On May 22th2015 Jose Mourinho was chosen as the Premier League Manager of the Season. Jose Mourinho have been the coach in the Chelsea and Chelsea has won the English Premier League. For sure it is a huge accomplishment, but, maybe it is not enough to be named with this award. It is well known that this kind of prizes used to reward the head coach of one of the strongest teams as it can be seen in either in the list of NBA coach of the year or in the list of World Soccer coach of the year. However, this kind of prizes should not be to one of the head coach of the best teams but to coach that has obtained the most given its rooster. An alternative to evaluate objectively the managers’ performance is to compare the actual results with those expected from betting odds. The probability of the three possible outcomes in a game (i.e., local victory, draw and away victory) is embedded in betting odds so that it is enabled to calculate the probability of getting each of the possible number of victories.
Odds for football matches offered in the betting market can be reconverted into probabilities for each possible result (home win, draw, away win). If the betting market were efficient, these probabilities would reflect the true probabilities of each event. Although there is no consensus in the literature whether or not betting odds are efficient, it seems that any inefficiency that arises is very small. Thus, the probabilities embedded in betting odds can be seen as true probabilities. The European domestic football leagues are generally organized in a double round robin basis, where each team plays against the other teams once at home and once away. Winning teams are awarded three points, a draw earns one point for each team, and the losing team earns no points. The final league ranking is made on the basis of points earned at the end of the double round robin.
Basic probability theory tells us that the joint probability of two independent events (e.g., a victory of the same team in two different football matches) equals the product of their probabilities.Using this simple formula for all possible combinations of match results of each team, the probability of each team within a league obtaining a certain amount of points can be computed, that is, the density function of total points at the end of the season. The total points ranges between zero (i.e., the team loses all matches) and the product of the number of matches and three (i.e., the team wins all matches).
In particular, we use the betting odds from www.betexplorer.com, which provides the average of the betting odds from several bookmakers, in order to calculate the density functions for the 2014-15 season for English Premier League. The cumulative density function can be used to calculate the probability of getting more points than the actual result. The inverse of that probability can be viewed as an efficiency index for managers in the sense than the closer the value to one will reflect a better performance and the closer the value to zero will reflect a worse performance. The managers with higher efficiencies would be the teams that have overperformed the results expected from the odds. The overperforming could be due to luck or fortunate referees’ decisions, but the most plausible reason to overperform the expected results from the odds is good coaching, in the same way the underperformance of the teams could be due to injuries or bad luck but the most plausible is bad coaching. Thus, the efficiency index can be understood as a measure of the performance of the managers.
Table 1 shows the managers’ efficiency for each team in the season 2014/2015. It can be seen that the team most efficient was the Swansea, that obtained 56 points which is certainly a huge amount for the Swansea. It is followed by José Mourinho, but the second one in this list should not be named as the Premier League Manager of the season.
Table <!–[if supportFields]> SEQ Table * ARABIC <![endif]–>1<!–[if supportFields]><![endif]–>. Efficiencies of the managers/teams in the season 2014/2015
|
Manager
|
Team
|
Efficiency
|
Points
|
|
Garry Monk
|
Swansea
|
0.91
|
56
|
|
José Mourinho
|
Chelsea
|
0.85
|
84
|
|
Mark Hughes
|
Stoke City
|
0.82
|
51
|
|
Keith Millen and others
|
Crystal Palace
|
0.76
|
45
|
|
Mauricio Pochettino
|
Tottenham
|
0.74
|
61
|
|
Sam Allardyce
|
West Ham
|
0.69
|
47
|
|
Arsène Wenger
|
Arsenal
|
0.68
|
72
|
|
Alan Irvine and othrs
|
West Brom
|
0.60
|
44
|
|
Ronald Koeman
|
Southampton
|
0.59
|
60
|
|
Paul Lambert and others
|
Aston Villa
|
0.55
|
38
|
|
Manuel Pellegrini
|
Manchester City
|
0.54
|
76
|
|
Louis van Gaal
|
Manchester United
|
0.54
|
69
|
|
Gustavo Poyet and others
|
Sunderland
|
0.50
|
38
|
|
Brendan Rodgers
|
Liverpool
|
0.37
|
62
|
|
Nigel Pearson
|
Leicester
|
0.33
|
38
|
|
Harry Redknapp and others
|
QPR
|
0.25
|
30
|
|
Steve Bruce
|
Hull City
|
0.24
|
34
|
|
Sean Dyche
|
Burnley
|
0.22
|
30
|
|
Roberto Martínez
|
Everton
|
0.21
|
47
|
|
Alan Pardew and others
|
Newcastle Utd.
|
0.18
|
36
|
Notes: elaborated using the betting odds from www.betexplorer.com
Teams are ordered by the efficiency level.
Hence, it was not fair the election of Mourinho as the Premier League Manager of the Season, instead Garry Monk should have been awarded.
Lastly, it is important to note that these calculations have been carried out taking into account only the English Premier League.
Julio del Corral Cuervo is Associate professor in Economics at the University of Castilla-La Mancha (Spain)