Journal of Mathematics and System Science 6 (2016) 409-414 D doi: 10.17265/2159-5291/2016.10.004 DAVID PUBLISHING Performance Assessment of European Football Teams: Using Stochastic Data Envelopment Analysis Model Basma E. El-Demerdash1, Ihab A. El-Khodary2, Assem A. Tharwat3, Eslam R. Shaban4 1. Department of Operations Research and Decision Support, Faculty of Computers and Information, Cairo University, Egypt. [email protected] 2. Department of Operations Research and Decision Support, Faculty of Computers and Information, Cairo University, Egypt. [email protected] 3. College of Business Administration, American University in the Emirates, UAE. [email protected] 4. Department of Operations Research and Decision Support, Faculty of Computers and Information, Cairo University, Egypt. [email protected] Received: August 27, 2016 / Accepted: September 26, 2016 / Published: October 25, 2016. Abstract: Data Envelopment Analysis (DEA) is a powerful mathematical optimization method widely used for measuring, evaluating and improving the performance of Decision Making Units (DMUs). These used in the various forms, such as hospitals, government agencies, educational institutions, air force, bank branches, business firms, sport teams and even people including the performance of countries, regions, etc. Recently DEA has been extended to examine the performance through the different sport types. In this paper, a Stochastic Input Oriented Data Envelopment Analysis (SIODEA) Model is conducted for measuring and evaluating the relative efficiency scores of football teams selected from different European countries during 2014/2015 season each with some of inputs are stochastic with normally distributed and recent inputs are deterministic and outputs, to shed light on the professional football teams performance. Keywords: Data Envelopment Analysis; Stochastic Variables; Efficiency Measurement; Football Efficiency; Performance Assessment. 1. Introduction game is between two sides either individuals or teams, each trying to win the opponent. Some sports allow a Assessment of performance is a crucial component draw game; others provide tie-breaking method, to of the management process in any type of organization ensure that there is a winner and a loser at the end of the (i.e. educational institutions, banks, business firms, game. A number of such two sided games may be hospitals, sport teams, etc.…). Today’s Sports life arranged in a game producing a champion. Many sports takes a very important place as a mean to stay fit and leagues make an annual champion by arranging games healthy along with the entertainment. Sports are in a regular sports season, followed in some cases by considered one of the types of competitive activity via playoffs. It has several various kinds such as football, casual or organized involvement, aiming to use, basketball, tennis, handball, volleyball, cricket, etc… maintain or enhance skills while providing Football is considered the most popular sport in most entertainment to players and spectators. Usually any countries around the world, especially in Europe for Corresponding author: Basma E. El-Demerdash, many reasons: Department of Operations Research and Decision Support, (1) In England 1863 was introduced, also in England Faculty of Computers and Information, Cairo University, Egypt. E-mail: [email protected]. the first football association was formed. 410 Performance Assessment of European Football Teams: Using Stochastic Data Envelopment Analysis Model (2) The famous top leagues in the world are the especially in football. Haas [6] used the traditional European leagues such as Spain, England, Italy, and DEA model to assess the relative efficiency of 20 Germany. English football teams in the 2000/01 season to (3) The most prestigious club competition in investigate how close to their potential English Premier European football and one of the most prestigious League Clubs play. Haas et al. [7] applied the tournaments in the world is considered the Champions deterministic CRS (Constant Return to Scale) and League. deterministic VRS (Variable Return to Scale) DEA In addition to, football sports is considered the most models for studied the relative efficiency of the widely followed sport. Since in over 200 countries German football teams in the 1999/2000 season. around the world, it is played by approximately 250 Barros and Santos [8] used deterministic DEA model to million players and over 1.3 billion are interested measure and analyze the relative efficiency of the people in football sports; a combined television Portuguese football clubs in their football league. audience of more than 26 billion watched football Barros and Leach [9] used DEA to assess the tournaments in 2010 [1, 2]. In European football there performance of English Premier League football clubs are many various forms of competitions which are from 1998/99 season to 2002/03 season. national (domestic) competitions including league García-Sánchez [10] applied the DEA deterministic and cup for each country and after finishing in a model to measure the offensive and defensive domestic league at top position, teams qualify for efficiency during the 2004/05 season for Spanish playing in the international competitions such as the football teams. Boscá et al. [11] used DEA model to Europa (UEFA) League and Champions League. evaluate and analyze the relative efficiency during Given the behavioral objectives set by the football seasons from 2001/02 to 2002/03 for Italian and clubs, it makes evaluating the efficiency of football Spanish football teams in order to detect differences teams is not an easy task. between their performance when they play at home and DEA as originally proposed by Charnes et al. [3], is away. González-Gómez and Picazo-Tadeo [1] applied a non-parametric frontier estimation methodology DEA technique to assess the sporting performance of based on mathematical programming for evaluating the Spanish football teams during seasons from 2001/02 to relative efficiencies and performance of a collection of 2006/07 at League, King’s Cup and European related comparable entities (called Decision Making competitions. Picazo-Tadeo and González-Gómez [12] Units or DMUs) in transforming multiple inputs into evaluated the relative efficiency of Spanish football multiple outputs. The objective of DEA approach is to teams using traditional DEA model from seasons assess the relative efficiency of each DMU in relation 2001/02 to 2007/08 in the League controlling, and for to its peers with the result as a classification of all the extra games played in the King’s Cup, Champions DMUs as either “efficient” or “inefficient”. Not only League and UEFA Cup. Hamidi et al. [13] utilized classifying the DMUs, but also determining the level of DEA technique for evaluating the relative efficiency of inefficiency and the corresponding amount to enhance the Iranian teams that played in their premier football the performance [4]. In addition to, the main DEA league. Kounetas [14] applied DEA deterministic advantage is that it does not require any prior model to examine the relative efficiency of Greek assumptions on the relationships between the input football clubs, taking into account an 8-year-period variables and output variables [5]. which has been divided into two intervals before the There are many publications that address the Euro 2004 victory from 2000 to 2004 and after the applications of DEA in different sectors of sports and Euro 2004 victory from 2005 to 2008. Performance Assessment of European Football Teams: Using Stochastic 411 Data Envelopment Analysis Model Zambom-Ferraresi et al. [15] evaluated the sports 2. Methodology performance during seasons from 2004/05 to 2013/14 The basic DEA model is developed by Charnes et al. via DEA approach for the teams that have participated [3] working under the concept of CRS, which means in the Union of European Football Associations, regardless of the size of the DMU, the outputs change Champions League. in direct proportion to the change in inputs, assuming From all the previous applications, and Kounetas that the scale of operations does not influence [14], we have reached to: efficiency. Then extended by Banker et al. [16] under (1) Most of the DEA applications that were related the concept of VRS, which means changing inputs may to determining the efficiency of football teams, it was not result in proportional changes in outputs, a obvious that those applications focused on comparing preferred DEA assumption. El-Demerdash et al. [4] teams within the same country, such as England, Spain, modified the standard DEA model to measure the Portugal, Brazil and Germany. relative efficiency in the presence of random variation (2) Little (if not none), was oriented on comparing in some of inputs from given outputs. In the Chance the efficiency of football teams from different countries Constrained Input Oriented DEA Model, the outputs with each other. A team’s efficiency measure could not are assumed to be deterministic while some of inputs necessarily depend only on the domestic league competition, but could also depend on its performance are stochastic variables and remaining inputs are deterministic variables, each stochastic input , in the domestic cup competition and/or the is normally distributed with mean and variance international league competitions based on the team’s level, e.g. Europa League and Champions League. and the relation between the same stochastic input