Spanish researchers analysed performance of Spain's football players and have come up with a mathematical method quantifying their productivity.
Research results, published in the European Journal of Sport Science, were based on data from the 2000/2001 to 2008/2009 seasons. The team of scientists said they had made use of Bayesian statistics - a statistics sub-discipline that expresses the true state of affairs in terms of degrees of belief. The method makes it possible to predict the number of goals each player will score, taking into account their individual qualities.
The researchers explained that the rate of players’ success in scoring goals depends on a few easily quantifiable factors. What matters most is the number of minutes or matches played, whether the player is a defender, midfielder or striker, and the quality of his team. The latter is measured by the team’s position in the league table.
"Other factors that are harder to measure can also influence performance, such as the individual characteristics of the player that make him different from all the rest," explained José María Pérez Sánchez, a University of Granada professor and co-author of the study. "With this, we can rank Spanish league players according to this factor of individual ability."
By looking at the number of goals scored by each player and comparing it with the number that would be expected of a footballer playing at the same time, in the same position and on the same team, researchers can mathematically evaluate players’ performance.
So how did the individual Spanish players stand in this assessment? Among defenders, the five best from top to bottom were Ezequiel Garay, Roberto Carlos, Campano, Cristian Álvarez and Larrazábal. Among midfielders Rivaldo, Robert, Luis Cembranos, Mark González and Mostovoi reached the best score. In the category of strikers Messi, Ronaldo Nazário, Makkay, Villa and Etoo made it to the top. After analysing each category separately, the researchers created complex ranking including players from all categories – the results were rather surprising.
"It is remarkable that strikers do not rank very high in terms of overall performance," said Pérez Sánchez. "In fact, apart from Messi, who ranks the sixth, the rest are below 15th place."
It is possible though, that the strikers are assessed more harshly, as the model takes into account the fact that strikers are naturally expected to score more goals. Subsequently, a goal scored by a midfielder or a defender has a greater value for the model, as scoring goals is not the primary objective of these players.