory misfit (such as when a prevention focused person is in a gain
frame), they might be more prone to unethical behavior. In this vein, the
primary objectives of our research are to test the effects of frames and
regulatory focus on unethical behavior in a large-scale field study in
order to provide more conclusive evidence. Viewed this way, our research
attempts to replicate previous research on frames and regulatory focus,
and extend it in three important ways: first, by studying unethical
behavior in a context that contains a relatively high risk of getting
caught; second, by examining a relatively unstudied form of unethical
behavior – one that is both self-serving and benefits others; and third,
by documenting the effects of regulatory misfit in influencing unethical
behavior. The latter objective will help determine whether the previous
research on gain/loss frames and unethical behavior has yielded equivocal
results because the research has not accounted for an individual’s
character and traits that are relevant to predicting unethical behavior.

\section{Study Overview}

To conduct our investigation, we examined 2,917 games across eleven seasons
of the NFL (2002--2012). We analyzed these particular seasons because our
data are from a publicly available website that contains every
play-by-play description for these seasons, and only these seasons. By
play-by-play, we mean that the data contain every instance that something
notable happened during a game, like a tackle, a kick, a pass, an
incomplete pass, etc. In total, this amounts to 473,899 plays. Because our
investigation is on the impact of gain/loss frame and regulatory focus, we
excluded plays that occur: (1) when teams are tied, since tied teams are
in neither a gain nor a loss frame; (2) when one team punts to another,
since during a punt, ball-possession changes from one team to the other,
therefore it is not obvious which team possesses the ball; and (3) when
penalties are called on both teams during a play, because the play-by-play
descriptions data do not follow a consistent, decipherable pattern in
these cases. Following these exclusions, our data contain 332,239 plays,
including 27,350 penalties.

For each penalty, we recorded whether a player committed it when his team
was winning or losing, and whether the player was on offense or defense.
Respectively, these classifications furnish our measures of frame and
regulatory focus. To conduct our main test, we carried out a fixed-effects
Poisson regression model.\footnote{ The variance-to-mean ratio (VRM) in
our data is 1.06, which greenlights our using a Poisson regression model.
Given the low VRM ratio in our data, our approach is not susceptible to
the high rate of false positive findings that recent research has found to
occur among Poisson regressions with especially high VRM ratios (Ryan,
Evers \& Moore, 2018).} Following it, we carried out a series of
robustness checks which account for factors that might plausibly alter a
tendency to cheat and break the rules (e.g., player fatigue, penalty
severity, so-called “good penalties”, player position, etc.); we also
examined coach- and referee-decisions. In all, we find that our effects
are robust to each of the extraneous factors that might plausibly affect
when a player breaks the rules.

%Table 1
\begin{table}[t]\centering
\caption{Number of penalties according to
gain/loss frame and regulatory focus. Rate of penalties (in parentheses) is
penalties per cell divided by plays per cell; total plays is 332,239
(145,620 plays while offense is winning, and defense is losing; 186,619
plays while offense is losing, and defense is winning.}
\begin{tabular}{lccc}\toprule
 & \bfseries Gain & \bfseries Loss & \bfseries Total\\\midrule
\textbf{Promotion Focus} & 6557 (0.0450) & 9106 (0.0488) & 15663\\
\textbf{Prevention Focus} & 6967 (0.0373) & 4720 (0.0324) & 11687\\
\bfseries Total & 13524 & 13826 & \\\bottomrule
\end{tabular}
\end{table}

\section{Preliminary Results}

Before conducting our main analysis, we compared the proportion of
penalties to total plays among gain- and loss-framed teams, promotion- and
prevention-focused players, and in the respective four cells that interact
frame with focus. These descriptive statistics enumerate the raw
probability that a player commits a penalty according to frame and focus.
Table 1 shows the results. We found a marginally significant main effect
of gain/loss frame: the odds of a penalty are 2.33\% higher while losing
versus winning (95\% confidence interval [CI] = [-0.09\%, 4.75\%],
\textit{z} = 1.86, \textit{p} = .062). And we found a significant main
effect of regulatory focus: the odds of a penalty are 35.7\% higher for
promotion- versus prevention-focused players (95\% CI = [33.26\%,
38.15\%], \textit{z} = 24.47, \textit{p} {\textless} .001). Taken
together, this pair of results provides modest-to-strong support for the
separate findings in the literature that show that loss frames and
promotion focus are, respectively, related to more cheating behavior than
gain frames and prevention focus. Furthermore, these results extend the
prior work by evidencing the effects in a field setting where cheating is
carefully monitored (though, notably, the effect is smaller for frame than
focus).

Crucially, we found a significant interaction between gain/loss frame and
regulatory focus, which reveals a strong crossover effect, $\chi^2$(3) =
682.38, \textit{p} {\textless} .001. Among the 332,239 plays, we found that
promotion focused players attempt to cheat more when losing (9,106/186,619)
versus winning (6,557/145,620). In contrast, these results flipped among
prevention focused players; they attempt to cheat more when winning
(6,967/186,619) versus losing (4,720/145,620). Thus, in a relatively strong
way – the effect sizes (odds ratios) are 1.16 (95\% CI = [1.12,
1.20],\textit{ z} = 7.63, \textit{p} {\textless} .001) and 1.09 (95\% CI =
[1.06, 1.12],\textit{ z} = 5.08, \textit{p} {\textless} .001), respectively
– we found that among prevention focused players, the odds of cheating are
16\% greater when in a gain frame than in a loss frame; whereas among
promotion focused players, the odds of cheating are 9\% greater when in a
loss frame than in a gain frame.

\section{Main Results}

It is possible that our preliminary results are due to an omitted,
confounding variable associated with specific games that affect players’
tendency for committing fouls. This might include the personnel features
of a game, such as the teams, coaches, and referees; or the temporal
features of a game, such as the weather, time-of-day, or time-in-season;
or physical features, such as the stadium or city. To account for these
potential omitted variables which could bias our results, we estimated a
Poisson regression model with \textit{game-level fixed-effects}. This
analysis allows us to test if the crossover effect is robust across
game-level effects. For example, if, say, coach-decisions or weather are
surmised to produce the crossover effect, then by including game-level
fixed-effects, our analysis accounts for the unobserved heterogeneity
among coaches and weather – which rules out the possibility that the
crossover effect can be attributed to coach-decisions or weather.

Specifically, the model estimates the number of penalties in game
\textit{j} under frame \textit{f} and focus \textit{s}, such that:
\[
 \mbox{Pr}(\mbox{\textit{Penalty}}_{\mbox{\footnotesize\textit{jfs}}} = k|\lambda_{\mbox{\footnotesize\textit{jfs}}}) =\]\vspace{-3.5ex}
\[
 \frac{\Gamma(\alpha+\kappa)}{\Gamma(\alpha)\Gamma(\kappa+1)}
\Big(\frac{\alpha}{\alpha+\lambda_{\mbox{\footnotesize\textit{jfs}}}}\Big)^{\alpha}
\Big(\frac{\lambda_{\mbox{\footnotesize\textit{jfs}}}}{\alpha+\lambda_{\mbox{\footnotesize\textit{jfs}}}}\Big)^{\kappa}
\]
Where we adopt the standard log-link function for
\textit{${\lambda}$}\textit{\textsubscript{jfs}}, such that:
ln(\textit{${\lambda}$}\textit{\textsubscript{jfs}}) =
\textit{${\beta}$}\textsubscript{0}\textit{\textsubscript{j }}+
\textit{${\beta}$}\textsubscript{1}(\textit{Promotion}\textit{\textsubscript{jfs}})
+
\textit{${\beta}$}\textsubscript{2}(\textit{Gain}\textit{\textsubscript{jfs}})
+
\textit{${\beta}$}\textsubscript{3}(\textit{Promotion}\textit{\textsubscript{jfs}})(\textit{Gain}\textit{\textsubscript{jfs}})
+
\textit{${\beta}$}\textsubscript{4}(\textit{Plays}\textit{\textsubscript{jfs}})

Here, \textit{Promotion}\textit{\textsubscript{jfs}} is an
indicator equal to one when the penalized player is on offense, and zero
otherwise; \textit{Gain}\textit{\textsubscript{jfs}} is an indicator equal
to one when the penalized player’s team is winning, and zero otherwise;
\textit{Plays}\textit{\textsubscript{jfs}} is the count of plays per cell;
\{\textit{${\beta}$}\textsubscript{1},\textit{
}\textit{${\beta}$}\textsubscript{2},\textit{
}\textit{${\beta}$}\textsubscript{3},\textit{
}\textit{${\beta}$}\textsubscript{4}\} are parameters to be estimated; and
\{\textit{${\beta}$}\textsubscript{0}\textit{\textsubscript{j}}\} is a
vector of estimated game-specific fixed-effects controlling for any
omitted variable that is constant within a game. 

Because our outcome is the count of penalties,
\textit{Plays}\textit{\textsubscript{jfs}} is a critical
control in this model. It is possible that more plays occur under certain
game conditions, making it reasonable to expect more penalties in these
situations even in the absence of any psychological effects.
Encouragingly, under the rules of football, this cannot affect our main
effects related to frame and focus, because the counts associated with the
main effects are consistent across offense and defense; i.e., each play
involves both an offense and a defense, and one team is losing if the
other is winning. However, it is possible that the crossover effect may
simply reflect the volume of plays and not the propensity for cheating
behaviors. Congruent with this hypothesis, we observe that the offense is
losing on 56.2\% of plays analyzed.
\textit{Plays}\textit{\textsubscript{jfs}} allows us to control
for the discrepancy in the number of plays per condition. 

% Table 2
\begin{table}[t]\centering
\caption{Poisson regression of gain/loss frame
and regulatory focus on unethical behavior. Standard errors in
parentheses. All coefficients are $p<.001$ except $-$0.022.}
\begin{tabular}{ld{2.4}d{2.4}d{2.4}}\toprule
 & \mc{1}{c}{\bfseries Model 1} & \mc{1}{c}{\bfseries Model 2} & \mc{1}{c}{\bfseries Model 3}\\\midrule
\bfseries Gain Frame &  -0.022 &  &  0.131\\
 &  (0.012) &  &  (0.020)\\
\textbf{Promotion Focus} &  & 0.293 &  0.399\\
 &  & (0.012) &  (0.020)\\
\textbf{Gain × Promotion} &  &  &  -0.201\\
 &  &  &  (0.030)\\
\bfseries Plays &  0.022 &  0.022 &  0.020\\
 & (0.001) &  (0.001) &  (0.001)\\
\bfseries Game Fixed Effects & \mc{1}{c}{Included} & \mc{1}{c}{Included} & \mc{1}{c}{Included}\\
\bfseries Log-Likelihood & \mc{1}{c}{$-$13340.93} & \mc{1}{c}{$-$13052.57} & \mc{1}{c}{$-$13028.12}\\
\bfseries Num.\ Obs. & \mc{1}{c}{11,644} & \mc{1}{c}{11,644} & \mc{1}{c}{11,644}\\\bottomrule
\end{tabular}
\end{table}

The results of the fixed-effects Poisson regression are available in Table
2. We estimated three models to test for the separate effects of frame
(Model 1), regulatory focus (Model 2), and their interaction (Model 3). As
expected, the number of penalties is positively related to the number of
plays; the resulting parameter estimate for
\textit{Plays}\textit{\textsubscript{jfs}} is positive and
significant in each model. While controlling for
\textit{Plays}\textit{\textsubscript{jfs}} and game-level fixed-effects,
we find differences associated with both frame and regulatory focus:
penalties are more likely while losing versus winning (\textit{b} =
-0.022, \textit{t} = 1.83, \textit{p} = .067) in Model 1, and penalties
are more likely for promotion- versus prevention-focused players
(\textit{b} = 0.293, \textit{t} = 24.42, \textit{p} {\textless} .001) in
Model 2. In lock-step with the preliminary analysis, this pair of findings
replicates the separate findings that show that loss frames and promotion
focus are, respectively, related to more cheating behavior than are gain
frames and prevention focus.

It bears noting that the effect of frame in both the preliminary analysis
and Model 1 is marginally significant. Evidently, the effect of frame has
a small impact on unethical behavior, which is perhaps expected
considering the research shows that both gain and loss frames will
increase unethical behavior. In our analysis, the estimated effect of
frame reflects the difference between gain and loss frames. To the extent
that both frames impact unethical behavior in the same direction, the
difference in their influence is the net effect of one frame’s impact over
the other. Such, then, is the small effect of loss frame on unethical
behavior: the effect of loss frame may not be small per se; rather, the
net effect between loss frame and gain frame is in favor of a slightly
stronger loss frame than gain frame.

Of import, the interaction (Model 3) between gain/loss frame and regulatory
focus is significant, revealing a crossover effect. We found that
prevention focused players attempt to cheat more when winning versus
losing (\textit{b} = 0.131, \textit{t} = 6.40, \textit{p} {\textless}
.001). In contrast, these results flipped among promotion focused players;
they attempt to cheat less when winning versus losing (\textit{b} =
-0.070, \textit{t} = 3.87, \textit{p} {\textless} .001). Here, the effect
size is the sum of the main effect of gain frame (\textit{b} = 0.131,
\textit{t} = 6.40, \textit{p} {\textless} .001) and the interaction
between gain frame and promotion focus (\textit{b} = -0.201, \textit{t} =
6.81, \textit{p} {\textless} .001). The corresponding standard error is
calculated via the delta method.

Notably, by incorporating fixed-effects at the game-level, the crossover
effect cannot be due to any omitted variable or combination of omitted
variables that are fixed within games. For example, games are played on
different days of the week, at different times (from morning to evening),
during different weather (from sunny to snowy), in different cities and
stadiums, etc. The crossover effect that we document here is significant
irrespective of these factors which could, conceivably, influence
unethical behavior (e.g., in previous research, time-of-day, weather, and
jersey-color have been found to relate to committing unethical behaviors;
Kouchaki \& Smith, 2014; Frank \& Gilovich, 1988; Ranson, 2014).

To better understand the impact of gain/loss frame and regulatory focus, we
exponentiate the parameter estimates from Model 3 to transform them into
incident rate ratios. These ratios indicate the expected percentage change
in the rate at which penalties are committed in the corresponding
condition. For example, we expect penalties to increase by 2.0\%
(exp(0.020) ${\approx}$ 1.02) for each additional play, all else held
constant. Turning to the impact of frame and focus, when prevention
focused players are in a gain frame versus a loss frame, we expect the
penalty rate to increase by 14.0\% (exp(0.131) ${\approx}$ 1.140). In
contrast, promotion focused players commit 6.7\% (exp(-0.07) ${\approx}$
0.93) fewer penalties when in a gain frame versus a loss frame. Thus,
promotion focused players commit more penalties in a loss frame, while
prevention focused players commit more penalties in a gain frame.

\section{Discussion and Robustness Checks}

In sum, we found a crossover effect between frame and focus. Among
defensive players, the probability of cheating increases by 14.0\% while
in a gain- versus loss-frame; whereas among offensive players, the
probability of cheating decreases by 6.7\% while in a gain- versus
loss-frame. The sizes of these effects are surprising. The players in our
data face high stakes and receive high incentives; they are experienced
professionals yet they could appear to behave in tune with the whims of
regulatory fit. Frankly, it is precisely among highly paid and highly
experienced professionals whom we ought \textit{not} to expect evidence of
biased decision making (Levitt \& List, 2008). Which is to say that
despite players’ extensive training and experience, and despite the
well-defined rules of the game, and despite the high risk of detecting
misbehavior, players appear to behave in unison with the socio-situational
effects of regulatory fit. Moreover, we find that the crossover effect is
robust to game-level fixed-effects. By including game-level fixed-effects
in our regression, our results preclude many alternative explanations, in
the form of factors that distinguish one game from another game, such as
differences between coaches or weather. 

However, a major downside of our field data is that we cannot directly
measure players’ regulatory focus which limits what we can confidently
conclude about the role of regulatory fit in our findings. Other
explanations may be possible. For example, players could be making a
deliberate trade-off between the risk of getting caught and the acquired
benefit of cheating. In the spirit of understanding the findings further,
we examined several unique game-factors and -situations which could shed
further light. The primary benefit of these additional analyses is to
assess the generalizability of the crossover pattern. We tested if the
same crossover pattern would emerge in different cases, such as when a
team is down by more than one possession, or in the final two minutes of a
game, or when a passing play is likely (in addition, we looked at
game-factors, like team-quality, player position, etc.). If the crossover
pattern surfaces across situations, then we can be more confident that the
crossover pattern (irrespective of what causes it) is indeed robust. A
secondary benefit of these analyses is that the results could permit
speculation as to the theory, be it regulatory fit or an alternative
theory. Crucially, as we demonstrate next, the crossover findings are
consistent after accounting for other possible factors that vary within a
game.

\subsection{Costs and Benefits of Cheating}

%Table 3
\begin{table}[t]\centering
\caption{Top 5 most common penalties by defense and offense.}
\begin{tabular}{llr}\toprule
\bfseries Side & \textbf{Penalty} & \bfseries Frequency\\\midrule
Defense & Defensive Offside & 2,974 { ~ } \\
Defense & Defensive Pass Interference & 2,362 { ~ } \\
Defense & Defensive Holding & 1,758 { ~ } \\
Defense & Illegal Contact & 1,216 { ~ } \\
Defense & Roughing the Passer & 978 { ~ } \\\midrule
Offense & False Start & 7,679 { ~ } \\
Offense & Offensive Holding & 5,360 { ~ } \\
Offense & Delay of Game & 1,224 { ~ } \\
Offense & Offensive Pass Interference & 865 { ~ } \\
Offense & Illegal Formation & 677 { ~ } \\\bottomrule
\end{tabular}
\end{table}

In many sports, penalties may provide the penalized team with a strategic
advantage. For example, losing basketball teams will frequently foul their
opponent to stop the clock in the closing seconds of a basketball game. In
contrast, the NFL, which oversees the rules and regulations under which
the games in our data were played, has gone to considerable lengths to
ensure that penalties are unlikely to provide a strategic advantage to the
penalized player’s team. For example, teams have the right to decline the
consequences of any penalty committed against them during a play.
Therefore, if Team B receives a penalty and benefits from the penalty
(akin to committing a strategic foul), then Team A has the right to
decline the penalty, thus annulling the benefit Team B receives. This is
unlike the rules in basketball, in which a team may benefit despite
committing a foul. In this vein, “beneficial penalties” that are strategic
to commit do not generally exist in football.

%Table 4: 
\begin{table*}[t]\centering
\caption{Effects of Gain/Loss Frame and Regulatory Focus According to Penalty Type.}
\begin{tabular}{lccccr}\toprule
\bfseries Penalty & \textbf{Regulatory Focus} & \textbf{Gain} & \bfseries
Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Defensive Offside & Prevention & 0.007 & 0.006 & $\chi^2$(1,
\textit{N}=332,239)=14.96 & {\textless}0.001\\
Defensive Pass Interference & Prevention & 0.006 & 0.005 & $\chi^2$(1,
\textit{N}=332,239)=23.92 & {\textless}0.001\\
Defensive Holding & Prevention & 0.004 & 0.004 & $\chi^2$(1,
\textit{N}=332,239)=2.95 & 0.086\\
Illegal Contact & Prevention & 0.003 & 0.002 & $\chi^2$(1,
\textit{N}=332,239)=30.04 & {\textless}0.001\\
Roughing the Passer & Prevention & 0.003 & 0.002 & $\chi^2$(1,
\textit{N}=332,239)=41.76 & {\textless}0.001\\\midrule
False Start & Promotion & 0.016 & 0.019 & $\chi^2$(1,
\textit{N}=332,239)=35.77 & {\textless}0.001\\
Offensive Holding & Promotion & 0.014 & 0.013 & $\chi^2$(1,
\textit{N}=332,239)=0.70 & 0.404\\
Delay of Game & Promotion & 0.003 & 0.003 & $\chi^2$(1,
\textit{N}=332,239)=5.51 & 0.019\\
Offensive Pass Interference & Promotion & 0.002 & 0.002 & $\chi^2$(1,
\textit{N}=332,239)=3.77 & 0.052\\
Illegal Formation & Promotion & 0.001 & 0.002 & $\chi^2$(1,
\textit{N}=332,239)=2.42 & 0.12\\\bottomrule
\end{tabular}
\end{table*}

However, if “beneficial penalties” did exist and were driving our effect,
one might reasonably expect that our findings would hold for just a small
subset of penalties. This is because it is unlikely that all, or even
many, types of penalties are strategically advantageous. To test this
alternative explanation, we examined whether our findings hold for
individual types of penalties. Table 3 contains the five most frequently
called penalties on both the offense and the defense, respectively. These
ten penalties amount to 91.7\% of all penalties. Many of these penalties
can only be called on either the offense or the defense (i.e., defensive
offside cannot be called on the offense), so we cannot examine the role of
regulatory focus at this level. However, we can still examine the impact
of frame for the respective penalties on offensive and defensive players.
To do this, we ran separate $\chi^2$ analyses for each
of the penalties. The resulting proportions and \textit{p}{}-values are
available in Table 4. Our preceding main analysis revealed that the gain
frame has a positive impact on defensive penalties and a negative impact
on offensive penalties. Of the ten comparisons, nine are in the direction
of the crossover pattern (the likelihood of this happening by chance is
0.0098 percent), including five comparisons that are significant
(\textit{p} {\textless} 0.05) and two that are marginally significant
(\textit{p} {\textless} 0.10). In general, our findings are robust to the
type of penalty committed, indicating that the results are not
attributable to a few strategically committed examples.

Similarly, if players are committing penalties with strategic intent, we
would expect that they are evaluating the potential benefits of each
infraction with respect to their costs, and would likely opt for a lower
cost infraction all else equal. Thus, if strategic behavior were driving
our findings, we would expect that our findings hold for small- but not
large-cost penalties. The most direct cost of a penalty is the yardage
assessed. For 85.2\% of the penalties in our data, we can determine the
assessed yardage from the play description (for the remaining 14.8\% the
yardage was not noted in the description, nearly always because the
penalty was declined). Among these plays, the median was five yards for a
penalty. We subset the data based on whether the assessed yardage exceeded
five yards or not, and ran separate $\chi^2$ analyses by
group. The resulting proportions and \textit{p}{}-values are available in
Table 5. Again, all findings are directionally robust, and three of the
four are statistically significant at \textit{p} {\textless} 0.001. Thus,
it does not appear that players are strategically evaluating the benefits
of an infraction vis-à-vis the potential costs.

%Table 5: 
\begin{table*}[t]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to high- and low-penalty severity.}
\begin{tabular}{lccccr}\toprule
\textbf{Penalty Severity} & \bfseries Regulatory Focus & \bfseries Gain & \bfseries Loss & \textbf{Test Statistic} & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Low & Promotion & 0.023 & 0.026 & $\chi^2$(1, \textit{N}=328,171)=27.541 & {\textless}0.001\\
 & Prevention & 0.018 & 0.016 & $\chi^2$(1, \textit{N}=328,171)=24.257 & {\textless}0.001\\
High & Promotion & 0.017 & 0.018 & $\chi^2$(1, \textit{N}=328,171)=1.195 & 0.274\\
 & Prevention & 0.012 & 0.010 & $\chi^2$(1, \textit{N}=328,171)=30.042 & {\textless}0.001\\\bottomrule
\end{tabular}
\end{table*}
Another situation that could provide evidence of strategic intent is a
game’s point-differential. When a team is down by one possession, the game
is closer than if the score is separated by two or more possessions.
Possibly, the benefit to cheating would be higher in closer games, because
the score can change more easily; a currently losing team can become the
winning team in just one play. We subset the data based on whether the
current point-differential exceeds 8 points or not. We chose 8 points
because this is the differential at which the losing team can become the
winning team in just one possession. A score-differential of more than 8
points would require at least two possessions. Our results are robust to
such a split. The crossover pattern is significant in both instances: when
the score-differential is currently 8 points or lower vs.\ greater than 8
points (Table 6).

%Table 6: 
\begin{table*}[t]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to one and more-than-one possession score.}
\begin{tabular}{lccccr}\toprule
\bfseries One Possession & \bfseries Regulatory Focus & \bfseries Gain & \bfseries Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
No & Promotion & 0.043 & 0.049 & $\chi^2$(1, \textit{N}=142,972)=23.23 & {\textless}0.001\\
 & Prevention & 0.039 & 0.032 & $\chi^2$(1, \textit{N}=142,972)=49.91 & {\textless}0.001\\
Yes & Promotion & 0.046 & 0.049 & $\chi^2$(1, \textit{N}=189,267)=6.82 & 0.009\\
 & Prevention & 0.036 & 0.033 & $\chi^2$(1, \textit{N}=189,267)=14.99 & {\textless}0.001\\\bottomrule
\end{tabular}
\end{table*}

Finally, if players were making strategic decisions with respect to the
expected costs and benefits of committing a penalty, then this trade-off
may look different among more-fatigued players compared to less-fatigued
players (Lambourne \& Tomporowski, 2010). In football, the offense
earns a new set of four downs each time they move the ball forward ten
yards. This can lead to the offense and defense remaining on the field for
many consecutive plays and could produce fatigue, though not necessarily
disparately by offense and defense.\footnote{ Both the offense and the
defense participate in each play, meaning that each team’s offense has
appeared in the same number of plays as the opposing team’s defense.} To
control for this type of fatigue, we created a variable, \textit{Fatigue},
which is equal to one when the current series of plays has lasted longer
than the average in our data (6.3), and zero otherwise. We ran separate
$\chi^2$ analyses by group (the results are presented in
Table 7). All findings are directionally robust to differences in fatigue,
and three of the four differences are statistically significant at
\textit{p} {\textless} 0.001.

%Table 7: 
\begin{table*}[t]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to high- and low-fatigued players.}
\begin{tabular}{lccccr}\toprule
\bfseries Fatigue & \bfseries Regulatory Focus & \bfseries Gain & \bfseries
Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Low & Promotion & 0.045 & 0.050 & $\chi^2$(1, \textit{N}=248,707)=29.78 & {\textless}0.001\\
 & Prevention & 0.037 & 0.032 & $\chi^2$(1, \textit{N}=248,707)=41.95 & {\textless}0.001\\
High & Promotion & 0.045 & 0.046 & $\chi^2$(1, \textit{N}=83,532)=0.607 & 0.436\\
 & Prevention & 0.039 & 0.034 & $\chi^2$(1, \textit{N}=83,532)=14.66 & {\textless}0.001\\\bottomrule
\end{tabular}
\end{table*}

The above findings, coupled with the carefully refined rules of the game,
does not definitively rule out the potential for making strategic
trade-off decisions, in the form of committing strategic penalties. How
the crossover effect evidences among transgressions that are more or less
planned (i.e., intentional vs.\ less intentional) is an interesting and
still open question – in part because it is not obvious whether regulatory
misfit would only influence misbehavior that is, say, unplanned. Research
has found that misbehavior, in the form of dishonesty, has both
intentional and unplanned (automatic) origins (Köbis, Verschuere,
Bereby-Meyer, Rand \& Shalvi, 2019). And in the fast-paced game of
football, cheating may stem from both planning and impulse. Due to the
richness of our data, we can provide additional empirical speculation on
whether fouls that are committed intentionally are more or less consistent
with the crossover pattern.

One penalty-type in particular, intentional grounding, is a foul that is
intentionally committed. In our data, the effect is notably stronger for
intentional grounding, $\chi^2$(1, \textit{N} =
332,239) = 17.788, compared with most of the penalties that comprise the
top ten (as shown in Table 4, the preceding effect of intentional
grounding exceeds six of the top ten penalties). Notably, there are likely
cross-penalty differences in intentionality. However, as Tables 4 and 5
show, the crossover effect is robust across penalty-type and -severity,
which suggests that if some penalty-types are inherently more intentional,
then regardless if committing a penalty is planned or impulsive, the
crossover effect is observed all the same.

\subsection{Other Game- and Situation-Factors}

In addition to players’ strategic intent, there exist many other factors
that might explain, or at least contribute to, our findings. In order to
demonstrate that the crossover pattern is robust across such factors, we
carried out the following robustness checks. 

\subsubsection{Coach Decisions}

We examined two in-game scenarios that stem from coach decisions. First, we
explored whether the offense was in the red zone (i.e., within 20 yards of
the end-zone). Certain plays become infeasible when the offense is near the
end-zone (e.g., long passing plays would end up out of bounds), and this
limits what decisions coaches typically make. In our data, 16.1\% of plays
occur in the red-zone. To explore whether our findings generalize across
plays, we subset our data based on regulatory focus and whether the play
occurred in the red zone or not. We then ran separate $\chi^2$ analyses on
each of the subsets. The results are available in Table 8. All findings
were statistically significant (\textit{p} {\textless} 0.05) in the the
form of the crossover pattern.  Thus, our effects do not depend on whether
a play occurred in the red zone.

%Table 8: 
\begin{table*}[t]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to red zone play.}
\begin{tabular}{lccccr}\toprule
\bfseries Red Zone & \bfseries Regulatory Focus & \bfseries Gain & \bfseries Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Yes & Promotion & 0.037 & 0.041 & $\chi^2$(1, \textit{N}=53,530)=7.12 & 0.008\\
 & Prevention & 0.034 & 0.031 & $\chi^2$(1, \textit{N}=53,530)=5.63 & 0.018\\
No & Promotion & 0.047 & 0.050 & $\chi^2$(1, \textit{N}=278,709)=17.48 & {\textless}0.001\\
 & Prevention & 0.038 & 0.033 & $\chi^2$(1, \textit{N}=278,709)=51.66 & {\textless}0.001\\\bottomrule
\end{tabular}
\end{table*}

Second, we explored a subset of plays in which the offense is considerably
more likely to pass the ball, and the defense is likely to be aware of this
tendency. This occurs on third (and some fourth) down plays where there are
seven or more yards to go for a first down. In our data, probable passing
plays represent 11.5\% of all plays. We subset the data based on regulatory
focus and this criterion, and ran separate $\chi^2$ analyses. The results
are in Table 9. Our findings are directionally consistent across all
conditions. Specifically, the findings are statistically significant
(\textit{p} {\textless} 0.001) when it is not a probable passing play, and
marginally statistically significant for promotion focused players on
probable passing plays.

%Table 9:
\begin{table*}[t]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to a probable pass.}
\begin{tabular}{lccccr}\toprule
\bfseries Probable Pass & \bfseries Regulatory Focus & \bfseries Gain & \bfseries Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Yes & Promotion & 0.064 & 0.069 & $\chi^2$(1, \textit{N}=38,229)=3.36 & 0.067\\
 & Prevention & 0.050 & 0.046 & $\chi^2$(1, \textit{N}=38,229)=2.06 & 0.151\\
No & Promotion & 0.044 & 0.048 & $\chi^2$(1, \textit{N}=282,002)=17.41 & {\textless}0.001\\
 & Prevention & 0.036 & 0.031 & $\chi^2$(1, \textit{N}=282,002)=54.35 & {\textless}0.001\\\bottomrule
\end{tabular}
\end{table*}
\subsubsection{Referee Decisions}

NFL referees are evaluated on a weekly basis in a process that considers
both the penalties they called and those they may have missed. For each
referee, every play in every game is evaluated. Through this process, they
are graded and ranked among the other NFL referees. Those with the highest
ranks are awarded prestigious positions, such as the opportunity to
referee the Super Bowl. Those in the lower third are put on performance
improvement plans, and in the absence of observed improvements they are
fired. As a result, the referees have an incentive to be correct and
consistent in their play calling.

However, no system is perfect, and referees may be subject to biases. For
example, Green and Daniels (2014) documented an “impact-aversion” bias
among baseball umpires. Not wanting to make a mistake that could alter the
outcome of a game, Green and Daniels found that baseball umpires make calls
that are measurably less pivotal (i.e., less “game-changing”), in the form
of favoring a ball-call over a strike-call in situations that allow play to
continue. In football, impact-aversion could manifest in calling fewer
penalties following the “two minute warning” in which there are two minutes
left in a game. Calling a penalty at the end of a game has the potential to
alter the final outcome. Accordingly, referees may behave differently and
make different decisions during the final two minutes of a game. In our
data, 8.6\% of plays were executed in the final two minutes of a game. We
again subset the data based on regulatory focus and this criterion, and ran
separate $\chi^2$ analyses. The results are available in Table 10. All
findings were consistent with the crossover pattern and statistically
different from zero (\textit{p} {\textless} 0.05).

%Table 10: 
\begin{table*}[t]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to final 2-minutes of game.}
\begin{tabular}{lccccr}\toprule
\bfseries Final 2 Minutes & \bfseries Regulatory Focus & \bfseries Gain & \bfseries Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Yes & Promotion & 0.031 & 0.041 & $\chi^2$(1, \textit{N}=28,727)=19.26 & {\textless}0.001\\
 & Prevention & 0.038 & 0.018 & $\chi^2$(1, \textit{N}=28,727)=85.64 & {\textless}0.001\\
No & Promotion & 0.046 & 0.050 & $\chi^2$(1, \textit{N}=303,512)=20.13 & {\textless}0.001\\
 & Prevention & 0.037 & 0.033 & $\chi^2$(1, \textit{N}=303,512)=30.61 & {\textless}0.001\\\bottomrule
\end{tabular}
\end{table*}

\subsubsection{Team}

Although our game-level fixed-effects factor in the Poisson regression
already controls for team, we conducted a separate analysis to test the
extent that the crossover effect is consistent across teams. We conducted
64 separate $\chi^2$ analyses, one for each team in our
data. The resulting team-specific estimates are available in Table 11.
Across the 64 analyses, the effects are in the direction of the crossover
pattern for 52 analyses (the likelihood of this happening by chance is
1.78 × 10$^{-7}$ percent). Of the 52 analyses, 14 are
statistically significant (\textit{p} {\textless} 0.05). None of the 12
results that were in a counter-direction were statistically significant.
Thus, we do not have evidence that runs counter to our core results for
any of the NFL’s 32 teams.

%Table 11: 
\begin{table*}[t!]\centering
\caption{Effects of gain/loss frame and regulatory focus according to team.}
\begin{tabular}{l|@{\quad}cccc|@{\quad}cccc}\toprule
\mc{1}{c}{}& \mc{4}{c}{Promotion} & \mc{4}{c}{Prevention}\\\cmidrule(r{3ex}){2-5}\cmidrule(r{1ex}){6-9}
\bfseries Team & \bfseries Gain & \bfseries Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}
& \bfseries Gain & \bfseries Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
SF &  0.042 & 0.056 & $\chi^2$(1, \textit{N}=10,064)=9.995 & 0.002 &  0.036 & 0.029 & $\chi^2$(1, \textit{N}=10,543)=4.009 & 0.045\\
ARI &  0.052 & 0.051 & $\chi^2$(1, \textit{N}=10,405)=0.053 & 0.818 &  0.040 & 0.037 & $\chi^2$(1, \textit{N}=10,528)=0.455 & 0.500\\
ATL &  0.041 & 0.046 & $\chi^2$(1, \textit{N}=10,122)=1.24 & 0.265 &  0.032 & 0.028 & $\chi^2$(1, \textit{N}=10,513)=0.896 & 0.344\\
BAL &  0.045 & 0.051 & $\chi^2$(1, \textit{N}=10,851)=2.352 & 0.125 &  0.040 & 0.038 & $\chi^2$(1, \textit{N}=10,530)=0.142 & 0.707\\
DAL &  0.054 & 0.058 & $\chi^2$(1, \textit{N}=10,012)=0.475 & 0.491 &  0.042 & 0.032 & $\chi^2$(1, \textit{N}=9,539)=7.004 & 0.008\\
DET &  0.050 & 0.051 & $\chi^2$(1, \textit{N}=10,143)=0.022 & 0.882 &  0.042 & 0.038 & $\chi^2$(1, \textit{N}=10,565)=0.978 & 0.323\\
IND &  0.037 & 0.034 & $\chi^2$(1, \textit{N}=11,092)=0.438 & 0.508 &  0.031 & 0.029 & $\chi^2$(1, \textit{N}=10,933)=0.255 & 0.613\\
KC &  0.045 & 0.043 & $\chi^2$(1, \textit{N}=10,245)=0.079 & 0.778 &  0.030 & 0.024 & $\chi^2$(1, \textit{N}=10,079)=2.964 & 0.085\\
MIN &  0.049 & 0.053 & $\chi^2$(1, \textit{N}=10,340)=0.707 & 0.401 &  0.043 & 0.035 & $\chi^2$(1, \textit{N}=10,589)=4.11 & 0.043\\
NO &  0.039 & 0.046 & $\chi^2$(1, \textit{N}=11,093)=2.775 & 0.096 &  0.038 & 0.029 & $\chi^2$(1, \textit{N}=10,426)=5.900 & 0.015\\
NYJ &  0.042 & 0.043 & $\chi^2$(1, \textit{N}=10,094)=0.038 & 0.846 &  0.033 & 0.032 & $\chi^2$(1, \textit{N}=9,732)=0.099 & 0.753\\
PHI &  0.045 & 0.044 & $\chi^2$(1, \textit{N}=10,917)=0.04 & 0.842 &  0.043 & 0.034 & $\chi^2$(1, \textit{N}=10,970)=5.317 & 0.021\\
SD &  0.044 & 0.042 & $\chi^2$(1, \textit{N}=10,488)=0.222 & 0.638 &  0.041 & 0.035 & $\chi^2$(1, \textit{N}=10,645)=2.142 & 0.143\\
SEA &  0.044 & 0.045 & $\chi^2$(1, \textit{N}=10,666)=0.024 & 0.876 &  0.034 & 0.031 & $\chi^2$(1, \textit{N}=11,044)=1.114 & 0.291\\
STL &  0.054 & 0.055 & $\chi^2$(1, \textit{N}=10,325)=0.003 & 0.957 &  0.036 & 0.035 & $\chi^2$(1, \textit{N}=10,087)=0.119 & 0.730\\
PIT &  0.045 & 0.044 & $\chi^2$(1, \textit{N}=10,597)=0.173 & 0.677 &  0.035 & 0.029 & $\chi^2$(1, \textit{N}=10,053)=2.669 & 0.102\\
MIA &  0.035 & 0.048 & $\chi^2$(1, \textit{N}=9,755)=9.064 & 0.003 &  0.043 & 0.033 & $\chi^2$(1, \textit{N}=9,912)=6.047 & 0.014\\
BUF &  0.053 & 0.045 & $\chi^2$(1, \textit{N}=9,620)=2.939 & 0.086 &  0.035 & 0.027 & $\chi^2$(1, \textit{N}=10,050)=5.005 & 0.025\\
CAR &  0.044 & 0.049 & $\chi^2$(1, \textit{N}=10,067)=1.31 & 0.252 &  0.041 & 0.033 & $\chi^2$(1, \textit{N}=10,471)=3.956 & 0.047\\
CIN &  0.049 & 0.046 & $\chi^2$(1, \textit{N}=10,259)=0.377 & 0.539 &  0.035 & 0.027 & $\chi^2$(1, \textit{N}=10,135)=4.753 & 0.029\\
CLE &  0.048 & 0.053 & $\chi^2$(1, \textit{N}=9,466)=1.009 & 0.315 &  0.033 & 0.029 & $\chi^2$(1, \textit{N}=10,179)=1.566 & 0.211\\
GB &  0.039 & 0.043 & $\chi^2$(1, \textit{N}=11,077)=0.837 & 0.360 &  0.039 & 0.037 & $\chi^2$(1, \textit{N}=10,578)=0.117 & 0.732\\
WAS &  0.048 & 0.058 & $\chi^2$(1, \textit{N}=9,871)=4.554 & 0.033 &  0.033 & 0.027 & $\chi^2$(1, \textit{N}=9,967)=2.412 & 0.120\\
CHI &  0.042 & 0.053 & $\chi^2$(1, \textit{N}=10,000)=7.032 & 0.008 &  0.030 & 0.033 & $\chi^2$(1, \textit{N}=10,354)=0.545 & 0.460\\
HOU &  0.043 & 0.049 & $\chi^2$(1, \textit{N}=9,999)=2.054 & 0.152 &  0.041 & 0.035 & $\chi^2$(1, \textit{N}=10,190)=2.495 & 0.114\\
NE &  0.042 & 0.038 & $\chi^2$(1, \textit{N}=11,731)=1.292 & 0.256 &  0.036 & 0.031 & $\chi^2$(1, \textit{N}=11,111)=1.886 & 0.170\\
NYG &  0.048 & 0.050 & $\chi^2$(1, \textit{N}=10,916)=0.338 & 0.561 &  0.037 & 0.029 & $\chi^2$(1, \textit{N}=10,708)=5.628 & 0.018\\
TB &  0.057 & 0.054 & $\chi^2$(1, \textit{N}=10,132)=0.185 & 0.667 &  0.033 & 0.032 & $\chi^2$(1, \textit{N}=9,624)=0.091 & 0.763\\
TEN &  0.047 & 0.048 & $\chi^2$(1, \textit{N}=9,980)=0.033 & 0.855 &  0.047 & 0.039 & $\chi^2$(1, \textit{N}=10,439)=3.174 & 0.075\\
DEN &  0.042 & 0.047 & $\chi^2$(1, \textit{N}=10,526)=1.419 & 0.234 &  0.034 & 0.036 & $\chi^2$(1, \textit{N}=10,243)=0.23 & 0.631\\
OAK &  0.055 & 0.064 & $\chi^2$(1, \textit{N}=10,055)=2.808 & 0.094 &  0.050 & 0.044 & $\chi^2$(1, \textit{N}=10,503)=1.842 & 0.175\\
JAC &  0.045 & 0.047 & $\chi^2$(1, \textit{N}=10,151)=0.152 & 0.697 &  0.037 & 0.031 & $\chi^2$(1, \textit{N}=9,749)=2.803 & 0.094\\\bottomrule
\end{tabular}
\end{table*}

\subsubsection{Team Quality}

In order to look at teams in more detail, we assessed the crossover effect
among “good” and “bad” teams (i.e., team quality), based on the total
number of wins a team has at the end of each season. NFL teams generally
play 16 regular season games, followed by a four round sudden death
playoff among the top 12 teams. By considering only the number of wins
(vs.\ percentage of wins or number of losses), we avoid penalizing teams
that make the playoffs (i.e., have more opportunities for losses). We
define a low-quality team (a “bad” team) as a team with fewer wins than
losses, and a high-quality team (a “good” team) as a team with more wins
than losses, at the season-level. We subset our data based on this
criterion and ran separate $\chi^2$ tests for each
group. The resulting proportions are presented in Table 12 along with the
corresponding \textit{p}{}-values from the $\chi^2$
tests. Directionally, all findings are robust to differences in team
quality. Further, three of the four differences are statistically
significant at \textit{p} {\textless} 0.01.

%Table 12: 
\begin{table*}[t!]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to team quality (net win-loss differential).}
\begin{tabular}{lccccr}\toprule
\bfseries Team Quality & \bfseries Regulatory Focus & \bfseries Gain & \bfseries Loss & \textbf{Test Statistic} & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Bad & Promotion & 0.027 & 0.027 & $\chi^2$(1, \textit{N}=285,113)=0.089 & 0.765\\
 & Prevention & 0.021 & 0.018 & $\chi^2$(1, \textit{N}=287,595)=44.15 & {\textless}0.001\\
Good & Promotion & 0.023 & 0.026 & $\chi^2$(1, \textit{N}=287,595)=16.955 & {\textless}0.001\\
 & Prevention & 0.020 & 0.018 & $\chi^2$(1, \textit{N}=285,113)=8.429 & 0.004\\\bottomrule
\end{tabular}
\end{table*}

%Table 13: 
\begin{table*}[t!]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to team quality (no.\ wins by season-end)}
\begin{tabular}{lccccr}\toprule
\bfseries Team Quality & \bfseries Regulatory Focus & \bfseries Gain & \bfseries Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Worse & Promotion & 0.048 & 0.050 & $\chi^2$(1, \textit{N}=152,207)=1.95 & 0.162\\
 & Prevention & 0.038 & 0.033 & $\chi^2$(1, \textit{N}=155,533)=30.49 & {\textless}0.001\\
Better & Promotion & 0.043 & 0.046 & $\chi^2$(1, \textit{N}=155,533)=5.72 & 0.017\\
 & Prevention & 0.037 & 0.032 & $\chi^2$(1, \textit{N}=152,207)=21.49 & {\textless}0.001\\\bottomrule
\end{tabular}
\end{table*}

%Table 14: 
\begin{table*}[t!]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to player position.}
\begin{tabular}{lccccr}\toprule
\bfseries Position & \textbf{Regulatory Focus} & \bfseries Gain & \bfseries
Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
Defensive Back & Prevention & 0.009 & 0.007 & $\chi^2$(1,
\textit{N}=332,239)=32.11 & {\textless}0.001\\
Defensive End & Prevention & 0.005 & 0.004 & $\chi^2$(1,
\textit{N}=332,239)=16.25 & {\textless}0.001\\
Line Backer & Prevention & 0.004 & 0.003 & $\chi^2$(1,
\textit{N}=332,239)=9.73 & 0.002\\
Defensive Tackle & Prevention & 0.003 & 0.003 & $\chi^2$(1,
\textit{N}=332,239)=0.99 & 0.321\\
Cornerback & Prevention & 0.0002 & 0.0002 & $\chi^2$(1,
\textit{N}=332,239)=0 & 1.000\\
Offensive Tackle & Promotion & 0.009 & 0.011 & $\chi^2$(1,
\textit{N}=332,239)=46.26 & {\textless}0.001\\
Guard & Promotion & 0.009 & 0.010 & $\chi^2$(1, \textit{N}=332,239)=7.26 & 0.007\\
Tight End & Promotion & 0.004 & 0.004 & $\chi^2$(1,
\textit{N}=332,239)=2.36 & 0.125\\
Wide Receiver & Promotion & 0.003 & 0.004 & $\chi^2$(1,
\textit{N}=332,239)=6.35 & 0.012\\
Quarterback & Promotion & 0.003 & 0.003 & $\chi^2$(1,
\textit{N}=332,239)=0.41 & 0.522\\\bottomrule
\end{tabular}
\end{table*}

%Table 15: 
\begin{table*}[t!]\centering
\caption{Effects of gain/loss frame and
regulatory focus according to season.}
\begin{tabular}{lccccr}\toprule
\bfseries Season & \textbf{Regulatory Focus} & \bfseries Gain & \bfseries
Loss & \bfseries Test Statistic & \textbf{\textit{p}}\textbf{{}-value}\\\midrule
2002 & Promotion & 0.046 & 0.049 & $\chi^2$(1, \textit{N}=28,987)=0.73 & 0.394\\
 & Prevention & 0.040 & 0.034 & $\chi^2$(1, \textit{N}=28,987)=7.68 & 0.006\\
2003 & Promotion & 0.050 & 0.052 & $\chi^2$(1, \textit{N}=29,716)=0.95 & 0.329\\
 & Prevention & 0.036 & 0.031 & $\chi^2$(1, \textit{N}=29,716)=6.62 & 0.010\\
2004 & Promotion & 0.050 & 0.056 & $\chi^2$(1, \textit{N}=29,689)=3.72 & 0.054\\
 & Prevention & 0.043 & 0.034 & $\chi^2$(1, \textit{N}=29,689)=16.69 & {\textless}0.001\\
2005 & Promotion & 0.049 & 0.060 & $\chi^2$(1, \textit{N}=30,163)=18.17 & {\textless}0.001\\
 & Prevention & 0.041 & 0.037 & $\chi^2$(1, \textit{N}=30,163)=2.55 & 0.110\\
2006 & Promotion & 0.042 & 0.047 & $\chi^2$(1, \textit{N}=29,826)=3.43 & 0.064\\
 & Prevention & 0.037 & 0.030 & $\chi^2$(1, \textit{N}=29,826)=11.99 & 0.001\\
2007 & Promotion & 0.042 & 0.048 & $\chi^2$(1, \textit{N}=29,464)=4.58 & 0.032\\
 & Prevention & 0.033 & 0.028 & $\chi^2$(1, \textit{N}=29,464)=6.55 & 0.010\\
2008 & Promotion & 0.042 & 0.046 & $\chi^2$(1, \textit{N}=30,355)=2.92 & 0.087\\
 & Prevention & 0.034 & 0.031 & $\chi^2$(1, \textit{N}=30,355)=2.23 & 0.135\\
2009 & Promotion & 0.042 & 0.047 & $\chi^2$(1, \textit{N}=29,739)=3.46 & 0.063\\
 & Prevention & 0.033 & 0.033 & $\chi^2$(1, \textit{N}=29,739)=0.00 & 1.000\\
2010 & Promotion & 0.045 & 0.046 & $\chi^2$(1, \textit{N}=30,861)=0.26 & 0.613\\
 & Prevention & 0.034 & 0.029 & $\chi^2$(1, \textit{N}=30,861)=5.50 & 0.019\\
2011 & Promotion & 0.045 & 0.045 & $\chi^2$(1, \textit{N}=31,387)=0.01 & 0.922\\
 & Prevention & 0.039 & 0.034 & $\chi^2$(1, \textit{N}=31,387)=6.30 & 0.012\\
2012 & Promotion & 0.042 & 0.042 & $\chi^2$(1, \textit{N}=32,052)=0.05 & 0.819\\
 & Prevention & 0.039 & 0.036 & $\chi^2$(1, \textit{N}=32,052)=2.31 & 0.129\\\bottomrule
\end{tabular}
\end{table*}

We conducted a second test of team quality, one that compares which team
has more wins by the end of the season. This provides a test of relative
team quality. With this test, we assigned team quality such that the
“better” team in each game had more wins while the “worse” team had fewer,
as measured at the end of the season. Note, this is different from the
preceding analysis because it assigns relative team quality within each
game. For example, a 12--4 team has net-8 wins (and would be classified as
a “good” team in the preceding analysis) but it would be classified as the
“worse” team in this analysis when facing a team with 13 or more wins. By
assessing the relative quality of the competing teams, we are better able
to capture the impact of being a “better” or “worse” team within each
game. As with the previous measure of team quality, all four findings are
directionally robust, with three of the four differences as statistically
significant at \textit{p} {\textless} 0.05 (Table 13).

\subsubsection{Player Position}

To explore whether our findings generalize across player positions, we
subset our data to focus only on penalties committed by each of the top
five penalized positions on offense and defense (listed in Table 14), and
ran separate $\chi^2$ analyses on each. For the ten
positions, we find that all but one are in the direction of the crossover
pattern (the likelihood of this happening by chance is 0.0098 percent),
with significant differences for six of the ten positions. Thus, it
appears that our results generalize across player positions.

\subsubsection{Season}

As with team, the game-level fixed-effects factor in the Poisson regression
already accounts for season. However, in a separate analysis, we examined
whether our results are driven by one or a few seasons, or if our results
tend to apply more generally, by subsetting the data by season. The
resulting season-specific estimates are available in Table 15. Across all
22 comparisons, all effects were in the direction of the crossover pattern
(the likelihood of this happening by chance is 2.38 ×
10$^{-7}$ percent); nine of the 22 tests were significant
(\textit{p} {\textless} 0.05). Thus, our effects appear robust across
seasons.

\section{General Discussion}

In the ongoing exploration of the impact of self-regulatory mechanisms on
affect, behavior, and cognition, the effects of gain/loss frames and
regulatory focus on unethical behavior have emerged as a prominent topic
of research. Yet to date, research on unethical behavior has been limited
to people making mainly risk-free (detection-free) choices. For contrast,
our investigation illuminates how fairly people behave in an interactive
context when their deception can be found out, punished, and responded to
(in kind). In addition, our study included both gain/loss frames and
regulatory focus, which may help disentangle past, mixed findings.
Constituting the largest dataset combining gain/loss frames and regulatory
focus ever assembled, our data replicated past separate effects of loss
frame and promotion focus – and revealed the heretofore undocumented
circumstances when \textit{both} frames and foci could significantly
foster unethical behavior. 

Only a small handful of studies have investigated unethical behavior in
natural conditions (e.g., Griffin, Kruger \& Maturana, 2019; Millar,
White \& Zheng, 2019; Rajgopal \& White, 2015). Our study contained
27,350 transgressions in a sports context, which allowed us to demonstrate
that cheating may be less prevalent when there is regulatory fit, compared
to misfit. Still, our study has its limitations, discussed next. 

\subsection[Limitations]{Limitations}

We did not manipulate gain/loss frame nor regulatory focus. We presumed
these variables in our data. These variables have high face validity to the
extent that past research has tested and manipulated frames and regulatory
focus in precisely the same way that we have coded them in our research. In
research on gain/loss frames, it is not uncommon to test an athlete’s or a
gambler’s current state of contest-winning versus -losing in terms of gain
and loss frame, respectively (Bartling, Brandes \& Schunk, 2015; Berger \&
Pope, 2011; Bucciol, Hu \& Zarri, 2018; De Martino, Kumaran, Seymour \&
Dolan, 2006). Furthermore, past work on regulatory focus in the sports
psychology literature supports our operationalizing the offensive and
defensive players as respectively promotion- and prevention-focused
(Converse \& Reinhard, 2016; Krawietz, 2013; Memmert et al., 2015;
Plessner, Unkelbach, Memmert, Baltes \& Kolb, 2009; Unkelbach, Plessner,
\& Memmert, 2009; Yen, Chao \& Lin, 2011). As Shao, Grace, and Ross (2015)
put it, “A person exhibiting a high promotion/low prevention focus may be
considered to be playing on the offense while a person exhibiting a high
prevention/low promotion focus may be considered to be playing on the
defense” (p.\ 615).

Although it is encouraging that past research has documented a connection
between offensive and defensive positions and promotion and prevention
foci, we have also conducted tests at the player-position level which
provides its own support. We found that for the top five fouling positions
on both offense and defense, nine are in the direction of the crossover
pattern (with six being significant). As noted, the likelihood of this
happening by chance is 0.0098 percent. Although we cannot verify in our
data that offensive and defensive players are respectively promotion- and
prevention-focused, these results show that the fouls committed by
offensive and defensive players are generally consistent with the fouls we
would predict among promotion- and prevention-focused players.

However, because we did not manipulate these variables, our conclusions
could appear ambiguous on grounds of causality and theory. First, one
might counter-argue that regulatory misfit is not, as we argue,
influencing unethical behavior; but rather, the direction of the bona fide
effect could be in reverse, as though unethical behavior is influencing
regulatory misfit. However, unlike most correlational field studies,
questions about reverse causality are untenable in our research. Consider
that in our data, both frame and regulatory focus cannot be altered after
a player commits a penalty; therefore, our findings would struggle to be
re-interpreted as a case whereby unethical behavior is influencing
regulatory misfit. Even if one considers that our data include only
misbehaviors that were detected (vs.\ undetected) – which we acknowledge
leaves open the possibility that the frame could change after cheating
(because \textit{undetected} cheating could subsequently change the score
and therefore frame) – it still would not be possible to argue that
unethical behavior is influencing regulatory misfit, because when
undetected cheating leads to a change in frame, it can only change from
losing to winning – it cannot change from winning to losing (i.e., after a
player cheats, his team’s points cannot \textit{drop} below the
pre-cheating score; the score can only stay the same, or increase if the
cheating is undetected). Therefore, in order for unethical behavior to
affect regulatory misfit, both frames must be allowed to change – e.g.,
when the frame cannot change from winning to losing, this renders it
impossible for a promotion focused player’s regulatory fit to change from
fit to misfit. Quite simply, since the frame cannot change in our data
after committing a penalty, neither can regulatory fit, which renders
regulatory fit unmalleable to changes in ethical behavior – at least in
our data. Theoretically, it is still possible for unethical behaviors to
influence regulatory (mis)fit – but in our research it is not a plausible
candidate interpretation of the findings.

Second, other theories besides regulatory fit could explain the crossover
pattern that we observe. Since our data are field data, it can only go so
far with ruling in regulatory fit. That said, it is encouraging that we
have a lot of data, and are thus able to provide some comment or light on
potential explanations and boundary conditions. One alternative
explanation is that players could be making deliberate cost-benefit (or
risk-reward) trade-off decisions. In light of the crossover pattern, this
would imply that for offensive players, the perceived reward of cheating
is greater than its cost when losing, whereas for defensive players, the
perceived reward of cheating is greater than its cost when winning. From a
cost-benefit perspective, in football (and most sports), the benefit to
cheating may in fact be greater than its cost when currently losing,
especially close to the end of a game. This is because most sports’
outcomes are binary; teams post a win or a loss (and it typically matters
less by how much a team wins or loses). Therefore, if a team is already
down, there is little cost to cheating to get ahead. At worst, the losing
team will lose by more points if caught, but the final outcome will be the
same regardless if a team unsuccessfully cheats or plays fair. 

This line of thinking could explain offensive players’ behaviors, but it
struggles to explain defensive players’ behaviors since the trade-off
decision reverses for defensive players; they cheat more when winning –
which is a costly strategy because a team can quickly lose its lead if
caught cheating. What could otherwise explain why defensive players cheat
while winning? It could be a piqued concern for not wanting to “blow the
lead”. When a team that is currently winning loses its lead, it is most
likely because the opposing team scored on its defense. This could place
blame on the defense; their primary role is to stop points from being
scored, and this role is crucial when the opposing team’s offense could
change the score in their favor – as though the stakes are higher for
stopping points while currently winning compared to stopping points while
currently losing. This could be the case because for a currently winning
defense, the score could qualitatively and unfavorably change when scored
on (from currently winning to currently losing), whereas for a currently
losing defense, the game’s victor-loser status is unchanged when scored
on. 

While theoretically possible, our robustness checks can speak a little to
whether blame-aversion or deliberate cost-benefit decision making are
observed in our data. For one, we find that defensive players commit more
fouls while winning in both cases in which the game-score is separated by
one possession or by multiple possessions. For a one-possession
game-score, the current victor-loser game status can change in one play,
which should place more pressure or blame on the defense when it is scored
on, compared with a multiple-possessions game-score. As Table 6 shows, the
defense fouls more in both cases; in fact, the effect is bigger for
multiple possessions, for which there is theoretically less blame. 

Relatedly, we can also speculate a little on whether the effects are due to
making strategic or deliberate cost-benefit decisions. If players are
making a deliberative trade-off and this is driving our results, then one
might expect our findings to hold only when the underlying penalties are
of lower cost. In contrast, we found our results to be robust across a
range of penalty types and with respect to the yardage assessed (the most
direct cost of a penalty). Further, if strategic decisions are driving our
results, this trade-off may look different among more-fatigued players
compared to less-fatigued players (Lambourne \& Tomporowski, 2010). In
our data, we observed the same pattern among low- and high-fatigued
players. We also observed the effect among both intentional fouls
(intentional grounding) and other fouls. We cannot assess if the other
fouls were intentional or not, but we do see evidence of the crossover
pattern across a range of fouls. Assuming that fouls are more or less
intentionally committed, the data do not clearly locate a role for
strategic decision making in our findings. All told, the robustness checks
demonstrate the breadth and generalizability of the finding, but they can
only speak a little to the prevalence of the theory, which leaves open the
role of regulatory fit, and other possible theories as well.

Of relevance, it may be argued that fouls in sports are qualitatively
different from committing unethical behaviors, perhaps because of how
frequently fouls occur in sports. Yet in keeping with a straightforward
definition of cheating (from the \textit{Oxford English Dictionary}: “to
act dishonestly or unfairly in order to gain an advantage, especially in a
game, a competition, an exam, etc.”), it follows that rule-breaking in
sports qualifies as cheating. This behavior not only violates the rules but
is committed to gain an advantage. Still, what is considered unethical is
subjective. For self-serving reasons, fouling players (and their fans) may
not consider the fouls as cheating, but fouled players (and their fans) may
feel differently and classify the fouls as cheating (Hastorf \& Cantril,
1954). On the discussion of whether rule-breaking in sports is unethical,
the sport ethicist, Warren Fraleigh (1984), argues that any rule-breaking
behavior in a sports contest committed by a player to gain advantage is
committing a moral violation. For instance, Fraleigh writes that breaking
the rules is “a moral concern because it is an exploitation of those who
competed in good faith” (p.\ 73). Despite Fraleigh’s conclusion, cheating
in sports is not the same as cheating in other domains like school or work
or taxes. Therefore it is an open question whether our results would apply
to other kinds of unethical behavior, including other kinds of cheating
behavior. People may hold divergent perceptions of cheating behavior
according to whether cheating happens in sports versus other domains.

Although what is considered cheating may not be widely agreed on, a benefit
to conducting research on fouls in sports contests is
\textit{observability}. As put by Balafoutas, Chowdhury, and Plessner
(2019): 

… contrary to many situations in business, politics, or other domains of
public and economic life in which individuals can conceal their behavior
(or are legally obliged to do so), behavior in sports is observable and
very well documented. Most sports events are nowadays televised and
recorded, and either the full events or at least informative summaries
thereof are widely available to the public. This feature is of particular
importance for the analysis of \textit{unethical behavior.} (emphasis
added; p.\ 2) 

Thus, on account of the observability of unethical behaviors in sports, we
are able to replicate past findings while also uncovering something new to
the research: the putative crossover effect between frame and regulatory
focus on unethical behavior. To our knowledge, our work is the first to
examine fouls in sports from a moral- and decision-theoretic perspective,
in a large-scale field study to boot. In this vein, our work also
complements a burgeoning area of research on testing behavioral science
phenomena in non-laboratory settings, like football (e.g., Harlow \&
Oswald, 2016; Massey \& Thaler, 2013). Notably, data drawn from football
games have led to the discovery of well-established findings in psychology,
such as motivated thinking and BIRGing (Cialdini et al., 1976; Hastorf \&
Cantril, 1954).

\subsection{Directions for Future Research}

Despite the benefits of our field study, future laboratory studies would
help clarify the effect of regulatory (mis)fit on influencing (un)ethical
behavior. Without a control condition, an open question is whether
regulatory misfit provokes unethical behavior, or whether regulatory fit
fosters ethical behavior. It would be informative to measure unethical
behavior with a control condition and compare it with manipulated
regulatory misfit and fit conditions. In this regard, the results could
reveal a possible downside to regulatory fit. Some researchers have
theorized that the same basic variables that predict motivation will also
predict unethical behavior (Hirsh, Lu \& Galinsky, 2018). And because
regulatory fit has been shown in research to foster motivation (Higgins,
2005), it could therefore potentially provoke unethical behavior (compared
to a control condition).

Future laboratory research might also employ manipulations of high- and
low-risk of detecting misbehavior, as well as manipulations of misbehavior
that are self- and other-serving. Such methods would allow for greater
insight into other-serving misbehaviors that are easily detected and
punishable – the kinds of misbehaviors that are rarely explored in
research on unethical behavior. While this is an oversight of most
research on unethical behavior, it is also a promising area for future
research, since punishable (vs.\ non-punishable) behaviors resemble more
the kinds of misbehaviors that occur outside of the laboratory. In the
present research, we have studied and highlighted these behaviors;
however, we could not conduct comparisons between them and self-serving
behaviors that are relatively free of detection and punishment. 

Finally, we are reminded of the work by Frank and Gilovich (1998) that
found that professional football and hockey players who wear black
uniforms commit more penalties than players who wear non-black uniforms.
Most importantly, their findings were attributed to both self-perception
and social perception processes, meaning the effect is based on players’
own behaviors, as well as the biased judgments of others (the referees who
were calling the penalties). In our research, we have discussed the
present findings in terms of self-perception. In particular, we did not
find evidence (in our analysis) that referees’ decisions precipitate the
crossover effect (we found the effect was consistent in situations in
which referees would be more or less likely to call a penalty; moreover we
found the effect was robust to game-level fixed-effects, which account for
games’ referees). But quite possibly, the findings could be helpfully
propped up by both self- and social perception. It remains to be seen, but
future research could assess whether regulatory (mis)fit is understood and
judged by others in this way – which is to say that, just as experiencing
regulatory (mis)fit influences one’s propensity for (un)ethical behavior,
so too might it lead observers to render a more or less punitive judgment
upon someone experiencing regulatory (mis)fit. In particular, research
might also consider the extent that status-judgments (e.g., judgments of
high-profile actors) interact with judgments of unethical behavior, in
juxtaposition to regulatory fit, considering judgments of unethical
behavior are influenced by transgressors’ status (Polman, Pettit \& Wiesenfeld, 2013).

Beyond replicating past research, our study found a heretofore untested and
significant crossover effect. We found that promotion focus was associated
with more misbehavior in a loss (vs.\ a gain) frame, whereas prevention
focus was associated with more misbehavior in a gain (vs.\ a loss) frame.
This crossover effect is consistent with regulatory fit theory. When there
is fit between frame and regulatory focus, people feel right about what
they are doing, which produces a sense of “moral rightness” (Camacho et
al., 2003, p.\ 499). In line with this view, we found unethical behavior is
highest when one’s frame is mismatched (misfit) with one’s regulatory
focus. This highlights the importance of taking a social-personality
psychological approach to the study of ethical decision making. As
evidenced by past research, unethical behavior has been traditionally
modeled in social-situational terms (e.g., by changing the frame), or in
person-dispositional terms (e.g., by examining personality variables) but
rarely both. Going forward, in order to better understand unethical
behaviors – between individuals, or between groups – researchers should
account for the person-situation framework, such as regulatory fit, for
understanding unethical decision making. This will help facilitate the
goal of generating ways to deter unethical decision making (e.g., Van
Swol, Polman \& Ahn, 2019).

While the present findings suggest evidence for the robustness of
regulatory fit effects, the mechanisms underlying regulatory fit effects
are still elusive. It is plausible that regulatory misfit may reduce
cognitive resources, precisely what are needed to keep one’s moral compass
on course (Gino, Schweitzer, Mead \& Ariely, 2011). In a related vein, it
could be argued that, depending on the regulatory focus, different moral
reasoning structures are accessible, and that the applicability of the
accessible moral reasoning depends on boundary conditions (Cornwell \&
Higgins, 2016, 2015), such as frame. Thus, as a result of a (mis)fit
between frame and regulatory focus, different rules for behavior may be
generated.

\section{Conclusion}

Going forward, researchers should account for regulatory fit. Seminal work
on motivation and persuasion has demonstrated the importance of regulatory
fit (Higgins \& Freitas, 2007). Work on unethical behavior is apt to
benefit from a similar perspective. Such approaches would dovetail with a
broader trend that regulatory fit leads to better quality of life outcomes
(Langsam, Freitas \& Higgins, 2005). As we have shown here, when it
“feels right,” people play by the rules (literally). 

\section*{References}
\begin{hangparas}{1em}{1}

Balafoutas, L., Chowdhury, S. M., \& Plessner, H. (2019). Applications of
sports data to study decision making. \textit{Journal of Economic
Psychology}, \textit{75}, 102153.

Bartling, B., Brandes, L., \& Schunk, D. (2015). Expectations as reference
points: Field evidence from professional soccer. \textit{Management
Science}, \textit{61}(11), 2646--2661.

Berger, J., \& Pope, D. (2011). Can losing lead to
winning?. \textit{Management Science}, \textit{57}(5), 817--827.

Brewer, M. B., \& Kramer, R. M. (1986). Choice behavior in social dilemmas:
Effects of social identity, group size and decision framing.
\textit{Journal of Personality and Social Psychology, 50}, 543--549.

Camacho, C. J., Higgins, E. T., \& Luger, L. (2003). Moral value transfer
from regulatory fit: What feels right is right and what feels wrong is
wrong. \textit{Journal of Personality and Social
Psychology}, \textit{84}(3), 498--510.

Cameron, J. S., \& Miller, D. T. (2009). Different ethical standards in
gain versus loss frames. In D. de Cremer (Ed.), \textit{Psychological
Perspectives on Ethical Behavior and Decision Making} (pp.\ 91–106).
Charlotte, NC: Information Age Publishing.

Cialdini, R. B., Borden, R. J., Thorne, A., Walker, M. R., Freeman, S., \&
Sloan, L. R. (1976). Basking in reflected glory: Three (football) field
studies. \textit{Journal of Personality and Social Psychology},
\textit{34}(3), 366--375.

Converse, B. A., \& Reinhard, D. A. (2016). On rivalry and goal pursuit:
Shared competitive history, legacy concerns, and strategy
selection. \textit{Journal of Personality and Social
Psychology}, \textit{110}(2), 191--213.

Cornwell, J. F., \& Higgins, E. T. (2016). Eager feelings and vigilant
reasons: Regulatory focus differences in judging moral
wrongs. \textit{Journal of Experimental Psychology: General},\textit{
145}(3), 338--355.

Cornwell, J. F., \& Higgins, E. T. (2015). The “ought” premise of moral
psychology and the importance of the ethical “ideal”.\textit{ Review of
General Psychology}, \textit{19}(3), 311--328.

Deis Jr, D. R., \& Giroux, G. A. (1992). Determinants of audit quality in
the public sector. \textit{Accounting Review}, 462--479.

De Martino, B., Kumaran, D., Seymour, B., \& Dolan, R. J. (2006). Frames,
biases, and rational decision-making in the human
brain. \textit{Science}, \textit{313}(5787), 684--687.

Fischbacher, U., \& Föllmi-Heusi, F. (2013). Lies in disguise—An
experimental study on cheating. \textit{Journal of the European Economic
Association}, \textit{11}(3), 525--547. 

Fraleigh, W. P. (1984). \textit{Right Actions in Sport: Ethics for
Contestants}. Champaign, IL: Human Kinetics Publishers. 

Frank, M. G., \& Gilovich, T. (1988). The dark side of self-and social
perception: Black uniforms and aggression in professional
sports. \textit{Journal of Personality and Social Psychology},
\textit{54}(1), 74--85.

Gino, F., Ayal, S., \& Ariely, D. (2009). Contagion and differentiation in
unethical behavior: The effect of one bad apple on the
barrel. \textit{Psychological Science}, \textit{20}(3), 393--398. 

Gino, F., \& Margolis, J. D. (2011). Bringing ethics into focus: How
regulatory focus and risk preferences influence (un)ethical
behavior. \textit{Organizational Behavior and Human Decision
Processes}, \textit{115}(2), 145--156.

Gino, F., Schweitzer, M. E., Mead, N. L., \& Ariely, D. (2011). Unable to
resist temptation: How self-control depletion promotes unethical
behavior. \textit{Organizational Behavior and Human Decision
Processes}, \textit{115}(2), 191--203.

Green, E., \& Daniels, D. P. (2014).\textit{ What does it take to call a
strike? Three biases in umpire decision making}. Paper presented at the
MIT Sloan Sports Analytics Conference, Boston MA.

Griffin, J. M., Kruger, S., \& Maturana, G. (2019). Personal infidelity and
professional conduct in 4 settings. \textit{Proceedings of the National
Academy of Sciences}, \textit{116}(33), 16268--16273. 

Grolleau, G., Kocher, M. G., \& Sutan, A. (2016). Cheating and loss
aversion: Do people cheat more to avoid a loss?. \textit{Management
Science}, \textit{62}(12), 3428--3438.

Harlow, L. L., \& Oswald, F. L. (2016). Big data in psychology:
Introduction to the special issue. \textit{Psychological Methods},
\textit{21}(4), 447--457.

Hastorf, A. H., \& Cantril, H. (1954). They saw a game; a case study.
\textit{Journal of Abnormal and Social Psychology}, \textit{49}(1),
129-134.

Higgins, E. T. (1998). Promotion and prevention: Regulatory focus as a
motivational principle. \textit{Advances in Experimental Social
Psychology}, \textit{30}, 1--46.

Higgins, E. T. (2000). Making a good decision: Value from
fit. \textit{American Psychologist}, \textit{55}(11), 1217--1230. 

Higgins, E. T. (2005). Value from regulatory fit. \textit{Current
Directions in Psychological Science, 14}(4), 209--213.

Higgins, E.T., \& Freitas, A.L. (2007). Regulatory fit: Its nature and
consequences. In C. Ostroff \& C. Judge (Eds.), \textit{Perspectives in
Organizational Fit}. Mahwah, NJ: Lawrence Erlbaum Associates. 

Hildreth, J. A. D., Gino, F., \& Bazerman, M. (2016). Blind loyalty? When
group loyalty makes us see evil or engage in it. \textit{Organizational
Behavior and Human Decision Processes}, \textit{132}, 16--36.

Hirsh, J. B., Lu, J. G., \& Galinsky, A. D. (2018). Moral utility theory:
Understanding the motivation to behave (un)ethically. \textit{Research in
Organizational Behavior}, \textit{38}, 43--59.

Idson, L. C., Liberman, N., \& Higgins, E. T. (2000). Distinguishing gains
from nonlosses and losses from nongains: A regulatory focus perspective on
hedonic intensity. \textit{Journal of Experimental Social
Psychology}, \textit{36}(3), 252--274.

Kahneman, D., \& Tversky, A. (1984). Choices, values, and frames.
\textit{American Psychologist}, \textit{39}(4), 341--350.

Kern, M. C., \& Chugh, D. (2009). Bounded ethicality the perils of loss
framing. \textit{Psychological Science}, \textit{20}(3), 378--384.

Köbis, N. C., Verschuere, B., Bereby-Meyer, Y., Rand, D., \& Shalvi, S.
(2019). Intuitive honesty versus dishonesty: Meta-analytic
evidence. \textit{Perspectives on Psychological Science}, \textit{14}(5),
778-796.

Kouchaki, M., \& Smith, I. H. (2014). The morning morality effect: The
influence of time of day on unethical behavior. \textit{Psychological
Science}, \textit{25}(1), 95--102.

Krawietz, S. A. (2013). \textit{Alleviating choking under pressure using
imagery }(Doctoral dissertation). University of Notre Dame. 

Kühberger, A. (1998). The influence of framing on risky decisions: A
meta-analysis. \textit{Organizational Behavior and Human Decision
Processes}, \textit{75}(1), 23--55.

Lambourne, K., \& Tomporowski, P. (2010). The effect of exercise-induced
arousal on cognitive task performance: A meta-regression
analysis. \textit{Brain research}, \textit{1341}, 12--24.

Langsam, K.L., Freitas, A.L., \& Higgins, E.T. (2005). Self-regulatory fit
and quality of life. In W. Lenderking and D. Revicki (Eds.),
\textit{Advances in Health Outcomes Research: Methods, Measurement,
Statistical Analysis, and Clinical Applications} (pp.\ 249-264). Dordrecht,
Netherlands: Kluwer Academic Press. 

Levine, E. E., \& Schweitzer, M. E. (2015). Prosocial lies: When deception
breeds trust. \textit{Organizational Behavior and Human Decision
Processes}, \textit{126}, 88--106. 

Levitt, S. D., \& List, J. A. (2008). \textit{Homo Economicus}
evolves. \textit{Science}, \textit{319}(5865), 909--910.

Massey, C., \& Thaler, R. H. (2013). The loser’s curse: Decision making and
market efficiency in the National Football League
draft. \textit{Management Science}, \textit{59}(7), 1479--1495.

Millar, M., White, R. M., \& Zheng, X. (2019). \textit{Substance abuse and
workplace fraud: Evidence from physicians}. Available at SSRN:
https://ssrn.com/abstract=3147938

Memmert, D., Plessner, H., Hüttermann, S., Froese, G., Peterhänsel, C., \&
Unkelbach, C. (2015). Collective fit increases team performances: extending
regulatory fit from individuals to dyadic teams. \textit{Journal of Applied
  Social Psychology}, \textit{45}(5), 274--281.

Neale, M. A., \& Bazerman, M. H. (1985). The effects of framing and
negotiator overconfidence on bargaining behaviors and
outcomes. \textit{Academy of Management Journal}, \textit{28}(1), 34--49.

Ordóñez, L. D., Schweitzer, M. E., Galinsky, A. D., \& Bazerman, M. H.
(2009). Goals gone wild: The systematic side effects of overprescribing
goal setting.\textit{ Academy of Management Perspectives}, \textit{23}(1),
6-16.

Padgett, M. Y., \& Morris, K. A. (2005). Keeping it “all in the family:”
Does nepotism in the hiring process really benefit the
beneficiary?. \textit{Journal of Leadership \& Organizational
Studies}, \textit{11}(2), 34--45.

Pettit, N. C., Doyle, S.P., Lount Jr., R. B. \& To, C. (2016). Cheating to
get ahead or to avoid falling behind? The effect of potential negative
versus positive status change on unethical behavior.
\textit{Organizational Behavior and Human Decision Processes},
\textit{137}(1), 172--183

Plessner, H., Unkelbach, C., Memmert, D., Baltes, A., \& Kolb, A. (2009).
Regulatory fit as a determinant of sport performance: How to succeed in a
soccer penalty-shooting. \textit{Psychology of Sport and
Exercise}, \textit{10}(1), 108--115.

Polman, E., Pettit, N. C., \& Wiesenfeld, B. M. (2013). Effects of
wrongdoer status on moral licensing. \textit{Journal of Experimental
Social Psychology}, \textit{49}(4), 614--623.

Rajgopal, S., \& White, R. (2015). \textit{Cheating when in the hole: The
case of New York City taxis}. Unpublished manuscript, Columbia University.

Ranson, M. (2014). Crime, weather, and climate change. \textit{Journal of
Environmental Economics and Management}, \textit{67}(3), 274--302.

Robben, H. S., Webley, P., Weigel, R. H., Wärneryd, K. E., Kinsey, K. A.,
Hessing, D. J., Martin, F. A., Elffers, H., Wahlund, R., Van Langenhove,
L., \& Long, S. B. (1990). Decision frame and opportunity as determinants
of tax cheating: An international experimental study. \textit{Journal of
Economic Psychology}, \textit{11}(3), 341--364.

Roczniewska, M., Retowski, S., \& Higgins, E. T. (2018). How
person-organization fit impacts employees’ perceptions of justice and
well-being. \textit{Frontiers in Psychology}, \textit{8}, 2318.

Ryan, W., Evers, E., \& Moore, D. A. (2018). \textit{False positive
Poisson}. Available at SSRN: https://ssrn.com/abstract=3270063

Schindler, S., \& Pfattheicher, S. (2017). The frame of the game:
Loss-framing increases dishonest behavior. \textit{Journal of Experimental
Social Psychology}, \textit{69}, 172--177. 

Schurr, A., \& Ritov, I. (2016). Winning a competition predicts dishonest
behavior. \textit{Proceedings of the National Academy of
Sciences}, \textit{113}(7), 1754--1759.

Schweitzer, M. E., DeChurch, L. A., \& Gibson, D. E. (2005). Conflict
Frames and the use of deception: Are competitive negotiators less
ethical?. \textit{Journal of Applied Social Psychology}, \textit{35}(10),
2123-2149. 

Schweitzer, M. E., Ordóñez, L., \& Douma, B. (2004). Goal setting as a
motivator of unethical behavior. \textit{Academy of Management
Journal}, \textit{47}(3), 422--432.

Shao, W., Grace, D., \& Ross, M. (2015). Self-regulatory focus and
advertising effectiveness. \textit{Marketing Intelligence \&
  Planning}, \textit{33}(4), 612--632.

Siniver, E., \& Yaniv, G. (2018). Losing a real-life lottery and dishonest
behavior. \textit{Journal of Behavioral and Experimental
Economics}, \textit{75}, 26--30.

Simkin, M. G., \& McLeod, A. (2010). Why do college students cheat?
\textit{Journal of Business Ethics}, \textit{94}(3), 441--453.

Skarlicki, D. P., \& Folger, R. (1997). Retaliation in the workplace: The
roles of distributive, procedural, and interactional
justice. \textit{Journal of Applied Psychology}, \textit{82}(3), 434--443.

Solgos, J. T. (2016). \textit{The effect of regulatory focus on ethical
decision-making }(Doctoral dissertation). Ohio University.

Spiegel, S., Grant-Pillow, H., \& Higgins, E. T. (2004). How regulatory fit
enhances motivational strength during goal pursuit. \textit{European
Journal of Social Psychology}, \textit{34}(1), 39--54.

Tenbrunsel, A. E., \& Thomas, J. (2015). \textit{The street, the bull and
the crisis: A survey of the US \& UK financial services industry}. New
York: Labaton Sucharow. 

Treviño, L. K., Weaver, G. R., \& Reynolds, S. J. (2006). Behavioral ethics
in organizations: A review. \textit{Journal of
Management}, \textit{32}(6), 951--990.

Unkelbach, C., Plessner, H., \& Memmert, D. (2009). “Fit” in sports:
Self-regulation and athletic performances. In J. Forgas, R. F. Baumeister,
\& D. M. Tice (Eds.), \textit{Psychology of Self-Regulation: Cognitive,
Affective, and Motivational Processes} (pp.\ 93-105). New York: Psychology
Press.

\vfill
\break

Van Swol, L. M., Polman, E., \& Ahn, H. P. (2019). Deterring deception:
Approaches to maximize ethical behavior in social interactions and
organizations. In T. Docan-Morgan (Ed.), \textit{The Palgrave Handbook of
Deceptive Communication }(pp.\ 673-688). Palgrave Macmillan. 

Vincent, L. C., Emich, K. J., \& Goncalo, J. A. (2013). Stretching the
moral gray zone: Positive affect, moral disengagement, and
dishonesty. \textit{Psychological Science}, \textit{24}(4), 595--599.

Vriend, T., Jordan, J., \& Janssen, O. (2016). Reaching the top and
avoiding the bottom: How ranking motivates unethical intentions and
behavior. \textit{Organizational Behavior and Human Decision
Processes}, \textit{137}(1), 142--155. 

Yen, C. L., Chao, C. H., \& Lin, C. Y. (2011). Field testing of regulatory
focus theory. \textit{Journal of Applied Social Psychology}, 41,
1565-1581.

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