# Teamwork and Spillover Effects in Performance Evaluations††thanks: We thank
Riccardo di Francesco, Daniel Goller and Tommy Krieger for valuable comments
on a previous draft of this paper.

Enzo Brox
University of St.Gallen University of St.Gallen, Swiss Institute for Empirical
Economic Research, Switzerland<EMAIL_ADDRESS>Michael Lechner
University of St.Gallen University of St.Gallen, Swiss Institute for Empirical
Economic Research, Switzerland<EMAIL_ADDRESS>Michael Lechner is
also affiliated with CEPR, London, CESIfo, Munich, IAB, Nuremberg, IZA, Bonn,
and RWI, Essen.

###### Abstract

This article shows how coworker performance affects individual performance
evaluation in a teamwork setting at the workplace. We use high-quality data on
football matches to measure an important component of individual performance –
shooting performance – isolated from collaborative effects. Employing causal
machine learning methods, we address the assortative matching of workers and
estimate both average and heterogeneous effects. There is substantial evidence
for spillover effects in performance evaluations. Coworker shooting
performance, meaningfully impacts both, manager decisions and third-party
expert evaluations of individual performance. Our results underscore the
significant role coworkers play in shaping career advancements and highlight a
complementary channel, to productivity gains and learning effects, how
coworkers impact career advancement. We characterize the groups of workers
that are most and least affected by spillover effects and show that spillover
effects are reference point dependent. While positive deviations from a
reference point create positive spillover effects, negative deviations are not
harmful for coworkers.

Keywords: Teams, Peer effects, Performance evaluation, Causal machine learning
JEL Classification: J31, D84, M51, M52, M54, Z22

"Great things in business are never done by one person. They’re done by a team
of people.”

(Steve Jobs, CEO, Apple Inc.)

"The nicest thing about teamwork is that you always have others on your side.”

(Margaret Carty, CEO, Maryland Library Association)

##  1 Introduction

Organizations increasingly embrace collaborative and team-based approaches to
enhance productivity and promote innovation Lazear and Shaw (2007); Deming
(2017). However, performance evaluations, which significantly impact workers’
compensation and career advancement, typically take place on the individual
level Prendergast (1999); De Janvry et al. (2023); Frederiksen et al. (2020).
This challenges conventional management practices, as it requires rewarding
and evaluating employees based on their contributions, even when these are not
perfectly observed or separable from coworker influences Jones (2021).
Consequently, it creates dependencies between workers that are crucial to
understand for organizations to accurately assess their employees and for
researchers that seek to understand inequalities in career outcomes.

The objective of performance evaluations is to recognize valuable signals of a
worker’s performance. In a teamwork context, dependencies between coworkers
make it difficult to obtain accurate information on individual contributions
to team performance Frederiksen et al. (2017). This requires employers often
to resort to subjective evaluations.111For a review of different approaches
studying the use of subjective performance evaluations, see kampkotter2016.
For another reference stressing the need of studying subjective performance
evaluations due to its ubiquitous use, see oyer2011. In this study, we
investigate whether and how the subjective evaluation of the performance of a
worker is affected by coworkers. We thereby test a complementary mechanism how
coworkers exert an influence on the career outcomes of their peers beyond
productivity and learning spillovers Arcidiacono et al. (2017); Jarosch et al.
(2021).

From a research perspective, pinpointing the impact of coworker performance on
individual performance evaluations encounters several challenges. First,
researchers do not have access to the complete array of information available
to employers regarding the employees. Second, evaluating the individual
performance of workers can be problematic, particularly within teamwork tasks
where their contributions may be less discernible. Third, coworker performance
is likely influenced by one’s own performance, making it difficult to untangle
the extent to which coworker performance should be attributed to one’s own
evaluation. Fourth, coworker assignment is not random and high-skilled workers
are likely to be matched with high-skilled coworkers. Thus, the assortative
matching of employers poses challenges to the causal interpretation.

This paper addresses the aforementioned challenges by utilizing a
comprehensive dataset on performance in sport contests. We focus on soccer
(football, German Bundesliga), and exploit the use of advanced player tracking
technologies to measure a specific aspect of players’ productivity – shooting
performance. Linking information about the quality of a chance to score a
goal, defined as a probability of a shot resulting in a goal (expected goals),
and the outcome of the shot allows assessing the shooting performance of a
player and abstracting it from collaborative effects.222The idea behind this
approach is similar to evaluating chess moves with a chess engine Künn et al.
(2021), where the pre move positioning (and post move positioning) of chess
figures is used to evaluate the quality of chess moves. We argue that, from
the perspective of a player on the field, coworkers shooting performance can
be considered as randomly assigned. We address the assortative matching of
workers using detailed information on worker quality, match circumstances,
manager characteristics, and methods from the causal machine learning
literature that enable flexible estimation of average and heterogeneous causal
effects.

Although the shooting performance of coworkers is beyond the control of the
individual worker, it significantly influences judgments and decisions related
to players’ performance. Coworker performance has a meaningful impact on
manager decisions regarding whether to field a player in the next match.
Comparing the highest degree of coworker performance to the lowest degree of
coworker performance under comparable circumstances decreases the probability
to be replaced in the starting line up on average by 13% relative to the
sample mean. The size of the effect is equivalent to one-third of the effect
of the own performance in the same task. While managers have strategic
interest to field the most successful team in the upcoming match, also expert
journalists’ evaluations of a players’ performance are substantially affected
by coworker performance. Again, comparing the highest degree of coworker
performance to the lowest degree of coworker performance leads to an almost
11% increase in the own evaluation. We present evidence against alternative
interpretations for our results and conduct various robustness checks to
support our identification strategy.

We further investigate whether good and bad performances cause asymmetric
spillover effects. A large literature documents that behavior in various
domains is reference point dependent (e.g., gneezy1997, pope2011). We use the
number of expected goals coworkers are exposed to as a natural reference
point, and investigating whether positive and negative deviations from this
reference point cause asymmetric spillover effects. There is substantial
evidence for asymmetric effects. Positive deviations have a substantial
positive impact on coworkers. Negative deviations, however, do not generate a
negative impact on coworkers. For journalists’ evaluations, large negative
deviations from the reference point are even less detrimental than small
negative deviations.

Despite documenting spillover effects in performance evaluations, it is
important to understand which type of workers are most and least affected by
spillover effects and to describe circumstances that trigger spillover
effects. We exploit recent advances in causal machine learning to investigate
heterogeneous treatment effects.

The first important observation is that the vast majority of players are
affected by spillover effects. In addition, for manager decisions, player
strength and tenure are negatively correlated with the size of the spillover
effect, suggesting that new and less skilled players are affected most by
coworker performance. This is in line with the idea that managers have less
trust or less information about these players. We also find stronger spillover
effects in lower quality teams, where good performance and success are less
frequently observed. However, there is no evidence that the responsibility for
a similar task is correlated with the effect size.333Shooting performance is
primarily important for offensive players who’s main task is to score goals,
while a defensive player’s main task is to prevent the opposing team from
scoring goals.

For journalists’ evaluations, we find that individual characteristics like
player skill-level or club-tenure are not related to the effect size. However,
spillover effects are highest for players who are responsible for a similar
task (offensive players). Furthermore, offensive players are not only most
affected by spillover effects, but theirs performances also exhibit the
highest spillover effects on other players. Results from a policy simulation
exercise and a k-means clustering approach to characterize the most and least
affected groups of players support our findings.

In the last part, we examine potential long-term effects. While fielding
decisions by managers already have career implications, as players receive
more playing time, season-level aggregates of our treatment are also
associated with elevated player evaluations over the following two years.
Hence, spillover effects from coworker performance in a teamwork setting
possess the potential to impact worker careers. This underscores an additional
channel through which coworkers shape the career outcomes of their peers
beyond their well documented effects on productivity Mas and Moretti (2009);
Gould and Winter (2009) and skill acquisition Amodio et al. (2023); Jarosch et
al. (2021).

Since the findings of this paper are obtained from an industry where every
action of a worker is observable, we argue that spillover effects from
coworker performance are even more likely to occur in other types of
organizations. In standard organizational settings, worker performance in a
teamwork task is less observable compared to our setting. This increased
difficulty in objectively rewarding individuals for their contributions to
team performance amplifies the reliance on subjective judgments. To the best
of our knowledge, this is the first paper studying the direct impact of
coworker performance on individual performance evaluation in a teamwork
setting and providing evidence for spillover effects in individual performance
evaluations at the workplace.

###  1.1 Relation to literature

Our study contributes to various strands of the literature. First, we add to
the existing research on peer effects in the workplace. There are multiple
potential factors that can result in productivity spillovers among coworkers.
One such factor is the nature of the production technology itself, where
coworkers impacting each other’s marginal productivity Gould and Winter
(2009); Arcidiacono et al. (2017). Additionally, observing coworkers’ efforts
motivates individuals to exert more effort themselves Kandel and Lazear
(1992); Falk and Ichino (2006); Cohen-Zada et al. (2023).444The designs of pay
structures, dismissal policies and input heterogeneity also generate
externalities among workers. For example, relative performance evaluations and
team-based assessments create interdependencies in coworkers’ effort choices
Bandiera et al. (2005); Mas and Moretti (2009); Amodio and Martinez-Carrasco
(2018). Beyond contemporaneous productivity spillover effects, several recent
studies emphasize the additional benefits of peer learning and knowledge
transfer among workers Papay et al. (2020). nix2020 found that an increase in
the average education level of peers positively impacts earnings in subsequent
years. akcigit2018 demonstrated that exposure to accomplished patent holders
increases the likelihood of patenting and improves the quality of patents,
underscoring the role of knowledge diffusion through peers. herkenhoff2018
explored learning with production complementarities, revealing how workers’
skills can be enhanced through peer interactions.555Outside workplace
settings, a substantial body of literature in education economics delves into
contemporaneous and lasting peer effects. For a review, refer to sacerdote2014
and bramoulle2020. Additionally, jarosch2021 documented a robust association
between having highly paid coworkers and future wage growth, highlighting
spillover effects in terms of career advancement.

Our study contributes to the existing literature by revealing an additional
channel through which workers shape the career outcomes of their peers. In a
team-based setting, we showcase a significant impact of coworkers on the
performance evaluations of their peers, extending beyond productivity
spillovers. Given the pivotal role of performance evaluations in compensation
and career advancement, our findings underscore the importance of coworkers,
especially in teamwork contexts. While our results do not negate the existence
of learning from coworkers, they highlight an additional and potentially
widespread mechanism through which workers influence their peers’ career
outcomes in modern organizations. These findings align with the reduced-form
evidence presented in jarosch2021 using German administrative labor market
data and speak to a broader literature studying how heterogeneity in workplace
conditions affects career outcomes Arellano-Bover (2024); von Wachter (2020).

Second, our findings contribute to the literature on performance evaluations,
which are pivotal in organizations for determining compensation, promotion
opportunities, and providing employee feedback De Janvry et al. (2023);
Frederiksen et al. (2020). The existing literature has explored various
dimensions of performance evaluations. First, research on performance
evaluation design has examined different approaches, such as relative
performance evaluations, objective metrics, and multidimensional assessments
Lazear and Shaw (2007); Baker and Hubbard (2003); Cascio and Aguinis (2008);
Manthei and Sliwka (2019). Second, studies have shown that performance
feedback influences employee motivation, job satisfaction, and subsequent
performance Ilgen et al. (2005); Kampkötter and Sliwka (2018). Third, biases
in performance evaluations have been extensively studied Ilgen and Feldman
(1983); Gauriot and Page (2019); Principe and van Ours (2022).666A related
literature studies whether women and men are differentially recognized for
performance Sarsons et al. (2021); Card et al. (2019, 2022). Several recent
studies use data from the sports industry to study biases in performance
evaluations, due to observability of individual performance. principe2022 uses
data from the top Italian soccer league to show that black players receive
worse evaluations compared to non-black players, despite no differences in
performance. gauriot2019 and lefgren2015 provide evidence for an outcome bias
using data from professional soccer and basketball. They exploit quasi-
experimental settings where luck, rather than effort and performance,
determines the outcome, affecting performance evaluations. This is argued to
violate the informativeness principle Holmström (1979), which states that only
valuable signals for performance should be rewarded.777There is also a
substantial psychological literature on the outcome bias. Following baron1988,
several studies have suggested that individuals tend to give too much
importance to information about the outcome when trying to assess the quality
of decisions made by an agent (e.g. alicke1994, gino2010). We contribute to
this literature by studying spillover effects in performance evaluations in a
teamwork setting and by providing evidence that coworkers present another
source of bias in individual performance evaluations.

Third, our findings contribute to a broader literature on teamwork spanning
various disciplines, including economics, business, organizational behavior,
and psychology. The economic literature extensively examines the benefits of
teamwork in terms of enhancing productivity and fostering innovation Smith and
Krueger (2000); Lazear (1999), focusing on the division of labor,
specialization, and coordination mechanisms within teams Akerlof and Kranton
(2005); Weidmann and Deming (2021); Marx et al. (2021); Brox and Krieger
(2022). From a business perspective, research explores how effective teamwork
can lead to improved organizational performance, customer satisfaction, and
competitive advantage Katzenbach and Smith (2015); Hackman and Wageman (2005).
The psychological literature examines individual and team-level factors
impacting team effectiveness, including team cohesion, trust, conflict
management, and motivation Mathieu et al. (2017); West (2012).

This paper contributes to this literature by examining spillover effects in
teams. Given the non-trivial nature of this task, the empirical literature on
peer effects in teamwork settings is relatively scarce Cornelissen et al.
(2017). weidmann2021 employ an experimental setup to study spillover effects
in teamwork, demonstrating that individuals with higher socio-emotional skills
have the potential to significantly enhance team performance. arcidiacono2017
use data from the North American Basketball League (NBA) to illustrate
substantial differences among basketball players in their contributions to the
performance of their peers, also arguing that players receive less credit for
spillover effects than for own performance. cohen2023effort provide evidence
of peer effects in effort provision using data from the professional Israeli
soccer league. Additionally, amodio2023b reveal skill adoption patterns among
coworkers using data from the North American Hockey League (NHL). Our
contribution to the understanding of teamwork settings lies in revealing
externalities arising from coworker performance.

The remainder of the paper is structured as follows. Section 2 outlines the
key elements of the German Bundesliga. Section 3 introduces the datasets
employed in our empirical analysis. Section 4 details the empirical strategy
and estimation procedures. Section 5 presents the findings of our empirical
analysis. In Section 6, we concentrate on long-run effects. Finally, Section 7
concludes.

##  2 Institutional Framework

To explore the impact of coworkers on individual performance evaluations, we
utilize data from the Bundesliga, the premier division of German male
football. The Bundesliga is widely regarded as one of the top-five football
leagues in Europe and consists of 18 clubs. The league operates in a double
round-robin format, with each club facing all other opponents twice in a
season, totaling 34 matches per club evenly distributed between home and away
games. Matches predominantly occur on weekends, with the first round typically
spanning from August to December, followed by a brief winter break. The second
round runs from January to May/June, with a change in the home field advantage
between the two rounds.

Teamwork in soccer is fundamental to the success of a team. It involves
coordinated efforts among players to achieve common objectives, such as
creating chances to score goals and preventing the opposing team from scoring
goals. Each match comprises two halves of 45 minutes each, and a team secures
a victory by scoring more goals than its opponent. The winning team earns
three ranking points, while the losing team receives none. In the event of a
draw, both teams are awarded one point. The final league position at the end
of the season is determined by the total accumulated ranking points,
influencing relegation decisions and participation in international
competitions in the following season. Before each match, the team manager
selects eleven starting players — a goalkeeper and ten field players
(defender, midfielder, attacker) — from the available squad. Additionally, up
to seven potential substitutes can be nominated, with the opportunity for up
to three substitutions during the match.

##  3 Data

We utilize data spanning from the 2010-2011 season to the 2019-2020 season,
with the primary data source being Opta, a private company specializing in
data collection and distribution for various
sports.888https://www.statsperform.com/opta/ Opta specializes in gathering in-
play information for football matches, capturing details such as passes,
duels, and shots on goal. With advanced tracking technology, they record
spatial coordinates, providing a comprehensive overview of player actions
during matches. The dataset includes the names of the involved players in
every event of the match, the time of each action, and the corresponding
spatial coordinates.999Event data quantifies what happens on the pitch in
relation to individual player actions. For example, each time a player passes
the ball, tackles an opponent, shoots on goal, or saves a shot is one event.

The analysis relies on two crucial features of this dataset. First, it
provides comprehensive information on every shot taken, encompassing the
player’s name, the outcome (whether it resulted in a goal or not), and a
quantitative assessment of the quality of the chance from which the shot
resulted (further details below in Section 4.1 and in Appendix B). We exploit
this information to measure a player’s shooting performance. Second, the
dataset offers detailed performance measures at the individual level. Through
Opta’s advanced tracking technology, player tracking is conducted throughout
the match, resulting in over 100 categories of performance metrics at the
individual level. This level of granularity provides precise insights into the
actions of each player. In addition to standard measures like goals scored, it
encompasses less observable performance indicators such as attempted dribbles
and successful crosses. A comprehensive description of these performance
measures is relegated to Appendix A (Table A.2 and Table A.3). We also gather
information on each team’s line-up and substitutions from this dataset.

We enhance this dataset by incorporating additional information from various
sources. First, we gather background details on the players, including their
date of birth, date of hiring by a Bundesliga club, playing position,
preferred foot, nationality, and physical attributes. Furthermore, the data is
augmented with two time-varying expert-based indicators of player quality. One
measure is derived from www.transfermarkt.com, a reputable platform for
tracking player market values. The other measure originates from the popular
video game FIFA, developed by Electronic Arts. Each player is assigned a
playing strength rating ranging from 0 to 100. This measure offers notable
advantages compared to market values. The game is widely played globally and
strives for realistic player evaluations, motivating game developers to ensure
accuracy. Additionally, the measure is age-independent. Finally, experts
evaluate players across various game-relevant attributes that capture
different aspects of a player’s skills. These include shooting skills, passing
skills, running skills, dribbling skills, physical skills, and defensive
skills Brox and Krieger (2022). An example of a player’s evaluation is
illustrated in Figure A.1 in Appendix A. To avoid endogeneity issues, we
utilize quality measures updated before the start of each half-season.

Second, we incorporate player ratings from Kicker, a popular sports newspaper
in Germany. After each match, since 1963, independent experts assign ratings
to players on a scale of 1 to 6 in 0.5 increments, with 1 being the best grade
and 6 being the worst grade. The grades appear in the online and print version
of the newspaper after each match day. For each match, there are two experts
assigned, and the observed grade is the joint evaluation of both experts. All
players who played for at least 30 minutes in a match receive a rating. For an
example of such an evaluation, see Figure A.2 in Appendix A.

Third, we enrich our dataset with match-related information to characterize
match circumstances. This includes for example whether a club has previously
participated in international competitions or is scheduled to participate in
an international match following the current one. Furthermore, we calculate
the number of days between each team’s previous and next match, capture
whether a match is played on the home ground, the ranking position of the
participating teams, whether a team has been relegated in the season before,
and details regarding the manager’s experience. For a comprehensive list,
please refer to Table A.1 in Appendix A.

##  4 Empirical Strategy

###  4.1 Identification

Identifying the effect of coworker performance on individual performance
evaluation is challenging for at least two reasons. First, in a teamwork
setting, coworker performance is likely to depend on individual performance.
This makes it difficult to isolate coworker performance from individual
performance, which naturally influences performance evaluations. Second,
coworker performance is likely to depend on coworker quality. As coworkers are
not randomly assigned, this introduces the potential for selection bias when
estimating the effect of coworker performance on individual performance
evaluations. The remainder of this section describes how we address these
challenges.

To address the former challenge, we leverage the richness of our data,
enabling us to measure the performance of workers in one specific dimension
isolated from coworker influences. From the point of view of the individual
worker, coworker shooting performance is as good as randomly assigned. For
simplicity, consider player A playing alongside player B. In two subsequent
matches, player B faces a chance to score a goal from a similar position. In
the first match, player B scores the goal, while in the second match, he fails
to score.101010Failing to score can be the result of multiple issues. Player B
may either perform worse, or be less lucky, or the opponent team (goalkeeper)
shows a better performance. However, none of these issues is influenced by
player A. The identifying assumption rests on the fact that we can adequately
control for the performance of player A in creating the scoring opportunity
for player B. This allows us to control for factors that jointly determine
shooting performance, as well as player A’s performance evaluation (details
are discussed in Section 4.2 below).

Although shooting performance is not influenced by coworkers, the assignment
of workers to coworkers is not random. Assortative matching between workers
and coworkers results in a positive association between coworker
quality/performance and performance evaluation. We address this issue using
state-of-the-art methods from causal machine learning and detailed information
on worker quality, teams and match circumstances. In particular, we control
for the quality of workers in all our specifications in a flexible way and
also include controls that describe the circumstances of the match, such as
the overall quality of the teams, their current form, the regeneration time of
each team before and after a match, and whether a team faces important matches
before and after the match.111111Note that since we control in a detailed way
for the quality of the worker, we eliminate concerns regarding worker quality
jointly affecting coworker performance and performance evaluation.

A remaining concern regarding the argument that coworker performance directly
affects individual performance evaluation is that coworker quality, even after
addressing assortative matching of workers, may affect individual performance
and thus individual performance evaluations. We consider this unlikely since
shooting performance is likely to be determined by shooting ability, which is
usually not the dominant skill/ability that creates the largest spillover
effects. However, shooting ability may be correlated with other skills that
are more prone to create coworker spillover effects in productivity. We
address this concern in the robustness checks in two ways. First, by adding
detailed coworker quality control measures. Second, we exploit the richness of
the data and include a large set of individual performance metrics. This
should eliminate the concern that productivity spillovers resulting from day-
to-day variation in coworker quality are driving our result (Table 5.2).

###  4.2 Shooting Performance

Measuring individual performance within a team-based task presents inherent
challenges due to the complex nature of performance observation and its
reliance on multiple contributors. Take, for instance, the example of a soccer
player’s pass. Whether player A is able to play a successful pass hinges not
only on the passer’s skill but also to a significant extent on the recipient’s
positioning and decision-making, as well as on the quality of the previous
pass before player A received the ball. In this study, we leverage recent
advancements in player monitoring within the sports industry and exploit a
method that enables the separation of players shooting performance from
collaborative effects.To do so, we leverage a widely used metric in modern
sports analytics called ’expected goals’ (xG).

The xG metric is extensively used in predictive modeling, player, and team
analysis. It quantifies the quality of a scoring opportunity at the moment
when a shot is taken, by employing machine learning to estimate the
probability of a shot resulting in a goal. These predictions are derived from
a training data set containing information from thousands of shots.
Importantly, xG probabilities are not influenced by the player’s skill level;
instead, they consider factors such as the shot’s location (distance and angle
to the goal), the positioning of other players of both teams, the goalkeeper’s
position, the type of assist, the shot type, and the flow of the game in the
second when a shot is taken.121212For a more comprehensive explanation of how
expected goals are calculated, refer to Appendix B.

Figure 4.1: Expected Goals

(a) Shots

(b) Individual

(c) Team

Notes: This figure shows histograms of expected goals at different aggregation
levels. Panel (a) displays the distribution of expected goal values at the
shot level. Panel (b) aggregates expected goals at the individual-match level,
while Panel (c) aggregates expected goals at the team-match level.

Figure 4.1 provides information on the xG metric. Figure 1(a) shows the
distribution of xG values over all shots in our sample. xG values range
between zero and one, with the majority of values close to zero. The small
spike between 0.7 and 0.8 constitutes penalties that have a fixed xG value.
Figure 1(b) displays the distribution of aggregated xGs per individual in a
match, ranging from 0 (if a player does not face a chance to score) to around
3.4. Approximately 40% of individual-match observations do not involve a
chance to score.131313In Appendix B, Figure B.1 shows the distribution of xG
by position. Reassuringly, strikers face the highest xG values, while
defenders face the lowest xG values. In Figure 1(c), we show aggregated xG
values by team in a match, ranging from 0 to around 6, with teams expected to
score slightly more than 1 goal on average.

We utilize the assessment of chance quality via xG to quantify the shooting
performance of individual players. Specifically, we measure shooting
performance by considering the number of goals a player scores under the
condition of the chance quality he encounters. This allows to isolate an
important component of individual performance, in a teamwork setting, from the
influence of coworkers.141414We conduct a further test to verify that our
approach indeed measures shooting performance by correlating expert
assessments of shooting ability and our approach to measure shooting
performance. For details, see Appendix B Table B.1.

###  4.3 Variable definitions

####  4.3.1 Outcome variables

We employ two performance evaluation metrics: manager decisions to field
players in subsequent matches and expert evaluations provided by journalists.
In this section, we provide a more detailed description of these outcome
variables.

Team managers play a crucial role in making decisions about player selection
throughout the season. They are tasked with assessing each player’s
performance at a particular moment and making decisions based on these
evaluations when forming match lineups Gauriot and Page (2019). Existing
research suggests that the primary objective of team managers is to maximize
the probability of winning matches, rather than solely focusing on profits
Sloane (1971); Garcia-del Barrio and Szymanski (2009). Therefore, managers are
motivated to select what they perceive as the best players for each match. Our
analysis focuses on the fielding decisions for starting line-ups, aiming to
determine whether a player’s chances of staying in the starting line-up vary
based on the shooting performance of their coworkers.151515It is important to
note that we lack information about the availability of players not in the
lineup for the next match. While we assume this absence is not correlated with
coworkers’ shooting performance due to its quasi-random nature, the lack of
control for this factor may introduce noise, potentially affecting the
likelihood of observing an effect, if one exists.

The second outcome variable are journalists’ ratings published in the sports
magazine Kicker. These ratings are presented after each match and represent a
subjective assessment of the players’ performance. To ensure easier
interpretation, we invert the scale, with our measure ranging from 1 (poor) to
6 (excellent). There are important differences between journalists’
evaluations and manager decisions. First, unlike manager decisions,
journalists’ evaluations do not have immediate career consequences. Second,
journalist do not have an incentive to field the most promising team for the
next match. However, the evaluation of soccer players by journalists is
subject to public debate and forms the basis for an interactive online manager
game. Therefore, journalists have incentives to evaluate as objectively as
possible the individual performance of each
player.161616https://www.sueddeutsche.de/sport/fussball-bundesliga-noten-
vielleicht-reicht-auch-mal-eine-fuenf-1.141370

####  4.3.2 Coworker Performance

The objective is to investigate the influence of coworkers’ shooting
performance on performance evaluation. The shooting performance of coworkers
is measured as follows. We utilize data on all 79,876 shots taken over the ten
seasons of German soccer and leverage information on the outcome of each shot,
the quality of the chance (xG), and the player who took the shot. For each
player $i$ and match $m$, we calculate the sum of goals scored by all his
coworkers $j$ in the starting lineup: $GC_{im}=\sum_{j\neq i}\text{goals}$.
This variable serves as the treatment variable in the main analysis.

To isolate the shooting performance of coworkers from the individual’s own
performance, a crucial control variable is the measure of the quality of
chances that all coworkers $j$ of an individual $i$ faced. We measure the
quality of chances that coworkers were exposed to in the same way as the
number of goals scored by coworkers. For each player $i$, we calculate the sum
of xG that his coworkers $j$ in match $m$ were exposed to:
$xGC_{im}=\sum_{j\neq i}xG$. This control variable is used in all
specifications.171717We show an alternative specification in which we define
coworker performance directly via the difference between $GC_{im}$ and
$xGC_{im}$ in Section 5.2.

####  4.3.3 Control variables

To approximate the identification prerequisites discussed in Section 4.1, a
vector of pre-determined variables $X_{i}$ is chosen to control for
assortative matching of coworkers. To control for assortative matching of
workers into teams, a set of individual background characteristics is included
in this vector. This set of variables includes various measures to control for
worker quality and skills in various categories, as discussed in detail in
Section 3 above. It also includes measures of the time a worker is already in
the club, their age, nationality, and physical composition. The overall
strength of the team is controlled for with a pre-season measure for team
strength that remains constant over the half-season. To control for sorting in
particular matches, a detailed set of characteristics of the match
circumstances is included in $X_{i}$. These include the season and half-season
in which the match takes place, whether a match is played at home, the
position of both teams in the league table, whether the team is engaged in
international competitions, information on whether international matches have
been taking place before or after a match, the number of days between the last
and the current match, and the number of days between the current and the next
match to control for potential strategic fielding decisions. Since the manager
takes the decision on which players to field, information on the time the
manager is in the club and about his experience as a coach is also added. For
the complete list of control variables used in the specification, refer to
Table A.1.

To avoid biases due to using bad controls, we focus on control variables,
which are predetermined before the observation period (match) Angrist and
Pischke (2009). Nonetheless, to enhance the robustness of the findings, we
conducted additional analyses by expanding the vector of controls to encompass
factors such as individual performance metrics in the match.

###  4.4 Sample

In general, information is available for all players who participated in a
match during the seasons 2010 to 2020. The sample is restricted in several
ways. First, it is limited to starting players. This simplifies the
interpretation of the managerial decision on whether to field a player in the
next match and allows interpreting the results as changes in the probability
of staying in the starting line-up. Additionally, for almost all players, the
necessary information is available, as players have to play at least 30
minutes to receive a grade. This ensures a comparable sample for both outcome
variables. Second, goalkeepers are excluded from the analysis since they
perform a very different task, are rarely replaced, and the quality measures
cannot characterize them in the same way as other players. Third, all matches
from the last match day of a season are dropped because the starting line-up
in the next match is not observed. The final sample consists of 58,968 player-
match observations.

###  4.5 Estimation

To assess the impact of coworker performance on performance evaluations, we
leverage advancements in the field of causal machine learning. The integration
of techniques from machine and statistical learning (e.g., athey2019machine)
with micro-econometric methodologies that aim to identify causal effects
(e.g., imbens2009), offers distinct advantages over traditional estimators.

We utilize the Modified Causal Forest (mcf) estimator, introduced by
lechner2018 and further investigated by lechner2024.181818In a Monte Carlo
analysis they demonstrate the good performance of the (mcf) compared to other
popular choices such as Double/debiased machine learning Chernozhukov et al.
(2018) or the Generalized Random Forest Athey et al. (2019). Compared to other
causal machine learning estimators (e.g. athey2019generalized), an important
advantage of the mcf is that it provides a framework to estimate all causal
parameters of interest in one unified estimation and a straightforward
approach to perform unified inference across all aggregation levels.191919We
show results for Average Treatment Effect (ATE), Group Average Treatment
Effect (GATE), and Individualized Average Treatment Effect (IATE). The IATEs
measure the treatment effect for units with features $x$ and present the
causal parameters at the finest aggregation level. For the GATEs we preselect
variables according to research and practitioners interest and show effect
heterogeneity with regard to the chosen parameters. Furthermore, the mcf
allows for applications in empirical settings involving multiple discrete
treatment variables, which is especially useful for the empirical application
in our study.202020For a comprehensive understanding of the estimator’s
technical aspects, the interested reader is directed to lechner2018 and
lechner2024. Additionally, for more in-depth insights into the implementation
of the Python package (mcf) available freely by PyPI, readers find detailed
information in bodory2022. We also test the robustness of the results using a
traditional linear regression framework and an alternative machine learning
estimator Kennedy et al. (2017) in Section 5.1 and Section 5.2.

For estimation purposes the treatment is restricted to the categories, zero,
one, two or more than two goals scored by coworkers, due to the lack of common
support on the higher levels of the treatment variable. Common support figures
for our preferred specification are subsumed in Figure C.1. To show that
results are not driven by extreme values, we perform a robustness check and
cut the sample and use only observation in which coworkers score zero, one or
two goals (Table C.1).212121Only around 10% of observations have coworkers
scoring more than two goals in a game. In general, specifications differ by
the set of covariates included to address assortative matching and to rule out
alternative interpretations.

###  4.6 Descriptive Statistics

Figure 4.2 shows how shooting performance of coworkers correlates with
individual performance evaluations. For this purpose, we plot the number of
goals scored by coworkers against the own performance evaluation of a player
for his expert evaluation in the newspaper and for the manager decision. We
find a substantial positive correlation between coworker shooting performance
and the own performance evaluations for both outcome variables. However, this
result might largely depend on assortative matching of workers and does not
account for the fact that goals are a product of team performance.

Table 4.1: Descriptive Statistics of selected variables by Treatment Status

| Goals scored by coworkers
---|---
| 0 | 1 | 2
_Outcome Variables_ |  |  |  |  |  |
Starting line-up next match | 0.77 | (0.42) | 0.78 | (0.41) | 0.81 | (0.39)
Journalist rating | 3.08 | (0.93) | 3.37 | (0.91) | 3.80 | (0.89)
_Covariates_ |  |  |  |  |  |
_Chance quality_ |  |  |  |  |  |
Expected goals coworker | 0.70 | (0.47) | 1.09 | (0.57) | 1.73 | (0.79)
_Individual controls_ |  |  |  |  |  |
Position | 2.82 | (0.74) | 2.77 | (0.72) | 2.70 | (0.69)
Time in club (years) | 2.31 | (2.16) | 2.41 | (2.23) | 2.60 | (2.41)
Age (years) | 26.17 | (3.68) | 26.14 | (3.69) | 26.06 | (3.74)
German | 0.44 | (0.50) | 0.44 | (0.50) | 0.43 | (0.50)
Market value (ln) | 15.06 | (1.08) | 15.17 | (1.11) | 15.40 | (1.19)
Player strength (Fifa) | 74.33 | (4.80) | 74.84 | (4.91) | 75.76 | (5.36)
_Team controls_ |  |  |  |  |  |
Rank last season | 10.35 | (4.99) | 9.64 | (5.09) | 8.39 | (5.31)
Number of league matches (manager) | 119.15 | (136.82) | 121.68 | (138.14) | 135.33 | (148.32)
Number of Top-5 matches (manager) | 137.80 | (158.35) | 145.77 | (168.44) | 174.75 | (196.65)
Average market value squad (ln) | 14.87 | (0.71) | 14.99 | (0.74) | 15.24 | (0.84)
Average market value Top 11 (ln) | 14.54 | (0.76) | 14.67 | (0.79) | 14.93 | (0.88)
Average squad strength (Fifa) | 70.62 | (2.38) | 71.06 | (2.48) | 71.76 | (2.77)
_Match controls_ |  |  |  |  |  |
Home team | 0.43 | (0.50) | 0.50 | (0.50) | 0.58 | (0.49)
Rank last season (opponent) | 8.94 | (5.37) | 9.43 | (5.17) | 10.21 | (4.91)
Number of league matches manager (opponent) | 130.44 | (148.82) | 126.20 | (139.25) | 116.84 | (132.95)
Number of Top-5 matches manager (opponent) | 166.94 | (194.94) | 152.52 | (171.14) | 133.47 | (151.50)
Average market value quad ln (opponent) | 15.14 | (0.83) | 15.03 | (0.77) | 14.89 | (0.70)
Average market value Top 11 ln (opponent) | 14.83 | (0.88) | 14.71 | (0.82) | 14.56 | (0.75)
Observations | 20,721 | 19,953 | 18,294

  * •

Notes: Means and standard deviations of selected variables by treatment
status. Standard deviation are reported in parentheses. For the full table,
see Table A.1 in Appendix A. Position: = 2; if the main position is defender;
= 3 if the main position is midfielder; = 4 if the main position is striker.

Table 4.1 shows the means and standard deviations (in brackets) by treatment
status for a number of selected variables used in the main specifications that
justify these concerns. Workers receive better evaluations when coworkers
score more goals. However, coworkers were exposed to more/better chances to
score goals, reflecting a better team performance. We also observe that
players of higher quality are exposed to more goals by coworkers and teams
that have ranked better in the last season, as well as teams playing on home
ground and against weaker opponents. We address these issues in Section 5.

Figure 4.2: Association of coworker performance and individual performance
evaluation

(a) Manager

(b) Expert

Notes: This figure shows the correlation of coworker performance with
performance evaluation for both outcome variables. The y-axis reports the mean
values of the outcome variable for each level of the treatment variable.

##  5 Results

In this section, we present the results of the empirical analysis. Section 5.1
shows the main results for the effect of coworker performance on individual
performance evaluation. In Section 5.2, we explore whether spillover effects
are influenced by reference points, distinguishing between coworker
performance below and above expectations. Section 5.3 investigates
heterogeneous treatment effects for a set of important variables. We also use
more data driven approaches, like an optimal policy simulation and k-mean
clustering, to investigate which group of players is most and least affected
by coworker performance. Finally, Section 5.4 investigates whether spillover
effects depend on the main responsibility of workers or whether the proximity
to coworkers affects the size of spillover effects.

###  5.1 Main Results

Table 5.1 presents the main findings across several model specifications.
Throughout all specifications, we control for the quality of chances coworkers
face (xG) to isolate coworker shooting performance. Columns differ in the way
we account for the assortative matching of workers. The first column
incorporates a comprehensive set of player characteristics to account for
assortative matching. Columns two and three progressively include additional
control variables at the team level (e.g. team quality, manager experience)
and match level (e.g. opponent, time of the season), respectively.222222For a
comprehensive list of covariates included in each specification, see Appendix
A Table A.1 The reported coefficients should be interpreted as a comparison of
being exposed to the lowest level of coworker performance compared to being
exposed to the highest level of coworker performance (specifically, 2 or more
goals vs. 0 goals scored by coworkers from comparable situations).

Table 5.1: Average effect of coworker performance on manager decisions

| Starting line-up next match
---|---
| (1) | (2) | (3)
Coworker performance |  0.038∗∗∗ |  0.036∗∗∗ |  0.033∗∗∗
| (0.012) | (0.011) | (0.010)
Mean probability to stay in the line-up | 78% | 78% | 78%
Individual controls | $\surd$ | $\surd$ | $\surd$
Team controls |  | $\surd$ | $\surd$
Match controls |  |  | $\surd$
Observations | 58,968 | 58,968 | 58,968

  * •

Notes: *, **, and *** represents statistical significance at the 10%, 5%, and
1% level respectively. Standard errors are clustered at the match level and
are presented in parentheses. For a full list of covariates included in each
specification, see Table A.1. All effects are population averages (ATE).

The results reveal a noteworthy and statistically significant positive effect
of coworker shooting performance on worker performance evaluation. We find
that when coworkers score two goals or more compared to coworkers scoring zero
goals, from similar chances, there is an increase of over 3 percentage points
in the likelihood for a worker to remain in the starting line-up. This effect
is both statistically significant and of practical importance. Considering the
sample mean of around 78%, the results suggest a 4% increase in the
probability to stay in the starting line-up for the next match or a 14%
decrease in the probability of being replaced in the starting line-up for the
next match.

The findings are indicative of spillover effects in performance evaluations. A
remaining concern associated with this interpretation involves the possibility
that coworker quality, which likely influences coworker shooting performance,
may exert an immediate impact on individual productivity, even after
accounting for assortative matching, This concern is supported by
arcidiacono2017, who present evidence of substantial spillover effects on
individual productivity within teamwork settings. Despite our efforts to
control for a comprehensive set of individual quality measures, team quality
measures and other match-related variables to address assortative matching, it
remains plausible that day-to-day fluctuations in coworker quality may jointly
influence both coworker shooting performance and individual performance. Such
a scenario would not allow us to rule out improvements in individual
productivity as an alternative explanation for the observed results.232323An
alternative scenario might be so-called momentum effects, where coworker
shooting performance does have an impact on individual productivity in the
reminder of the match. While this does not invalidate the chosen
identification approach, it would provide an alternative interpretation for
the observed result.

Table 5.2: Robustness to alternative explanation

| Starting line-up next match
---|---
| (1) | (2) | (3)
Coworker performance |  0.032∗∗∗ |  0.035∗∗∗ |  0.036∗∗∗
| (0.010) | (0.009) | (0.010)
Individual controls | $\surd$ | $\surd$ | $\surd$
Team controls | $\surd$ | $\surd$ | $\surd$
Match controls | $\surd$ | $\surd$ | $\surd$
Coworker controls | $\surd$ |  | $\surd$
Individual performance metrics |  | $\surd$ | $\surd$
Observations | 58,968 | 58,968 | 58,968

  * •

Notes: *, **, and *** represents statistical significance at the 10%, 5%, and
1% level respectively. Standard errors are clustered at the match level and
are presented in parentheses. All effects are population averages (ATE).

We consider the likelihood that fluctuations in coworker quality, which impact
shooting performance, directly impacting the productivity of other players to
be low in our setting. Shooting performance is mostly linked to a player’s
shooting skills. This type of skill is unlikely to have large spillover
effects on productivity, and players that exhibit good shooting skills are not
necessarily players with skills in other categories that contribute to
enhancing the overall play of teammates. Despite this reasoning, we
empirically address the potential issue that improvements in individual
productivity explain the result in several ways and report the results in
Table 5.2.

In Column one, we add a set of control variables for coworker quality to the
model. Specifically, coworker quality is controlled for similarly to the
approach for player quality. This involves explicitly accounting for the skill
levels of coworkers in the starting line-up across six game-relevant
dimensions, including passing and dribbling, which are likely to generate the
highest spillover effects on productivity. The result is insensitive to this
model extension. To further exclude the possibility that individual
productivity changes explain the observed result, we run an additional
regression and include an extensive set of individual performance metrics in
the match that should be able to adequately characterize individual
productivity (Column two).242424A list of performance metrics can be found in
Table A.2 and Table A.3. Lastly, we combine both sets of control variables in
our model (Column three). Importantly, the results remain virtually unaffected
by the extensions to the estimation model. This result strengthens the
interpretation of our findings as indications of spillover effects in
performance evaluations.

Table 5.3: Average effect of coworker performance on expert journalists’
ratings

| Expert evaluation
---|---
| (1) | (2) | (3) | (4) | (5) | (6)
Coworker performance |  0.432∗∗∗ |  0.391∗∗∗ |  0.333∗∗∗ |  0.298∗∗∗ |  0.339∗∗∗ |  0.337∗∗∗
| (0.036) | (0.032) | (0.027) | (0.026) | (0.021) | (0.021)
Mean expert evaluation | 3.33 | 3.33 | 3.33 | 3.33 | 3.33 | 3.33
Individual controls | $\surd$ | $\surd$ | $\surd$ | $\surd$ | $\surd$ | $\surd$
Team controls |  | $\surd$ | $\surd$ | $\surd$ | $\surd$ | $\surd$
Match controls |  |  | $\surd$ | $\surd$ | $\surd$ | $\surd$
Coworker controls |  |  |  | $\surd$ |  | $\surd$
Individual performance metrics |  |  |  |  | $\surd$ | $\surd$
Observations | 58,968 | 58,968 | 58,968 | 58,968 | 58,968 | 58,968

  * •

Notes: *, **, and *** represents statistical significance at the 10 %, 5 %,
and 1 % level respectively. Standard errors are clustered at the match level
and are presented in parentheses. All effects are population averages (ATE).
For a full list of covariates included in each specification, see Table A.1.

So far, we relied on manager decisions whether to field a player in the next
match as our measure of performance evaluations. We now show results using an
alternative measure of performance evaluation. Table 5.3 shows how coworker
performance affects journalists’ evaluations. While an obvious advantage of
manager decisions is that they have direct career implications for players,
expert journalists’ ratings also have advantages.252525Getting the chance to
play more often and to show his skills is important for career advancement
Hoey (2022). They are conducted by experts that are not part of the club.
Therefore, they are free from strategic considerations about team success in
the upcoming match as well as the availability of replacing players and more
likely to reflect a "public perception" of individual performance. In line-
with the results for manager decisions, we observe a substantial improvement
in the evaluation a player receives from the expert journalist, equivalent to
more than one-third of a full grade. The coefficient size corresponds to an
approximate 10% increase relative to the sample average grade.

To strengthen the validity of our results, we conduct two additional
robustness checks. First, we examine the robustness of the findings to
treatment outliers. In this robustness check, we exclude all observations
where coworkers scored more than two goals. The results, shown in Table C.1,
confirm the main result.262626Additionally, we show all treatment comparisons
(1 goal vs. 0 goals, 2 goals vs. 1 goal). For expert evaluations, positive and
significant coefficients are observed for both comparisons. However, the
impact of scoring two goals instead of one is larger than the effect of
scoring one goal instead of zero goals across all specifications. Turning to
manager decisions, a similar pattern is identified. Nevertheless, the effect
of coworkers scoring one goal compared to those scoring zero goals is not
significant in any specification. Second, we demonstrate that the results are
robust to the chosen estimator. We utilize a linear regression framework. The
results, presented in Table C.2, uphold our main findings. While the linear
regression framework limits the ability to flexibly control for the extensive
set of control variables, we also show results using individual or even
individual-season fixed effects that address assortative matching based on
observed and unobserved individual characteristics. Reassuringly, results
using the set of control variables used in our main specification and results
using individual or individual-season fixed effects are quantitatively very
similar, strengthening the credibility of the condition independence
assumption.

###  5.2 Reference point dependence

The previous section has shown that coworkers exhibit spillover effects on
individual performance evaluations. We now turn towards understanding further
circumstances that trigger spillover effects. This section investigates
whether good or bad performances differentially initiate spillover effects.
Specifically, we examine whether the coworker spillover effect is dependent on
a reference point, demonstrating a differential impact below and above
expectations.

Theoretical work has conceptualized expectations as reference points Kőszegi
and Rabin (2006) and several empirical studies from the lab and the field
provide evidence for reference point dependent behavior in various domains
Gneezy and Potters (1997); Pope and Schweitzer (2011); Allen et al. (2017). We
test whether coworker performance below and above reference points exhibits a
differential impact on a worker’s performance evaluations. To do so, we expand
our investigation by incorporating an additional method from causal machine
learning. We adopt the non-parametric kernel method for continuous treatment
proposed by kennedy2017. Instead of using a discrete treatment, the treatment
variable is defined as the difference between the number of goals scored by
coworkers and the number of expected goals coworkers were exposed to. In
addition to understanding whether spillover effects are reference point
dependent, this approach serves as an additional complementary estimation
strategy to test the robustness of the main result.272727In the first stage, a
pseudo-outcome is constructed:
$\xi(\pi,\mu)=\frac{Y-\mu(X,D)}{\pi(D|X)}\int\pi(D|x)dP(x)+\int\mu(x,D)dP(x),$
where $\mu(D|X)$ and $\mu(x,D)$, the nuisance functions, are estimated by a
random forest estimator Breiman (2001). The pseudo-outcome $\xi(\pi,\mu)$
eliminates the influence of confounding factors and possesses the desirable
characteristic of being doubly-robust. To estimate the average potential
outcome for each treatment level, we employ non-parametric kernel regression
on the pseudo-outcome. In determining the bandwidths of the kernels for this
regression, we adopt a data-driven approach using a cross-validation method.

Figure 5.1: Spillover effects and reference point behavior

(a) Manager

(b) Expert

Notes: Non-parametric kernel regression based on Table 5.1, Column one.
Subsample without treatment outliers (99%). The solid line shows the
performance evaluation for different levels of coworker performance. Dashed
lines show confidence intervals around the smoothed parameter.

The estimates are presented in Figure 5.1. We plot the estimated average
potential outcomes for each treatment level. For two different treatment
levels $D=d_{1}$ and $D=d_{0}$ (on the x-axis), the treatment effect can be
calculated as
$\theta(d_{1},d_{0})=\frac{E(Y(D=d_{1}))-E(Y(D=d_{0}))}{d_{1}-d_{0}}$. The
treatment intensity in this example is $d_{1}-d_{0}$, with $d_{0}$ being the
treatment level from which the intensity is evaluated.

We observe the following key findings: First, in both subfigures, we notice
some non-linearity. Positive deviations from the expectation have a
substantial positive impact on coworkers. Negative deviations are hardly
harmful for coworkers. This holds true for both manager decisions and expert
evaluations. Second, manager decisions exhibit a rather monotone relationship
across the entire distribution of the treatment variable, with a rather flat
relationship below expectations and a positive relationship above
expectations. However, this differs for expert evaluations. Workers receive
the lowest performance evaluation if coworkers perform marginally below
expectation. If they perform substantially below expectation, workers receive
a smaller penalty. This result may stem from coworker performance showing very
obvious mistakes that can be easily associated with them.

###  5.3 Effect heterogeneity

####  5.3.1 Heterogeneity in worker and firm characteristics

In this subsection, we concentrate on identifying which group of workers is
most and least affected by spillover effects. To start uncovering effect
heterogeneity, we present Group Average Treatment Effects (GATEs) for four
characteristics at the individual and firm level that have implications beyond
the sports industry.

First, in most organizations and teamwork settings, workers are assigned
different sub-tasks aligned with their primary responsibilities, known to the
manager. Shooting performance, for instance, is particularly crucial for
strikers, while defenders primarily focus on preventing the opposing team from
scoring. We investigate whether task responsibility affects the spillover
effect in performance evaluations. Panel (a) of Figure 5.2 shows how the
effect of coworker performance varies based on the player’s position, relying
on pre-season player classifications of their main positions collected by
Opta. We find that the effect of coworker performance on the manager’s
fielding decision is significantly different from zero for players in all
positions. The estimated GATEs are neither statistically different from the
average treatment effect nor from each other.282828While we also have access
to the precise position on matchday, we abstain from using it due to the
challenges of classifying players based on fluid positions and tactical
changes during a match. In results not shown in the paper, we also conducted
our main analysis including goalkeepers. There is no effect on the probability
of staying in the starting line-up in the next match, which is plausible given
the generally limited variation in goalkeeper positions.

Figure 5.2: GATEs for different player characteristics

(a) Manager

(b) Manager

(c) Manager

(d) Manager

Notes: The vertical axis denotes the respective GATE and its 90% confidence
interval for the comparison of coworkers scoring two goals, relatively to
coworkers scoring zero goals. The measure for player strength and team
strength is the video game measure (0 to 100).

Second, we explore whether more or less skilled players are differentially
affected. Player strength significantly influences the manager’s line-up
decisions, suggesting that more skilled players should be less susceptible to
variation in coworker performance compared to weaker players, especially
concerning manager decisions. As depicted in Panel (b) in Figure 5.2, we
observe a decreasing effect size with player strength. However, it’s
noteworthy that the vast majority of GATEs are positive, with only star
players being seemingly unaffected.

Third, we investigate heterogeneity concerning the time a player has been with
the club. The longer a player has been with the club, and the more familiar
the manager is with the player, the greater the trust and knowledge about the
player’s quality. Panel (c) shows that almost all GATEs are positive and
statistically different from zero. We also observe effect sizes ranging from 4
percentage points for new players to around 2 percentage points for players
who have been with the club for a substantial period.

Lastly, we investigate whether the experience of the manager or the quality of
the club matter for the importance of a coworker bias. Panel (d) therefore
shows GATEs with respect to the average quality of the whole team. Spillover
effects are substantially larger for lower levels of team quality, thus for
teams that are less frequently used to team success.

We also estimate effect heterogeneity for the alternative outcome variable.
For brevity reasons, results from heterogeneity analysis for journalists’
ratings are subsumed in Appendix D. In line with the idea that journalists’
views reflect a more public perception of players and the role of players in a
team matter less for journalists, we find no heterogeneity in the effect size
with regard to player strength and tenure level. However, we observe some
heterogeneity by the position of players. The effect of coworker performance
is significantly different from zero for players in each position, albeit the
effect of coworker shooting performance is notably smaller for defenders
compared to strikers.

####  5.3.2 Fine-grained heterogeneity

In the preceding section, we explored the extent to which effect heterogeneity
is linked to a set of relevant firm and worker characteristics. To complement
the heterogeneity analysis, we use data driven approaches to detect effect
heterogeneity and to characterize groups of players that are most and least
affected by spillover effects.292929Panel A in Figure C.2 provides a visual
representation of the distribution of Individualized Average Treatment Effects
(IATEs) when comparing coworkers scoring two goals with those scoring zero
goals. Additionally, Panel B in Figure C.2 presents the sorted effects along
with a 90%-confidence interval based on the estimated standard errors. Two
main observations arise from these figures. First, the majority of the IATEs
are positive for both outcome variables. Second, there is significant
variation in the effects, indicating meaningful heterogeneity in the treatment
effects. Complementary results for journalists’ ratings, see Figure D.2.
Detecting additional patterns of heterogeneity is challenging without some
additional structure. Therefore, we show the findings from an optimal policy
simulation. While our goal is not to learn treatment assignment policies,
since the treatment cannot be modified, an optimal policy simulation approach
offers the advantage of producing yet an interpretable characterization of the
groups that benefit most and least from the treatment with regard to a joint
characterization based on a set of predefined features.

Table 5.4: Most and least affected group of players - policy simulation

| Treatment shares in %
---|---
|  0 Goals |  1 Goal |  2 Goals
Observed |  33.69 |  34.13 |  32.18
Random |  32.65 |  35.14 |  32.21
Decision tree 3 levels |  5.01 |  0 |  94.99
| Mean of features in assignment of decision tree
Player quality |  85.83 |  – |  74.51
Time in club |  4.35 |  – |  2.33
German |  0.44 |  – |  0.43
Manager experience |  469.33 |  – |  136.54
Team strength |  76.72 |  – |  70.91
Position |  2.86 |  – |  2.75

  * •

Notes: This table provides treatment shares in percentage for different
outcome categories in a policy simulation related to "Starting line-up." The
second part of the table shows the mean of features for each category.

We derive policy rules based on a modification of the approach by zhou2023,
implemented in decision trees of depth 3 (8 strata) in the mcf package. Table
5.4 displays the description of the simulated allocation rule and the shares
of the population allocated to the different treatments (in %). We also depict
the observed shares and the shares that would have been observed under random
assignment. A decision tree of depth 3 assigns 95% of observations to the
highest treatment dose, while 5 % are assigned to the zero treatment. This is
reassuring given that the vast majority of IATEs and GATEs are above
zero.303030The fact that the assigned shares under random assignment and the
observed shares are almost identical reveals that managers do not seem to base
their fielding decisions on the effect heterogeneity of spillover effects.
This is reassuring, given that managers do not intend to keep the same
starting line-up, but seek to maximize success.

In the lower part of Table 5.4, we present the average characteristics of
features used in constructing the decision tree, categorized by assigned
treatment status. Consistent with the previous sections, the decision tree
tends to assign high-quality players from stronger teams, with more club
tenure, and under the guidance of experienced managers to the no-goal
treatment. This aligns closely with our earlier findings. Table C.3 shows that
only two out of eight final leaves are assigned to the no-goal treatment, with
the remaining leaves assigned to the two-goal treatment. The assignment rules
mirror the patterns observed in Section 5.3.1. Notably, some degree of
substitutability between manager experience and player quality emerges, with
the first leaf featuring highly experienced managers and high player quality,
while the second leaf showcases very high player quality, albeit with lower
manager experience.313131Complementing results using a k-means++ clustering
approach can be found in Table C.4. The results align with our previous
results. Spillover effects range from 0.12 in the highest cluster to 0 in the
lowest cluster.

For our alternative outcome variable, the optimal policy simulation does not
result in a useful characterization of players that are most and least
affected by spillover effects, since all observations are assigned to the two
goal treatment. Therefore, we depict the dependence of the effects on
covariates using k-means++ clustering Arthur and Vassilvitskii (2007). The
results are shown in Table D.1 in Appendix D along with a detailed
description.

The analysis reveals substantial heterogeneity in the degree of spillover
effects. The spillover effects on journalists’ evaluations range from 0.18 in
the least affected cluster to 0.51 in the most affected cluster. To facilitate
interpretation, consider one example. A 0.51 increase in the evaluation
received by journalists is roughly equivalent to 0.5 times the effect of
scoring one goal oneself, given the faced chances. The size of the spillover
effect is, thus, one-quarter of the effect of one’s own performance in the
same task.323232Results used for this comparison are shown in Appendix C Table
C.5. The characterization of clusters aligns with our results from the
previous section. Manager and team strength matter less compared to the
manager’s decision. The group benefiting the most from spillover effects is
characterized by players with high offensive skills and a good team
performance (xG), while player exhibiting high defensive skills are prevalent
in the group of player who benefit least from their coworkers.

###  5.4 Proximity to coworkers

In Section 5.3.1, we explored whether players who are responsible for a
similar task (goal scoring is the primary task of offensive players) are
differentially affected than players who’s primary task is to prevent goals
(defensive players). While we identified a larger impact on offensive players
in journalists’ evaluations, no such variation was observed for manager
decisions. This section extends the analysis. First, we ask whether players,
who’s main task is scoring goals, exhibit higher spillover effects on other
workers than workers who’s main task is different (defensive task). Then, we
ask whether the proximity to coworkers (shared responsibilities), rather than
the own or the coworker responsibilities, affect the size of the spillover
effect.

Tables C.6 and C.7 present separate analyses for manager and expert
evaluations. We calculate coworkers’ shooting performance for different
subgroups based on their main positions and estimate the effects on
performance evaluations, considering the player’s own position. We focus on
strikers and defenders, since task responsibilities are more straightforward
compared to midfielders. Due to common support issues, the sample is
restricted to observations where coworkers score zero or one goal.

Table C.6 reveals no differential impact of coworker shooting performance
depending on the main responsibilities of coworkers. Neither are shared
responsibilities associated with a heterogeneous effects size. This may
suggest that the primary driver for spillover effects is team performance. For
journalists’ ratings (Table C.7), we find that shooting performance of
strikers has a stronger impact compared to shooting performance of defenders
(Column one). Thus, coworkers main responsibilities matter for the size of the
spillover effect they exhibit on coworkers. We also find that the effect of
coworkers shooting performance always tend to be stronger for strikers,
independent of the position of the player who provided the performance.
Proximity to coworkers, shared responsibilities, are thus not associated with
an additional premium.

##  6 Career effects

To explore the long-term consequences of coworker performance, we investigate
whether aggregates of our measure of shooting performance are associated with
player assessments in subsequent periods. To do so, we aggregate the main
dataset at the player-by-season level, resulting in approximately 3,900
player-season observations. Our measure of coworker performance at the season
level is the aggregated number of goals scored by coworkers and the aggregated
xG coworkers were exposed to in a given season $t$. We then examine the
relationship between these aggregated coworker performance variables and
expert-based player evaluations in the subsequent season ($t+1$) and the
season after next ($t+2$), using data from transfermarkt.de. This source
provides expert-based evaluations that are highly correlated with transfer
fees, offering a valuable indicator of a player’s perceived value in the
football market Prockl and Frick (2018); Coates and Parshakov (2022). An
important advantage of these evaluations compared to transfer fees is that
they are observed independent of a player changing the club, which avoids
selection issues. Furthermore, in contrast to wage information, they are
unlikely to depend on players bargaining power or other sources apart from the
actual or perceived productivity.

Table 6.1: Career perspective

| Player evaluation (market value)
---|---
| $t+1$ | $t+2$
Coworker performance |  75,659∗∗∗ |  75,204∗∗ |  127,784∗∗∗ |  91,666∗∗∗
| (23,795) | (30,738) | (37,116) | (34,039)
Individual controls | $\surd$ | $\surd$ | $\surd$ | $\surd$
Team controls | $\surd$ | $\surd$ | $\surd$ | $\surd$
Season Fixed effects |  | $\surd$ |  | $\surd$
Individual Fixed effects |  | $\surd$ |  | $\surd$
Observations | 3903 | 3903 | 3903 | 3903

  * •

Notes: Linear regression. Standard errors are clustered at the team-season
level. $t$ is the current season, $t+1$ refers to the next season and $t+2$
refers to the season after the next season. Individual controls are the same
as used in 5.1. Team controls are proxies for team quality. *, **, and ***
represents statistical significance at the 10%, 5%, and 1%.

Relating coworker shooting performance over a season to player assessments in
subsequent years is complicated by endogeneity issues. To get as close as
possible towards a causal interpretation of the results, we address the issue
of selection into particular clubs by incorporating various control variables
and fixed effects. Table 6.1 presents the results for two specifications. In
the first specification, we control for the same set of individual and team
characteristics as presented in Table 5.1. The second specification adds
season fixed-effects and, more crucially, individual fixed-effects. These
individual fixed-effects help to account for any differences between players
at the player level. In all specifications, we also control for the number of
xG coworkers are exposed to in a season.

The findings indicate a significant positive association between coworker
performance and the market value evaluations of workers in subsequent seasons.
Specifically, for each goal scored by coworkers, given the chance quality they
were exposed to, a worker’s market value increases by 75,000 Euros in the
subsequent season and by 90,000 Euros in the season after the next. Given that
the average market value of all players in our sample in 2010 is approximately
4 million Euros, ten more goals scored by coworkers (equivalent to less than
one in every third match) result in an almost 20% increase in the market value
of a worker in the next period relative to the sample mean.

##  7 Conclusion

Coworkers exert considerable influence on their peers, impacting productivity
and effort provision Arcidiacono et al. (2017); Cohen-Zada et al. (2023).
Moreover, exposure to high-quality peers contributes positively to earnings
and subsequent career outcomes Jarosch et al. (2021). While existing
explanations focus on learning from peers leading to skill acquisition and
enhanced work ethics Amodio et al. (2023); Nix (2020), this paper introduces
an additional and potentially widespread channel through which coworkers shape
the career trajectories of their peers.

Modern organizations extensively utilize teamwork to harness the advantages of
specialization Deming (2017). However, teamwork introduces challenges,
particularly in isolating individual contributions within the context of team
performance. This complexity creates the potential for spillover effects in
performance evaluations, where coworker performance causally influences
individual performance assessments, extending beyond coworkers’ impact on
individual productivity. Considering the pivotal role of performance
evaluations in shaping careers, understanding the conditions and extent to
which these evaluations depend on coworker performance becomes crucial.

We examine spillover effects in performance evaluations using highly detailed
individual data from the professional soccer industry. Leveraging player
tracking data, we identify situations where coworker performance appears as
good as random, while controlling for a comprehensive and relevant set of
variables to account for assortative matching of workers. Methods from causal
machine learning allow estimating average and heterogeneous treatment effects.

Our results indicate significant spillover effects in performance evaluations.
Managers’ decisions to field players and expert evaluations are notably
influenced by coworker performance, with substantial effects. The effect size
is equivalent to one-third of the effect of the own performance in the same
task and reduces the likelihood to be replaced in the starting line-up by up
to 13% relative to the sample mean. Also, third party evaluation of
performance, are impacted, showing an 11% change relative to the control mean.
We further characterize groups of players and circumstances that trigger
spillover effects. Interestingly, spillover effects exhibit a reference point
dependent behavior. Positive deviations from a reference point create large
positive spillover effects, while negative deviations do not harm coworker
evaluations. Furthermore, we find that less skilled worker, or worker with
limited tenure in the club, are most effected by spillover effects in manager
decisions. However, the vast majority of players are affected. For third-party
experts, we document that shared responsibilities are driving effect
heterogeneity.

Given the pronounced spillover effects observed in our setting, we believe
such effects are likely to be even more prevalent in other organizational
contexts. The visibility of soccer performance, with players tracked by
cameras and detailed statistics available, makes it an environment where
coworker effects are noticeable. We posit that these spillover effects are
widespread in situations where actions are less monitored, and decision-makers
may not have strong incentives to make optimal choices. This has significant
implications, introducing inefficiencies and inequities in reward allocation
and promotions. Moreover, it has substantial consequences for the career
trajectories of workers.

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##  Appendix A Data and Descriptive Statistics

In this section we present details about our data and descriptive statistics.

Figure A.1: Examples of Fifa player evaluation cards

(a) Thomas Müller

(b) Marco Reus

(c) Patrick Herrmann

Notes: PAC = Pace; SHO = Shooting; PAS = Passing; DRI = Dribbling; DEF =
Defensive skills; PHY = Physical skills.

Figure A.2: Example of Newspaper evaluation

Notes: Player evaluations are a topic of public debate
(https://www.sueddeutsche.de/sport/fussball-bundesliga-noten-vielleicht-
reicht-auch-mal-eine-fuenf-1.141370). For more details on the construction of
evaluations, see https://www.news.de/sport/855093240/die-zeugnisse-der-
profis/1/.

Table A.1: Descriptive Statistics by Treatment Status

| Goals scored by coworkers
---|---
| 0 | 1 | 2
_Outcome Variables_ |  |  |  |  |  |
Starting line-up next match | 0.766 | (0.423) | 0.780 | (0.414) | 0.813 | (0.390)
Journalist rating | 3.083 | (0.927) | 3.374 | (0.907) | 3.800 | (0.889)
_Covariates_ |  |  |  |  |  |
_Chance quality_ |  |  |  |  |  |
expected goals coworker | 0.704 | (0.474) | 1.087 | (0.573) | 1.733 | (0.792)
_Individual controls_ |  |  |  |  |  |
Position | 2.819 | (0.742) | 2.766 | (0.722) | 2.699 | (0.693)
Foot | 1.362 | (0.668) | 1.351 | (0.657) | 1.344 | (0.631)
Time in club | 2.309 | (2.162) | 2.407 | (2.234) | 2.603 | (2.413)
Age | 26.170 | (3.683) | 26.140 | (3.691) | 26.057 | (3.736)
German | 0.440 | (0.496) | 0.439 | (0.496) | 0.433 | (0.496)
Market value (ln) | 15.058 | (1.080) | 15.173 | (1.107) | 15.404 | (1.187)
Player strength (Fifa) | 74.334 | (4.803) | 74.835 | (4.914) | 75.760 | (5.363)
Defensive Skills (Fifa) | 57.895 | (18.968) | 59.455 | (18.793) | 61.725 | (18.470)
Pace Skills (Fifa) | 71.340 | (10.379) | 71.522 | (10.281) | 71.960 | (10.454)
Passing Skills (Fifa) | 65.780 | (8.729) | 66.430 | (8.782) | 67.535 | (9.078)
Physical Skills (Fifa) | 70.857 | (7.535) | 71.061 | (7.498) | 71.328 | (7.635)
Shooting Skills (Fifa) | 59.735 | (14.364) | 59.419 | (14.363) | 59.312 | (14.339)
Dribling Skills (Fifa) | 69.197 | (9.960) | 69.557 | (10.033) | 70.171 | (10.450)
_Team controls_ |  |  |  |  |  |
Days since previous match | 7.788 | (6.059) | 7.489 | (5.572) | 7.491 | (5.824)
Days to next match | 7.499 | (5.090) | 7.696 | (5.933) | 7.173 | (4.948)
Upcoming Cup match | 0.125 | (0.331) | 0.155 | (0.362) | 0.198 | (0.398)
Following Cup match | 0.145 | (0.352) | 0.153 | (0.360) | 0.202 | (0.402)
Relegated last season | 0.152 | (0.359) | 0.125 | (0.331) | 0.084 | (0.277)
Rank last season | 10.353 | (4.985) | 9.640 | (5.091) | 8.385 | (5.310)
Number of previous clubs (manager) | 2.379 | (1.984) | 2.413 | (2.006) | 2.608 | (2.142)
Number of League Matches (manager) | 119.149 | (136.819) | 121.681 | (138.139) | 135.330 | (148.318)
Number of Top-5 matches (manager) | 137.803 | (158.349) | 145.770 | (168.444) | 174.753 | (196.653)
Average market value squad (ln) | 14.869 | (0.713) | 14.994 | (0.744) | 15.239 | (0.838)
Std. market value squad (ln) | 14.798 | (0.834) | 14.941 | (0.850) | 15.209 | (0.929)
Average market value Top 11 (ln) | 14.539 | (0.760) | 14.670 | (0.791) | 14.930 | (0.881)
Std. market value Top 11 (ln) | 14.607 | (0.911) | 14.747 | (0.912) | 15.010 | (0.965)
Average squad strength (Fifa) | 70.618 | (2.375) | 71.058 | (2.481) | 71.763 | (2.766)
Std. squad strength (Fifa) | 6.492 | (1.350) | 6.667 | (1.434) | 7.067 | (1.645)
_Match controls_ |  |  |  |  |  |
Home team | 0.430 | (0.495) | 0.503 | (0.500) | 0.578 | (0.494)
Played on an unusual match day | 0.065 | (0.247) | 0.074 | (0.261) | 0.067 | (0.250)
Played in the evening | 0.161 | (0.368) | 0.158 | (0.365) | 0.155 | (0.362)
Played after an international break | 0.124 | (0.330) | 0.125 | (0.330) | 0.134 | (0.341)
Played before an international break | 0.129 | (0.335) | 0.128 | (0.334) | 0.133 | (0.339)
WM/EM Season | 0.494 | (0.500) | 0.500 | (0.500) | 0.507 | (0.500)
Season after a WM/EM | 0.093 | (0.291) | 0.083 | (0.275) | 0.089 | (0.284)
Season before a WM/EM | 0.087 | (0.282) | 0.091 | (0.288) | 0.091 | (0.287)
Africa Cup Season | 0.510 | (0.500) | 0.495 | (0.500) | 0.495 | (0.500)
Match is played during Africa Cup | 0.152 | (0.359) | 0.150 | (0.357) | 0.142 | (0.349)
Days since previous match (opponent) | 7.611 | (6.127) | 7.490 | (5.587) | 7.693 | (5.733)
Days to next match (opponent) | 7.234 | (5.081) | 7.622 | (5.742) | 7.555 | (5.204)
Upcoming Cup match (opponent) | 0.186 | (0.389) | 0.152 | (0.359) | 0.133 | (0.340)
Following Cup match (opponent) | 0.187 | (0.390) | 0.156 | (0.363) | 0.152 | (0.359)
Relegated last season (opponent) | 0.109 | (0.311) | 0.123 | (0.328) | 0.137 | (0.344)
Rank last season (opponent) | 8.941 | (5.370) | 9.428 | (5.170) | 10.211 | (4.909)
Number of previous clubs manager (opponent) | 2.598 | (2.159) | 2.452 | (2.032) | 2.309 | (1.900)
Number of league matches manager (opponent) | 130.438 | (148.815) | 126.196 | (139.250) | 116.838 | (132.946)
Number of Top-5 matches manager (opponent) | 166.936 | (194.943) | 152.520 | (171.142) | 133.470 | (151.504)
Average market value quad ln (opponent) | 15.140 | (0.832) | 15.031 | (0.771) | 14.892 | (0.702)
Std. market value squad ln (opponent) | 15.091 | (0.934) | 14.980 | (0.879) | 14.838 | (0.816)
Average market value Top 11 ln (opponent) | 14.825 | (0.879) | 14.710 | (0.817) | 14.563 | (0.747)
Std. market value Top 11 ln (opponent) | 14.879 | (0.974) | 14.790 | (0.939) | 14.657 | (0.897)
Observations | 20,721 | 19,953 | 18,294

  * •

Notes: Means and standard deviations (in parentheses) for all variables
included in Table 5.1.

Table A.2: List of individual performance metrics

Variable | Variable | Variable
---|---|---
Playing time | accurate back zone pass | accurate corners into box
accurate cross | accurate cross no corner | accurate fwd zone pass
accurate goal kicks | accurate keeper throws | accurate launches
accurate layoffs | accurate long balls | accurate pass
accurate through ball | accurate throws | aerial lost
aerial won | att bx centre | att obx centre
att bx right | att bx left | att corner
att fastbreak | att freekick goal | att freekick target
att freekick total | att freekick miss | att freekick post
att goal high centre | att goal high left | att goal high right
att goal low centre | att goal low left | att goal low right
att hd goal | att hd miss | att hd post
att hd target | att hd total | att ibox blocked
att ibox goal | att ibox miss | att ibox post
att ibox target | att lf goal | att lf target
att lf total | att miss high | att miss high left
att miss high right | att miss left | att miss right
att one on one | att cmiss high | att cmiss high right
att cmiss high left | att cmiss left | att cmiss right
att openplay | att pen goal | att pen miss
att pen post | att pen target | att post high
att post left | att post right | att setpiece
attempts conceded ibox | attempts conceded obox | attempts ibox
attempts obox | back pass | ball recovery
blocked scoring att | challenge lost | clean sheet
clearance off-line | corner taken | cross not claimed
crosses 18yardplus | dangerous play | dispossessed
dive catch | dive save | duel lost
effective clearance | effective head clearance | error lead to goal
error lead to shot | final third entries | fouls
fouled final third | gk smother | goal assist
goal assist intentional | goal kicks | goals
goals conceded | goals conceded ibox | goals conceded obox
good high claim | goals open play | hand ball
head clearance | head pass | interceptions in box
keeper pick up | keeper throws | last man tackle
long pass own to opp | long pass own to opp success | offside provoked
off target att assist | on target att assist | on target scoring att
outfielder block | own goals | pen goals conceded
penalty conceded | penalty save | penalty won
post scoring att | punches | red card
saves | second yellow | second goal assist
shot off target | total att assist | total back zone pass
total clearance | total contest | total corners into box
total cross | total cross no corner | total fastbreak

  * •

Notes: This table includes a list of individual performance metrics used in
Table 5.2. The list is continued in Table A.3. fwd: forward; rf: right foot;
lf: left foot; hd: header; att: attempt; ctrl: control; pen: penalty; ibox: in
box.

Table A.3: List of individual performance metrics

Variable | Variable | Variable
---|---|---
total fwd zone pass | total high claim | total launches
total long balls | total offside | total pass
total scoring att | total sub off | total sub on
total tackle | total through ball | total throws
touches | turnover | was fouled
won contest | won corners | won tackle
yellow card | penalty faced | goal assist open play
goal assist setplay | att assist open play | att assist setplay
overrun | interception won | big chance created
big chance missed | big chance scored | unsuccessful touch
fwd pass | backward pass | successful final third passes
total final third passes | diving save | poss won def 3rd
poss won mid 3rd | poss won att 3rd | poss lost all
poss lost ctrl | goal fastbreak | shot fastbreak
pen area entries | hit woodwork | goal assist deadball
freekick cross | accurate freekick cross | open play pass
successful open play pass | attempted tackle foul | fifty fifty
successful fifty fifty | blocked pass | failed to block
put through | successful put through | assist pass lost
assist blocked shot | assist attempt saved | assist post
assist free kick won | assist handball won | assist own goal
assist penalty won | touches in opp box | formation place
times tackled | winning goal | interception
expected goals | expected goals non penalty | expected goals open play
expected goals set play | expected goals hd | expected goals lf
expected goals rf | expected goals freekick | expected goals conceded

  * •

Notes: This table includes a list of individual performance metrics used in
Table 5.2. The list is continued in Table A.2. fwd: forward; rf: right foot;
lf: left foot; hd: header; att: attempt; ctrl: control; pen: penalty; ibox: in
box.

##  Appendix B Expected Goals

In this section, we explain details on the calculation of expected goals.
Expected goals (xG) quantify the quality of a scoring opportunity based on
historical data from nearly a million shots. The name “expected goals” is
derived from the mathematical concept of “expected value” and it is a measure
of the likelihood of an outcome occurring. Variance from the expected value is
inevitable, and provides valuable information, which we exploit in this
paper.333333https://theanalyst.com/eu/2023/08/what-is-expected-goals-xg/

Each scoring opportunity is assigned a value on a scale from zero to one. A
zero implies an impossible-to-score chance, while a one signifies a situation
where a player is expected to score every time. This provides us with a way to
express the likelihood of goals in different scenarios. For instance, if a
chance inside the penalty area is assigned an xG of 0.1, it means that, on
average, a player would score once in every ten attempts from that position,
or 10% of the time.

While watching a game, football enthusiasts often assess the likelihood of a
goal being scored based on factors like the shooter’s proximity to the goal,
the shot angle, whether it’s a one-on-one, or a header. However, individually
evaluating the scoring likelihood for each of these unique scenarios would is
a laborious task. xG models employ machine learning, specifically gradient
boosting algorithms. The model leverages various variables, including those
leading up to the shot and immediately before it. Over 20 factors are assessed
to determine the likelihood of a goal. Some key factors include:

  * •

Distance to the goal

  * •

Angle to the goal

  * •

Goalkeeper’s position, providing insight into their ability to make a save

  * •

The shooter’s view of the goal, considering the positions of other players

  * •

The level of defensive pressure from opponents

  * •

Shot type, including which foot the shooter used and whether it was a volley,
header, or one-on-one

  * •

Pattern of play (e.g., open play, fast break, direct free-kick, corner kick,
throw-in, etc.)

  * •

Information about the previous action, such as the type of assist (e.g.,
through ball, cross, etc.)

Figure B.1: Expected Goals by position

(a) Defender

(b) Midfielder

(c) Striker

Notes: Distribution of expected goals players from different positions are
exposed to during a match. For further discussion, see Section 4.2.

We use expected goals as a measure of the quality of chances to separate
shooting performance from collaborative efforts. Since the setting and the way
of measuring individual performance are non-standard, we present further
evidence that goals and xG allow for an evaluation of shooting performance. We
conduct a test by correlating our shooting performance measure with expert-
based assessments of shooting abilities.343434For more details about the
origin of these expert based skill assessments, see Section 4.3.3. Table B.1
shows the beta coefficients of regressions of several specific ability
measures on the number of goals scored conditional on xG and an overall
assessment of players’ strength. Reassuringly, we find that only the expert
assessment of shooting ability is statistically significantly positively
correlated with the number of goals scored. This result supports the argument
that we are measuring shooting performance in a meaningful way and that
shooting performance is an important aspect of the performance of soccer
players.

Table B.1: Player skills and shooting performance

| $Shooting$ | $Passing$ | $Dribbling$ | $Pace$ | $Physical$ | $Defense$
---|---|---|---|---|---|---
$\hat{\beta}$ | 0.346 | 0.164 | 0.207 | 0.123 | -0.266 | -0.815
$s.e.$ | [0.176] | [0.103] | [0.100] | [0.138] | [0.098] | [0.241]
$p$-value | 0.013 | 0.110 | 0.126 | 0.371 | 0.007 | 0.000

  * •

Notes: $\hat{\beta}$, standard error, and p-value of separate regressions of
the form: $y_{i}=\beta goals_{i}+\gamma xG_{i}+\sigma X_{i}+\epsilon_{i}$.
$Y_{i}$ is the ability measure based on the FIFA video game. $X_{i}$ is the
overall quality of a player.

##  Appendix C Further results and robustness checks

Figure C.1: Common support figures

(a) Treatment level: 0

(b) Treatment level: 1

(c) Treatment level: 2

Notes: Common support figures for each treatment level based on the
specification in Column three of Table 5.1

Figure C.2: Manager decisions - Distribution of estimated IATEs and overall
effect heterogeneity

(a) Manager

(b) Manager

Notes: Estimates based on our main specification (Column 3 in Table 5.1).
Panel a shows the distribution of estimated IATEs. The horizontal axis
measures the effect of coworkers scoring two goals relative to coworkers
scoring zero goals in the corresponding outcome variables. Kernel smooth with
Epanechnikov Kernel and Silverman (normality) bandwidth. Panel b shows IATEs
sorted according to their size. 90%-confidence interval of IATEs based on
estimated standard errors and normal distribution. The vertical axis measures
the average increase in performance evaluation from coworkers scoring two
goals, relatively to coworkers scoring zero goals. The horizontal axis shows
the rank of the ordered observations.

Table C.1: Robustness to treatment outliers

Dependent Variable: | Starting line-up next match | Expert evaluation
---|---|---
2 vs. 0 |  0.036∗∗∗ |  0.040∗∗∗ |  0.037∗∗∗ |  0.410∗∗∗ |  0.365∗∗∗ |  0.315∗∗∗
| (0.011) | (0.010) | (0.008) | (0.038) | (0.030) | (0.028)
1 vs. 0 | 0.004 | 0.006 | 0.004 |  0.176∗∗∗ |  0.160∗∗∗ |  0.126∗∗∗
| (0.010) | (0.010) | (0.008) | (0.023) | (0.021) | (0.021)
2 vs. 1 |  0.032∗∗∗ |  0.034∗∗∗ |  0.033∗∗∗ |  0.232∗∗∗ |  0.205∗∗∗ |  0.190∗∗∗
| (0.011) | (0.010) | (0.010) | (0.036) | (0.028) | (0.026)
Individual controls | $\surd$ | $\surd$ | $\surd$ | $\surd$ | $\surd$ | $\surd$
Team controls |  | $\surd$ | $\surd$ |  | $\surd$ | $\surd$
Match controls |  |  | $\surd$ |  |  | $\surd$
Observations | 51,794 | 51,794 | 51,794 | 51,794 | 51,794 | 51,794

  * •

Notes: *, **, and *** represents statistical significance at the 10 %, 5 %,
and 1 % level respectively. Standard errors are clustered at the match level
and presented in parentheses. All coefficients are population averages (ATE).
For a full list of covariates included in each specification, see Table A.1.

Table C.2: OLS estimates

Model: | (1) | (2) | (3) | (4)
---|---|---|---|---
_Starting line-up next match_ |  |  |  |
Coworker performance |  0.023∗∗∗ |  0.020∗∗∗ |  0.020∗∗∗ |  0.019∗∗∗
| (0.003) | (0.003) | (0.002) | (0.002)
_Expert evaluation_ |  |  |  |
Coworker performance |  0.234∗∗∗ |  0.234∗∗∗ |  0.227∗∗∗ |  0.224∗∗∗
| (0.011) | (0.010) | (0.010) | (0.010)
Individual controls | $\surd$ |  |  |
Team controls | $\surd$ |  | $\surd$ |
Match controls | $\surd$ |  | $\surd$ | $\surd$
Individual FE |  | $\surd$ | $\surd$ |
Individual-Season FE |  |  |  | $\surd$
Observations | 58,968 | 58,968 | 58,968 | 58,968

  * •

Notes: Linear regression. *, **, and *** represents statistical significance
at the 10 %, 5 %, and 1 %, respectively. We additionally control for the
quality of chances coworkers are exposed to (xG).

Table C.3: Assignment rules of shallow trees

Tree depth = 3
---
0 Goals |  1 Goal |  2 Goals
Managers with more than 258 matches |  |
in Top-5 leagues & |  |
Player quality above 75 & |  |
Team strength above 74.654 |  |
or |  Nobody |  All other
Managers with less than 259 matches |  |
in Top-5 leagues & |  |
Player quality above 83 & |  |
Team strength above 74.654 |  |

  * •

Notes: The outcome variable used is a binary indicator, whether a player is
fielded in the starting line-up in the next match. For the sake of brevity, we
do not list the specific sectors selected by the decision tree.

Results from k-means clustering. K-means clustering groups similar data points
into distinct clusters by assigning each point to the cluster whose mean is
closest. The "k" in k-means denotes the predetermined number of clusters. The
algorithm iteratively adjusts centroids to minimize within-cluster variance,
resulting in a partitioning of data into k clusters. In our implementation,
k-means$++$ clustering utilizes Individualized Average Treatment Effects
(IATEs) relative to the no-goal treatment to categorize players into
clusters.353535K-means$++$ compared to k-means clustering improves initial
center selection for faster computation.

Table C.4: Means of IATEs and covariates by cluster obtained from k-means
clustering

Cluster | 1 | 2 | 3 | 4
---|---|---|---|---
| IATE for the comparison 2 vs 0
| -0.010 | 0.025 | 0.059 | 0.116
| Mean of selected features
xG Coworker | 1.31 | 1.17 | 1.23 | 0.23
Player quality (Fifa) | 76.79 | 74.89 | 73.52 | 73.53
Defensive Skills (Fifa) | 62.77 | 60.53 | 56.06 | 55.70
Pace (Fifa) | 71.86 | 71.08 | 71.91 | 71.22
Passing Skills (Fifa) | 66.74 | 66.25 | 66.80 | 64.79
Physical Skills (Fifa) | 72.46 | 71.28 | 69.46 | 70.20
Dribbling Skills (Fifa) | 69.41 | 69.10 | 70.52 | 68.60
Shooting Skills (Fifa) | 58.93 | 58.79 | 60.86 | 59.55
Time in club | 3.03 | 2.45 | 1.89 | 2.00
Age | 26.08 | 26.16 | 26.07 | 25.91
German | 0.44 | 0.44 | 0.42 | 0.43
Position | 3.65 | 3.73 | 3.78 | 3.75
Manager experience | 174.15 | 144.92 | 140.32 | 143.41
Team strength (Fifa) | 72.40 | 71.02 | 70.24 | 70.29
Relegated from 2nd to 1st division | 0.05 | 0.11 | 0.20 | 0.19
Rank last season | 6.83 | 9.62 | 11.50 | 11.35
Opponent strength (MW) | 15.33 | 14.99 | 14.66 | 15.22
Rank last season opponent | 7.98 | 9.73 | 11.21 | 8.49

  * •

Notes: Summary of results from k-means clustering approach. Cluster 1 is the
least beneficial group, while cluster 4 is the most beneficial group. In the
bottom part, we drop a set of covariates for which we do not observe
meaningful differences across cluster. The outcome variable used is a binary
indicator, whether a player is fielded in the starting line-up in the next
match.

The analysis reveals substantial heterogeneity in the degree of spillover
effects. The spillover effects on fielding decisions in the next match range
from 0.01 to 0.12. To facilitate interpretation, let’s consider one examples.
The average chances of being replaced in the match are around 20%. In the
group most affected by spillover effects, there is a more than 50% decrease in
the likelihood of being replaced in the next match.

In the bottom part of Table C.4 we report means per cluster for selected
features. For manager decisions, we find that the group benefiting the least
from spillover effects is broadly characterized by higher team performance
(xG) and higher individual quality—especially marked by superior defensive
skills. On average, this group has also spent more time in the club, and the
club manager is more experienced compared to the most beneficial group. As
observed in previous sections, team strength and position do not exert a
substantial impact.

Table C.5: Own shooting performance and performance evaluation

| (2 vs 0) | (1 vs 0) | (2 vs 1)
---|---|---|---
_Starting line-up next match_ |  |  |
Coworker performance |  0.100∗∗ |  0.086∗∗∗ | 0.014
| (0.044) | (0.011) | (0.045)
_Expert evaluation_ |  |  |
Coworker performance |  1.965∗∗∗ |  1.058∗∗∗ |  0.907∗∗∗
| (0.256) | (0.028) | (0.257)
Individual controls | $\surd$ | $\surd$ | $\surd$
Team controls | $\surd$ | $\surd$ | $\surd$
Match controls | $\surd$ | $\surd$ | $\surd$
Observations | 58,968 | 58,968 | 58,968

  * •

Notes: *, **, and *** represents statistical significance at the 10%, 5%, and
1% level respectively. Standard errors are clustered at the match level and
sre presented in parentheses. All effects are population averages (ATE). For a
full list of covariates included in each specification, see Table A.1.

Table C.6: Subsample analysis - Type of coworker and type of worker

Dependent Variable: | Manager decision
---|---
| (All) | (Defender) | (Striker)
_Defender_ |  |  |
Shooting Performance |  0.019∗ |  0.021∗ | 0.013
| (0.011) | (0.012) | (0.011)
_Striker_ |  |  |
Shooting Performance | 0.011 | 0.011 | 0.004
| (0.010) | (0.010) | (0.016)
Individual controls | $\surd$ | $\surd$ | $\surd$
Team controls | $\surd$ | $\surd$ | $\surd$
Match controls | $\surd$ | $\surd$ | $\surd$
Observations | 58,968 | 23,293 | 10,044

  * •

Notes: Subsample analysis based on types of coworkers. The outcome variable is
the manager decision. *, **, and *** represents statistical significance at
the 10 %, 5 %, and 1 %, respectively.

Table C.7: Subsample analysis - Type of coworker and type of worker

Dependent Variable: | Expert evaluation
---|---
| (All) | (Defender) | (Striker)
_Defender_ |  |  |
Shooting Performance |  0.080∗∗∗ |  0.057∗∗ |  0.101∗∗∗
| (0.024) | (0.026) | (0.028)
_Striker_ |  |  |
Shooting Performance |  0.137∗∗∗ |  0.127∗∗∗ |  0.146∗∗∗
| (0.020) | (0.019) | (0.031)
Individual controls | $\surd$ | $\surd$ | $\surd$
Team controls | $\surd$ | $\surd$ | $\surd$
Match controls | $\surd$ | $\surd$ | $\surd$
Observations | 58,968 | 23,293 | 10,044

  * •

Notes: Subsample analysis based on types of coworkers. The outcome variable is
the journalists’ ratings. *, **, and *** represents statistical significance
at the 10 %, 5 %, and 1 %, respectively.

##  Appendix D Effect heterogeneity journalists’ ratings

Figure D.1: GATEs for different player characteristics

(a) Expert

(b) Expert

(c) Expert

Notes: The vertical axis denotes the respective GATE and its 90% confidence
interval for the comparison of coworkers scoring two goals, relatively to
coworkers scoring zero goals.

Figure D.2: Journalists’ ratings - Distribution of estimated IATEs and overall
effect heterogeneity

(a) Manager

(b) Manager

Notes: Estimates based on our main specification (Column 3 in Table 5.1).
Panel a shows the distribution of estimated IATEs. The horizontal axis
measures the effect of coworkers scoring two goals relative to coworkers
scoring zero goals in the corresponding outcome variables. Kernel smooth with
Epanechnikov Kernel and Silverman (normality) bandwidth. Panel b shows IATEs
sorted according to their size. 90%-confidence interval of IATEs based on
estimated standard errors and normal distribution. The vertical axis measures
the average increase in performance evaluation from coworkers scoring two
goals, relatively to coworkers scoring zero goals. The horizontal axis shows
the rank of the ordered observations.

Results k-means clustering. Since we could not derive informative results for
the journalists’ ratings using the policy simulation exercise, as all
observation were assigned to the highest treatment level, we depict the
dependence of the effects on covariates using k-means++ clustering Arthur and
Vassilvitskii (2007). The analysis reveals substantial heterogeneity in the
degree of spillover effects. The spillover effects on journalists’ evaluations
range from 0.18 in the least affected cluster to 0.51 in the most affected
cluster. To facilitate interpretation, let’s consider one examples. A 0.51
increase in the evaluation received by journalists is roughly equivalent to
0.5 times the effect of scoring one goal oneself, given the faced chances. The
size of the spillover effect is, thus, one-quarter of the effect of one’s own
performance in the same task.363636Results used for this comparison are shown
in Appendix C Table C.5.

In the bottom part of Table D.1, we report means per cluster for selected
features. The group benefiting the most from spillover effects is roughly
characterized by higher team performance (xG), with individual quality
negatively correlated with the treatment effect size. Specifically, players
with high defensive skills are prevalent in the group of least beneficial
players, while players with high offensive skills are in the group that
benefits the most from coworker shooting performance. These findings align
with the fact that strikers are more likely to be in the group of most
beneficial players. Manager and team strength matter less compared to the
manager’s decision.

Table D.1: Means of IATEs and covariates by cluster obtained from k-means
clustering.

Cluster | 1 | 2 | 3 | 4 | 5 | 6
---|---|---|---|---|---|---
| IATE for the comparision 2 vs 0
| 0.179 | 0.250 | 0.290 | 0.371 | 0.387 | 0.510
| Mean of selected features
xG Coworker | 2.08 | 1.37 | 0.75 | 1.09 | 0.91 | 1.51
Player quality (Fifa) | 75.98 | 74.31 | 73.78 | 74.73 | 74.72 | 78.29
Defensive Skills (Fifa) | 74.83 | 67.61 | 63.46 | 57.52 | 53.01 | 42.11
Pace (Fifa) | 67.02 | 69.46 | 70.08 | 71.53 | 73.30 | 77.93
Passing Skills (Fifa) | 61.88 | 63.85 | 64.70 | 67.37 | 68.23 | 72.44
Physical Skills (Fifa) | 75.17 | 72.86 | 71.78 | 70.76 | 69.31 | 66.83
Dribbling Skills (Fifa) | 61.66 | 65.49 | 66.99 | 70.91 | 72.61 | 79.08
Shooting Skills (Fifa) | 47.74 | 52.79 | 55.70 | 62.24 | 64.17 | 73.10
Time in club | 3.12 | 2.60 | 2.32 | 2.47 | 2.17 | 2.15
Age | 26.29 | 26.35 | 26.17 | 26.20 | 25.69 | 25.86
German | 0.45 | 0.46 | 0.46 | 0.43 | 0.42 | 0.37
Position | 2.20 | 2.52 | 2.72 | 3.13 | 3.23 | 3.72
Manager experience | 148.88 | 142.55 | 104.94 | 191.98 | 133.05 | 216.83
Team strength (Fifa) | 71.94 | 70.83 | 70.37 | 71.19 | 71.02 | 72.56
Relegated from 2nd to 1st division | 0.07 | 0.15 | 0.17 | 0.13 | 0.10 | 0.06
Rank last season | 7.21 | 9.95 | 10.75 | 9.66 | 9.59 | 7.54
Opponent strength (MW) | 15.01 | 14.98 | 15.06 | 15.06 | 14.94 | 14.93
Rank last season opponent | 9.68 | 9.72 | 9.23 | 9.35 | 9.82 | 10.06

  * •

Notes: Summary of results from k-means clustering approach. Cluster 1 is the
least beneficial group, while cluster 6 is the most beneficial group. In the
bottom part, we drop a set of covariates for which we do not observe
meaningful differences across cluster. The outcome variable are the
journalists’ evaluations.