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Within-season dismissal of football coaches: Statistical analysis of causes and consequences
European Journal of Operational Research 181 (2007) 362–373 www.elsevier.com/locate/ejor
O.R. Applications
Within-season dismissal of football coaches: Statistical analysis of causes and consequences Juan de Dios Tena
a,b,1
, David Forrest
c,*
a
b
Departamento de Economı´a, Universidad de Concepcio´n, Victoria 471, Concepcio´n, Chile Dipartamento di Economia, Impresa e Regolamentazione, Universita di Sassari, Via Torre Tonda 34, 07100 Sassari, Italy c School of Accounting, Economics and Management Science, University of Salford, Salford, M5 4WT, UK Received 20 September 2005; accepted 22 May 2006 Available online 20 July 2006
Abstract The paper examines the triggers for, and, consequences of, within-season dismissals of managers (head coaches) in the top division of the Spanish Football League during seasons 2002–2003 to 2004–2005. A major reason for directors deciding on dismissal is shown to have been concern that the club in question was in danger of demotion out of the division. This suggests that the clubs hoped to bring about short-term improvement in performance by changing manager. Employing an ordered probit model of match results, we demonstrate that an improvement in results tended to be achieved but only in home matches. The finding vindicates the decisions taken by club directors who dismissed their managers and implies that appeasing fans can have on-the-field benefits. It is consistent with the importance attributed to crowd support in the literature on home advantage in sports. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Football; Managerial change; Scapegoat hypothesis; Ordered probit; Home advantage
1. Introduction In most sorts of organisation, there is a natural time for changing leadership. In a political party, it may be after an election defeat. In a business, it may be when the contract of the Chief Executive Officer (CEO) comes up for renewal or when he reaches a certain age. In a sports club, it is certainly at the end of a season. Then a new manager will *
Corresponding author. Tel.: +44 161 295 3674. E-mail addresses: [email protected], [email protected] (J. de Dios Tena), [email protected] (D. Forrest). 1 Tel.: +56 41203204.
have time to train his players to adapt to his strategic approach and to recruit new personnel where appropriate. This mitigates any tendency for disruption to productivity to be associated with the replacement of the old regime. Despite the arguments that there is benefit to switching management only at convenient predetermined times for which preplanning is possible, organisations occasionally dismiss their leadership with unconventional timing. Bad opinion poll ratings may lead to a no-confidence motion on the leader of a political party. Falling market share may induce a board of directors to dismiss their CEO. Similarly, faced with a series of losses on the field, the owners
0377-2217/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2006.05.024
J. de Dios Tena, D. Forrest / European Journal of Operational Research 181 (2007) 362–373
of a sports team may decide to dismiss the manager (or head coach, as he is termed in many countries). It is of interest whether decision takers typically achieve their goals when they act in this apparently precipitate way, which runs the risk of disruption to the organisation and which may involve high direct costs in the form of compensation payments for termination of contract. It may be that decision takers correctly assess when a situation is sufficiently serious and sufficiently attributable to the behaviour of the current leadership to justify immediate dismissal. On the other hand, they may often act out of panic or may be indulging in scapegoating to appease stakeholders such as party members, shareholders or fans of the team. In the literature on managerial change in firms, there is general agreement that poor prior performance is correlated with the enforced departure of management (see, for example, Groves et al., 1995) and some studies point to the policy tending to be successful (Weisbach, 1988; Groves et al., 1995; Warzynski, 2000; Hudson et al., 2004). However, difficulties arise in selecting which indicators of firm performance, over what time period, are relevant in testing. Where stock market performance was the yardstick, Warner et al. (1988) and Cools and van Praag (2003) found no evidence that managerial change induced better performance. We examine the issue here in a sports context. We focus below on 20 within-season involuntary changes of manager in the Spanish Premier (football) League during the seasons from 2002–2003 to 2004–2005. We show that a significant predictor of dismissal of management was the club falling into the part of the standings where demotion from the division occurs at the end of the season. It is fair, then, to characterise dismissal in this context as a response to a situation where the club urgently needs league points. At this end of the standings, a small difference in points accumulated through a season can make a very substantial difference to the finances of the club as those forced into the immediately inferior division will suffer a major loss in revenue earning capacity. Compared to the literature on the impact of managerial change in business generally, there is the advantage here of no ambiguity about what needs to be measured to assess whether sacking managers has been a successful strategy: we need to model the impact of managerial change on on-the-field outcomes (which themselves are clear cut and not open to massaging by discretionary accounting).
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In Section 2, we review relevant studies in the sports economics literature. In Section 3, we model the determinants of managerial change. Section 4 employs an ordered probit model to assess the short-term impact of managerial change on team performance in home and away matches. Section 5 offers a more detailed analysis, with calculation of marginal effects for a team facing the threat of relegation. Section 6 concludes. 2. Previous sports studies In their comprehensive text on The Economics of Football, Dobson and Goddard (2001, Chapter 6) include a review of studies, in North America and elsewhere, of the impact of change of coach on team performance. Much of the work looks at whether team output improves in the season(s) following managerial succession but this is more relevant to the assessment of between-seasons change of manager. Here our concern is with whether dismissal of a manager during the season (and a crisis) has typically reaped short-term dividends. We refer therefore only to those studies which relate management change to subsequent results in the same season. Gamson and Scotch (1964) were early contributors to the literature. Their tests were inconclusive: they reported that win-ratios improved in 13 of the 22 cases of within-season managerial change observed in Major League Baseball between 1954 and 1961. For American Football, Brown (1982) reported a number of tests that allowed him to compare the subsequent win-ratios of teams which had performed badly early in the season and fired their coach and a control group of teams with similarly bad records but which had continued under the same management. Recovery from on-the-field slump was similar as between the two groups. The finding was suggestive that firing the coach was irrelevant to the resolution of the slump in results; but we would point out that a conceivable alternative explanation might be that club owners could correctly distinguish between slumps being attributable to bad management and bad luck and that the first group of teams may not have recovered at all without the crisis response. In soccer, Audas et al. (1997) for English leagues, and Bruinshoofd and ter Weel (2003) for the top division in The Netherlands, compared the recovery of teams that had sacked the manager during a slump with that of those that had not. In each case,
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the recovery rate of the first group was actually worse than that of the control group, casting further doubt on the efficacy of a dismissal strategy. However, the same caveat concerning selection bias again applies: the boards of clubs that left their manager in place may have been just those who (correctly) anticipated that the team’s fortunes would soon turn around. A more recent approach is based on econometric modelling of individual match results. This avoids issues of how to select a control group and takes into account the quality of opposition a team faces before and after managerial change. Results have, however, again failed to vindicate decisions by club directors to fire their coach. Koning (2003) modelled team rankings and individual match results in the Dutch Premier (football) League. The model for determining match results had as dependent variable the difference in goals scored between the two teams in a match. Explanatory variables were quality indicators of the two teams and a dummy to reflect which was playing at home. The parameters of the model were permitted to vary with change of manager. Koning analysed five seasons of data from the Dutch Premier League. In this time, there were 28 coaches fired of which four were terminated during the first season, 1993–1994. For 1993–1994, Koning found a significant change of coach effect, with improvement detected in team quality and in the extent of home advantage. However, the result was not replicated for any of the four following seasons (though home advantage improved following dismissals in 1996–1997) and Koning concluded as follows: ‘‘firing a coach occurs too often. Since it is not clear that the results on the field improve after a change of coach, it is likely that the board of a team intervenes for other reasons. It is likely that fan and media pressure are also strong determinants of the tenure of a coach’’. Recently, a popular approach amongst economists in the field of modelling match results has been ordered probit or logit with three ranked outcomes, home win, draw and away win (see, for example, Kuypers, 2000; Forrest and Simmons, 2000; Goddard and Asimakopoulos, 2004). Work reported by Audas et al. (2002) and Dobson and Goddard (2001, Chapter 6.8) adapts a very detailed ordered probit model to address the issue of whether match outcomes are influenced by recent changes in manager. This is achieved by adding to the regressors variables that reflect whether one of the teams has
recently changed manager: there are separate dummies for whether it is the first or second (and so on) game since the change in regime. Total impact is measured by summation of the coefficient estimates on these dummy variables. The finding is that managerial change tends to have a negative effect on team performance in the remaining weeks of the season, further evidence for the scapegoating hypothesis of managerial change: during a poor run of results, directors may dismiss the coach to appease club supporters rather than in any real hope of short-term amelioration of the club’s plight. Although scapegoating has been associated in the sports literature with the need to ‘‘placate disgruntled fans’’ (Dobson and Goddard, 2001, p. 265), this abstracts from the possibility that the latter will itself be a route through which change in management can lead to improved performance on the pitch. Players talk of the importance of fans ‘‘getting behind the team’’ and this belief, that the enthusiasm of the crowd matters, that it affects the performance of the team and perhaps the decisions of the referees, is reflected in academic analysis of the sources of home advantage. If firing the manager rekindles the enthusiasm of a crowd grown sullen from repeatedly adverse results, the policy may have a payoff in terms of league results even if it may be characterised in one sense, that of punishing an innocent man, as ‘‘offering a scapegoat’’. There is a hint of this in Koning’s finding that, in two of five seasons analysed, home advantage strengthened for those clubs that had changed manager in the Dutch League. To test the hypothesis further, we will make a distinction, in our empirical analysis below, between impact of managerial change on home and away performance. In contrast to some previous studies, our analysis will control for the quality of opposition faced in matches played subsequent to a change of manager. First though, we present statistical analysis of what triggered managerial change in our context of Spanish football. 3. Causes of managerial change The Spanish Premier League is structured in the same way as, for example, that in England to the extent that there are 20 teams that play each other on a home-and-away basis to give 38 rounds of matches (380 individual games). Three clubs are demoted to the immediately inferior division at the end of each season, to be replaced by three clubs promoted from that division.
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Our sample covers seasons 2002–2003 to 2004– 2005. There were 20 involuntary changes of manager during this period. We exclude from our analysis two voluntary departures, from Villarreal following the 26th round of matches in 2003–2004 and from Real Madrid after the third round in 2004–2005. Of course, whether resignations are truly voluntary may, in some circumstances, be ambiguous, since a coach may be willing to leave ‘‘by mutual consent’’ given adequate compensation for the shortening of his contract. However, for the two particular cases at Villarreal and Real Madrid, we were satisfied, after an examination of contemporary newspaper reports, that the terminations were initiated by the coaches themselves. Neither of them sought any financial compensation for early departure. The frequency of within-season dismissals in Spain appears to compare closely with that in the top division in English football: Dobson and Goddard (2001, p. 275) report there to have been 156 such terminations in 27 seasons up to 1998–1999, a rate of 5.8 per season. In the slightly smaller Dutch Premier League, Koning (2003) tabulates experience during five seasons when an average of 5.6 managers per season were fired. The relative frequency with which Spanish coaches are dismissed is therefore of a similar order of magnitude as in other European leagues. We constructed a probit model to account for within-season dismissal of the coach. The variable to be explained took the value one if the coach of team i was dismissed between match round t 1 and match round t. With three seasons’ data, and with the first round of each season excluded, there were 2220 observations. Relevant information, for example, on match scores, league positions and club budgets, were obtained from the newspaper websites, www.elmundo.es and www.marca.es. Our period of analysis was constrained by the limits on the period for which some of these old data continue to be displayed on the websites. Explanatory variables in the probit specification included the time of season (represented by the match round number and its square) and a measure of ‘‘managerial efficiency’’ (the number of places by which a club’s current position in the League is superior to its ranking in terms of its (wage) budget). There were also dummy variables set equal to one to signify, respectively, that the team was in a relegation position in the standings, that the team had lost its match in round t 1, and that the team
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had already dismissed a manager in the current season. Variables with which we experimented in an earlier specification but which were ultimately excluded on grounds of extreme non-significance included: dummy variables for newly promoted teams and for teams playing in the European Champions League; size of club (wage) budget; an interaction term equal to ‘‘efficiency’’ multiplied by the relegation zone dummy; and, to represent club culture, the number of within-season dismissals of the coach in the preceding three years. Some of these variables had appeared to be important from inspection of simple correlations with the incidence of dismissal. For example, the mean budget for clubs which did dismiss their manager in a given season was much lower than for clubs which did not (€33.24m compared with €58.65m). However, multivariate analysis reveals that low spending per se was not the ‘‘cause’’ of dismissals. Rather, the threat of relegation proved to be the principal trigger to change manager and, naturally, this threat is most commonly faced by the lowest spending clubs, hence the correlation. In respect of certain other covariates that failed to be significant, it should be noted that much less than one percent of the observations were positive: it is then to be expected that some plausible variables will fail to account, in a statistical sense, for the pattern of dismissals. Results from our final specification are displayed as Table 1. In the result on managerial ‘‘efficiency’’, there is evidence that boards of directors were realistic to the extent that they assessed coach performance by considering league position relative to what was to be expected given wage expenditure. Generally, the raw data indicate that dismissals typically occurred at clubs, which were underperforming relative to the size of budget. The mean value of the efficiency variable at the time of dismissal was 3.85. Often this improved subsequent to a dismissal, so that the mean value of ‘‘efficiency’’ at the end of the season (or at the next change of manager if sooner) at clubs which had fired was 2.18. Thus, on the face of it, changing manager tended to be a successful strategy; but this result cannot be considered definitive without econometric testing reported below. A key trigger of deciding to dismiss the coach appears to be that a team is in one of the relegation places in the standings. The ‘‘relegation’’ dummy, and another used to signify that a team had lost
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Table 1 Probit results: Manager dismissed before match t Coefficient Match round number Square of match round number Dummy: team lost last game Dummy: club is in relegation zone Managerial ‘‘efficiency’’ Dummy: ‘‘failing top team’’ Dummy: club has already dismissed a manager in the current season
0.095 0.002 0.525 1.025 0.046 0.584 0.771
Standard error 0.046 0.001 0.203 0.226 0.024 0.378 0.278
t
p 2.06 1.72 2.58 4.54 1.96 1.55 2.78
.039 .086 .010 .000 .050 .122 .005
Number of observations: 2220. Pseudo-R2: 0.21.
its most recent fixture, attracted highly significant, positive coefficient estimates. On the other hand, results from fixtures two and three matches ago (entered individually or represented by categorical variables representing successive defeats) did not prove significant and are omitted from our model as reported; this indicates that it was the relegation threat that was key rather than a run of poor results per se. Therefore, we may generalise that the threat of relegation is a strong proximate cause of managerial dismissal; but if the team has at least not suffered defeat in its most recent match, the manager is likely to be given another chance. So far as timing is concerned, the coefficient estimates on the round number of the next match and its square, which give a turning point of 26.04, imply that directors are most likely to act between the 25th and 26th matches of the 38 match schedule. If a club is in the relegation zone at this stage in the season, it is safe to say that relegation is a distinct possibility: but there are enough games left that a new manager might have time to engineer an escape. The situation described by our result appears similar to that in English football. Dobson and Goddard (2001, p. 273) link the record high number of dismissals across the English leagues in season 1994–1995 to a restructuring of divisions that meant that, in that year, more clubs than usual would be relegated. Relegation is the worst development possible from the perspective of fans and is also likely to cause financial problems for the owners. It is not surprising, therefore, that firing the manager in-season can be characterised as being often a response to the crisis of possible relegation. If the manager can be blamed for the club’s plight, the situation cannot be righted by waiting to the end of the season to dismiss him because, by then, the club may be out of the division. The manager in such a case is in a similar position to the chief executive
of a corporation, which is not merely delivering disappointing results but faces the possibility of actual liquidation. It might be speculated that, near the top of the standings, there are also especially severe financial consequences to underperformance relative to sums committed to player salaries. While in the middle rankings of the division, it will not make much difference financially if the club gains a few more or less points, amongst the leading clubs these points might determine success or failure to qualify for the highly lucrative European Champions League. We therefore included an additional variable related to the performances of three leading clubs, Barcelona, Real Madrid and Valencia. These are the clubs with the highest budgets, the only clubs to have won the League Championship in the last five years and the only clubs, which would regard playing in the Champions League as routine. The variable (failing top team) takes the value one whenever one of these clubs is, at the time of the observation, outside the qualifying zone for the Champions League. There is some evidence, consistent with the notion of nonlinear financial consequences, that these clubs may indeed be more ready to dismiss the coach than would be expected simply from the value taken by the managerial ‘‘efficiency’’ variable. However ‘‘failing top team’’ is not statistically significant at conventional levels (p = .12). This is unsurprising to the extent that a large majority of dismissals observed are in fact at clubs in or immediately adjacent to the relegation zone. This description applied to 17 of the 20 cases of dismissal in our data period. The trend continues. At the time of writing, there have been eight more dismissals subsequent to our data period and seven of the clubs concerned were in, or close to, the relegation zone. If relegation is the dominant cause of instigating managerial change, it follows that the effectiveness
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of the policy should be judged in terms of the shortterm impact on results and therefore the accumulation of points for survival. This we investigate in the next section. 4. Impact of managerial change on subsequent results We present now the results from an ordered probit model to account for match outcomes of Spanish Premier League fixtures played in the seasons from 2002–2003 to 2004–2005. The first three rounds of matches each season were excluded from the sample because league positions were used as regressors and these are likely to contain a lot of noise when based on only one or two games played by each team. Outcomes were ordered across three categories, from home win (2) through draw (1) to away win (0). Our focus variables were dummies to capture recent managerial change. Controls included were the current league positions, where 1 is top and 20 bottom, of the home and away teams and the most recent home result of the home team, represented as win = 2, draw = 1 and loss = 0 (the most recent away result of the home team and the most recent home or away result of the away team were insignificant in preliminary estimation). The two league position variables attracted very strong coefficients of expected sign. More surprisingly, the coefficient on the most recent result of the home team was significant and negative. This presumably reflects the apparent difficulty in football of putting together sequences of wins. Like Audas et al. (2002) we represent recent managerial change with a series of dummy variables according to whether a team was playing its first or second (and so on) match under new management. The particular managerial change variable defined by Audas et al. took the value +1 if the home team had a new manager and 1 if the away team had a new manager. This imposed a restriction that any impact on performance will be the same in home and away matches. For our study of Spain, we do not impose this restriction because we hypothesise that the impact of managerial change will work partly by influencing degree of crowd support for the home team. Accordingly, we have separate dummy variables to indicate that either the home or away team had a new manager. The variable HOMENEWONE indicates that the home team in a match was playing its first home fixture following a new appointment (this may or may
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not be the first game since the dismissal of the previous coach, depending on whether there is a delay in announcing a replacement). Variables HOMENEWTWO to HOMENEWSEVEN indicate that the home team was playing its second or third (and so on up to seventh) home match since the arrival of a new coach. A similar set of seven dummy variables captures similar information for the away club (for example, AWAYNEWONE is equal to one if the away team is playing its first away game following regime change). We restricted investigation to 14 rounds of matches (seven home, seven away) because of the number of dismissals that occurred with fewer than 15 matches remaining in the season. Results are displayed as Table 2. We consider first the impact on the match outcome of the home team having recently changed manager. The estimated coefficients on the manager change dummies, HOMENEWONE to HOMENEWSEVEN, are positive in every case, indicating that the information that a home team is playing under a new coach raises the probability that it will win the game. They are statistically significant in the cases of the first and second home matches under new management. Thereafter, however, none of the coefficient estimates is individually significantly different from zero at the 5% level. This may indicate that any positive effect on home performance is short-term. On the other hand, given the amount of ‘‘noise’’ in the outcomes of football games, it is unsurprising if no statistically significant impact is identified when attention is confined to the nth match in the tenure of a new coach, particularly since some dismissals in our data set occurred with as few as two home games remaining (thus the number of cases where the variable equals one falls below 20 from HOMENEWTHREE onwards). We therefore tested whether there was any effect on performance in the group of games from the third to the seventh home match: a Wald test was employed to evaluate whether the sum of the five individual coefficient estimates was different from zero. There was some indication albeit weak (p = .178) that a residual effect from new management was still felt in this run of games. The crucial question to a club is whether a positive effect on performance emerges over the remainder of the season following replacement of the coach. For home games, we seek to answer this question by summation of the coefficient estimates on HOMENEWONE to HOMENEWSEVEN. The sum here is +2.245. Whether this is significantly
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Table 2 Ordered probit results on match outcome (away win = 0, draw = 1, home win = 2) Coefficient Home position Away position Result of home team’s last home match HOMENEWONE HOMENEWTWO HOMENEWTHREE HOMENEWFOUR HOMENEWFIVE HOMENEWSIX HOMENEWSEVEN AWAYNEWONE AWAYNEWTWO AWAYNEWTHREE AWAYNEWFOUR AWAYNEWFIVE AWAYNEWSIX AWAYNEWSEVEN
0.077 0.062 0.103 0.649 0.600 0.171 0.151 0.168 0.369 0.137 0.438 0.458 0.118 0.146 0.166 0.224 0.235
Standard error 0.007 0.007 0.047 0.259 0.273 0.271 0.282 0.316 0.322 0.349 0.309 0.294 0.321 0.297 0.365 0.324 0.313
t
p 10.37 8.87 2.19 2.50 2.20 0.63 0.53 0.53 1.14 0.39 1.42 1.56 0.37 0.49 0.45 0.69 0.75
.000 .000 .029 .012 .028 .529 .593 .595 .253 .694 .156 .119 .714 .622 .650 .490 .453
Number of observations: 1050. Pseudo-R2: 0.10.
different from zero may be evaluated by a Wald test. In this case, the null hypothesis of no effect over seven home matches is decisively rejected (p = .010). The result is not dependent on the choice of seven for the number of home games over which the impact of managerial change was to be measured. It was impractical to extend the horizon beyond seven home games because of shrinking sample size (the season lasts for 19 home games and some dismissals occur with more than 12 already played). However, Table 3 shows the cumulative impact over shorter runs. Whatever the time horizon considered up to seven home games, there is an effect on performance that is significant at about, or better than, the 1% level. We tested the robustness of our findings to a respecification that replaced current home and away league positions with information on the teams’ performances over a full season, i.e., points gained over their preceding 38 matches. Using an index of club performances over a longer period than the season to date might be argued to defend yet more strongly than in the first model against the possibility that mean reversion effects (an improvement in results following a poor run) could be misinterpreted as real effects from dismissing the coach. Account was taken of whether points were won in the current or previous season and an adjustment made where previous season points had been awarded while the team was playing in the Second Division. Data from the previous season have been found to be sig-
Table 3 Cumulative impact of a new manager (away win = 0, draw = 1, home win = 2) Coefficient HOMENEWONE HOMENEWTWO HOMENEWTHREE HOMENEWFOUR HOMENEWFIVE HOMENEWSIX HOMENEWSEVEN AWAYNEWONE AWAYNEWTWO AWAYNEWTHREE AWAYNEWFOUR AWAYNEWFIVE AWAYNEWSIX AWAYNEWSEVEN
0.649 1.249 1.420 1.571 1.739 2.108 2.245 0.438 0.020 0.138 0.284 0.449 0.674 0.909
p .010 .001 .004 .007 .011 .007 .010 .157 .963 .803 .659 .553 .425 .324
Number of observations: 1050. Pseudo-R2: 0.10.
nificant in accounting for results in English football (Dobson and Goddard, 2001). In analysis of the English game, distance between the stadia of the two clubs has also been found to play a role and accordingly we also include this in our alternative and more information-rich model. Table 4 presents the results of the estimation. HPTSCURR is total League points achieved by the home club in the season to date; HPTSPREV is total League points achieved by the home team in its final (38-n) matches of the previous season,
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Table 4 Ordered probit results on match outcome (alternative model) (away win = 0, draw = 1, home win = 2) Coefficient Distance HPTSCURR HPTSPREV HPTSPREV * HPROM APTSCURR APTSPREV APTSPREV * APROM Result of home team’s last home match HOMENEWONE HOMENEWTWO HOMENEWTHREE HOMENEWFOUR HOMENEWFIVE HOMENEWSIX HOMENEWSEVEN AWAYNEWONE AWAYNEWTWO AWAYNEWTHREE AWAYNEWFOUR AWAYNEWFIVE AWAYNEWSIX AWAYNEWSEVEN
0.0009 0.043 0.004 0.002 0.041 0.009 0.003 0.051 0.548 0.400 0.110 0.102 0.200 0.433 0.267 0.546 0.406 0.089 0.112 0.067 0.278 0.157
Standard error 0.011 0.004 0.005 0.003 0.004 0.005 0.003 0.046 0.260 0.270 0.274 0.284 0.319 0.326 0.352 0.311 0.223 0.318 0.297 0.366 0.330 0.318
t
p 0.01 9.56 0.78 0.57 9.58 0.02 1.03 1.12 2.10 1.48 0.40 0.36 0.63 1.33 0.76 1.76 1.38 0.28 0.38 0.18 0.84 0.50
.994 .000 .436 .570 .000 .986 .305 .264 .035 .139 .689 .720 .529 .184 .448 .079 .167 .779 .706 .854 .399 .620
Number of observations: 1050. Pseudo-R2: 0.09.
where n is the number of games played so far in the current season; HPTS PREV * HPROM is a slope dummy to allow a different coefficient for teams that had been promoted from the division below at the end of the previous season. Similar controls for past performance by the away team are defined symmetrically with those for the home team. The results from this alternative model indicate that it is in fact less effective than our main model in accounting for the set of match outcomes, with distance and results from the previous season failing to add statistically significant explanatory power. The lack of role for geographical distance between the home bases of the two clubs is interesting in that it contrasts with results from English soccer. The explanation may be that absolute distances in Spain tend to be much larger. Players in the top division are likely to be transported by air so that fatigue and disruption for visiting teams will differ little according to the distance involved; and the presence of travelling supporters, whose numbers may influence performance on the field, is much more limited across the League than in a small country like England. As in the main model, we find a positive effect on home performance following a change of manager. Estimated coefficients on all seven ‘‘home new’’
dummy variables are positive. While only the first is individually significant (p = .035), the sum over seven games is positive and significant with a p-value of .019. In further experimentation, we repeated the analysis with an additional covariate, a dummy variable set equal to one (minus one) if the home (away) team finished the game with more players than its opponent because of sending(s)-off. The variable proved highly significant in accounting for match results though there is a problem of potential endogeneity if dismissals by referees are correlated with the scoreline at the time of an incident. Therefore, we do not report the estimates here but note that the results on the managerial change variables were essentially unchanged: the impact of a change in manager measured over seven home games was positive with a p-value of .003. There is therefore robust evidence from these three seasons of experience in the Spanish Premier League that sacking the coach produced tangible results at home in the following weeks. Note that this does not imply that dismissal is a good option for all clubs in urgent need of league points since, if boards of directors possess even limited powers of discrimination, the set of clubs that fired the coach will be biased towards those in a situation
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where such an action was most likely to yield results (for example, these were cases where the club’s plight was least attributable merely to bad luck or cases where fan support had been most dangerously eroded). What is being tested here is rather whether clubs that opted for a new manager acted wisely. Our findings were different in respect of away performance. In both our main and our alternative models, the coefficient estimates on the dummy variables for a new away team manager indicated a negative effect on performance in the first away match though this was not statistically significant; thereafter, signs point to a positive effect but none of the coefficient estimates was close to being statistically significant. We summed them to assess cumulative impact over seven away matches. We found no significant difference in performance in this group of away matches following management change (p = 0.324; p = .541 in the case of our alternative model) and this finding was robust to choosing alternative lengths of sequence than seven (Table 3). A new coach appeared to have no effect on the set of away match outcomes following his appointment. A caveat to this finding is that there was some weak indication of improved away results if the first away game was excluded from consideration. The contrast between the results for home and away performance suggest that any gain in points achieved by those clubs that fired their manager was not primarily the result of reversion to mean effects or to technical improvements introduced by a new coach. These factors would have been reflected equally at home and away. It is though consistent with the hypothesis that, where a team’s run of results provokes fan disillusion, there may be real effects from ‘‘doing something’’ if the fans respond by supporting their team more enthusiastically at the home stadium. Of course, the support a team receives at a home match could depend both on the number of fans attending and on how positive their attitude is. In the present case, there is no evidence that more supporters purchased tickets when a new manager arrived. Comparing the three home games before and after the arrival of a new coach (two matches where the dismissal was so late in the season that only two home games remained), 10 clubs experienced an increase and 10 a decrease in attendance. Further, in case these data were unduly influenced by which teams happened to be the visitors before and after changes in coach, we also estimated a conventional attendance demand function for the whole
sample of 1050 matches, with new manager dummies included as additional regressors. Again, there was no evidence of a relationship between attendance and the appointment of a new coach: none of the coefficients on the variables HOMENEWONE to HOMENEWSEVEN was significant. Any positive effects on home performance when a new manager arrives appears, therefore, to be attributable not to crowd size but to crowd enthusiasm. Evidence that crowd enthusiasm, as opposed to crowd size or density, affects match outcomes is limited in the literature on home advantage, the issue being hard to test because of the difficulty in measuring the emotional atmosphere in a stadium. However, Nevill et al. (2002) employed an experimental method. Senior English referees were shown films of incidents in games with crowd noise either included or silenced. Their opinions were shown to run more in favour of the home team when they were exposed to the noise of the crowd and such bias could of course influence match outcomes. The potential for officials’ decisions, and perhaps therefore match results, to be influenced by the crowd received further support from Dohnen (2005). He found evidence of referee home bias in German stadia without moats but not in stadia where the crowd was set back behind a moat. Whether or not performances of players themselves respond to an increased level of enthusiasm from a crowd of a given size is an issue yet to be resolved in the home advantage literature though findings that measures of home advantage at the team-specific level are unstable are consistent with the notion that fans can sometimes help and sometimes hinder their team (Smith, 2005). Football supporters certainly believe their behaviour in the stadium is important. Wolfson et al. (2005) surveyed 461 English fans and established that by far the most important factor behind the phenomenon of home advantage was, according to those who attend games, crowd support. On the other hand, in openended responses, many noted the potential of a discontented home crowd to harm their team, for example, ‘‘Home players in a poor team can suffer at home due to pressure of disgruntled supporters’’ and ‘‘Home fans can in fact distil fear and show frustration to their own team . . . home advantage has gone and the players feel the pressure and tensions between their home supporters’’. Our findings are at least consistent with these fan beliefs. The crowd is likely to be disaffected when a team is facing relegation; but a new manager potentially repre-
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bulk of the expected effect relates to the first two games). Note that the sum of marginal effects on draw probabilities is not statistically significant, so we attribute no extra points from that source. A gain of two to three League points is, of course, modest but this is a typical margin separating the last team safe from relegation at the end of the season from those below it. A gamble that a new coach might save the team from relegation by improving home results is therefore by no means to be viewed as reckless. We also computed (but do not report) marginal effects of away team manager change on away win and draw probabilities in the case where an away team lies 18 in the standings (the home team was assumed to be mid-table and to have had an ‘‘average’’ result in its last home game). The effect on win/ draw probabilities over seven away matches proved to be far from statistically significant. We therefore attribute no additional points gain to managerial change in respect of away fixtures. We investigated the sensitivity of our estimates of expected gain in points earned at home to the toughness of the schedule faced by a club. We recalculated marginal effects for the case where opponents were at the upper quartile (ap = 5.25) rather than in the middle (ap = 10.5) of the League table. With such a pessimistic scenario (and other assumptions as before), the point estimate of a home win is .169 and that of a draw .270. In these circumstances, there was a statistically significant positive effect on both the expected number of home wins and the expected number of draws. Combined, these yielded an expected gain in League points of 2.24 over seven
sents a new start and fans may rally behind him. This could account for the improvement in home performances identified by our analysis. 5. Marginal effects In this section, we attempt more precise estimation of the benefits that accrued to those clubs that sacked their manager by calculating the marginal effects from managerial change, evaluated at values for variables that reflect typical circumstances of clubs facing the threat of relegation. Table 5 presents estimates of marginal effects on home win and draw from the ‘‘main’’ ordered probit model whose results were discussed in the previous section. They are evaluated with home position = 18, reflecting the situation of a club which is in the relegation zone. It is presumed only to have drawn its last home game (result = 1) and to be playing against a mid-table club (away position = 10.5). All managerial change variables are set to zero. With this configuration of values of the regressors, the point estimate of the probability of a home win is .258 (and that of a draw .304). The effect of changing manager on the team’s expected number of home wins in the following seven home matches is given by the sum of the seven marginal effects, which is +0.807. In Spanish football, as is normal in Europe, three league points are awarded for a win and one for a draw. Change in manager is therefore expected to raise the number of ‘‘win’’ points earned from this group of games by approximately 2.42 points. This is equivalent to 0.35 points per match (though the
Table 5 Marginal effects On home win dy/dx
On draw se
t
dy/dx
se
t
Home position Away position
.025 .020
.002 .002
15.02 7.99
.005 .004
.002 .001
2.85 3.52
Result of home team’s last home match HOMENEWONE HOMENEWTWO HOMENEWTHREE HOMENEWFOUR HOMENEWFIVE HOMENEWSIX HOMENEWSEVEN
.033 .241 .222 .058 .051 .057 .131 .046
.015 .102 .107 .096 .099 .112 .123 .122
2.20 2.37 2.07 0.61 0.52 0.51 1.07 0.38
.007 .014 .009 .008 .008 .008 .007 .007
.004 .028 .027 .008 .009 .009 .013 .012
1.80 0.50 0.34 1.06 0.83 0.93 0.53 0.59
Marginal effects, calculated from the ordered probit model reported in Table 2, are evaluated at: home position = 18, away position = 10.5, result of home team’s last home match = 1 (draw), all other variables = 0.
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League matches. Our estimate of benefit was therefore lowered only slightly for a quite extreme assumption about the quality of opponents in remaining matches. 6. Conclusions Sport often offers a laboratory for the testing of general ideas about business and economic behaviour. In the case of changes of management in a crisis, and whether they typically improve performance or merely reflect scapegoating, professional league football is an appropriate setting for testing hypotheses: it is very public information when a manager is fired; given the typical circumstances, the aim of the policy is very clearly defined; and the extent to which the aim is met is readily measurable in the league standings. Two previous studies of European football leagues found little evidence that clubs dismissing their manager in mid-season benefited in terms of results though, in The Netherlands in some seasons, change of coach appeared to improve the extent to which clubs exploited home advantage. For the case of Spain, we have examined the impact of changing coach on subsequent match results. New coaches appear to have made a modest positive difference to match results in the shortterm; but this effect was derived entirely from an improvement in results at the home stadium. No change in away performance, measured over a run of games, was detected. We are mindful that evidence from a relatively small number of seasons may not generalise to lengthier periods (Koning, 2003); but our results suggests that future researchers should distinguish carefully between home and away results when assessing the effects of manager dismissal. The implication from our evidence is that a new coach does not typically bring technical solutions to the weaknesses of the team since away performance is little altered. That home results nevertheless improve suggests a role for crowd support in the determination of match outcomes. Clubs typically fire the manager when faced with the threat of relegation and in those circumstances supporter morale is liable to be low. Perhaps, to appease them, the directors offer a scapegoat; but in this context ‘‘scapegoating’’ may not be mere gesturing, still less irrational, since, as discussed in the literature on home advantage, support from the crowd can be an input in the process of the team producing wins.
Our general proposition is, then, that scapegoating can have positive effects if the goals of an organisation are capable of being influenced by the stakeholders being appeased. Acknowledgements We are grateful to Oscar Callejo from Comite´ Nacional de Entrenadores for providing very helpful information about managerial dismissals, to three anonymous referees for incisive suggestions, and to Ian McHale and Andy Tremayne for valuable comments on an earlier draft. References Audas, R., Dobson, S., Goddard, J., 1997. Team performance and managerial change in the English football league. Economic Affairs 17, 30–36. Audas, R., Dobson, S., Goddard, J., 2002. The impact of managerial change on team performance in professional sports. Journal of Economics and Business 54, 633–651. 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. Brown, M., 1982. Administrative succession and organizational performance: The succession effect. Administrative Science Quarterly 27, 1–16. Cools, K., van Praag, C., 2003. The value relevance of forced top management departures. Discussion Paper 03-051/3, Tinbergen Institute. Dobson, S., Goddard, J., 2001. The Economics of Football. Cambridge University Press, Cambridge. Dohnen, T., 2005. Social pressure influences the decisions of individuals: Evidence from the behavior of football referees. Discussion paper 1595, IZA, Bonn. Forrest, D., Simmons, R., 2000. Forecasting sport: The behaviour and performance of football tipsters. International Journal of Forecasting 16, 317–331. Gamson, W., Scotch, N., 1964. Scapegoating in baseball. American Journal of Sociology 70, 69–72. Goddard, J., Asimakopoulos, I., 2004. Forecasting football results and the efficiency of fixed-odds betting. Journal of Forecasting 23, 51–66. Groves, T., Hong, Y., McMilan, J., Naughton, B., 1995. China’s evolving managerial labor market. Journal of Political Economy 103, 873–891. Hudson, R., Malatesta, P., Parrino, R., 2004. Managerial succession and firm performance. Journal of Financial Economics 74, 237–275. Koning, R., 2003. An econometric evaluation of the effect of firing a coach on team performance. Applied Economics 35, 555–564. Kuypers, T., 2000. Information and efficiency: An empirical study of a fixed odds betting market. Applied Economics 32, 1353–1363. Nevill, A.M., Balmer, N.J., Williams, A.M., 2002. The influence of crowd noise and experience upon refereeing decisions in
J. de Dios Tena, D. Forrest / European Journal of Operational Research 181 (2007) 362–373 association football. Psychology of Sport and Exercise 3, 261– 272. Smith, D.R., 2005. Disconnects between popular discourse and home advantage research: What can fans and media tell us about the home advantage phenomenon?. Journal of Sports Sciences 23 351–364. Warner, J., Jerold, B., Ross, L., Karen, H., 1988. Stock prices and top management changes. Journal of Financial Economics 20, 461–492.
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Weisbach, M., 1988. Outside directors and CEO turnover. Journal of Financial Economics 20, 431–460. Warzynski, F., 2000. The causes and consequences of managerial change in Ukraine and the complementarity of reforms. Working paper, LIKOS Centre for Transition Economics. Wolfson, S., Wakelin, D., Lewis, M., 2005. Football supporters’ perceptions of their role in the home advantage. Journal of Sports Sciences 23, 365–374.
O.R. Applications
Within-season dismissal of football coaches: Statistical analysis of causes and consequences Juan de Dios Tena
a,b,1
, David Forrest
c,*
a
b
Departamento de Economı´a, Universidad de Concepcio´n, Victoria 471, Concepcio´n, Chile Dipartamento di Economia, Impresa e Regolamentazione, Universita di Sassari, Via Torre Tonda 34, 07100 Sassari, Italy c School of Accounting, Economics and Management Science, University of Salford, Salford, M5 4WT, UK Received 20 September 2005; accepted 22 May 2006 Available online 20 July 2006
Abstract The paper examines the triggers for, and, consequences of, within-season dismissals of managers (head coaches) in the top division of the Spanish Football League during seasons 2002–2003 to 2004–2005. A major reason for directors deciding on dismissal is shown to have been concern that the club in question was in danger of demotion out of the division. This suggests that the clubs hoped to bring about short-term improvement in performance by changing manager. Employing an ordered probit model of match results, we demonstrate that an improvement in results tended to be achieved but only in home matches. The finding vindicates the decisions taken by club directors who dismissed their managers and implies that appeasing fans can have on-the-field benefits. It is consistent with the importance attributed to crowd support in the literature on home advantage in sports. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Football; Managerial change; Scapegoat hypothesis; Ordered probit; Home advantage
1. Introduction In most sorts of organisation, there is a natural time for changing leadership. In a political party, it may be after an election defeat. In a business, it may be when the contract of the Chief Executive Officer (CEO) comes up for renewal or when he reaches a certain age. In a sports club, it is certainly at the end of a season. Then a new manager will *
Corresponding author. Tel.: +44 161 295 3674. E-mail addresses: [email protected], [email protected] (J. de Dios Tena), [email protected] (D. Forrest). 1 Tel.: +56 41203204.
have time to train his players to adapt to his strategic approach and to recruit new personnel where appropriate. This mitigates any tendency for disruption to productivity to be associated with the replacement of the old regime. Despite the arguments that there is benefit to switching management only at convenient predetermined times for which preplanning is possible, organisations occasionally dismiss their leadership with unconventional timing. Bad opinion poll ratings may lead to a no-confidence motion on the leader of a political party. Falling market share may induce a board of directors to dismiss their CEO. Similarly, faced with a series of losses on the field, the owners
0377-2217/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2006.05.024
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of a sports team may decide to dismiss the manager (or head coach, as he is termed in many countries). It is of interest whether decision takers typically achieve their goals when they act in this apparently precipitate way, which runs the risk of disruption to the organisation and which may involve high direct costs in the form of compensation payments for termination of contract. It may be that decision takers correctly assess when a situation is sufficiently serious and sufficiently attributable to the behaviour of the current leadership to justify immediate dismissal. On the other hand, they may often act out of panic or may be indulging in scapegoating to appease stakeholders such as party members, shareholders or fans of the team. In the literature on managerial change in firms, there is general agreement that poor prior performance is correlated with the enforced departure of management (see, for example, Groves et al., 1995) and some studies point to the policy tending to be successful (Weisbach, 1988; Groves et al., 1995; Warzynski, 2000; Hudson et al., 2004). However, difficulties arise in selecting which indicators of firm performance, over what time period, are relevant in testing. Where stock market performance was the yardstick, Warner et al. (1988) and Cools and van Praag (2003) found no evidence that managerial change induced better performance. We examine the issue here in a sports context. We focus below on 20 within-season involuntary changes of manager in the Spanish Premier (football) League during the seasons from 2002–2003 to 2004–2005. We show that a significant predictor of dismissal of management was the club falling into the part of the standings where demotion from the division occurs at the end of the season. It is fair, then, to characterise dismissal in this context as a response to a situation where the club urgently needs league points. At this end of the standings, a small difference in points accumulated through a season can make a very substantial difference to the finances of the club as those forced into the immediately inferior division will suffer a major loss in revenue earning capacity. Compared to the literature on the impact of managerial change in business generally, there is the advantage here of no ambiguity about what needs to be measured to assess whether sacking managers has been a successful strategy: we need to model the impact of managerial change on on-the-field outcomes (which themselves are clear cut and not open to massaging by discretionary accounting).
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In Section 2, we review relevant studies in the sports economics literature. In Section 3, we model the determinants of managerial change. Section 4 employs an ordered probit model to assess the short-term impact of managerial change on team performance in home and away matches. Section 5 offers a more detailed analysis, with calculation of marginal effects for a team facing the threat of relegation. Section 6 concludes. 2. Previous sports studies In their comprehensive text on The Economics of Football, Dobson and Goddard (2001, Chapter 6) include a review of studies, in North America and elsewhere, of the impact of change of coach on team performance. Much of the work looks at whether team output improves in the season(s) following managerial succession but this is more relevant to the assessment of between-seasons change of manager. Here our concern is with whether dismissal of a manager during the season (and a crisis) has typically reaped short-term dividends. We refer therefore only to those studies which relate management change to subsequent results in the same season. Gamson and Scotch (1964) were early contributors to the literature. Their tests were inconclusive: they reported that win-ratios improved in 13 of the 22 cases of within-season managerial change observed in Major League Baseball between 1954 and 1961. For American Football, Brown (1982) reported a number of tests that allowed him to compare the subsequent win-ratios of teams which had performed badly early in the season and fired their coach and a control group of teams with similarly bad records but which had continued under the same management. Recovery from on-the-field slump was similar as between the two groups. The finding was suggestive that firing the coach was irrelevant to the resolution of the slump in results; but we would point out that a conceivable alternative explanation might be that club owners could correctly distinguish between slumps being attributable to bad management and bad luck and that the first group of teams may not have recovered at all without the crisis response. In soccer, Audas et al. (1997) for English leagues, and Bruinshoofd and ter Weel (2003) for the top division in The Netherlands, compared the recovery of teams that had sacked the manager during a slump with that of those that had not. In each case,
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the recovery rate of the first group was actually worse than that of the control group, casting further doubt on the efficacy of a dismissal strategy. However, the same caveat concerning selection bias again applies: the boards of clubs that left their manager in place may have been just those who (correctly) anticipated that the team’s fortunes would soon turn around. A more recent approach is based on econometric modelling of individual match results. This avoids issues of how to select a control group and takes into account the quality of opposition a team faces before and after managerial change. Results have, however, again failed to vindicate decisions by club directors to fire their coach. Koning (2003) modelled team rankings and individual match results in the Dutch Premier (football) League. The model for determining match results had as dependent variable the difference in goals scored between the two teams in a match. Explanatory variables were quality indicators of the two teams and a dummy to reflect which was playing at home. The parameters of the model were permitted to vary with change of manager. Koning analysed five seasons of data from the Dutch Premier League. In this time, there were 28 coaches fired of which four were terminated during the first season, 1993–1994. For 1993–1994, Koning found a significant change of coach effect, with improvement detected in team quality and in the extent of home advantage. However, the result was not replicated for any of the four following seasons (though home advantage improved following dismissals in 1996–1997) and Koning concluded as follows: ‘‘firing a coach occurs too often. Since it is not clear that the results on the field improve after a change of coach, it is likely that the board of a team intervenes for other reasons. It is likely that fan and media pressure are also strong determinants of the tenure of a coach’’. Recently, a popular approach amongst economists in the field of modelling match results has been ordered probit or logit with three ranked outcomes, home win, draw and away win (see, for example, Kuypers, 2000; Forrest and Simmons, 2000; Goddard and Asimakopoulos, 2004). Work reported by Audas et al. (2002) and Dobson and Goddard (2001, Chapter 6.8) adapts a very detailed ordered probit model to address the issue of whether match outcomes are influenced by recent changes in manager. This is achieved by adding to the regressors variables that reflect whether one of the teams has
recently changed manager: there are separate dummies for whether it is the first or second (and so on) game since the change in regime. Total impact is measured by summation of the coefficient estimates on these dummy variables. The finding is that managerial change tends to have a negative effect on team performance in the remaining weeks of the season, further evidence for the scapegoating hypothesis of managerial change: during a poor run of results, directors may dismiss the coach to appease club supporters rather than in any real hope of short-term amelioration of the club’s plight. Although scapegoating has been associated in the sports literature with the need to ‘‘placate disgruntled fans’’ (Dobson and Goddard, 2001, p. 265), this abstracts from the possibility that the latter will itself be a route through which change in management can lead to improved performance on the pitch. Players talk of the importance of fans ‘‘getting behind the team’’ and this belief, that the enthusiasm of the crowd matters, that it affects the performance of the team and perhaps the decisions of the referees, is reflected in academic analysis of the sources of home advantage. If firing the manager rekindles the enthusiasm of a crowd grown sullen from repeatedly adverse results, the policy may have a payoff in terms of league results even if it may be characterised in one sense, that of punishing an innocent man, as ‘‘offering a scapegoat’’. There is a hint of this in Koning’s finding that, in two of five seasons analysed, home advantage strengthened for those clubs that had changed manager in the Dutch League. To test the hypothesis further, we will make a distinction, in our empirical analysis below, between impact of managerial change on home and away performance. In contrast to some previous studies, our analysis will control for the quality of opposition faced in matches played subsequent to a change of manager. First though, we present statistical analysis of what triggered managerial change in our context of Spanish football. 3. Causes of managerial change The Spanish Premier League is structured in the same way as, for example, that in England to the extent that there are 20 teams that play each other on a home-and-away basis to give 38 rounds of matches (380 individual games). Three clubs are demoted to the immediately inferior division at the end of each season, to be replaced by three clubs promoted from that division.
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Our sample covers seasons 2002–2003 to 2004– 2005. There were 20 involuntary changes of manager during this period. We exclude from our analysis two voluntary departures, from Villarreal following the 26th round of matches in 2003–2004 and from Real Madrid after the third round in 2004–2005. Of course, whether resignations are truly voluntary may, in some circumstances, be ambiguous, since a coach may be willing to leave ‘‘by mutual consent’’ given adequate compensation for the shortening of his contract. However, for the two particular cases at Villarreal and Real Madrid, we were satisfied, after an examination of contemporary newspaper reports, that the terminations were initiated by the coaches themselves. Neither of them sought any financial compensation for early departure. The frequency of within-season dismissals in Spain appears to compare closely with that in the top division in English football: Dobson and Goddard (2001, p. 275) report there to have been 156 such terminations in 27 seasons up to 1998–1999, a rate of 5.8 per season. In the slightly smaller Dutch Premier League, Koning (2003) tabulates experience during five seasons when an average of 5.6 managers per season were fired. The relative frequency with which Spanish coaches are dismissed is therefore of a similar order of magnitude as in other European leagues. We constructed a probit model to account for within-season dismissal of the coach. The variable to be explained took the value one if the coach of team i was dismissed between match round t 1 and match round t. With three seasons’ data, and with the first round of each season excluded, there were 2220 observations. Relevant information, for example, on match scores, league positions and club budgets, were obtained from the newspaper websites, www.elmundo.es and www.marca.es. Our period of analysis was constrained by the limits on the period for which some of these old data continue to be displayed on the websites. Explanatory variables in the probit specification included the time of season (represented by the match round number and its square) and a measure of ‘‘managerial efficiency’’ (the number of places by which a club’s current position in the League is superior to its ranking in terms of its (wage) budget). There were also dummy variables set equal to one to signify, respectively, that the team was in a relegation position in the standings, that the team had lost its match in round t 1, and that the team
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had already dismissed a manager in the current season. Variables with which we experimented in an earlier specification but which were ultimately excluded on grounds of extreme non-significance included: dummy variables for newly promoted teams and for teams playing in the European Champions League; size of club (wage) budget; an interaction term equal to ‘‘efficiency’’ multiplied by the relegation zone dummy; and, to represent club culture, the number of within-season dismissals of the coach in the preceding three years. Some of these variables had appeared to be important from inspection of simple correlations with the incidence of dismissal. For example, the mean budget for clubs which did dismiss their manager in a given season was much lower than for clubs which did not (€33.24m compared with €58.65m). However, multivariate analysis reveals that low spending per se was not the ‘‘cause’’ of dismissals. Rather, the threat of relegation proved to be the principal trigger to change manager and, naturally, this threat is most commonly faced by the lowest spending clubs, hence the correlation. In respect of certain other covariates that failed to be significant, it should be noted that much less than one percent of the observations were positive: it is then to be expected that some plausible variables will fail to account, in a statistical sense, for the pattern of dismissals. Results from our final specification are displayed as Table 1. In the result on managerial ‘‘efficiency’’, there is evidence that boards of directors were realistic to the extent that they assessed coach performance by considering league position relative to what was to be expected given wage expenditure. Generally, the raw data indicate that dismissals typically occurred at clubs, which were underperforming relative to the size of budget. The mean value of the efficiency variable at the time of dismissal was 3.85. Often this improved subsequent to a dismissal, so that the mean value of ‘‘efficiency’’ at the end of the season (or at the next change of manager if sooner) at clubs which had fired was 2.18. Thus, on the face of it, changing manager tended to be a successful strategy; but this result cannot be considered definitive without econometric testing reported below. A key trigger of deciding to dismiss the coach appears to be that a team is in one of the relegation places in the standings. The ‘‘relegation’’ dummy, and another used to signify that a team had lost
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Table 1 Probit results: Manager dismissed before match t Coefficient Match round number Square of match round number Dummy: team lost last game Dummy: club is in relegation zone Managerial ‘‘efficiency’’ Dummy: ‘‘failing top team’’ Dummy: club has already dismissed a manager in the current season
0.095 0.002 0.525 1.025 0.046 0.584 0.771
Standard error 0.046 0.001 0.203 0.226 0.024 0.378 0.278
t
p 2.06 1.72 2.58 4.54 1.96 1.55 2.78
.039 .086 .010 .000 .050 .122 .005
Number of observations: 2220. Pseudo-R2: 0.21.
its most recent fixture, attracted highly significant, positive coefficient estimates. On the other hand, results from fixtures two and three matches ago (entered individually or represented by categorical variables representing successive defeats) did not prove significant and are omitted from our model as reported; this indicates that it was the relegation threat that was key rather than a run of poor results per se. Therefore, we may generalise that the threat of relegation is a strong proximate cause of managerial dismissal; but if the team has at least not suffered defeat in its most recent match, the manager is likely to be given another chance. So far as timing is concerned, the coefficient estimates on the round number of the next match and its square, which give a turning point of 26.04, imply that directors are most likely to act between the 25th and 26th matches of the 38 match schedule. If a club is in the relegation zone at this stage in the season, it is safe to say that relegation is a distinct possibility: but there are enough games left that a new manager might have time to engineer an escape. The situation described by our result appears similar to that in English football. Dobson and Goddard (2001, p. 273) link the record high number of dismissals across the English leagues in season 1994–1995 to a restructuring of divisions that meant that, in that year, more clubs than usual would be relegated. Relegation is the worst development possible from the perspective of fans and is also likely to cause financial problems for the owners. It is not surprising, therefore, that firing the manager in-season can be characterised as being often a response to the crisis of possible relegation. If the manager can be blamed for the club’s plight, the situation cannot be righted by waiting to the end of the season to dismiss him because, by then, the club may be out of the division. The manager in such a case is in a similar position to the chief executive
of a corporation, which is not merely delivering disappointing results but faces the possibility of actual liquidation. It might be speculated that, near the top of the standings, there are also especially severe financial consequences to underperformance relative to sums committed to player salaries. While in the middle rankings of the division, it will not make much difference financially if the club gains a few more or less points, amongst the leading clubs these points might determine success or failure to qualify for the highly lucrative European Champions League. We therefore included an additional variable related to the performances of three leading clubs, Barcelona, Real Madrid and Valencia. These are the clubs with the highest budgets, the only clubs to have won the League Championship in the last five years and the only clubs, which would regard playing in the Champions League as routine. The variable (failing top team) takes the value one whenever one of these clubs is, at the time of the observation, outside the qualifying zone for the Champions League. There is some evidence, consistent with the notion of nonlinear financial consequences, that these clubs may indeed be more ready to dismiss the coach than would be expected simply from the value taken by the managerial ‘‘efficiency’’ variable. However ‘‘failing top team’’ is not statistically significant at conventional levels (p = .12). This is unsurprising to the extent that a large majority of dismissals observed are in fact at clubs in or immediately adjacent to the relegation zone. This description applied to 17 of the 20 cases of dismissal in our data period. The trend continues. At the time of writing, there have been eight more dismissals subsequent to our data period and seven of the clubs concerned were in, or close to, the relegation zone. If relegation is the dominant cause of instigating managerial change, it follows that the effectiveness
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of the policy should be judged in terms of the shortterm impact on results and therefore the accumulation of points for survival. This we investigate in the next section. 4. Impact of managerial change on subsequent results We present now the results from an ordered probit model to account for match outcomes of Spanish Premier League fixtures played in the seasons from 2002–2003 to 2004–2005. The first three rounds of matches each season were excluded from the sample because league positions were used as regressors and these are likely to contain a lot of noise when based on only one or two games played by each team. Outcomes were ordered across three categories, from home win (2) through draw (1) to away win (0). Our focus variables were dummies to capture recent managerial change. Controls included were the current league positions, where 1 is top and 20 bottom, of the home and away teams and the most recent home result of the home team, represented as win = 2, draw = 1 and loss = 0 (the most recent away result of the home team and the most recent home or away result of the away team were insignificant in preliminary estimation). The two league position variables attracted very strong coefficients of expected sign. More surprisingly, the coefficient on the most recent result of the home team was significant and negative. This presumably reflects the apparent difficulty in football of putting together sequences of wins. Like Audas et al. (2002) we represent recent managerial change with a series of dummy variables according to whether a team was playing its first or second (and so on) match under new management. The particular managerial change variable defined by Audas et al. took the value +1 if the home team had a new manager and 1 if the away team had a new manager. This imposed a restriction that any impact on performance will be the same in home and away matches. For our study of Spain, we do not impose this restriction because we hypothesise that the impact of managerial change will work partly by influencing degree of crowd support for the home team. Accordingly, we have separate dummy variables to indicate that either the home or away team had a new manager. The variable HOMENEWONE indicates that the home team in a match was playing its first home fixture following a new appointment (this may or may
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not be the first game since the dismissal of the previous coach, depending on whether there is a delay in announcing a replacement). Variables HOMENEWTWO to HOMENEWSEVEN indicate that the home team was playing its second or third (and so on up to seventh) home match since the arrival of a new coach. A similar set of seven dummy variables captures similar information for the away club (for example, AWAYNEWONE is equal to one if the away team is playing its first away game following regime change). We restricted investigation to 14 rounds of matches (seven home, seven away) because of the number of dismissals that occurred with fewer than 15 matches remaining in the season. Results are displayed as Table 2. We consider first the impact on the match outcome of the home team having recently changed manager. The estimated coefficients on the manager change dummies, HOMENEWONE to HOMENEWSEVEN, are positive in every case, indicating that the information that a home team is playing under a new coach raises the probability that it will win the game. They are statistically significant in the cases of the first and second home matches under new management. Thereafter, however, none of the coefficient estimates is individually significantly different from zero at the 5% level. This may indicate that any positive effect on home performance is short-term. On the other hand, given the amount of ‘‘noise’’ in the outcomes of football games, it is unsurprising if no statistically significant impact is identified when attention is confined to the nth match in the tenure of a new coach, particularly since some dismissals in our data set occurred with as few as two home games remaining (thus the number of cases where the variable equals one falls below 20 from HOMENEWTHREE onwards). We therefore tested whether there was any effect on performance in the group of games from the third to the seventh home match: a Wald test was employed to evaluate whether the sum of the five individual coefficient estimates was different from zero. There was some indication albeit weak (p = .178) that a residual effect from new management was still felt in this run of games. The crucial question to a club is whether a positive effect on performance emerges over the remainder of the season following replacement of the coach. For home games, we seek to answer this question by summation of the coefficient estimates on HOMENEWONE to HOMENEWSEVEN. The sum here is +2.245. Whether this is significantly
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Table 2 Ordered probit results on match outcome (away win = 0, draw = 1, home win = 2) Coefficient Home position Away position Result of home team’s last home match HOMENEWONE HOMENEWTWO HOMENEWTHREE HOMENEWFOUR HOMENEWFIVE HOMENEWSIX HOMENEWSEVEN AWAYNEWONE AWAYNEWTWO AWAYNEWTHREE AWAYNEWFOUR AWAYNEWFIVE AWAYNEWSIX AWAYNEWSEVEN
0.077 0.062 0.103 0.649 0.600 0.171 0.151 0.168 0.369 0.137 0.438 0.458 0.118 0.146 0.166 0.224 0.235
Standard error 0.007 0.007 0.047 0.259 0.273 0.271 0.282 0.316 0.322 0.349 0.309 0.294 0.321 0.297 0.365 0.324 0.313
t
p 10.37 8.87 2.19 2.50 2.20 0.63 0.53 0.53 1.14 0.39 1.42 1.56 0.37 0.49 0.45 0.69 0.75
.000 .000 .029 .012 .028 .529 .593 .595 .253 .694 .156 .119 .714 .622 .650 .490 .453
Number of observations: 1050. Pseudo-R2: 0.10.
different from zero may be evaluated by a Wald test. In this case, the null hypothesis of no effect over seven home matches is decisively rejected (p = .010). The result is not dependent on the choice of seven for the number of home games over which the impact of managerial change was to be measured. It was impractical to extend the horizon beyond seven home games because of shrinking sample size (the season lasts for 19 home games and some dismissals occur with more than 12 already played). However, Table 3 shows the cumulative impact over shorter runs. Whatever the time horizon considered up to seven home games, there is an effect on performance that is significant at about, or better than, the 1% level. We tested the robustness of our findings to a respecification that replaced current home and away league positions with information on the teams’ performances over a full season, i.e., points gained over their preceding 38 matches. Using an index of club performances over a longer period than the season to date might be argued to defend yet more strongly than in the first model against the possibility that mean reversion effects (an improvement in results following a poor run) could be misinterpreted as real effects from dismissing the coach. Account was taken of whether points were won in the current or previous season and an adjustment made where previous season points had been awarded while the team was playing in the Second Division. Data from the previous season have been found to be sig-
Table 3 Cumulative impact of a new manager (away win = 0, draw = 1, home win = 2) Coefficient HOMENEWONE HOMENEWTWO HOMENEWTHREE HOMENEWFOUR HOMENEWFIVE HOMENEWSIX HOMENEWSEVEN AWAYNEWONE AWAYNEWTWO AWAYNEWTHREE AWAYNEWFOUR AWAYNEWFIVE AWAYNEWSIX AWAYNEWSEVEN
0.649 1.249 1.420 1.571 1.739 2.108 2.245 0.438 0.020 0.138 0.284 0.449 0.674 0.909
p .010 .001 .004 .007 .011 .007 .010 .157 .963 .803 .659 .553 .425 .324
Number of observations: 1050. Pseudo-R2: 0.10.
nificant in accounting for results in English football (Dobson and Goddard, 2001). In analysis of the English game, distance between the stadia of the two clubs has also been found to play a role and accordingly we also include this in our alternative and more information-rich model. Table 4 presents the results of the estimation. HPTSCURR is total League points achieved by the home club in the season to date; HPTSPREV is total League points achieved by the home team in its final (38-n) matches of the previous season,
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Table 4 Ordered probit results on match outcome (alternative model) (away win = 0, draw = 1, home win = 2) Coefficient Distance HPTSCURR HPTSPREV HPTSPREV * HPROM APTSCURR APTSPREV APTSPREV * APROM Result of home team’s last home match HOMENEWONE HOMENEWTWO HOMENEWTHREE HOMENEWFOUR HOMENEWFIVE HOMENEWSIX HOMENEWSEVEN AWAYNEWONE AWAYNEWTWO AWAYNEWTHREE AWAYNEWFOUR AWAYNEWFIVE AWAYNEWSIX AWAYNEWSEVEN
0.0009 0.043 0.004 0.002 0.041 0.009 0.003 0.051 0.548 0.400 0.110 0.102 0.200 0.433 0.267 0.546 0.406 0.089 0.112 0.067 0.278 0.157
Standard error 0.011 0.004 0.005 0.003 0.004 0.005 0.003 0.046 0.260 0.270 0.274 0.284 0.319 0.326 0.352 0.311 0.223 0.318 0.297 0.366 0.330 0.318
t
p 0.01 9.56 0.78 0.57 9.58 0.02 1.03 1.12 2.10 1.48 0.40 0.36 0.63 1.33 0.76 1.76 1.38 0.28 0.38 0.18 0.84 0.50
.994 .000 .436 .570 .000 .986 .305 .264 .035 .139 .689 .720 .529 .184 .448 .079 .167 .779 .706 .854 .399 .620
Number of observations: 1050. Pseudo-R2: 0.09.
where n is the number of games played so far in the current season; HPTS PREV * HPROM is a slope dummy to allow a different coefficient for teams that had been promoted from the division below at the end of the previous season. Similar controls for past performance by the away team are defined symmetrically with those for the home team. The results from this alternative model indicate that it is in fact less effective than our main model in accounting for the set of match outcomes, with distance and results from the previous season failing to add statistically significant explanatory power. The lack of role for geographical distance between the home bases of the two clubs is interesting in that it contrasts with results from English soccer. The explanation may be that absolute distances in Spain tend to be much larger. Players in the top division are likely to be transported by air so that fatigue and disruption for visiting teams will differ little according to the distance involved; and the presence of travelling supporters, whose numbers may influence performance on the field, is much more limited across the League than in a small country like England. As in the main model, we find a positive effect on home performance following a change of manager. Estimated coefficients on all seven ‘‘home new’’
dummy variables are positive. While only the first is individually significant (p = .035), the sum over seven games is positive and significant with a p-value of .019. In further experimentation, we repeated the analysis with an additional covariate, a dummy variable set equal to one (minus one) if the home (away) team finished the game with more players than its opponent because of sending(s)-off. The variable proved highly significant in accounting for match results though there is a problem of potential endogeneity if dismissals by referees are correlated with the scoreline at the time of an incident. Therefore, we do not report the estimates here but note that the results on the managerial change variables were essentially unchanged: the impact of a change in manager measured over seven home games was positive with a p-value of .003. There is therefore robust evidence from these three seasons of experience in the Spanish Premier League that sacking the coach produced tangible results at home in the following weeks. Note that this does not imply that dismissal is a good option for all clubs in urgent need of league points since, if boards of directors possess even limited powers of discrimination, the set of clubs that fired the coach will be biased towards those in a situation
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where such an action was most likely to yield results (for example, these were cases where the club’s plight was least attributable merely to bad luck or cases where fan support had been most dangerously eroded). What is being tested here is rather whether clubs that opted for a new manager acted wisely. Our findings were different in respect of away performance. In both our main and our alternative models, the coefficient estimates on the dummy variables for a new away team manager indicated a negative effect on performance in the first away match though this was not statistically significant; thereafter, signs point to a positive effect but none of the coefficient estimates was close to being statistically significant. We summed them to assess cumulative impact over seven away matches. We found no significant difference in performance in this group of away matches following management change (p = 0.324; p = .541 in the case of our alternative model) and this finding was robust to choosing alternative lengths of sequence than seven (Table 3). A new coach appeared to have no effect on the set of away match outcomes following his appointment. A caveat to this finding is that there was some weak indication of improved away results if the first away game was excluded from consideration. The contrast between the results for home and away performance suggest that any gain in points achieved by those clubs that fired their manager was not primarily the result of reversion to mean effects or to technical improvements introduced by a new coach. These factors would have been reflected equally at home and away. It is though consistent with the hypothesis that, where a team’s run of results provokes fan disillusion, there may be real effects from ‘‘doing something’’ if the fans respond by supporting their team more enthusiastically at the home stadium. Of course, the support a team receives at a home match could depend both on the number of fans attending and on how positive their attitude is. In the present case, there is no evidence that more supporters purchased tickets when a new manager arrived. Comparing the three home games before and after the arrival of a new coach (two matches where the dismissal was so late in the season that only two home games remained), 10 clubs experienced an increase and 10 a decrease in attendance. Further, in case these data were unduly influenced by which teams happened to be the visitors before and after changes in coach, we also estimated a conventional attendance demand function for the whole
sample of 1050 matches, with new manager dummies included as additional regressors. Again, there was no evidence of a relationship between attendance and the appointment of a new coach: none of the coefficients on the variables HOMENEWONE to HOMENEWSEVEN was significant. Any positive effects on home performance when a new manager arrives appears, therefore, to be attributable not to crowd size but to crowd enthusiasm. Evidence that crowd enthusiasm, as opposed to crowd size or density, affects match outcomes is limited in the literature on home advantage, the issue being hard to test because of the difficulty in measuring the emotional atmosphere in a stadium. However, Nevill et al. (2002) employed an experimental method. Senior English referees were shown films of incidents in games with crowd noise either included or silenced. Their opinions were shown to run more in favour of the home team when they were exposed to the noise of the crowd and such bias could of course influence match outcomes. The potential for officials’ decisions, and perhaps therefore match results, to be influenced by the crowd received further support from Dohnen (2005). He found evidence of referee home bias in German stadia without moats but not in stadia where the crowd was set back behind a moat. Whether or not performances of players themselves respond to an increased level of enthusiasm from a crowd of a given size is an issue yet to be resolved in the home advantage literature though findings that measures of home advantage at the team-specific level are unstable are consistent with the notion that fans can sometimes help and sometimes hinder their team (Smith, 2005). Football supporters certainly believe their behaviour in the stadium is important. Wolfson et al. (2005) surveyed 461 English fans and established that by far the most important factor behind the phenomenon of home advantage was, according to those who attend games, crowd support. On the other hand, in openended responses, many noted the potential of a discontented home crowd to harm their team, for example, ‘‘Home players in a poor team can suffer at home due to pressure of disgruntled supporters’’ and ‘‘Home fans can in fact distil fear and show frustration to their own team . . . home advantage has gone and the players feel the pressure and tensions between their home supporters’’. Our findings are at least consistent with these fan beliefs. The crowd is likely to be disaffected when a team is facing relegation; but a new manager potentially repre-
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bulk of the expected effect relates to the first two games). Note that the sum of marginal effects on draw probabilities is not statistically significant, so we attribute no extra points from that source. A gain of two to three League points is, of course, modest but this is a typical margin separating the last team safe from relegation at the end of the season from those below it. A gamble that a new coach might save the team from relegation by improving home results is therefore by no means to be viewed as reckless. We also computed (but do not report) marginal effects of away team manager change on away win and draw probabilities in the case where an away team lies 18 in the standings (the home team was assumed to be mid-table and to have had an ‘‘average’’ result in its last home game). The effect on win/ draw probabilities over seven away matches proved to be far from statistically significant. We therefore attribute no additional points gain to managerial change in respect of away fixtures. We investigated the sensitivity of our estimates of expected gain in points earned at home to the toughness of the schedule faced by a club. We recalculated marginal effects for the case where opponents were at the upper quartile (ap = 5.25) rather than in the middle (ap = 10.5) of the League table. With such a pessimistic scenario (and other assumptions as before), the point estimate of a home win is .169 and that of a draw .270. In these circumstances, there was a statistically significant positive effect on both the expected number of home wins and the expected number of draws. Combined, these yielded an expected gain in League points of 2.24 over seven
sents a new start and fans may rally behind him. This could account for the improvement in home performances identified by our analysis. 5. Marginal effects In this section, we attempt more precise estimation of the benefits that accrued to those clubs that sacked their manager by calculating the marginal effects from managerial change, evaluated at values for variables that reflect typical circumstances of clubs facing the threat of relegation. Table 5 presents estimates of marginal effects on home win and draw from the ‘‘main’’ ordered probit model whose results were discussed in the previous section. They are evaluated with home position = 18, reflecting the situation of a club which is in the relegation zone. It is presumed only to have drawn its last home game (result = 1) and to be playing against a mid-table club (away position = 10.5). All managerial change variables are set to zero. With this configuration of values of the regressors, the point estimate of the probability of a home win is .258 (and that of a draw .304). The effect of changing manager on the team’s expected number of home wins in the following seven home matches is given by the sum of the seven marginal effects, which is +0.807. In Spanish football, as is normal in Europe, three league points are awarded for a win and one for a draw. Change in manager is therefore expected to raise the number of ‘‘win’’ points earned from this group of games by approximately 2.42 points. This is equivalent to 0.35 points per match (though the
Table 5 Marginal effects On home win dy/dx
On draw se
t
dy/dx
se
t
Home position Away position
.025 .020
.002 .002
15.02 7.99
.005 .004
.002 .001
2.85 3.52
Result of home team’s last home match HOMENEWONE HOMENEWTWO HOMENEWTHREE HOMENEWFOUR HOMENEWFIVE HOMENEWSIX HOMENEWSEVEN
.033 .241 .222 .058 .051 .057 .131 .046
.015 .102 .107 .096 .099 .112 .123 .122
2.20 2.37 2.07 0.61 0.52 0.51 1.07 0.38
.007 .014 .009 .008 .008 .008 .007 .007
.004 .028 .027 .008 .009 .009 .013 .012
1.80 0.50 0.34 1.06 0.83 0.93 0.53 0.59
Marginal effects, calculated from the ordered probit model reported in Table 2, are evaluated at: home position = 18, away position = 10.5, result of home team’s last home match = 1 (draw), all other variables = 0.
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League matches. Our estimate of benefit was therefore lowered only slightly for a quite extreme assumption about the quality of opponents in remaining matches. 6. Conclusions Sport often offers a laboratory for the testing of general ideas about business and economic behaviour. In the case of changes of management in a crisis, and whether they typically improve performance or merely reflect scapegoating, professional league football is an appropriate setting for testing hypotheses: it is very public information when a manager is fired; given the typical circumstances, the aim of the policy is very clearly defined; and the extent to which the aim is met is readily measurable in the league standings. Two previous studies of European football leagues found little evidence that clubs dismissing their manager in mid-season benefited in terms of results though, in The Netherlands in some seasons, change of coach appeared to improve the extent to which clubs exploited home advantage. For the case of Spain, we have examined the impact of changing coach on subsequent match results. New coaches appear to have made a modest positive difference to match results in the shortterm; but this effect was derived entirely from an improvement in results at the home stadium. No change in away performance, measured over a run of games, was detected. We are mindful that evidence from a relatively small number of seasons may not generalise to lengthier periods (Koning, 2003); but our results suggests that future researchers should distinguish carefully between home and away results when assessing the effects of manager dismissal. The implication from our evidence is that a new coach does not typically bring technical solutions to the weaknesses of the team since away performance is little altered. That home results nevertheless improve suggests a role for crowd support in the determination of match outcomes. Clubs typically fire the manager when faced with the threat of relegation and in those circumstances supporter morale is liable to be low. Perhaps, to appease them, the directors offer a scapegoat; but in this context ‘‘scapegoating’’ may not be mere gesturing, still less irrational, since, as discussed in the literature on home advantage, support from the crowd can be an input in the process of the team producing wins.
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