Usefulness of Dismissing and Changing the Coach in Professional Soccer
ABSTRACT Whether a coach dismissal during the mid-season has an impact on the subsequent team performance has long been a subject of controversial scientific discussion. Here we find a clear-cut answer to this question by using a recently developed statistical framework for the team fitness and by analyzing the first two moments of the effect of a coach dismissal. We can show with an unprecedented small statistical error for the German soccer league that dismissing the coach within the season has basically no effect on the subsequent performance of a team. Changing the coach between two seasons has no effect either. Furthermore, an upper bound for the actual influence of the coach on the team fitness can be estimated. Beyond the immediate relevance of this result, this study may lead the way to analogous studies for exploring the effect of managerial changes, e.g., in economic terms.
- [Show abstract] [Hide abstract]
ABSTRACT: Statistics of soccer tournament scores based on the double round robin system of several countries are studied. Exploring the dynamics of team scoring during tournament seasons from recent years we find evidences of superdiffusion. A mean-field analysis results in a drift velocity equal to that of real data but in a different diffusion coefficient. Along with the analysis of real data we present the results of simulations of soccer tournaments obtained by an agent-based model which successfully describes the final scoring distribution [da Silva et al., Comput. Phys. Commun. 184, 661 (2013)]. Such model yields random walks of scores over time with the same anomalous diffusion as observed in real data.Physical Review E 08/2013; 88(2):022136. · 2.31 Impact Factor
- [Show abstract] [Hide abstract]
ABSTRACT: Scoring goals in a soccer match can be interpreted as a stochastic process. In the most simple description of a soccer match one assumes that scoring goals can be described by a constant goal rate for each team, implying simple Poissonian and Markovian behavior. Here a general framework for the identification of deviations from this behavior is presented. For this endeavor it is essential to formulate an a priori estimate of the expected number of goals per team in a specific match. The analysis scheme is applied to approximately 40 seasons of the German Bundesliga. It is possible to characterize the impact of the previous course of the match on the present match behavior. This allows one to identify interesting generic features about soccer matches and thus to learn about the hidden complexities behind scoring goals.07/2012;
- [Show abstract] [Hide abstract]
ABSTRACT: Scoring goals in a soccer match can be interpreted as a stochastic process. In the most simple description of a soccer match one assumes that scoring goals follows from independent rate processes of both teams. This would imply simple Poissonian and Markovian behavior. Deviations from this behavior would imply that the previous course of the match has an impact on the present match behavior. Here a general framework for the identification of deviations from this behavior is presented. For this endeavor it is essential to formulate an a priori estimate of the expected number of goals per team in a specific match. This can be done based on our previous work on the estimation of team strengths. Furthermore, the well-known general increase of the number of the goals in the course of a soccer match has to be removed by appropriate normalization. In general, three different types of deviations from a simple rate process can exist. First, the goal rate may depend on the exact time of the previous goals. Second, it may be influenced by the time passed since the previous goal and, third, it may reflect the present score. We show that the Poissonian scenario is fulfilled quite well for the German Bundesliga. However, a detailed analysis reveals significant deviations for the second and third aspect. Dramatic effects are observed if the away team leads by one or two goals in the final part of the match. This analysis allows one to identify generic features about soccer matches and to learn about the hidden complexities behind scoring goals. Among others the reason for the fact that the number of draws is larger than statistically expected can be identified.PLoS ONE 11/2012; 7(11):e47678. · 3.53 Impact Factor
Usefulness of Dismissing and Changing the Coach in
Andreas Heuer1*, Christian Mu ¨ller2, Oliver Rubner1, Norbert Hagemann3, Bernd Strauss4
1Institute of Physical Chemistry, University of Muenster, Muenster, Germany, 2Institute of Organic Chemistry, University of Muenster, Muenster, Germany, 3Institute of
Sports Sciences, University of Kassel, Kassel, Germany, 4Institute of Sports Sciences, University of Muenster, Muenster, Germany
Whether a coach dismissal during the mid-season has an impact on the subsequent team performance has long been a
subject of controversial scientific discussion. Here we find a clear-cut answer to this question by using a recently developed
statistical framework for the team fitness and by analyzing the first two moments of the effect of a coach dismissal. We can
show with an unprecedented small statistical error for the German soccer league that dismissing the coach within the
season has basically no effect on the subsequent performance of a team. Changing the coach between two seasons has no
effect either. Furthermore, an upper bound for the actual influence of the coach on the team fitness can be estimated.
Beyond the immediate relevance of this result, this study may lead the way to analogous studies for exploring the effect of
managerial changes, e.g., in economic terms.
Citation: Heuer A, Mu ¨ller C, Rubner O, Hagemann N, Strauss B (2011) Usefulness of Dismissing and Changing the Coach in Professional Soccer. PLoS ONE 6(3):
Editor: Bard Ermentrout, University of Pittsburgh, United States of America
Received August 6, 2010; Accepted February 10, 2011; Published March 22, 2011
Copyright: ? 2011 Heuer et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: These authors have no support or funding to report.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: email@example.com
Fred Everiss, responsible for the soccer team of West Bromwich
Albion (UK) coached his team over 46 years (1902–1948) without
any interruption. This is probably the all time world record for
coaches in professional soccer. In Germany, for instance, Volker
Finke is the record holder. He coached the professional soccer team
of SC Freiburgfor almost16 years (1991–2007) without interruptions
(German record), although due to the relegation into the Second
German soccer league his team had to leave the Premier German
Soccer league (the so called ‘‘Erste Bundesliga’’, established 1963)
four times.However,such loyalty isveryunusual in professional team
sports. Frequently, the usual response to a continuing series of recent
lost matches is to dismiss and replace the coach mid-season. For
example in the German Bundesliga the club ‘‘Eintracht Frankfurt’’ is
leading in dismissing a coach during mid season (20 times in 47 years
of the German Premier soccer league). Fired coaches are often hired
by competitors who also dismissed the coach. For example, Gyula
Lorant as well as Joerg Berger are the most often dismissed head
coaches in the German Bundesliga (six times each).
The reason to fire a coach mid-season  is often due to
disappointed expectations in comparison to the team wage bill 
and to the widespread assumption of clubs, fans, and the media
that changing the coach has a major positive effect on a
subsequent team’s performance (one-way causality hypothesis)
. This is opposed to the Ritual Scapegoating Hypothesis, i.e.
dismissing the coach will have no effect on a team’s performance
(the nil hypothesis) . The latter follows the assumption that a
coach has only a small impact on the performance of the team
which the coach is responsible for.
Already in 1964  preferred the hypothesis of ritual
scapegoating. However, a closer inspection of their empirical
findings in professional Baseball could not clearly support any of
their presented hypotheses. Not surprisingly, whether mid-season
coach dismissals have effects on the subsequent team performance
has long been a subject of controversial discussions, mainly in the
Sport Sciences  and Economic Sciences as well [1,5].
Many of these studies focused on coach dismissals in
professional soccer in different national leagues. These studies
disagree with respect to the final result as well as the used research
design. Partly these results have to be questioned due to design
problems like a sub-optimal choice of the performance criterion
[1,6–15], the use of a very small data basis (e.g., Dutch soccer
[8,9], Spanish soccer ), missed control teams [1,8,10], or a
biased choice of control teams (English soccer [11,12], German
soccer [13–15], Dutch soccer ).
Team Fitness in Soccer from a Statistical Perspective
N Heuer and Rubner  have recently shown theoretically that
the mathematically optimal measure of a soccer team’s fitness
is the goal difference (DG). Therefore, to optimize the
predictability it is essential to use DG rather than the number
of points or the rank as a characteristic of the team fitness (as
almost always used by the studies mentioned above, a rare
exception is ). Stated differently, the number of points
contains a larger random contribution than the goal difference.
Qualitatively, the superiority of goal differences as compared
to points expresses the fact that a 5:0 and a 1:0 win is counted
identically in terms of points although in general this difference
indicates the presence of different fitness values for both teams.
Quantitatively, the identification of random contributions can
be achieved via a straightforward correlation analysis of
PLoS ONE | www.plosone.org1March 2011 | Volume 6 | Issue 3 | e17664
subsequent sets of matches (e.g., by comparing the first and the
second half of the season).
Most importantly, a team’s fitness remains just about constant
throughout a season. Any variations during the season are due to
temporal fluctuations (like weather conditions, red cards) whereas
systematic variations mainly occur between different seasons [6,7].
This observation already gives a hint to formulate our main
hypothesis in line with  that changing the coach during the
season is useless and would have no effects in the subsequent team
performance. Using optimized statistical approaches to avoid the
design problems mentioned above these questions will be
answered in this work. Additionally, to classify these mid-season
dismissal effects on subsequent performances we will also analyze
the effects of changing the coach between seasons.
Analysis of Coach Dismissals (CDs)
We analyze the Premier German soccer league (as we already
mentioned, the so-called German ‘‘Erste Bundesliga’’) which
started in the season 1963/64. We consider all mid-seasonal coach
dismissals (CDs) for all 46 seasons until 2008/09. Almost in each
season every team has to play 34 games (except the three seasons
1963/64, 64/65 as well as 1991/1992). The entire data set covers
14,018 games. Since during the first decades of the Bundesliga
several matches have been adjourned due to weather conditions
etc. it is essential to take into account the correct order of matches
for each team. The key procedure of our approach can be
summarized as follows
1. To be able to quantify possible fitness variations due to the CD
we require that before and after the CD the team plays at least
m=10 matches in that season, i.e. 10#tCD#24 where tCDis
the match day just before the CD. During the m=10 matches
before the CD no other CD is allowed. Our final data basis
contains 154 CDs out of 361 mid-seasonal CDs in total. To first
approximation the CDs are equally distributed in the time
interval 10#tCD#24 with an average value of around 17.
2. To quantify the effect of a CD we choose an appropriate
control group. For a specific CD event, occurring after match
day tCD(by construction tCD$10), we identify all events where
some other or the same team during any season displays a
similar goal difference (more specifically with a difference of the
goal difference DG between control team and CD team in the
interval [0.185,20.215]) during tCDsubsequent matches and
has still at least 10 matches to play after this time interval. The
minor asymmetry of the selection interval for control teams
guarantees an identical average value of DG of control and CD
teams and just reflects the Gaussian-type distribution of DG
-values around zero . We use always normalized goal
differences (per match). In this way we obtain approximately
100 control teams per CD, except for a single extreme case in
the year 1965/66 where no control teams could be found.
Additionally, we have chosen a control group by two separate
conditions. First, during the matches 3 to 10 before the CD
event the deviation of the average goal difference DG between
control team and CD team had to be in the interval
[0.196,20.204] and second, during the two matches before
the CD event (matches 1 and 2) a per-match-deviation of the
goal difference by 60.5 was allowed. The reason for these
different choices is discussed in the main part.
3. Going beyond most previous studies we have also corrected the
home/away-asymmetry [7,8], i.e. the match results are
projected on the fictive results in a neutral stadium, in order to
extract the respective team fitness without the home/away-bias.
More specifically, we have substituted DG by DG6Dh (2: home
match;+:awaymatch)whereDh (.0)denotes the average home
advantage. It turns out that the home advantage depends on the
season, but is independent of the specific team .
Our procedure implies some important methodological aspects
that have to be kept in mind:
1. The value of m=10 has been selected by the condition that the
final result displays a minimum error. In case of a larger
interval the number of CDs would be smaller, in case of a
smaller interval the characterization of the team fitness would
2. A few times it occurs that within the m=10 matches a new
coach is already replaced by another coach. Sometimes this is
planned (in case of a caretaker coach) or is the consequence of
successive bad performance. As implied by our approach we
have in that case incorporated the first CD but not the second
one. This is motivated by the fact that otherwise we cannot
judge the team quality during the short time (less than m
matches) between the first and the second CD. In any event,
our setup implies that the results exactly hold for all CDs where
the coach was active for at least m matches.
3. Previous studies (see above) have restricted the control group to
teams which did not dismiss the coach during the relevant
period. This, however, introduces a bias towards a more
positive expectation because teams with a bad future
performance tend to be excluded. To overcome this statistical
problem it is essential to use unbiased control groups.
4. The identification of control teams via all tCDmatches before
the CD is motivated by our previous observation that the
change of the team fitness during the season is neglible so that
as many matches as possible should be taken into account for
the estimation of the team fitness. However, based on the
subsequent results we will conclude that a minor modification
of the selection process might be appropriate. In any event, this
will be discussed further below.
Analysis of Changes of Coaches (CCs)
We have also studied all cases where a coach was changed (as a
regular change or a dismissal) during the summer break. This
event is denoted as CC (change of coach). We have considered
those 141 cases (starting 1966/67) where the corresponding team
played in the German Premier League in both seasons before and
after the CC. Here we start somewhat later in order to have
enough seasons to estimate the team fitness before the CC (see
An important aspect for the CC analysis deals with the
prediction of the expected outcome of a season. If during one
season the goal difference is given by DG (old) the expected
average fitness F(est) in the next season can be consistently
estimated via F(est)=cF+dFDG (old) . Here F(est) can represent
the expected goal difference or the number of points in the new
season. The parameters cFand dFare calculated from a regression
analysis for all teams which are not relegated. An even better
estimator is obtained by averaging (for all teams where this is
possible) the outcome over the previous three years with weighting
factor 1.0, 0.7 and 0.5 for the determination of DG (old). These
parameters have been estimated by optimizing the prediction
process. If a team was not playing in the Bundesliga in the second
and/or third last season, these seasons were just omitted from the
calculation of DG (old). Note that our results are insensitive to the
specific choice of these weighting factors.
The Usefulness of Coach Dismissal and Change
PLoS ONE | www.plosone.org2March 2011 | Volume 6 | Issue 3 | e17664
CD: Analysis of Possible Effects
The temporal evolution of CD and CC events is explicitly
shown in Fig. 1. Interestingly, the total number does not show any
significant time dependence. It seems, however, that the number
of CC events was larger during the initial period of the Bundesliga
whereas at the same time the number of CD events during the
initial or final period of the season was smaller. This might be a
consequence of the increased presence of media and the
corresponding pressure to act in case of a bad performance.
In Fig. 2 we show the goal difference of an average CD team vs.
time (measured in units of matches). There is a naive interpre-
tation of this plot. First the teams, which later on will dismiss the
coach, display an average value of DG=20.5. Then the fitness
further deteriorates down to DG=21.3 which prompts the CD.
Afterwards the average value of DG is 20.25, suggesting a
As already noted in literature [1,8,10–15] a group of teams with
an average negative goal difference will on average also have
experienced bad luck. After the selection procedure, i.e. in the
prediction period (final 10 matches), any positive or negative
random effects will average out. To quantify this effect we analyse
the performance of the control teams as introduced in the method
section. By our construction we obtain an identical average value
of DG of control and CD teams ((DG=20.53960.002 and
DG=20.53960.035, respectively. Time resolved average DG
-values are also displayed in Fig. 2. For the prediction period we
obtain an average DG -value of 20.25760.044 for the CD teams
and of 20.28760.002 for the control teams, yielding D
(DG)=0.03060.044, supporting the nil hypothesis. A more
detailed error analysis which takes into account the statistical
uncertainty of DG in the selection period, yields a slightly larger
statistical error of 0.046 as compared to 0.044. With an optimistic
estimationof a residualimprovement
0.046=0.076 our result amounts to a total improvement during
half a season, i.e. 17 matches, of DG<1.3.
Repeating this analysis for different values of m, i.e. different
time intervals to define the selection and prediction period, the nil
hypothesis is supported for all choices, albeit with larger statistical
errors. An objective approach to judge the size of this effect is to
compare the square of this maximum possible improvement with
the variance of the fitness distribution which is 0.27 (see also  for
a similar value determined for the last 23 seasons). Thus we obtain
0.0762/0.27=0.02. This again clearly shows that any possible
improvement is absolutely negligible. Using a different measure of
the effect size, as standard in statistical literature, yields a similarly
small value .
This apparent improvement in Fig. 2 is known as regression
towards the mean [13–15]. Qualitatively, this effect reflects the
fact that a subgroup which is selected based on a negative
accomplishment during a finite time interval will seemingly
improve in the future. This is just a direct consequence of the
presence of statistical fluctuations and is fully reflected by the
behavior of the control teams. In the present case it can be
expressed as the ratio rDG of the average DG value in the
prediction period and the DG value in the selection period. For the
control teams one empirically obtains rDG=0.53. Previous work
has developed a general formula stating the rDGis approximately
equal to 1/(1+f/tCD),1 with f<13; see . With this expression at
hand we can perform a consistency check of our approach.
Additionally taking into account the distribution of tCDvalues as
well its average value of 17 the relevant factor here is c(13.5,
17)<0.56 which is indeed close to 0.53. The slight variation of f
reflects the difference between ,1/tCD. and 1/,tCD..
Please note that there is no gradual improvement during the m
matches after the CD event. First, this result is consistent with the
Figure 1. The number of CD and CC events. In particular we show the intra-seasonal CD events after the 10thmatch and before the 25thmatch.
Figure 2. Comparison of the CD (coach dismissal) with the
control teams based on the average goal difference. The time
axis is shifted with respect to the time of the CD (occurring directly after
match day tCD) to enable comparison of different events. The average
values for the prediction period are included as solid lines. No effect of
the CD is present within statistical errors.
The Usefulness of Coach Dismissal and Change
PLoS ONE | www.plosone.org3March 2011 | Volume 6 | Issue 3 | e17664
general observation that the team fitness does not change during
the season. Second, this also implies that the cases where a
carekeeper coach is replaced after less than m=10 matches does
not yield a further significant positive (or negative) shift.
We have repeated the analysis by restricting ourselves to the last
23 years of the Bundesliga. Here we find D (DG)=0.0860.06.
Within the error bars this result is identical to that of the whole
period and is thus again compatible with the nil hypothesis. Thus,
there is no significant time dependence in the efficiency of CD
Interestingly, the CD teams play worse during the last two
matches before the CD event. Thus one might speculate that the
CD event at least helps to stop this emerging negative streak. This
hypothesis can be checked by selecting control teams which also
have two worse results at the end of the selection period (see above
for details). The results are shown in Fig. 3. Except for 14 CD
teams it was always possible to find appropriate control teams,
albeit with a smaller number (due to the more detailed
constraints). This shows up in larger fluctuations. Again the
average results in the prediction period are basically identical. This
result is compatible with our previous finding  that two
consecutively lost matches are not sufficient to identify the
beginning of a negative streak (in contrast to four consecutively
Furthermore we checked that the CD events are not related to
any effects of the home/away-asymmetry. Since we have corrected
out this asymmetry no effects should be present. However, we
explicitly checked that within statistical noise the number of
home/away and away/home matches before the CD event is
nearly equal and the fraction of two subsequent home or two
subsequent away matches before the CD event is both less than
The results, reported so far, deal with the average effect of a CD
event. In particular they are still compatible with the hypothesis
that the CD has a positive effect for some teams and a negative
effect for other teams. This can be tested by analyzing the variance
of DG -values. Results are shown in Fig. 4. The variance increases
by 0.0560.1. This result is compatible with a zero effect. Of
course, the value of 0.05 would still allow for the (extreme)
scenario that half of the CD events result in an improvement of
DG<0.2 (<!0.05) and the other half in a deterioration of DG<
–0.2. This explicitly shows that the resulting effect, if present at all,
is very small effect.
In practice one is particularly interested in points P rather than
in the goal difference DG. Because of the important implications of
our results we have repeated the same analysis as in Fig. 2 by using
points to characterize the fitness of teams. To standardize all
games beginning in 1963 we have always used 3 points for a win
and 1 for a draw following the worldwide established FIFA rules. It
should be noted, that in the German Premier League 2 points
were used for a win until 1994/95.
As seen in Fig. 5 the qualitative behavior is fully identical as
discussed in the context of Fig. 2. The average values in the
prediction period are P=1.34760.036 and P=1.32960.004 for
the CD teams and the control teams, respectively. Their difference
reads DP=0.01860.036. Note that DP=0.018 per match
corresponds too much less than one point per half season. In
any event, the nil hypothesis is fully supported.
However, comparisons of the results for DG and P explicitly
show that the information content of the goal difference is by far
superior. As shown in  an approximate scaling of DG to P
values can be performed by using a factor of approx.1.6 (see ).
Indeed, this factor is approximately recovered when comparing D
(DG)=0.030 with DP=0.019. However, the relative statistical
error is significantly larger for DP, i.e. 0.2, as compared to D(DG),
i.e. 0.13. Furthermore, also the strong apparent fitness decrease
during the two matches before the coach dismissal is significantly
more pronounced for DG as compared to P. This is partly due to
the fact that points are (trivially) bounded from below whereas no
such bound exists for DG.
Motivation for a CD
A further important question deals with the motivation to
dismiss a coach. Naturally, an unsatisfactory performance is
expected to be the main reason. As already discussed above the
data in Fig. 2 suggest that beyond this general performance
argument (see below for a closer discussion) the occurrence of two
bad results trigger the dismissal of the coach. This observation has
consequences for the consistency of our approach. Based on our
previous results  we expect that fitness fluctuations are very
small during a season. Due to the relative shifting of the data (via
Figure 3. Analogous representation as in Figure 2, but with the
additional constraint that the control teams also display
correspondingly bad results during the two matches before
the CD event. Again no effect of the CD is present.
Figure 4. Comparison of the CD teams with the control teams
based on the variance of the goal differences. In analogy to
Figure 1 the average values over the prediction period are given as solid
lines. Again no effect is present.
The Usefulness of Coach Dismissal and Change
PLoS ONE | www.plosone.org4March 2011 | Volume 6 | Issue 3 | e17664
t–tCD) we systematically identify two matches where the teams just
had particular bad luck. It is consistent to exclude these two
matches from the fitness estimation of a team because these two
data points are biased. As a consequence the control teams on
average should have the same DG for t–tCD,21.
This argument can be rationalized with a simple example. In
the ‘‘dice throwing premier league’’ a coach is dismissed after 2
times throwing a 1. Of course, in principle all teams have equal
properties (average fitness 3.5). However, if the 10 matches before
a CD event were analyzed exactly in analogy to our procedure one
finds an average fitness of 3.3. The reduction is due to the
systematic inclusion of the final two results with a 1. Thus, the
fitness estimate is lower than the true fitness of 3.5. Excluding the
last two results for the CD from the analysis yields a fitness value of
3.6. Now the value is larger as the true fitness because in our
approach no second (1,1)-pair is allowed to occur during the 10
matches before the CD event. Thus we conclude that a better
fitness estimate is obtained if we omit the two matches before the
CD event. However, since this estimation would be slightly too
optimistic, the optimum estimation lies in between both approach-
es (with and without the final two matches) as exemplified above.
Adapting the choice of control teams to this condition (omission
of the last two matches) the average value of DG in the selection
period reads 20.431 instead of 20.539. Correspondingly the
optimized set of control teams also plays better in the prediction
period (20.235 instead of 20.287). Thus the effect of the CD gives
rise to a negative value of D(DG)=20.02260.048 rather than
D(DG)=0.03060.046 (as mentioned above). As a consequence
our finding of a nil effect is further corroborated by this self-
consistently modified procedure. As discussed in the previous
paragraph for general reasons the ‘‘true’’ value is expected to lie
between the original (0.030) and the new estimate (20.022) which
even better agrees with the nil hypothesis.
It is to be expected that beyond this triggering effect also the
performance in the whole season is unsatisfactory. To quantify this
effect we determine the expected number of points in a season
P(est) as well as the expected goal difference DG(est) for all CD
teams with the procedure, introduced in the method section. Then
one can assess the degree of frustration of a team from comparison
with the actual outcome. For this comparison we choose the
number of points, i.e. P(true) – P(est), since this observable is
relevant for managerial decision processes. Since the CD does not
change the fitness of the team we can use the outcome of the total
season to get an optimum statistical accuracy. To obtain an even
more specific correlation we additionally correlate the difference
P(true) – P(est) with DG(est), the latter representing the fitness of a
team. In this way we can distinguish between the motivation of a
CD for good and bad teams.
The results are displayed in Fig. 6. Obviously, most (82%) of all
teams have indeed performed worse than the pre-season
expectation. Thus, the motivation to dismiss a coach is not only
pure imagination but is indeed backed by a bad performance
(which, unfortunately, does not change after the CD). Interesting-
ly, the deviations from expectation are stronger for good teams (on
average up to 9 points for the whole season) as compared to bad
teams with approximately half of the number of points. This may
have a simple psychological explanation. Even with a somewhat
poorer performance good teams are still significantly distant from
the relegation positions. Thus, for these teams the need for action
results from the mere comparison with the expected outcome. For
bad teams, however, already a minor negative deviation will push
these teams to positions very close to relegation. This may
immediately increase the pressure to act and thus to dismiss the
coach as the most simple action.
We have repeated the analysis with evaluating the number of
points after midseason, i.e.at the average time of the coach
dismissal. The graph looks similar albeit with slightly smaller
values for the number of points (because only half of the season is
over). In any event, the interpretation remains exactly the same as
CC: Analysis of Possible Effects
Having found no signature of the in-season CDs one may
wonder whether changing the coach during the summer break, i.e.
a CC, has an influence on the team performance. This question
has two facets. First, independent of the quality of the coach the
mere act of changing a coach may bring in a systematic shift in
fitness. Of course, this shift may be positive (e.g. due to bringing in
new stimulus in saturated structures) or negative (e.g. due to
corrosion of well-established team structures). Second, beyond this
systematic effect the different qualities of coaches might lead to the
effect that some teams profit whereas other teams may suffer from
this change (relative to the average). Whereas the systematic effect
Figure 5. Analogous to Figure 2, using points rather than the
goal difference as the observable of interest. Again no effect of
the CD is present within statistical errors.
Figure 6. Correlation of the deviation from the expectation of
points with the expected fitness in a season where a CD takes
please. The solid line is the regression line. From this graph the
motivation to dismiss a coach can be extracted.
The Usefulness of Coach Dismissal and Change
PLoS ONE | www.plosone.org5March 2011 | Volume 6 | Issue 3 | e17664
can be studied from the first moment of the appropriate
performance distribution, the variance of this distribution contains
additional information about the quality variation of different
coaches, as already discussed in the context of CD.
In analogy to above we start by correlating P(true) – P(est) with
DG(est); see Fig. 7. It turns out that the average value of P(true) –
P(est) is 20.360.6. Thus, no significant overall improvement of
deterioration is seen. Furthermore, no significant correlation with
DG(est) is observed since the relative error of the slope of the
regression line is approx. 70% of the slope itself. Thus we may
conclude that a possible systematic effect of a CC is less than one
point per season, i.e. totally negligible. Repeating the same analysis
for DG(true) - DG(est) (as before defined as the average goal
difference per match) we obtain 20.0260.04 which again indicates
that any effect, if present at all, is very small. We may conclude that
changing the coach has no systematic positive or negative effect.
In the next step we study the variance of DG(true) - DG(est) of
the CC teams. In what follows we restrict ourselves to the
distribution of goal differences due to its superior properties as
compared to the number of points. For the variance we obtain the
value of 0.19760.026. Here the statistical error is smaller than in
the CD analysis because we include information from a complete
season rather than just from 10 matches. To identify the statistical
contribution (due to the random effects in a soccer match beyond
the actual team fitness) we also determine the variance for all
teams. We take the same seasons as for the CC teams and, of
course, also require that the team was playing in the Bundesliga in
the previous season (for the determination of DG(est)). Here the
variance is given by 0.21260.013. The difference of the variances
thus reads 20.01560.029. Within the statistical error no
difference to the variance of the CC teams is present. Note that
a significant quality variation among the coaches would have
resulted in a positive value of that difference. In any event, the
hypothesis that all coaches basically have the same or similar
quality (or their quality is irrelevant for the team performance) and
that a CC has no direct effect cannot be ruled out by studying the
data of more than 40 years Bundesliga.
Taking into account the size of the statistical error one may
estimate the possible relevance of the specific coach on the team
performance. With an optimistic view the maximum increase of
the variance is given by 20.015+260.029<0.04. The value has to
be compared with the fitness variance of all teams in the
Bundesliga which is 0.27 (see above). This implies that with this
optimistic estimation the relative contribution of the coach to the
team fitness is 0.04/0.27, i.e. 15%. Most likely, however, this
contribution is even smaller. This small value also reflects the fact
that the group of coaches, which is considered to be hired in the
Bundesliga, fulfills already high quality criteria so that the quality
variation within this group is quite small.
This work can support the results of some previous studies [11–
15], but now ruling out several methodological weaknesses and
covering a very large data set with respect to effects of coach
dismissals. The underlying team fitness does not improve due to
coach dismissal. The increase immediately after the coach
dismissal can be completely traced back to a simple statistical
selection effect (regression towards the mean). The idea to dismiss
a coach emerges from a bad performance as compared to
expectation (see Fig. 6) and the actual dismissal is triggered by two
particularly unfortunate matches. Furthermore, for teams below
the average a smaller deviation from the pre-season expectation
may be sufficient to dismiss the coach as compared to better teams
where typically a larger deviation is required.
Changing the coach during the summer break results in the
same nil effect. Most interestingly, even the variance of the
appropriate distribution of teams changing the coach during two
seasons does not show any effect. This has the immediate
consequence that the impact of coaches as ‘‘fitness producers’’
for the teams is limited and is most likely (on average) much
smaller than 15% as compared to other factors (like the team wage
bill ), determining the quality of a soccer team. Stated
differently, the quality of coaches, working in the Premier German
Soccer league and hired successively by a team is either quite
similar or does not have much impact on the quality of the team as
already assumed before . Our results do not exclude the
possibility that it is favorable to work with a coach several years in
a row. This aspect will be studied in future work along similar
Conceived and designed the experiments: AH CM OR NH BS. Performed
the experiments: AH CM OR NH BS. Analyzed the data: AH CM OR
NH BS. Contributed reagents/materials/analysis tools: AH CM OR NH
BS. Wrote the paper: AH CM OR NH BS.
1. Frick B, Barros CP, Prinz J (2010) Analysing head coach dismissals in the
German ‘‘Bundesliga’’ with a mixed logit approach. European Journal of
Operational Research 200: 151–159.
2. Barros CP, Frick B, Passos J (2009) Coaching for survival: The hazards of
head coach careers in the German ‘Bundesliga’. Applied Economics 41:
3. Gamson WA, Scotch NA (1964) Scapegoating in baseball. American Journal of
Sociology 70: 69–72.
4. Carron AV, Hausenblas HA, Eys MA (2005) Group dynamics in sport.
Morgentown, WV: Fitness Information Technology.
5. Dobson S, Goddard J (2001) The economics of football. Cambridge: Cambridge
6. Heuer A, Mu ¨ller C, Rubner O (2010) Soccer: Is scoring goals predictable
poissonian process? Europhysics Letters 89: 38007.
7. Heuer A, Rubner O (2009) Fitness, chance, and myths: An objective view on
soccer results. European Physical Journal B 67: 445–458.
Figure 7. Correlation of the deviation from the expectation of
points with the expected fitness in a season where the coach
has been changed in the previous summer break. The solid line is
the regression line. From this graph the effect of changing a coach in
the summer break can be extracted.
The Usefulness of Coach Dismissal and Change
PLoS ONE | www.plosone.org6March 2011 | Volume 6 | Issue 3 | e17664
8. Koning RH (2003) An econometric evaluation of the effect of firing a coach on
team performance. Applied Economics 35: 555–564.
9. van Dalen HP (1994) Loont het om een voetbaltrainer te ontslaan? Economisch
Statistische Berichten 79: 1089–1092.
10. de Dios Tena J, Forrest D (2007) Within-season dismissal of football coaches:
Statistical analysis of causes and consequences. European Journal of Operational
Research 181: 362–373.
11. Audas R, Dobson S, Goddard J (2002) The impact of managerial change on
team performance in professional sports. Journal of Economics and Business 54:
12. Audas R, Dobson S, Goddard J (1997) Team performance and managerial
change in the English Football League. Economic Affairs 17: 30–36.
13. Breuer C, Singer R (1996) Trainerwechsel im Laufe der Spielsaison und ihr
Einfluss auf den Mannschaftserfolg (Mid-season coach dismissal and its impact
on team success]. Leistungssport 26: 41–46.
14. Salomo S, Teichmann K (2000) The relationship of performance and
managerial succession in the German premier soccer league. European Journal
for Sport Management 7: 99–119.
15. Tippenhauer A, Strauss B (2003) Trainerentlassungen in der Fußballbundesliga
(Coach-dissimals in the German Soccer league). In: Strauss B, Hagemann N,
Tietjens M, Falkenberg-Gurges G, eds. Sport goes media. Hamburg, Germany:
Czwalina. 334 p.
16. Bruinshoofd A, Ter Weel B (2003) Manager to go? Performance dips
reconsidered with evidence from Dutch football. European Journal of
Operational Research 148: 233–246.
17. Cohen J (1988) Statistical power analysis for the behavioral sciences (2ndedition).
Hillsdale (New Jersey): Erlbaum.
18. Simmons R, Forrest D (2004) Buying success: Team performance and wage bills
in U.S. and European Sports leagues. In International Sports economics
comparisons Fort R, Fitzel J, eds. Santa Barbara (California): Praeger. pp
The Usefulness of Coach Dismissal and Change
PLoS ONE | www.plosone.org 7March 2011 | Volume 6 | Issue 3 | e17664