One of the most important decisions to be taken by professional football teams is choosing an adequate manager. This decision should be made taking into account the manager’s performance in previous seasons, either in the current team or in other teams. However, it is not straightforward to calculate the performance of the managers given that in most leagues the quality of the players is very different between teams.
One alternative to evaluate the performance of a particular manager in a league is to compare the number of points actually achieved by the team with the expectations of the team. If a team has obtained better results than the expectations, this would be due to the good performance of the manager. Similarly, if a team has obtained worse results than expected, this would be due to a poor performing manager. One way to obtain the expectations for a team is using betting odds.
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 on whether 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 organised on 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 for 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 its matches) and the product of the number of matches and three (i.e. the team wins all its matches). The graph below shows the probability that betting companies attributed to FC Barcelona of getting each of the possible number of points by the end of the 2012/13 season. The red vertical line indicates the actual number of points achieved by the club in the season.
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 the teams, in the sense than a value closer will reflect a better performance and a value closer to zero will reflect a worse performance.
The table below shows the mean, minimum and maximum efficiency for each coach among the studied seasons (from 2000/01 to the 24th match day of 2013/14). The most efficient coach has been Simeone, followed by Montanier. It is important to note that the current Manchester City manager, Pellegrini, is the most efficient coach among the subsample of coaches with four or more seasons. Mourinho and Guardiola are tied in a good position in the ranking, with Rafa Benítez, ex Liverpool manager, following.