The impact of managerial change on performance: the role of team heterogeneity.
Muehlheusser, Gerd ; Schneemann, Sandra ; Sliwka, Dirk 等
The impact of managerial change on performance: the role of team heterogeneity.
I. INTRODUCTION
In many organizations, the dismissal of a manager is typically
triggered by unsatisfactory performance of the unit (e.g., team,
subdivision) for which the manager is responsible. Consequently, in
replacing the current manager by a new one, executives hope for enhanced
performance. But whether and how a new manager can affect a firm's
or a team's performance intricately depends on the role of the
manager within the organization. In this article, we study a particular
channel through which a manager can affect performance, namely through
the selection of team members and its effects on within-team competition
for attractive positions.
Hoffler and Sliwka (2003) have analyzed within-team competition in
a theoretical model in which a manager picks among team members to fill
an important position. The article builds on Lazear and Rosen's
(1981) tournament theory and endogenizes a manager's selection
choice under incomplete information about individuals' ability or
talent. When a manager has been in place before, she knows the abilities
of the team members quite well and therefore should have a clear idea in
mind who should be picked. In turn, competition for being selected is
weaker. When, however, a new manager is brought in from outside, this
new manager knows less about the respective abilities and in turn,
within-team competition is reinforced. But, whether a management
replacement can indeed trigger such a push in incentives crucially
depends upon the composition of the team. In particular, when team
members differ strongly in their abilities, the new manager will most
certainly pick the same individuals as the old manager had--in this
case, dismissals only have weak effects in this respect. But, if the
team composition is more homogeneous, management replacements are more
effective in reinvigorating within-team competition.
On a more general level, this prediction builds on a theoretically
robust mechanism that has been established across a large number of
models on asymmetric contests and tournaments, in which it has been
shown that equilibrium efforts tend to be the higher the more symmetric
(and hence the more competitive) the contest. (1) From this perspective,
the dismissal of a manager can be viewed as an instrument to reduce the
asymmetries in contests.
We study this question empirically in an area where the selection
of subordinates for important tasks is one of the core responsibilities
of a manager, namely in professional team sports. To do this, we are
using a large dataset on the German Bundesliga, one of the biggest
soccer leagues in the world. A key task of a head coach in soccer is the
selection of the starting line-up of 11 players for each game from a
larger number (on average 25) of players employed by the respective
club. As the players' career advances, their popularity and often
also their remuneration depend crucially on the number of matches in
which they were being fielded; competition among team members for these
positions is an important element of team sports. In turn, the dismissal
of the coach should have a substantial impact on the nature of this
within-team competition. It is the key purpose of this article to test
empirically whether indeed dismissals have a stronger effect on the
performance in teams, which are homogeneous with respect to the
abilities of the team members.
In general, the empirical evaluation of management dismissals is
nontrivial because of a number of caveats: First, there is often a lack
of available performance measures for managers' unit of control. In
addition, managerial change either occurs rarely and/or is often
accompanied by further changes in the surrounding conditions, which
obscures the identification of the causal succession effect.
Furthermore, organizations will typically be heterogeneous with respect
to a number of crucial dimensions which makes it difficult to assess the
contribution of a single manager. And last but not least, dismissal
decisions are unlikely to be random, but often occur after a period of
low performance. When part of the actual performance is outside a
manager's control ("luck"), then the organization's
expected performance may increase after managerial change simply because
of mean reversion. (2)
In response to these difficulties, a major part of the existing
literature has aimed at measuring succession effects in the context of
professional team sports. Apart from being of interest in its own right,
since the sports sector has long been recognized as a valuable
"labor-market laboratory" (Kahn 2000), it is particularly well
suited for the analysis of succession effects. In particular, in
European soccer, managerial changes occur rather frequently and, in most
cases they occur within a season (i.e., between two match days). The
German Bundesliga consists of 18 teams, and during our observation
period of 16 seasons there were on average 7.13 within-season
replacements per season. One key benefit of within-season replacements
for the purpose of the evaluation of dismissal effects is that most
other crucial determinants for team success (e.g., composition of roster
or team budget) remain constant between two match days, which is also
helpful when aiming to control for mean reversion. (3)
There now exists a large number of empirical studies that have
attempted to assess the effects of management changes in professional
sports. Early studies typically use seasonal data from U.S. sports
leagues (and hence mainly consider between-season managerial changes),
and the evidence is mixed: Grusky (1963), Theberge and Loy (1976), and
Allen, Panian, and Lotz (1979) do find a negative relationship between
managerial change and the performance in different U.S. sports leagues.
Other studies do not find a statistically significant effect and
interpret this as evidence in favor of "ritual scapegoating"
(Brown 1982; Gamson and Scotch 1964; McPherson 1976). A final set of
studies does find a mild positive effect (Fabianic 1994; Gamson and
Scotch 1964; McTeer, White, and Persad 1995), where the measured effects
are typically stronger in the short run and often vanish shortly after
the replacement takes place. (4) However, the older studies often do not
fully account for performance prior to dismissals and are prone to
mean-reversion effects (i.e., if a coach is dismissed after a series of
losses, the probability of a performance increase is necessarily
larger). In more recent studies, match-level data are used which allows
to directly control for the prior performance of each team and account
for mean reversion. In particular, the large bulk of studies of
different European soccer leagues either find detrimental (e.g., Audas,
Dobson, and Goddard 2002; Audas, Goddard, and Dobson 1997; Bruinshoofd
and ter Weel 2003) or no effects (e.g., De Paola and Scoppa 2012; Koning
2003), while only de Dios Tena and Forrest (2007) provide some evidence
for performance increases after a dismissal. However, most of these
studies do not discuss potential biases due to the endogeneity of coach
dismissals beyond potential mean-reversion effects.
Our article adds to the literature in two respects. First of all,
we analyze in more detail potential selection effects and argue that the
typical approaches (including our own) tend to underestimate the effects
of coach dismissals. The reason is that the effect of a dismissal is
typically identified by comparing the average performance of teams
dismissing the coach with the performance of nondismissing teams, which
exhibit similar values for a set of observable variables. This would
identify a causal effect if the (counterfactual) performance of teams
with dismissals was identical to the performance of nondismissing teams
with the same set of observables. As we show in a simple formal model in
which the executives who decide on the dismissal of the manager receive
a private signal that contains additional information on the benefits of
a dismissal, this will typically not be the case under very plausible
assumptions: the fact that a team dismissed a manager reveals
unfavorable information about the future performance without a
dismissal. Hence, the conditional expectation about counterfactual
performance of the team that dismissed the coach should therefore be
smaller than the performance of the teams that did not dismiss the coach
in the same situation. In turn, the typical estimates should give a
lower bound on the true effects of coach dismissals. Hence, from these
considerations, we can reconcile the two apparently contradictory
observations in the previous literature--that is, that coach dismissals
were estimated to be mostly useless, but that there are still so many of
them. (5)
But more importantly, while nearly all other studies investigate
the average consequences of coach dismissals in soccer, our approach is
to study under which contingencies a dismissal can be expected to be
beneficial. In particular, we study the importance of the team
composition prior to the dismissal. Indeed, we find that teams that
replaced their coach significantly increase their performance as
compared with other teams exhibiting the same set of observables--but
only when the team is sufficiently homogeneous prior to the dismissal.
Given the above arguments that we identify a lower bound to the true
effects, we conclude that coach dismissals on average have substantially
positive performance effects in homogeneous teams. Moreover, we also
investigate the effect of coach dismissals on the performance of
individual players and show that individual performance increases to a
stronger extent in homogeneous teams. To the best of our knowledge,
there has been no empirical evidence so far concerning the impact of
heterogeneity in the context of dismissals and our analysis reveals that
this is a key factor determining the success of a replacement. Moreover,
our results are consistent with recent findings from the empirical
literature on asymmetric contests, which often finds a negative
correlation between effort levels and the degree of heterogeneity of
contestants (see, e.g., Berger and Nieken 2014; Brown 2011; Lynch 2005;
Nieken and Stegh 2010; Orrison, Schotter, and Weigelt 2004; Schotter and
Weigelt 1992; Sunde 2009).
The remainder of the article is organized as follows: Section II
lays out the empirical framework. In Section III, we present our
empirical results concerning the impact of coach dismissals on the
performance of teams and individual players. Section IV discusses our
findings and concludes.
II. EMPIRICAL FRAMEWORK
A. Institutional Background and Data
Our aim is to estimate to what extent the effect of a coach
dismissal depends upon team heterogeneity. But, a key challenge is of
course the potential endogeneity of the dismissal itself. Coach
dismissals are not exogenously imposed and will typically be driven by
the (observed) performance history of a team but may also be influenced
by (unobserved) private information of the club's management on the
future performance of the team. Hence, a careful discussion of potential
selection effects is of crucial importance for any study of management
dismissals with observational data. But first, it is important to
understand the structure of the data that we use and the basic
econometric approach.
The German Bundesliga consists of 18 teams, and each team plays
twice against each other team (one home match each) resulting in 34
match days per season and 306 matches overall. In each match, a winning
(losing) team is awarded 3 (0) points. In case of a draw, each team is
awarded 1 point and teams are ranked according to their accumulated
points. (6) At the end of the season, the team with the highest number
of points wins the championship (there are no playoffs), while the two
(resp. three) teams with the lowest number of points are delegated to
the second division and replaced by the best two resp. three teams from
that division. (7) During our observation period, both the league winner
and the second best team were automatically qualified to participate in
the highly prestigious UEFA Champions League in the subsequent season;
the third best team also had the chance of participation by prevailing
in a preliminary tournament against corresponding teams from other
European leagues. The next two teams participated in the UEFA Euro
League. The incentives (both financially and with respect to reputation)
to qualify for one of the two UEFA leagues are very strong; the same is
true for avoiding relegation. (8)
The unit of observation in our dataset is a specific match. The
dataset contains all matches played in the German Bundesliga for the 16
seasons from 1994/1995 until 2009/2010 (9 matches played on each of 544
match days leading to a total of 4,896 matches). For each match, we have
detailed information about match- and team-specific characteristics, as
well as the involved managers and players.
For most of the analysis, the dependent variable is the number of
points [y.sub.ijt] won by the home team in a match between the home team
i and the away team j at match day t. As there are three possible match
outcomes, home team win, draw, or away team win, resulting in 3 (0), 1
(1), or 0 (3) point(s), respectively, for the home (away) team, both
teams have a strictly monotone (but reversed) preference order with
respect to it.
Overall, there are 184 dismissals in our sample, out of which 137
occurred within a season. In 23 out of these 137 cases, the new manager
was (and was ex ante known to be) an interim solution, supposed to step
down as soon as the "true" successor was available. These were
dropped from the main analysis, which leaves us with 114 within-season
dismissals. (9)
B. Identification and Selection Bias
As our baseline specification, we estimate by ordinary least
squares a number of regression models of the following form: (10)
(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Euro League are smaller, but still significant. On the other side
of the spectrum, relegation typically comes along with severe budgets
cuts, which is due to lower TV fees (on average, 18.5 million Euro per
season in the Bundesliga vs. 4.9 million in the lower division), gate
revenues, and merchandizing revenues. As a consequence, teams are forced
to sell some (in many cases most) of their best players.
The dummy [new.sup.[tau].sub.it] (new.sup.[tau].sub.jt]) indicates
whether, prior to match day t, the home (away) team's manager is
"new" in the sense that he has been hired within the last
[tau] home (away) matches of the home (away) team. Throughout, we will
consider three different time horizons [tau] [member of] {2,4,6} for the
effects of managerial change to materialize. The variables [het.sub.it]
and [het.sub.jt] are measures for the heterogeneity of each team
(explained in detail below). The vectors [X.sub.it] and [X.sub.jt]
contain (1) a dummy variable indicating the importance of a match for a
team (crucial), (11) and (2) a measure for a team's ability to
attract top players, where we use a proxy of its relative annual budget
(budget), that is, an estimate of its absolute budget divided by the
average absolute budget in the league in a given season. (12) Finally,
the vectors [Y.sub.it] and [Y.sub.jt] contain different measures for the
respective team's past performance, which are explained in detail
below.
As for the causal effect of a dismissal, it is crucial to consider
the underlying conditional independence assumption. To understand this
point, note that we could obtain a perfectly clean estimate of the
effect of a coach dismissal if dismissals were randomly assigned as in
an experiment--which is of course highly unlikely and infeasible in the
field. An important question is therefore to ask in what direction
regression estimates may deviate from the true causal effects. To save
on notation, define [X.sub.ijt] = ([X.sub.it], [X.sub.jt], [new.sub.jt])
and [Y.sub.ijt] = ([Y.sub.it], [Y.sub.jt]) which contain all relevant
match-specific covariates. Moreover, denote by [y.sub.ijt](1) the
outcome for team i upon dismissing its manager, and by [y.sub.ijt](0)
the (potentially counterfactual) outcome when there is no dismissal.
Then, our approach allows us to identify a causal effect of a dismissal
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
That is, conditional on the observed control variables, the
counterfactual performance of dismissing teams in case of nondismissal
should be equal to the performance of teams that did not dismiss the
coach in the same situation (see, e.g., Angrist and Pischke 2008, 16).
Intuitively, the effect of a coach dismissal is here estimated by
comparing the performance of teams that recently dismissed the coach
with the performance of other teams that did not dismiss the coach under
the same set of observables.
If dismissals were randomly assigned, this condition would always
be met. But, if there are unobserved factors that have an impact on the
likelihood of a dismissal and performance, afterwards this is not
necessarily the case. A first potential endogeneity issue that has
already been acknowledged in the previous literature is that dismissals
are typically triggered by low team performance in the last games prior
to the dismissal. A performance increase after a dismissal may then, for
instance, be simply a mean-reversion phenomenon. As this is a selection
issue based on observable variables (past performance), we account for
this by following a lagged-dependent variable approach, where the
vectors [Y.sub.it] and [Y.sub.jt] contain the following variables for
each team: (13) First, we take into account a team's long-term
performance history, measured by the average league position in the last
three seasons (PerfHist). Second, as a measure for a team's
performance in the current season, we use the average number of points
accumulated in the season up to the match under consideration. Because
there is typically a considerable difference between a team's
performance in home and away matches (see Table 1 in Section II.D), we
distinguish between the two match types (HomePerf and AwayPerf) for both
the home and the away teams. Finally, as each team's exact sequence
of outcomes in the most recent games can be crucial for both--the
decision to dismiss a coach and the pattern of mean reversion--we employ
a saturated approach concerning the most recent performance by including
dummy variables to indicate its exact performance history in the last
four matches, (14) thereby allowing for nonlinearities. In this sense,
we come close to a matching approach comparing teams with identical
short-term performance histories. (15)
Even though we control for the past performance of each team in a
detailed manner, the assumption expressed in Equation (2) will still
clearly be violated when the firing decision is based on unobservable
variables determining the expected future performance of a team under
its current or a new manager. For example, executives who decide on a
dismissal will typically have observed further information (for instance
from communicating with influential players or by observing the team
also between games) that should influence their decision. An important
question is, for instance, whether a performance dip is only due to bad
luck, while the team is in principle still in "good hands"
under the current manager, or whether his relationship with the team is
substantially disturbed.
To see that, consider the following simple formal model. Suppose
that prior to match day t the executive receives a private signal sit
which contains some additional information on the team's expected
subsequent performance, and that the latter is increasing in the signal,
that is, ([partial derivative]/[partial
derivative][s.sub.it])E[[y.sub.ijt](0)|[new.sub.it] = 0, [X.sub.ijt],
[Y.sub.ijt], [s.sub.it]] > 0. Suppose now that the coach will be
dismissed (and thus [new.sub.it] = 1) if and only if
E[[y.sub.ijt](0)|[new.sub.it] = 0, [X.sub.ijt], [Y.sub.ijt], [s.sub.it]]
is sufficiently small. In turn, this leads to a critical signal value
[bar.s] ([X.sub.ijt], [Y.sub.ijt]) such that a dismissal occurs if and
only if [s.sub.it] < [bar.s] ([X.sub.it], [Y.sub.it]). But then
(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Hence, the conditional independence assumption (2) is violated and
the estimates will be biased. But, these considerations also lead to
another insight, namely that the selection bias
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
is negative, and thus, coefficients obtained from estimating
specification (1) will be conservative in the sense that they
underestimate the true average treatment effect. The reason is that the
teams in which managers are fired are those whose performance under the
old manager would be particularly low (as otherwise they would not have
dismissed him). Those teams that did not fire the coach in the same
situation should on average have a better performance--in turn, the true
performance effect from a dismissal must be larger than the difference
in performance between the dismissing and the nondismissing teams. (16)
In our view, these considerations are helpful in resolving a puzzle
in the prior discussion about the effect of coach dismissals as there
are two contradictory patterns: on one hand, within-season dismissals
are very frequent. (17) But on the other hand, the existing studies
mostly find negative or no effects of these dismissals, which would
suggest highly irrational behavior on the part of the club executives
because of the large cost associated with a dismissal in the form of
payments to the outgoing coaches. (18) As we have now argued, studies
with observational data will most likely underestimate the effect of a
dismissal. Hence, it may well be the case that coach dismissals may
indeed be more effective than previously thought. Moreover, the benefits
of dismissals may depend on the degree of team heterogeneity. And it is
this conjecture that we now explore in the remainder of this article.
C. Measuring Team Heterogeneity
Our key hypothesis is that coach dismissals are more beneficial
when teams are homogeneous. In the regression model (1), the variables
[het.sub.it] and [het.sub.jt] are measures for team heterogeneity. These
are constructed from the players' individual performance grades as
assigned by Impire AG, Germany's largest professional provider of
sports data services. They track each individual Bundesliga match and,
for each player being active for at least 15 minutes, assign index
points for a large number of both team- and position-specific
performance indicators (see Appendix A for more detailed information on
how this index is constructed). Each player's accumulated index
points in a given match are then converted into a performance grade on a
scale from 1 (lowest) to 10 (highest). (19)
We then construct a measure of team heterogeneity as follows: For
each team and each match day, we compute the average grade for each of
its players in all matches prior to the match day and then rank players
according to these average grades. In each match, each team fields 11
players, and it can replace up to three of these by players from the
bench. (20) Therefore, we start by comparing two groups of players:
those on rank positions 8-11 (i.e., the weakest ones among the top 11
players) and those at rank positions 12-15 (i.e., the strongest
contenders), and the average grades of these two groups are denoted by
[G.sup.8-11.sub.t] and [G.sup.12-15.sub.t], respectively. For each team
and each match day, we then compute the ratio [g.sub.t] =
([G.sup.8-11.sub.t] - [G.sup.l2-15.sub.t])/[G.sup.8-11.sub.t] as a
measure of how much worse on average the players on rank positions 12-15
are compared with those on positions 8-11 prior to match day t. While
the measure [g.sub.t] will be used in the main part of the article, as
detailed in Appendix C, our results are robust with respect to
alternative ways of measuring heterogeneity, including measures such as
the Gini coefficient or the coefficient of variation, where all graded
players in the roster are considered. Hence, our results do not hinge on
the specific boundaries for the contested ranks.
Because of the higher variance in prior grades early in a season,
the expected value of [g.sub.t] is decreasing in the match day of a
given season. Therefore as a last step, for each match day, we normalize
the measure by dividing each team's g, by the average value across
all teams at this match day. This normalized measure of team
heterogeneity prior to match day t is denoted [het.sub.t], where
[het.sub.t] > (<) 1 indicates a degree of heterogeneity above
(below) average. Consequently, we refer to teams satisfying [het.sub.t]
> (<)1 at match day t as heterogeneous and homogeneous,
respectively. When a team hires a new manager at match day t, we use
([het.sub.t] + [het.sub.t-1])/2 (i.e., the team's average degree of
heterogeneity of the last home and the last away match under the old
manager) as a measure for the "inherited" team heterogeneity
for the upcoming [tau] match types under the new manager. (21) Thus,
heterogeneity of a team after a coach dismissal is measured by the
heterogeneity of the grades in the matches prior to the first game of
the new coach, such that the heterogeneity measure is not affected by
the dismissal.
Note that our measures of team heterogeneity are not position
specific as they can, for example, contain both strikers and defenders,
so that the competitive pressure between such players might appear as
being not too strong. This might suggest that it is superior to use
position-specific measures instead. However, such an approach is
problematic for at least two reasons: First that even within positions,
players such as left and right defenders might not exert too much
competitive pressure on each other, which rather arises from defensive
midfielders who can play on the same side. (22) In fact, except
goalkeepers, most players are typically observed on several positions,
suggesting that competitive pressure indeed does arise across positions.
For example, in our dataset, out of the 1,639 non-goalkeeper players
whom we observe for at least ten matches, only 26.2% are observed on one
position only, while the remainder is observed on two or even three
different positions, respectively. Hence, competitive pressure arises to
a large extent across positions. When excluding goalkeepers from the
computation of the measure [g.sub.t], all of our results remain
qualitatively robust (see Table C3).
D. Descriptive Statistics
Table 1 summarizes the descriptive statistics for the main
variables used in the analysis. As can be seen, match outcomes are not
uniformly distributed, but the home team wins about half of the matches,
while the other half is evenly split between draws and wins of the away
team. Annual (relative) budgets are ranging from one third of the
average budget to more than twice as much, which indeed suggests that
teams are highly heterogeneous with respect to their ability to attract
good players. (23)
There are no roster limits in the German Bundesliga, and teams have
rosters of up to 35. The average roster size is 25, that is, the average
team contracts with more than twice as many players as it can field in a
single match. While also the possibility of injuries needs to be taken
into account, this suggests that within-team competition for the scarce
slots in the squad is an importance aspect in this context. (24) In
fact, Figure 1 plots the average frequency of being fielded as a
function of a player's rank with respect to his average grade, and
it shows that match participation is strongly driven by players'
rank within the roster, where for example, players in the top ranks are
fielded more than three times as often as those in the lowest ranks.
Table 1 also shows that teams differ strongly with respect to our
(normalized) measure of heterogeneity based on grades (het): For
example, the degrees of heterogeneity in the 90th and 10th percentile of
the distribution differ by a factor 2.5. This holds for both the whole
sample and, in case of dismissals, for the degrees of heterogeneity
which the new managers inherit from their predecessors.
Figure 2 illustrates the average player performance (grades) in
homogeneous and heterogeneous teams: As would be expected, heterogeneous
teams exhibit slightly better grades at the top performance ranks, while
the grades in homogeneous teams, being more balanced, are better at the
lower performance ranks. Overall, these differences appear to be small.
However, and consistent with our main hypothesis, it will turn out that
this relationship does become important in cases of manager dismissal.
As for the frequency of dismissals, Table 1 shows that in about a
third of the 288 team-season observations, at least one dismissal
occurred within the current season. At a season level, on average, there
were roughly seven within-season dismissals. As already pointed out in
the above, managerial change between two seasons occurs less often, on
average only in three teams per season. Figure 3 presents more detailed
information about the distribution of dismissals depending on a
season's match day and league positions, respectively. It is
evident from panel (b) that many dismissals occur when the respective
teams are facing the threat of being relegated.
Finally, panel (a) of Figure 4 shows the average of the number of
points won in the six games before and after dismissal for all teams
with a within-season dismissal, suggesting a negative trend in
performance as a key source of managerial change which points at the
importance of controlling for the exact short-term sequence of
performance to exclude mean reversion as a driver of the observed
performance increase.
Importantly, our key hypothesis, that positive succession effects
emerge in homogeneous rather than heterogeneous teams, should not be
driven by mean reversion. Rather, as argued by Hoffler and Sliwka
(2003), managerial change should be more successful in homogeneous teams
where it is easier for the new manager to invigorate the competition for
the available slots as players are operating in a now more competitive
environment. In contrast, when there is a large difference in abilities
between the top players in the team and the rest, a new manager will
basically have to pick the same starting line-up as his predecessor so
that within-team competition cannot be triggered anew through a
dismissal.
As a first step in assessing the validity of our main hypothesis,
panel (b) of Figure 4 plots again the average number of points achieved
in the last six games before and after a dismissal but, in contrast to
panel (a), separately for homogeneous and heterogeneous teams. While
both groups show a very similar performance dip prior to dismissal (with
a slightly better performance for heterogeneous teams), the performance
increase in the first matches under the new manager appears to be larger
in homogeneous teams at least for a short time frame. These issues will
be investigated in more detail in the following.
III. RESULTS
A. Coach Dismissals and Team Performance
As explained above, we estimate lower boundaries to the causal
effect of coach dismissals on team performance. Our main hypothesis is
that dismissals should increase performance to a stronger extent in
homogeneous teams. Note that we can test this hypothesis both with the
data from home and away teams. In turn, we expect that the coefficient
for the interaction term between our measure of heterogeneity (het) and
the dummy for managerial change (new) should be negative for home teams
and positive for away teams. We estimate three different models, looking
at the new manager's first 2, 4, and 6 match types (home and away),
respectively.
The regression results are shown in Table 2, and they provide
strong support for the main hypothesis. All coefficients of the
interaction terms have the expected sign and are also statistically
significant. (25)
In a next step, we investigate the economic significance of the
dismissal effect, depending on the degree of heterogeneity of the
respective team. To do this, we center the het_home and het_away
variables at different percentiles (10, 25, 50, 75, 90--see Table 1 for
the respective values) of their distributions and then estimate again
the New_home dummy, which then yields a lower bound on the average
treatment effect in home games for teams at this percentile. To evaluate
the effect of dismissals on away performance, Table B1 reports the
results of a second regression with the same set of covariates, but with
the number of points won by the away team as the dependent variable.
(26) Applying the same approach to these models, we obtain the average
treatment effect in away games for teams at the respective percentiles.
The overall average effect of a dismissal on the respective teams'
performance per match of either type is then the average of the
respective coefficients for New_home from Table 2 and New_away from
Table B1 (centering the heterogeneity measure het at the respective
percentile). The results are shown in Table 3. (27)
As conjectured, Table 3 reveals that there are highly significant
and substantial average dismissal effects (only) for homogeneous teams,
that is, at the lower percentiles of the distribution of het. For
example, when a team with a degree of heterogeneity at the lowest 10
(25)% percentile replaces its manager, it wins on average an additional
0.35 (0.23) points per game during the next four matches (two home and
two away), compared with a team in a comparable situation which keeps
its manager. Given that, at the time of dismissal, the average
dismissing team has only won 0.98 points per match in the respective
season (as opposed to an average in the whole sample of 1.68 points, see
Table 1), these numbers indeed indicate substantial performance effects;
a fortiori when recalling that, as argued above, the estimates are in
fact lower bounds on the true causal effects.
Moreover, the "new broom effect" becomes smaller as the
time horizon considered for the new manager ([tau]) increases. This is
consistent with the idea that the new manager's ability to trigger
within-team competition anew is strongest in the first few matches of
his new team. After some time in office, the new manager will again have
made up his mind about his most preferred team composition and, in turn,
within-team competition should again become weaker.
Last, but not least, disentangling this overall average effect of a
dismissal into home and away performance reveals that it is more
strongly driven by performance increases in away games. (28) One
interpretation for this result is that in home games the players'
motivation is substantially higher in any case because of the
monitoring, support, or even pressure from the team's own fans
(recall that home team wins occur twice as often as away wins and
draws). Hence, the additional motivational push from intra-team
competition from a coach replacement in a homogeneous team appears to be
stronger in away games where these other motivational mechanisms are
weaker. In this respect, it is also interesting to note that the
coefficient of the heterogeneity measure in our main regression reported
in Table 2 is significantly negative in away games, which is in line
with the idea that the motivational effect of within-team competition
matters more in these games. (29)
In order to check the robustness of our results, we have also
analyzed a number of alternative model specifications (all regression
results are reported in Appendix C): First, we have considered a number
of alternative measures of the teams' heterogeneity such as the
coefficient of variation or the Gini coefficient of the players'
grades. Table C2 replicates the results from Table 3 for each of the
alternative measures. While the size of the coefficients varies to some
extent, the results are qualitatively very robust. For instance, the
estimate for the average increase in the number of points in the next
four matches at the 10% percentile in terms of heterogeneity is 0.201
and 0.215 when using the coefficient of variation and the Gini
coefficient, respectively, as a measure of heterogeneity. We also
studied regressions where we include players up to rank 18 in the
"contested ranks" and again the results are robust.
Second, we also created a heterogeneity measure that does not
include goalkeepers, as they do not compete with players on other
positions, while changes on the goalkeeper position occur only rarely
(for instance, the goalkeeper with the largest number of appearances on
average plays in 29.3 of the 34 games of a season). The results of this
specification are shown in Table C3, and again, they are qualitatively
unchanged.
Third, in our main specifications, we used a lagged-dependent
variable approach as this allows us to control for the sequence of
performance in the most recent games (and as laid out in footnote 13
including both would lead to biased estimates). But, the results are
also robust when estimating a fixed-effects model instead, where
team-season fixed effects are included to allow for varying team
strength over time. The results of regressions including team-season
fixed effects for both the home and away performance are reported in
Table C4. Again, our results are robust also under this specification.
Finally, we also allowed for the possibility that the relationship
between past and future performance may also depend on team
heterogeneity. For instance, because of their better "bench
strength," homogeneous teams might find it easier to recover from a
string of bad results than heterogeneous teams that would create a
potential confounding effect. (30) In order to test this, we have added
interaction terms between the 81 x 2 = 162 dummies for most recent past
performance and our measure for team heterogeneity. Again, as can be
seen from Table C5, our results concerning the impact of team
heterogeneity on the effect of a coach dismissal turn out to be robust
also under this specification.
B. Manager Dismissals and Individual Players' Performance
Apart from the performance impact of managerial succession on the
(aggregate) team level, an alternative route is to directly consider the
(individual) player level and see whether there is any measurable direct
impact on the players' grades. Consistent with our underlying
mechanism based on within-team competition, we would expect that the
improvement of players' grades is stronger (1) in homogeneous teams
and (2) in the "contested" ranks, that is, those close to rank
11 which are the weakest players on the team or the strongest on the
bench. However, we expect a weaker response among the top players as
they will most certainly also be a part of the starting line-up under a
new coach.
Figure 5 plots the changes of grades for the players at the
different performance ranks again using the average grades obtained so
far in response to dismissals (the figure plots the average grade change
for players on rank 1-4, 5-8, ...). Panel (a) shows the change of
(average) grades between the first four matches under the new manager
and all previous matches (in a given season) before the dismissal, while
panel (b) extends the time horizon to cover all matches under new
manager until the end of the season. First, note that the changes are
increasing in a player's rank at the time of dismissal and are
negative at the top ranks and positive at the lower ranks. This
phenomenon is naturally explained by mean reversion of players who
received top grades in the past have less scope to improve; vice versa,
those at rather lower ranks have more scope for improvements. But the
important observation here is that players in homogeneous teams improve
to a stronger extent under a new coach (i.e., the players on the lower
ranks become better to a stronger extent and the players on the top
ranks show lower degrees of mean reversion) than players in
heterogeneous teams. Moreover, from panel (b) and in line with our
previous findings, we observe that the "new broom effect" gets
weaker as the tenure of the new manager increases--the patterns of the
homogeneous and heterogeneous teams do not differ that much when the
whole season is considered.
To investigate this issue in more detail, we estimated the
performance change of individual players around a coach dismissal. We
first constructed a dataset containing all players of teams in which a
coach has been replaced within a season. The dependent variable is the
difference between the average grade in first four matches under new
manager and that in all matches (in a given season) before the
dismissal. The key independent variables are a dummy indicating whether
the team's homogeneity is above average as well as the
player's rank prior to the dismissal. The key hypothesis is that
grade improvements because of coach replacements are stronger (1) in
more homogeneous teams and (2) for players at the lower performance
ranks.
The regression results are shown in Table 4. As can be seen from
the first column, the change in player performance as a result of
managerial change is on average stronger for homogeneous teams and for
players at lower ranks (at the time of dismissal). (31) In the second
column, we include an interaction term between the team homogeneity and
the performance rank (which we here normalize at the average rank of
11.52) testing the hypothesis that the lower ranks improve more in
homogeneous teams. While the coefficient of the interaction term is
positive, it is not statistically significant (p=.174), so that this
latter hypothesis is not supported by our results. Apparently, the
reinvigorated within-team competition in homogeneous teams affects all
players and not only those on the lower ranks.
C. The Impact of Team Heterogeneity under Interim Managers
Recall that we have excluded interim managers from the main
analysis, because their spell was usually very short (on average a mere
2.3 matches) and, more importantly, they are typically known to be
interim solutions, only responsible for the team until the arrival of
the "real" replacement for the old manager and mostly they
have worked for the same team before--typically as an assistant to the
outgoing manager. Given their very short tenure as responsible coach and
given that they are typically well acquainted with the players, our
theory based on within-team competition would predict that new interim
managers are less successful in triggering within-competition anew
compared with those new managers who are hired from the outside and
expected to stay for longer. As a result, and in contrast to our main
findings as reported in Table 2, we should expect to see no sizeable
effect of team heterogeneity on team performance when an interim coach
takes over. Table 5 shows the results of the same regressions as above
with an additional dummy indicating whether or not the new manager is an
interim coach. Indeed, the interaction terms are not significant for
interim managers so that, in contrast to their more permanent
counterparts, there is no effect with respect to team heterogeneity.
IV. CONCLUSION
The allocation of tasks to subordinates is a core management
responsibility not only in sports but also nearly any kind of
organization. When subordinates have preferences on tasks of different
importance, subordinates compete for the most important tasks that for
instance may help to advance their careers. And this competition can be
a powerful incentive mechanism. However, it will crucially depend upon
the manager's allocation choices. As shown by Hoffler and Sliwka
(2003), a manager who knows his subordinates very well will assign the
most important tasks to the subordinate which he perceives to be the
most able. However, when this is transparent, competition among the
subordinates will be rather weak as their roles are more or less fixed.
In such a situation, dismissing the manager may trigger the competition
for attractive tasks anew. A new manager who does not know the talents
of her subordinates as precisely as her predecessor will have to make up
her mind on the subordinates' talents. In turn the subordinates
have a strong incentive to exert effort to convince the new manager of
their abilities. We have explored this mechanism empirically in
professional sports, a field where it should be of substantial
importance as picking a subset of players from a larger team is a core
management task of any coach. Our key hypothesis was that coach
replacements have a stronger effect on team performance in more
homogeneous teams compared with heterogeneous ones. Indeed, we found
that coach replacements are beneficial when the abilities of the weakest
players just on the team and the strongest ones on the bench are
similar.
This result has direct implications for the decision to replace
coaches in professional sports. It is notable that in many sports, it is
used as a key mechanism to boost performance in the short run, for
instance, to avoid relegation or to qualify for the prestigious UEFA
leagues. As laid out above, in the German Bundesliga, one of the biggest
soccer leagues in the world and the largest in terms of the number of
spectators, nearly half of the clubs dismiss a coach at some point
within a season. As our results show this can indeed be a reasonable
policy--provided that within-team competition can be triggered by a
dismissal which, as we have shown, is the case only when teams are
rather homogeneous. Hence, a simple rule of thumb implied by our results
would be that dismissals are more likely to be beneficial when the
respective team's players do not differ too substantially in terms
of their quality. Indeed, club executives may intuitively have grasped
some of this intuition as we find that 57% of all coach dismissals occur
in teams with below average heterogeneity at the time of the dismissal.
But, the result also contains some insights for other
organizations. Firms frequently not only use dismissals but also job
rotation policies by exchanging managers across different functions or
departments, to bring in "fresh air." Our results indicate
that this can indeed reinvigorate the incentives of subordinates. But
again an important caveat is that this mechanism only works when these
subordinates are on a rather equal footing. If this is not the case, the
costs of a rotation or dismissal (for instance due to a loss in human
capital or specific investments) may outweigh the gains. Our results
also give some insights for the theory of tournaments or contests. A key
theoretical result established in the literature on contests and
tournaments is that competition creates the strongest incentives when
players are rather homogeneous. Our observations are well in line with
this result. Moreover, the results hint at a mechanism how homogeneity
can be increased in the real world even when the set of contestants
cannot be changed: replacing the decision maker to reinvigorate the race
for attractive positions by "destroying" some information on
relative performance differences.
Finally, the article also yields some methodological insights
concerning the econometric evaluation of the effect of managerial change
on performance. As we have pointed out, estimates in observational
studies where proper instrumental variables are unavailable will be
biased when executives who decide upon dismissals have further
unobservable private information on future states. But as we have shown
this mechanism induces a negative selection bias--and, in turn, typical
regression models will underestimate the true effect of dismissals.
Hence, the fact that previous studies have typically found no or even
negative effects does not tell us that coach dismissals are detrimental
or useless. To the contrary, as suggested by our article, they can lead
to substantial performance effects in homogeneous teams.
doi: 10.1111/ecin.12285
Online Early publication October 28, 2015
APPENDIX A: MEASURING PLAYER PERFORMANCE
Impire's Performance Index
Table A1 lists the criteria according to which Impire AG awards
index points to each player who plays for at least 15 minutes in a
match. Impire then converts each player's total number of index
points into a grade on a scale from 1 (lowest) to 10 (highest). (32)
These grades are then used to calculate our measure of team
heterogeneity (het,) as explained in the text. Apart from this 15-minute
rule, the playing time of a player does not enter directly in the
calculation of his index points and the grade. This implies that, say, a
good performance over the course of 90 minutes will on average lead to a
better grade than a good performance of a substitute player who plays
for 20minutes only. Moreover, as can be seen from Table Al, for some
events in a match, index points are only awarded if the player is
actually on the pitch at the time when the event occurred.
Relationship between Impire Grades and Team Performance
The Impire grades of individual players are highly correlated with
team performance. For example, the coefficient of correlation between
the average grades in the course of a season and the team's rank at
the end of the season is - 0.87. This tight relationship is also
confirmed in a regression analysis: Table A2 shows that the average
player grades of a team have a highly significantly effect on the number
of points won by the (home) team.
Relationship between Impire Grades and Future Playing Time
The Impire grades are also good predictors of players'
(future) playing time. In this respect, Table A3 shows that a
player's average grade in previous matches has a highly significant
effect on his likelihood of being fielded in future matches.
TABLE A1
Impire's Performance Index
General Assessment Points
1. Team win +25
2. Team loss -25
3. Goal scored (except penalty kick) +100
4. Penalty kick scored +50
5. Opener scored (bonus) +25
6. Equalizer scored (bonus) +15
7. Goal assist +75
8. Penalty/free kick scored +75
9. Own goal -75
10. Grave mistake leading to goal conceded -100
11. Causing penalty kick against team -50
12. Penalty kick missed -100
13. Missing good opportunity to score a goal -25
14. Shot on post/bar +25
15. Shot on goal in penalty area +20
16. Shot in penalty area +15
17. Shot on goal outside penalty area +10
18. Shot outside penalty area +5
19. Preventing goal on goal line (non-goalkeepers) +25
20. Yellow card -15
21. Yellow-red card -75
22. Red card -100
Position-Specific Assessment Points
Goalkeepers
1. Goal conceded -75
2. Penalty kick saved +100
3. Shot on goal saved +50
4. Saved cross or ball from corner +10
5. No goal conceded in match +50
Defenders
1. Tackle won +20
2. Tackle lost -20
3. Successful long pass +5
4. Assist shot on goal in penalty area +20
5. Assist shot on goal outside penalty +10
area
6. No goal conceded in match +40
7. Goal conceded by team (while -20
player is fielded)
8. Goal scored by team (while player +5
is fielded)
Midfielders
1. Assist shot on goal in penalty area +25
2. Assist long range shot +15
3. Tackle won +15
4. Tackle won -10
5. Successful long pass +5
6. Goal conceded (while player is -5
fielded)
7. Goal scored by team (while player +5
is fielded)
Strikers
1. Assist shot on goal in penalty area +20
2. Assist long range shot +10
3. Tackle won (on the ground) +5
4. Tackle won (in the air) +3
5. Goal scored by team (while player +5
is fielded)
TABLE A2
The Impire Grades as a Measure of Team Performance
Model 1 Model 2
HomePerf_home 0.1751 ***
(0.0364)
AwayPerf_home 0.1954 ***
(0.0384)
HomePerf_away -0.1322 ***
(0.0374)
-0.1716 ***
(0.0375)
GradeAvg_home 0.5556 ***
(0.0740)
-0.4782 ***
(0.0738)
PerfHist_home -0.0043 -0.0035
(0.0035) (0.0035)
PerfHist_away 0.0111 *** 0.0098 ***
(0.0034) (0.0034)
Budget_home 0.2784 *** 0.2658 ***
(0.0667) (0.0668)
Budget_away -0.2014 *** -0.1855 ***
(0.0690) (0.0691)
Crucial_home 0.0912 ** 0.0891 **
(0.0441) (0.0442)
Crucial_away -0.0216 -0.0234
(0.0444) (0.0444)
Constant 1.4844 *** 1.2010 *
(0.1837) (0.6462)
Observations 4,268 4,268
[R.sup.2] .083 .083
Adjusted [R.sup.2] .078 .078
Notes: Dependent variable: Number of points won by the home
team (Result). (Robust) Standard errors in parentheses. Both
regressions include season dummies. HomePerf (AwayPerf) represents the
average number of points won in all previous home (away) matches of
the current season, GradeAvg the average grade of the home respectively
away team in previous matches (of the respective season) and
PerfHist the average final ranking of a team in the last three seasons.
Budget indicates the relative budget of a team in a given season,
Crucial is a dummy indicating whether winning the match would lead the
team to either reach or lose a ranking position of special importance
(championship, qualification for international competition, and
relegation).
* p < .1, ** p < .05, *** [ < .01.
TABLE A3
The Impact of (Previous) Impire Grades on a Player's
Likelihood of Being Fielded
Model 1 Model 2
Grade Rank -0.1004 ***
(0.0011)
GradeAvg 0.6376 ***
(0.0086)
Player FE Yes Yes
Obs. 193,315 193,315
Pseudo [R.sup.2] .04 .028
Notes: Logit Regression, dependent variable: Dummy variable
indicating whether a player is fielded or not. Standard errors in
parentheses. Grade_Rank represents the rank of a player regarding his
average grade prior to a match and GradeAvg the average grade a player
has received in previous matches (of a season). FE, fixed effects.
*** p < .01.
APPENDIX B: IMPACT OF MANAGERIAL CHANGE AND TEAM HETEROGENEITY IN
AWAY GAMES
Table B1 shows the results when replicating the analysis of Section
IIIA (see Table 2), the only difference being that the dependent
variable is now the number of points won by the away team.
TABLE B1
Impact of Managerial Change and Team Heterogeneity in
Away Games
Model 1 Model 2 Model 3
Short-Term Intermediate-Term Long-Term
([tau] = 2) ([tau] = 4) ([tau] = 6)
New_home -0.3742 -0.3537 * -0.3170 *
(0.2568) (0.1964) (0.1686)
New * het_home 0.3339 0.3613 * 0.2974 *
(0.2438) (0.1910) (0.1650)
het_home -0.0111 -0.0129 -0.0082
(0.0575) (0.0587) (0.0596)
New_away 0.9167 *** 0.5789 *** 0.5663 ***
(0.2485) (0.2036) (0.1710)
New * het_away -0.8060 *** -0.4461 ** -0.5047 ***
(0.2308) (0.1974) (0.1649)
het_away 0.1368 ** 0.1462 ** 0.1576 ***
(0.0563) (0.0576) (0.0587)
HomePerf_home -0.1183 *** -0.1159 *** -0.1195 ***
(0.0414) (0.0418) (0.0421)
AwayPerf_home -0.1376 *** -0.1321 *** -0.1331 ***
(0.0448) (0.0451) (0.0453)
HomePerf_away 0.1157 *** 0.1216 *** 0.1211 ***
(0.0432) (0.0435) (0.0439)
AwayPerf_away 0.1814 *** 0.1905 *** 0.1885 ***
(0.0426) (0.0429) (0.0433)
PerfHist_home 0.0039 0.0042 0.0040
(0.0034) (0.0034) (0.0035)
PerfHist_away -0.0090 *** -0.0086 *** -0.0090 ***
(0.0033) (0.0033) (0.0033)
Budget_home -0.2834 *** -0.2830 *** -0.2853 ***
(0.0641) (0.0641) (0.0639)
Budget_away 0.2263 *** 0.2237 *** 0.2229 ***
(0.0684) (0.0684) (0.0684)
Crucial_home -0.0780 * -0.0804 * -0.0789 *
(0.0427) (0.0428) (0.0429)
Crucial_away 0.0379 0.0326 0.0336
(0.0434) (0.0435) (0.0437)
Constant 1.0352 *** 0.9994 *** 1.0269 ***
(0.2474) (0.2488) (0.2497)
Observations 4,263 4,259 4,255
Adjusted [R.sup.2] .072 .073 .073
Notes: Dependent variable: Number of points won by the away team
(Result). (Robust) Standard errors in parentheses. All regressions
include [3.sup.4] = 81 dummy variables for the exact sequence of
performance in the last four matches both for home and away teams, as
well as season dummies. New is a dummy indicating if match is played
under a new coach, het is the measure of team heterogeneity, HomePerf
(AwayPerf) represents the average number of points won in all
previous home (away) matches of the current season, PerfHist the
average final ranking of a team in the last three seasons. Budget
indicates the relative budget of a team in a given season, Crucial is
a dummy indi-cating whether winning the match would lead the team to
either reach or lose a ranking position of special importance
(championship, qual-ification for international competition,
relegation). Starting from the total number of matches 4,896 (see
Table 1), we lose 579 observations due to controls for short-term
performance not yet being available (i.e., all 36 matches before
match day 5 in each of 16 seasons, and 3 cases due to a postponed
match), and 52 due to interim managers. Moreover, one managerial
change occurred so early in the season that no average value of team
heterogeneity under the old manager is available in the first matches
under the new manager so that we lose 2 observations for [tau] = 2
and further observations as [tau] increases.
* p <. 1, ** p < .05, *** p < .01.
APPENDIX C: RESULTS FOR ROBUSTNESS CHECKS
In the following, we report the results for the robustness checks
as discussed at the end of Section III.A in the main text.
Alternative Measures of Heterogeneity
Table C2 replicates the analysis underlying Table 3 using six
alternative measures of heterogeneity, again each evaluated and
normalized at each match day t. In the upper three panels, we use
measures which are also based on the average grades of each team's
players at the contested ranks 8-15:
[g.sup.1.sub.it] = [G.sup.8-11.sub.it] - [G.sup.12-15.sub.it],
[g.sup.2.sub.it] = [G.sup.8-11.sub.it] / [G.sup.12-15.sub.it]
and [g.sup.3.sub.it] = ([G.sup.8-11.sub.it] - [G.sup.12-15.sub.it])
/ [G.sup.12-15.sub.it].
The lower left panel relates the performance difference of the
players at the contested ranks to the average of all [K.sub.it] active
players in team i up to match day t:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Finally, in the last two panels, we use the coefficient of
variation ([g.sup.5.sub.it]) and the Gini coefficient
([g.sup.6.sub.it]). As teams have different roster sizes and hence
differ with respect to the number of graded players at each match day,
for the sake of comparison, both measures are based on the team with the
minimum number of graded players up to match day t. (33)
As in the main analysis, these measures are then normalized for
each match day t, so that each team's degree of heterogeneity
[het.sup.h=1 ... 6].sub.it] is given by its value of [g.sup.h.sub.it]
divided by the average value of all teams at match day t. Table C1
provides some summary information on these alternative heterogeneity
measures, which are then used in the regressions reported in Table C2.
As can be seen, for all these alternative measures, the results are very
similar to those reported in Table 3, so that we consider our insights
to be robust in that respect.
Regressions Excluding Goalkeepers
Table C3 replicates the analysis of Section III.A (see Table 2)
with goalkeepers excluded.
Regressions with Team-Season Fixed Effects
Table C4 replicates the analysis of Section III.A (see Table 2)
where we use team-season fixed effects instead of lagged-dependent
variables (i.e., our measures of past performance).
Interacting short-term performance and heterogeneity
Table C5 replicates the analysis of Section III.A (see Table 2)
where we allow teams of different degrees of heterogeneity to also
exhibit a different relationship between past and future performances,
in particular, recovery after a string of bad results and a managerial
change. This is achieved by also interacting the 81 dummies indicating
each team's most recent performance history with our measure of
team heterogeneity (het).
TABLE C1 Descriptive Statistics for Alternative
Measures of Heterogeneity
Std.
Variable Obs. Mean Dev. Min Max
Team heterogeneity [g.sup.1.sub.it] 9,481 1 0.35 0.08 2.74
(het) based on [g.sup.2.sub.it] 9,481 1 0.03 0.83 1.85
[g.sup.3.sub.it] 9.481 1 0.37 0.06 4.56
[g.sup.4.sub.it] 9,481 1 0.35 0.07 2.68
[g.sup.5.sub.it] 9,481 1 0.20 0.37 1.93
[g.sup.6.sub.it] 9,481 1 0.19 0.36 1.90
TABLE C2
Average Impact of Managerial Change on Team Performance: Different
Measures of Heterogeneity
[g.sup.1.sub.it] = [G.sup.8-11.sub.it] -
[G.sup.12-15.sub.it]
Intermediate-
Short-Term Term Long-Term
(2[tau] = 4) (4[tau] = 8) (6[tau] = 12)
New 0.6619 *** 0.4600 *** 0.4665 ***
(het = 0) (0.0001) (0.0004) (0.0000)
New 0.3120 *** 0.2271 *** 0.2141 ***
(het = 10% percentile) (0.0006) (0.0009) (0.0003)
New 0.2029 *** 0.1544 *** 0.1355 ***
(het = 25% percentile) (0.0058) (0.0049) (0.005)
New 0.0449 0.0493 0.0216
(het = mean) (0.4819) (0.3233) (0.6280)
New -0.0954 -0.0441 -0.0796
(het = 75% percentile) (0.2115) (0.4757) (0.1462)
New -0.2493 ** -0.1466 * -0.1906 **
(het = 90% percentile) (0.0170) (0.0848) (0.0105)
[g.sup.2.sub.it] = [G.sup.8-11.sub.it]/
[G.sup.12-15.sub.it]
Intermediate-
Short-Term Term Long-Term
(2[tau] = 4) (4[tau] = 8) (6[tau] = 12)
New 7.0684 *** 3.6174 ** 4.3162 ***
(het = 0) (0.0010) (0.0335) (0.0025)
New 0.2726 *** 0.1712 ** 0.1647 ***
(het = 10% percentile) (0.0022) (0.0104) (0.0042)
New 0.1775 ** 0.1229 ** 0.1065 **
(het = 25% percentile) (0.0134) (0.0227) (0.0243)
New 0.0597 0.0631 0.0345
(het = mean) (0.3498) (0.2049) (0.4369)
New -0.0417 0.0117 -0.0274
(het = 75% percentile) (0.5649) (0.8411) (0.5967)
New -0.1673 * -0.0519 -0.1041
(het = 90% percentile) (0.0846) (0.5131) (0.1304)
[g.sup.3.sub.it] = ([G.sup.8-11.sub.it] -
[G.sup.12-15.sub.it]/[G.sup.12-15.sub.it]
Intermediate-
Short-Term Term Long-Term
(2[tau] = 4) (4[tau] = 8) (6[tau] = 12)
New 0.6784 *** 0.4654 *** 0.4487 ***
(het = 0) (0.0000) (0.0003) (0.0000)
New 0.3348 *** 0.2399 *** 0.2182 ***
(het = 10% percentile) (0.0003) (0.0006) (0.0003)
New 0.2245 *** 0.1676 *** 0.1442 ***
(het = 25% percentile) (0.0029) (0.0030) (0.0036)
New 0.0583 0.0585 0.0327
(het = mean) (0.3585) (0.2365) (0.4581)
New -0.0869 -0.0367 -0.0646
(het = 75% percentile) (0.2361) (0.5395) (0.2216)
New -0.2483 ** -0.1426 * -0.1729 **
(het = 90% percentile) (0.0127) (0.0835) (0.016)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE
IN ASCII]
Intermediate-
Short-Term Term Long-Term
(2[tau] = 4) (4[tau] = 8) (6[tau] = 12)
New 0.7268 *** 0.4992 *** 0.4834 ***
(het = 0) (0.0000) (0.0002) (0.0000)
New 0.3460 *** 0.2481 *** 0.2266 ***
(het = 10% percentile) (0.0002) (0.0005) (0.0002)
New 0.2268 *** 0.1695 *** 0.1462 ***
(het = 25% percentile) (0.0026) (0.0027) (0.0031)
New 0.0594 0.0592 0.0334
(het = mean) (0.3492) (0.2310) (0.4485)
New -0.0932 -0.0415 -0.0695
(het = 75% percentile) (0.2074) (0.4902) (0.1912)
New -0.2516 ** -0.1459 * -0.1763 **
(het = 90% percentile) (0.0115) (0.0746) (0.0136)
[g.sup.5.sub.it] = Coefficient of Variation
Intermediate-
Short-Term Term Long-Term
(2[tau] = 4) (4[tau] = 8) (6[tau] = 12)
New 0.6305 * 0.7215 *** 0.7397 ***
(het=0) (0.0579) (0.0045) (0.0009)
New 0.2006 ** 0.2161 *** 0.2015 ***
(het = 10% percentile) (0.0395) (0.0033) (0.0019)
New 0.1448 * 0.1506 *** 0.1317 ***
(het = 25% percentile) (0.0559) (0.0084) (0.0094)
New 0.0661 0.0581 0.0332
(het = mean) (0.3010) (0.2368) (0.4495)
New -0.0018 -0.0217 -0.0518
(het = 75% percentile) (0.9819) (0.7218) (0.3386)
New -0.0814 -0.1152 -0.1514 **
(het = 90% percentile) (0.4673) (0.1877) (0.0497)
[g.sup.6.sub.it] = Gini Coefficient
Intermediate-
Short-Term Term Long-Term
(2[tau] = 4) (4[tau] = 8) (6[tau] = 12)
New 0.7160 ** 0.7489 *** 0.7731 ***
(het=0) (0.0362) (0.0043) (0.0007)
New 0.2149 ** 0.2182 *** 0.2049 ***
(het = 10% percentile) (0.0277) (0.0031) (0.0015)
New 0.1499 ** 0.1493 *** 0.1312 ***
(het = 25% percentile) (0.0463) (0.0085) (0.0090)
New 0.0615 0.0556 0.0309
(het = mean) (0.3363) (0.2589) (0.4824)
New -0.0190 -0.0296 -0.0603
(het = 75% percentile) (0.8122) (0.6370) (0.2748)
New -0.1048 -0.1205 -0.1577 **
(het = 90% percentile) (0.3522) (0.1740) (0.0415)
Notes: New is calculated as the average of the respective
coefficient(s) involving New_home and New_away. The p values (in
parentheses) are based on robust standard errors and estimated based
on Seemingly Unrelated Regressions (SUR) (Stata command suest).
* p <. 1, ** p < .05, *** p < .01.
TABLE C3
Managerial Change and Team Heterogeneity without Goalkeepers
Model 1 Model 2 Model 3
[tau] = 2 [tau] = 4 [tau] = 6
New_home 0.5820 ** 0.5101 ** 0.5062 ***
(0.2687) (0.2079) (0.1809)
New_home * het_home -0.5793 ** -0.5316 *** -0.5088 ***
(0.2537) (0.2017) (0.1773)
het_home 0.0425 0.0443 0.0501
(0.0592) (0.0605) (0.0613)
New_away -0.6961 *** -0.4313 ** -0.4008 **
(0.2555) (0.2067) (0.1768)
New_away * het_away 0.6018 ** 0.3030 0.3452 **
(0.2477) (0.2040) (0.1744)
Het_away -0.1245 ** -0.1301 ** -0.1302 **
(0.0581) (0.0596) (0.0608)
HomePerf_home 0.1456 *** 0.1455 *** 0.1492 ***
(0.0433) (0.0437) (0.0440)
AwayPerf_home 0.1631 *** 0.1575 *** 0.1576 ***
(0.0471) (0.0475) (0.0477)
HomePerf_away -0.1403 *** -0.1445 *** -0.1425 ***
(0.0453) (0.0456) (0.0460)
AwayPerf_away -0.1793 *** -0.1890 *** -0.1871 ***
(0.0447) (0.0450) (0.0454)
PerfHist_home -0.0047 -0.0050 -0.0048
(0.0036) (0.0036) (0.0036)
PerfHist_away 0.0096 *** 0.0093 *** 0.0096 ***
(0.0035) (0.0035) (0.0035)
Budget_home 0.2740 *** 0.2727 *** 0.2758 ***
(0.0683) (0.0682) (0.0682)
Budget_away -0.2216 *** -0.2189 *** -0.2185 ***
(0.0706) (0.0706) (0.0706)
Crucial_home 0.0888 ** 0.0904 ** 0.0875 *
(0.0449) (0.0450) (0.0451)
Crucial_away -0.0252 -0.0189 -0.0203
(0.0454) (0.0455) (0.0457)
Constant 1.6255 *** 1.6542 *** 1.3632 ***
(0.2625) (0.2644) (0.2582)
Observations 4,263 4,259 4,255
Adjusted [R.sup.2] .077 .079 .078
Notes: Dependent variable: Number of points won by the home team
(Result). (Robust) Standard errors in parentheses. All regressions
include [3.sup.4] = 81 dummy variables for the exact sequence of
performance in the last four matches both for home and away teams, as
well as season dummies. New is a dummy indicating if match is played
under a new coach, het is the measure of team heterogeneity, HomePerf
(AwayPerf) represents the average number of points won in all
previous home (away) matches of the current season, PerfHist the
average final ranking of a team in the last three seasons. Budget
indicates the relative budget of a team in a given season, Crucial is
a dummy indicating whether winning the match would lead the team to
either reach or lose a ranking position of special importance
(championship, qualification for international competition, and
relegation). The measure of heterogeneity het refers to the
difference between the average grades of players on rank 7-10 and
those on rank 11-14. Starting from the total number of matches 4,896
(see Table 1), we lose 579 observations due to controls for short-
term performance not yet being available (i.e., all 36 matches before
match day 5 in each of 16 seasons, and 3 cases due to a postponed
match), and 52 due to interim managers. Moreover, one managerial
change occurred so early in the season that no average value of team
heterogeneity under the old manager is available in the first matches
under the new manager so that we lose 2 observations for [tau] = 2
and further observations as [tau] increases.
* p <. 1, ** p < .05, *** p < .01.
TABLE C4 Managerial Change and Team Heterogeneity with Team-Season
Fixed Effects
Model 1 Model 2 Model 3
[tau] = 2 [tau] = 4 [tau] = 6
New_home 0.6283 ** 0.6438 *** 0.7117 ***
(0.2962) (0.2365) (0.2185)
New * het_home -0.5029 * -0.4936 ** -0.5149 **
(0.2867) (0.2330) (0.2185)
het_home 0.1437 * 0.1475 * 0.1503 *
(0.0769) (0.0780) (0.0788)
New_away -1.0082 *** -0.6687 *** -0.8043 ***
(0.2855) (0.2328) (0.2154)
New * het_away 0.7961 *** 0.3724 0.5341 **
(0.2784) (0.2310) (0.2131)
het_away -0.1112 -0.1108 -0.1115
(0.0766) (0.0775) (0.0789)
Crucial_home 0.0885 * 0.0891 * 0.0879 *
(0.0526) (0.0527) (0.0529)
Crucial_away -0.0216 -0.0142 -0.0119
(0.0526) (0.0528) (0.0531)
Constant 1.7563 *** 1 .7947 *** 1.7916 ***
(0.1436) (0.1421) (0.1439)
Hometeam * Season FE Yes Yes Yes
Awayteam * Season FE Yes Yes Yes
Observations 4,266 4,262 4,258
Adjusted [R.sup.2] .123 .126 .127
Notes: Dependent variable: Number of points won by the home
team (Result). (Robust) Standard errors in parentheses. New is a
dummy indicating if match is played under a new coach, het is the
measure of team heterogeneity. Crucial is a dummy indicating whether
winning the match would lead the team to either reach or lose a
ranking position of special importance (championship, qualification
for international competition, and relegation). Starting from the
total number of matches 4,896 (see Table 1), we exclude 576 matches
which took place before match day 5, and 52 due to interim managers.
Moreover, one managerial change occurred so early in the season
that no average value of team heterogeneity under the old manager
is available in the first matches under the new manager so that we
lose 2 observations for [tau] = 2 and further observations as [tau]
increases. FE, fixed effects.
* p < .1, ** p < .05, *** p < .01.
TABLE C5
Managerial Change and Team Heterogeneity: Additional
Interaction Terms
Model 1 Model 2 Model 3
[tau] = 2 [tau] = 4 [tau] = 6
New_home 0.5489 * 0.4222 ** 0.4399 **
(0.2862) (0.2114) (0.1843)
New * het_home -0.5172 * -0.4236 ** -0.4202 **
(0.2747) (0.2052) (0.1820)
het_home 0.1554 0.1481 0.1413
(0.3444) (0.3448) (0.3481)
New_away -0.7165 *** -0.4712 ** -0.4228 **
(0.2750) (0.2158) (0.1850)
New * het_away 0.6180 ** 0.3536 * 0.3771 **
(0.2657) (0.2120) (0.1825)
het_away -0.3901 -0.3131 -0.3461
(0.3159) (0.3275) (0.3278)
Home Perf_home 0.1471 *** 0.1485 *** 0.1570 ***
(0.0441) (0.0443) (0.0446)
AwayPerf_home 0.1590 *** 0.1526 *** 0.1533 ***
(0.0482) (0.0487) (0.0489)
HomePerf_away -0.1329 *** -0.1409 *** -0.1398 ***
(0.0463) (0.0466) (0.0471)
AwayPerf_away -0.1842 *** -0.1938 *** -0.1870 ***
(0.0457) (0.0460) (0.0462)
PerfHist_home -0.0057 -0.0059 -0.0052
(0.0037) (0.0037) (0.0037)
PerfHist_away 0.0104 *** 0.0100 *** 0.0104 ***
(0.0036) (0.0036) (0.0036)
Budget_home 0.2562 *** 0.2559 *** 0.2644 ***
(0.0698) (0.0697) (0.0695)
Budget_away -0.2256 *** -0 2221 *** -0.2202 ***
(0.0720) (0.0720) (0.0718)
Crucial_home 0.0762 0.0781 * 0.0793 *
(0.0465) (0.0467) (0.0468)
Crucial_away -0.0195 -0.0120 -0.0207
(0.0469) (0.0469) (0.0470)
Constant 1.8415 *** 1.8039 *** 1.5321 ***
(0.5201) (0.5252) (0.5240)
PastPerf * het_home Yes Yes Yes
PastPerf * het_away Yes Yes Yes
Observations 4,263 4,259 4,255
Adjusted [R.sup.2] .076 .079 .081
Notes: Dependent variable: Number of points won by the home team
(Result). (Robust) Standard errors in parentheses. All regressions
include [3.sup.4] = 81 dummy variables for the exact sequence of
performance in the last four matches both for home and away teams, as
well as season dummies. New is a dummy indicating if match is played
under a new coach, het is the measure of team heterogeneity, HomePerf
(AwayPetf) represents the average number of points won in all
previous home (away) matches of the current season, PerfHist the
average final ranking of a team in the last three seasons. Budget
indicates the relative budget of a team in a given season, Crucial is
a dummy indicating whether winning the match would lead the team to
either reach or lose a ranking position of special importance
(championship, qualification for international competition, and
relegation). Starting from the total number of matches 4,896 (see
Table 1), we lose 579 observations due to controls for short-term
performance not yet being available (i.e., all 36 matches before
match day 5 in each of 16 seasons, and 3 cases due to a postponed
match), and 52 due to interim managers. Moreover, one managerial
change occurred so early in the season that no average value of team
heterogeneity under the old manager is available in the first matches
under the new manager so that we lose 2 observations for [tau] = 2
and further observations as [tau] increases.
* p < .1, ** p < .05, *** p < .01.
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GERD MUEHLHEUSSER, SANDRA SCHNEEMANN and DIRK SLIWKA *
* We are grateful to two anonymous referees for their comments and
suggestions. Financial support from the State of North Rhine-Westphalia
(NRW), Ministry for Family, Children, Culture and Sport (MFKJKS) is also
gratefully acknowledged. Moreover, we thank the company Impire/Datatre
for kindly providing a large part of the data used in the article. We
also benefitted from comments by Jeff Borland, Berno Buchel, Ruud
Koning, Thomas Siedler and seminar participants at Adelaide, Bath,
Berlin (Humboldt), Bern, Frankfurt, Groningen, Seoul (SNU), Tubingen,
and the workshops on "Personnel Economics" (POEK) and
"Football and Finance" in Paderborn and Munster, respectively.
Last, but not least, we are grateful to Merle Gregor, Michaela Buscha,
Stefanie Kramer. Dennis Baufeld, Dennis Flebben, and Uwe Blank for their
excellent research assistance.
Muehlheusser: Professor, Department of Economics, University of
Hamburg, Hamburg 20146, Germany. Phone +49 40 42838 5575, Fax +49 40
42838 9226, E-mail gerd.muehlheusser@wiso.uni-hamburg.de
Schneemann: Ph.D. Candidate, Department of Sport Science, Bielefeld
University, Bielefeld 33615, Germany. Phone +49 521 106 6111, Fax +49
521 106 6489, E-mail sandra.schneemann@uni-bielefeld.de
Sliwka: Professor, Faculty of Management, Economics & Social
Sciences, University of Cologne, Cologne 50937, Germany. Phone +49 221
470 5887. Fax +49 221 470 1849, E-mail dirk.sliwka@uni-koeln.de
(1.) See, e.g., Baik (1994), Clark and Riis (2000), Feess,
Muehlheusser, and Walzl (2008), Gradstein (1995), Lien (1990), Moldovanu
and Sela (2006), Nti (1999), O'Keeffe, Viscusi, and Zeckhauser
(1984), and Szymanski and Valletti (2005). Moreover, the literature has
also considered the issue of excluding weak contestants as to not dilute
the incentives of their stronger counterparts (see, e.g., Fullerton and
McAfee 1999; Nalebuff and Stiglitz 1983; Taylor 1995).
(2.) A similar phenomenon has become known as
"Ashenfelter's dip" in the context of evaluating labor
market training programs, where trainees' often exhibited
preprogram earnings below average, thereby obscuring the measurement of
the effectiveness of the training program (see, e.g., Ashenfelter 1978;
Heckman, LaLonde, and Smith 1999).
(3.) In our view, this makes the European sports sector
particularly attractive for the analysis of succession effects as
compared with U.S. sports leagues because for the latter, (the typical)
between-seasons replacements are often accompanied by changes of other
crucial variables such as the team's roster.
(4.) There also exists a strand of literature concerned with the
reverse relationship, that is, with the impact of current performance on
the likelihood of a managerial change (see, e.g., Audas, Dobson, and
Goddard 1999; Barros, Frick, and Passos 2009; Porter and Scully 1982;
Scully 1994).
(5.) Note that dismissals are rather expensive for teams as the
sacked manager is entitled to receive his wage until his contract would
have expired. In many cases, teams and managers agree on a severance
payment in exchange for instantaneous mutual cancelation of the
contract.
(6.) When several teams have accumulated the same number of points,
the goal difference serves as the tie-breaking rule.
(7.) For the seasons 1992/1993-2007/2008, the three teams at the
bottom were relegated. Since season 2008/2009, the team ranked third to
last and the team ranked third in the second division compete in two
extra matches for the final Bundesliga slot for the next season.
(8.) For example, the UEFA Champions League earned Bayern Munich an
additional 58 Mio Euro in the season 2009/2010, as compared with an
average Bundesliga team's budget of 39.5 Mio Euro for that season.
The numbers for the
(9.) In our sample, the average spell duration of interim managers
was 2.3 matches. In Section III.C we will use the performance of teams
playing under interim managers as a robustness check for our main
results. We are grateful to Loek Groot for this suggestion.
(10.) Estimating ordered probit models leads to virtually identical
results. See, e.g., Angrist and Pischke (2008, 107) for a critical
discussion on the use of linear and nonlinear models when the outcome of
interest is a limited dependent variables.
(11.) A match is considered crucial for a team when, starting with
the second half of the season (match days 18 through 34), its distance
to either one of the ranks relevant for Championship and the UEFA
competitions or relegation is less than or equal to 3 points.
(12.) Note that football teams in Germany are not obliged to
publish their budgets--hence the information we use are estimates
compiled by public sources such as newspapers and specific reports from
banks and consulting firms. These estimates are based on core parts of a
team's income such as TV revenues, revenues from participation in
the UEFA Leagues, ticket sales, and sponsoring which are in large parts
publicly available. Hence, while being noisy, they are likely to reflect
the relative financial strengths of the clubs within a season. All our
results remain qualitatively robust when this variable is omitted.
(13.) An alternative strategy would be to use team fixed-effects.
However, a fixed effects model with lagged dependent variables leads to
inconsistent estimates, see Nickell (1981) and also Angrist and Pischke
(2008, 243). As controlling for recent performance prior to the
dismissal is very important to reduce selection issues, we prefer the
lagged dependent variable approach. However, fixed effects models lead
to qualitatively very similar results, see Table C4 in the Appendix.
(14.) As shown in panel (a) of Figure 4 in Section II.D, teams
dismissing a coach indeed exhibit a particular performance pattern in
the four games prior to the dismissal.
(15.) For example, the home team's recent performance history
prior to match day t is ([y.sub.it-1], [y.sub.it-2], [y.sub.it-3],
[y.sub.it-4]), where [y.sub.it-k] [member of] {3,1,0) for k = 1 ... 4
denotes the number of points gained in the match played k match days
before match day t. Proceeding analogously with the away team leads to
[3.sup.4] = 81 of such history dummies for each team.
(16.) In an analogy to experiments, the estimation works as if a
control group is constructed which on average has a systematically
better performance outlook than the treatment group.
(17.) Apart from the German Bundesliga, within-season managerial
changes also occur frequently in other European soccer leagues such as
England (on average for 28.6% of all teams), Spain (36.7%), Italy (37%),
Portugal (54.6%), Austria (63%), Netherlands (38.4%), and Belgium
(35.7%). Managerial changes are also frequent in U.S. sports leagues,
but within-season replacements are much less common: For example, only
10.2% of all teams in Major League Baseball had a within-season
replacement during the period 1920-1973 (Allen, Panian, and Lotz 1979).
For the National Hockey League (NHL) the respective number is 18.4%
during the period 1942/1943-2001/2002 (Rowe et al. 2005).
(18.) As pointed out by Audas, Dobson, and Goddard (2002), while
dismissals might not be effective on average, they tend to increase the
variance of performance and hence might be optimal for teams facing the
threat of relegation.
(19.) In Appendix A, we provide further evidence for the validity
of these grades: First, they are highly correlated with overall team
performance. Second, they are good predictors of players' future
playing time. Last, but not least, there is a highly significant
correlation of [rho] = - 0.54 with an alternative, also frequently used
performance measure, the grades assigned by the German sports magazine
kicker with a scale from 1 (highest) to 6 (lowest). We are grateful to
an anonymous referee for suggesting these additional cross checks.
(20.) The manager is not obliged to exhaust the maximum number of
replacements (two in the first two seasons of our sample, and three
afterwards). In our sample, the number of replacements was at its
maximum in 76.8% of all matches.
(21.) Teams alternate between home and away matches from one match
day to the next. Given the different nature of the two match types
(e.g., in terms of the result or playing strategy), it appears
reasonable to take into account matches of either type when
approximating the team heterogeneity which the new manager inherits from
the old one. However, our results would not qualitatively change when
using a different rule such as the predecessor's last match only or
his last three or four matches.
(22.) In the data, we observe a player's position in a match
only as either goalkeeper, defender, midfielder, or striker, but not,
for example, on which side he played or whether he took a rather
offensive or defensive role on this position.
(23.) There are revenue-distribution mechanisms in place in the
Bundesliga, but less so than in many U.S. leagues, so that the income
distribution tends to be more uneven. For example, while the TV rights
are sold collectively and the revenue is then shared among all teams
according to a predefined sharing rule, unlike many U.S. leagues, there
is no sharing of gate revenues which heavily favors the teams with the
biggest crowd support and stadiums.
(24.) Moreover, a player's salary will typically depend on how
many times he has been fielded in a given season.
(25.) When including as controls the average team grades before a
given match as a measure for team strength (both instead of, and in
addition to, our other measures of past team performance), the results
for the impact of team heterogeneity are very similar to those reported
in Table 2.
(26.) Note that the number of points lost by the home teams are not
identical to the number of points gained by the away teams as the winner
(loser) of a match gets 3 (0) points, while each team gets 1 point in
case of a draw.
(27.) For example, the entries in the first row (het = 0) are
directly calculated as the average of the two coefficients in Tables 2
(New_home) and 9 (New_away), so that for the first column, we get
1/2(0.5671 +0.9167) = 0.7419. Similarly, at the 25% percentile (where
het = 0.7544), we get 1/2(0.5671-(0.5637 x 0.7544)+ 0.9167-(0.8060 x
0.7544)) = 0.2253. Because the set of covariates is identical in both
estimations, we obtain the same coefficients when estimating a system of
seemingly unrelated regressions (SUR), see, e.g., Greene (1997, 676).
This approach also allows us to test the joint significance of New_home
(Table 2) and New_away (Table B1) which leads to the p values reported
in the tables.
(28.) For instance, for the example given in footnote 2, at the 25%
percentile, the overall effect of 0.2253 points per game is the mean of
0.1418 points from home and 0.3087 from away games.
(29.) See Franck and Niiesch (2010) for a more detailed empirical
analysis of the relationship between team heterogeneity and team
performance in soccer.
(30.) We thank an anonymous referee for pointing out this
possibility.
(31.) The same is true when merging ranks into groups of four as in
Figure 5.
(32.) The exact conversion formula is a business secret of Impire
and hence not available to us.
(33.) To see the reason note the following example: When comparing
a team of say 7 strong and 8 weak players with another one which is
twice as large with 14 strong and 16 weak players, then both have
exactly the same Gini. But as only 11 players (plus substitutes) can be
fielded, the second team should be regarded as much more homogeneous
regarding the competition for one of these positions.
TABLE 1
Descriptive Statistics
Variable Obs.
Points home team 4,896
(result)
Home win 2,311
Draw 1,287
Away win 1,298
Budget (relative) 288
Roster size 288
Managerial change Within-season 288
(new) (a) Within-season 16
Between-season 16
Performance (grade) 9,784
Home team 4,892
Away team 4.892
Team heterogeneity 288
(het) All matches 8,640
Last two matches 113
of old Coach
(([het.sub.t] +
[het.sub.t-1])/2)
Variable Mean SD Min Max
Points home team Matches 1.68 1.30 0 3
(result)
(47.20%)
(26.29%)
(26.51%)
Budget (relative) Team/seasons 1 0.37 0.29 2.34
Roster size Team/seasons 25.88 2.75 19 35
Managerial change Team/seasons (b) 0.34 0.48 0 1
(new) (a) Seasons (c) 7.13 2.16 4 11
Seasons (c) 2.94 2.14 1 9
Performance (grade) Team avg./matches 6.11 0.80 3.73 8.31
(d)
Matches 6.35 0.74 3.73 8.31
Matches 5.86 0.78 3.78 7.99
Team heterogeneity Team/seasons 1 0.21 0.55 1.60
(het) Matches (e) 1 0.34 0.10 2.59
10% percentile 0.58
25% percentile 0.76
50% percentile 0.97
75% percentile 1.22
90% percentile 1.46
Upon dismissal 0.96 0.34 0.38 2.16
(f)
10% percentile 0.54
25% percentile 0.69
50% percentile 0.95
75% percentile 1.17
90% percentile 1.34
(a) Those cases where the new manager is an interim manager are
excluded.
(b) Average percentage of teams with at least one managerial change
in a given season.
(c) Average number of managerial changes within a season or between
two seasons, respectively.
(d) For four matches, the information on grades are missing so that
the number of observations for average team performance is 4,896 x 2-
8 = 9,784.
(e) In all regressions below, we include the teams' (short-term)
performance in the last four matches, and hence, in each season only
observations from match day 5 onwards are used. The values for het
reported here also refer to the same set of matches, which reduces
the number of observations by 1,152, so that 4,896 X 2 - 1,152 =
8,640 observations remain.
(f) There are 114 cases of (non-interim) within-season managerial
change during the observation period. However, in one case, the
change occurred already on match day 3, and only one previous
observation of het is available, as only 11 players were fielded in
match day 1.
TABLE 2
Managerial Change and Team Heterogeneity
Model 1 Model 2 Model 3
Short-Term Intermediate-Term Long-Term
([tau] = 2) ([tau] = 4) ([tau] = 6)
New_home 0.5671 ** 0.4475 ** 0.4308 **
(0.2718) (0.2064) (0.1791)
New * het_home -0.5637 ** -0.4654 ** -0.4297 **
(0.2578) (0.1999) (0.1752)
het_home 0.0549 0.0540 0.0538
(0.0601) (0.0614) (0.0623)
New_away -0.7789 *** -0.4683 ** -0.4577 ***
(0.2599) (0.2085) (0.1766)
New * het_away 0.6888 *** 0.3407 * 0.4038 **
(0.2514) (0.2038) (0.1720)
het_away -0.1311 ** -0.1337 ** -0.1406 **
(0.0588) (0.0602) (0.0614)
HomePerf_home 0.1469 *** 0.1456 *** 0.1484 ***
(0.0432) (0.0436) (0.0440)
AwayPerf_home 0.1624 *** 0.1567 *** 0.1565 ***
(0.0471) (0.0474) (0.0477)
HomePerf_away -0.1417 *** -0.1463 *** -0.1439 ***
(0.0452) (0.0456) (0.0460)
AwayPerf_away -0.1817 *** -0.1915 *** -0.1886 ***
(0.0446) (0.0450) (0.0453)
PeifHist_home -0.0048 -0.0050 -0.0049
(0.0036) (0.0036) (0.0036)
PerfHist_away 0.0096 *** 0.0093 *** 0.0096 ***
(0.0035) (0.0035) (0.0035)
Budget_home 0.2757 *** 0.2748 *** 0.2772 ***
(0.0683) (0.0683) (0.0682)
Budget_away -0.2245 *** -0.2215 *** -0.2217 ***
(0.0705) (0.0706) (0.0706)
Crucial_home 0.0857 * 0.0882 * 0.0862 *
(0.0449) (0.0450) (0.0452)
Crucial_away -0.0209 -0.0159 -0.0173
(0.0455) (0.0455) (0.0457)
Constant 1.6278 *** 1.6536 *** 1.6208 ***
(0.2566) (0.2582) (0.2592)
Observations 4,263 4.259 4,255
Adjusted [R.sup.2] .078 .078 .078
Notes: Dependent variable: Number of points won by the home
team (Result). (Robust) Standard errors in parentheses. All
regressions include [3.sup.4] = 81 dummy variables for the exact
sequence of performance in the last four matches both for home and
away teams, as well as season dummies. New is a dummy indicating if
match is played under a new coach, het is the measure of team
heterogeneity, HomePerf (AwayPerf) represents the average number of
points won in all previous home (away) matches of the current season,
PerfHist the average final ranking of a team in the last three
seasons. Budget indicates the relative budget of a team in a given
season, Crucial is a dummy indicating whether winning the match would
lead the team to either reach or lose a ranking position of special
importance (championship, qualification for international competition,
and relegation). Starting from the total number of matches 4,896 (see
Table 1), we lose 579 observations due to controls for short-term
performance not yet being available (i.e., all 36 matches before match
day 5 in each of 16 seasons, and three cases due to a postponed
match), and 52 due to interim managers. Moreover, one managerial
change occurred so early in the season that no average value of team
heterogeneity under the old manager is available in the first matches
under the new manager, so that we lose two observations for x = 2 and
further observations as x increases.
* p < .1, ** p < .05, *** p < .01.
TABLE 3
Average Impact of Managerial Change on Team
Performance at Different Percentiles of
Heterogeneity
Model HI Model H2 Model H3
Short-Term Intermediate-Term Long-Term
(2[tau] = 4) (2[tau] = 8) (2[tau] = 12)
New 0.7419 *** 0.5132 *** 0.4986 ***
{het = 0) (0.0000) (0.0002) (0.0000)
New 0.3457 *** 0.2495 *** 0.2282 ***
(het = 10% (0.0002) (0.0004) (0.0002)
percentile)
New 0.2253 *** 0.1694 *** 0.1461 ***
(het = 25% (0.0027) (0.0026) (0.0031)
percentile)
New 0.0571 0.0574 0.0314
{het = mean) (0.3681) (0.2453) (0.4771)
New -0.0971 -0.0452 -0.0739
{het = 75% (0.1902) (0.4541) (0.1671)
percentile)
New -0.2562 ** -0.1511 * -0.1824 **
(het = 90% (0.0103) (0.0663) (0.0111)
percentile)
Notes: New is calculated as the average of the respective
coefficients) involving New_home in Table 2 and New_away in Table B1.
The p values (in parentheses) are based on robust standard errors and
estimated based on Seemingly Unrelated Regressions (SUR) (Stata
command suest).
* p < .1, ** p < .05, *** p < .01.
TABLE 4
Impact of Dismissals on Individual Performance
Model 4 Model 5
Rank of player 0.0559 *** 0.0484 ***
(before (0.0049) (0.0068)
dismissal)
Homogeneous 0.1700 ** 0.1792 **
team (Dummy) (0.0814) (0.0833)
Rank * 0.0123
Homogeneous (0.0091)
team
Budget_Home 0.1387 0.1375
(0.1224) (0.1223)
PeifHist -0.0068 -0.0068
(0.0073) (0.0073)
PerfSeason (before -0.4473 ** -0.4492 **
dismissal) (0.1822) (0.1825)
PerfRecent (before 0.1087 0.1097
dismissal) (0.1024) (0.1025)
Constant -0.3762 -0.2972
(0.2719) (0.2703)
Season_dummies Yes Yes
Position_dummies Yes Yes
Observations 1,833 1.833
Adjusted [R.sup.2] .110 .110
Notes: Dependent variable: Difference between the (average)
grade in first four matches under new manager and (average) grade in
all matches (in a given season) before the dismissal. (Robust)
Standard errors in parentheses (clustered at each separate dismissal).
Rank represents the player's rank (according to his average grade)
prior to the dismissal, Homogeneous team is a dummy variable
indicating whether the team's homogeneity is above average (het < 1),
PerfHist refers to the average ranking of a team in the last three
seasons, PerfSeason to the average number of points won by a team in
all matches of the old coach and PerfRecent to the average number of
points won in the last four matches of the old coach, Position dummies
include dummies for strikers, midfielders, defenders, and goalkeepers.
The number of 1,833 observations is given by the number of players who
are observed under both the old manager and the new manager in a given
season.
* p < .1, ** p < .05, *** p < .01.
TABLE 5
(Interim) Managerial Change and Team
Heterogeneity
Model 7 Model 8 Model 9
Short-Term Intermediate-Term Long-Term
([tau] = 1) ([tau] = 2) ([tau] = 2)
New_home 0.9730 *** 0.5599 ** 0.4404 *
(0.3359) (0.2721) (0.2332)
New_home * -0.9517 *** -0.5576 ** -0.4193 *
het_home (0.3023) (0.2581) (0.2275)
het_home 0.0508 0.0525 0.0520
(0.0593) (0.0599) (0.0606)
Interim_home -1.6484 -0.6762 -0.7014
(1.1351) (1.0853) (1.0886)
Interim_home * 1.5842 0.6365 0.5783
het_home (1.0180) (0.9645) (0.9714)
New_away -0.8560 ** -0.7838 *** -0.4642 **
(0.3526) (0.2598) (0.2333)
New_away * 0.7857 ** 0.7008 *** 0.3675
het_away (0.3391) (0.2513) (0.2274)
het_away -0.1254 ** -0.1400 ** -0.1342 **
(0.0580) (0.0588) (0.0595)
Interim_away 1.6216 1.7391 ** 1.4285 *
(1.1224) (0.7999) (0.7942)
Interim_away * -0.7556 -0.5800 -0.5882
het_away (0.9129) (0.6715) (0.6733)
HomePerf_home 0.1479 *** 0.1497 *** 0.1501 ***
(0.0427) (0.0429) (0.0432)
AwayPerf_home 0.1668 *** 0.1691 *** 0.1676 ***
(0.0467) (0.0468) (0.0470)
HomePerf_away -0.1326 *** -0.1319 *** -0.1319 ***
(0.0450) (0.0451) (0.0453)
AwayPerf_away -0.1741 *** -0.1745 *** -0.1779 ***
(0.0443) (0.0444) (0.0446)
PerfHist_home -0.0051 -0.0053 -0.0054
(0.0035) (0.0036) (0.0036)
PerfHist_away 0.0107 *** 0.0106 *** 0.0104 ***
(0.0035) (0.0035) (0.0035)
Budget_home 0.2640 *** 0.2648 *** 0.2625 ***
(0.0678) (0.0678) (0.0678)
Budget_away -0.2145 *** -0.2167 *** -0.2168 ***
(0.0703) (0.0702) (0.0702)
Crucial_home 0.0821 * 0.0843 * 0.0842 *
(0.0449) (0.0449) (0.0450)
Crucial_away -0.0140 -0.0141 -0.0139
(0.0452) (0.0453) (0.0453)
Constant 1.5760 *** 1.6143 *** 1.6122 ***
(0.2545) (0.2552) (0.2567)
Observations 4,317 4,315 4,313
Adjusted [R.sup.2] .077 .077 .076
Notes: Dependent variable: Number of points won by the home
team (Result). (Robust) Standard errors in parentheses. All
regressions include [3.sup.4] = 81 dummy variables for the exact
sequence of performance in the last four matches both for home and
away teams, as well as season dummies. New is a dummy indicating if
match is played under a new coach, het is the measure of team
heterogeneity, Interim is a dummy indicating if the current coach is
an interim solution, HomePerf (AwayPerf) represents the average number
of points won in all previous home (away) matches of the current
season, PerfHist the average final ranking of a team in the last three
seasons. Budget indicates the relative budget of a team in a given
season, Crucial is a dummy indicating whether winning the match would
lead the team to either reach or lose a ranking position of special
importance (championship, qualification for international competition,
relegation). Starting from the 4,896 matches (see Table 1), we lose
579 observations due to controls for short-term performance not yet
being available (i.e., all 36 matches before match day 5 in each of 16
seasons, and three cases due to a postponed match). One managerial
change occurred so early in the season that no average value of team
heterogeneity under the old manager is available in the first matches
under the new manager. For x > 1, this further reduces the number of
observations slightly as x increases.
* p < .1, ** p < .05, *** p < .01.
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