Munich Personal RePEc Archive Optimal football strategies: AC Milan versus FC Barcelona Papahristodoulou, Christos Mälardalen University/Industrial Economics January 2012 Online at https://mpra.ub.uni-muenchen.de/35940/ MPRA Paper No. 35940, posted 14 Jan 2012 21:22 UTC Optimal football strategies: AC Milan versus FC Barcelona Christos Papahristodoulou* Abstract In a recent UEFA Champions League game between AC Milan and FC Barcelona, pla ed in Ital (final score 2-3), the collected match statistics, classified into four offensive and two defensive strategies, were in favour of FC Barcelona (b 13 versus 8 points). The aim of this paper is to e,amine to what e,tent the optimal game strategies derived from some deterministic, possibilistic, stochastic and fu-- LP models would improve the pa off of AC Milan at the cost of FC Barcelona. .e words/ football game, mi,ed strategies, fu-- , stochastic, 0ash e1uilibria *2epartment of Industrial Economics, M3lardalen Universit , 43ster5s, Sweden7 christos.papahristodoulou8mdh.se Tel7 94621543176 1. Introduction The main objective of the teams’ managers is to find their optimal strategies to win the match. Thus, it should be appropriate to use game theor to anal -e a football match. Moreover, as alwa s with game applications, the access of accurate data to estimate the pa offs of the selected strategies is ver difficult. According to Carlton & Perloff (2005), onl a few mi,ed strateg models have been estimated in Industrial Economics. In addition to that, contrar to professional business managers who have a solid managerial, mathematic or economic education, team managers lack the necessar formal knowledge to use the game theoretic methods. Football managers, when the decide their most appropriate tactical move or strateg , rel more on their a-priori beliefs, intuition, attitude towards risk and e,perience. In a football game if we e,clude fortune and simple mistakes, b pla ers and referees as well, goals scored or conceived are often the results of good offensive andCor bad defensive tactics and strategies. There are a var ing number of strategies and tactics. As is well known, tactics are the means to achieve the objectives, while strateg is a set of decisions formulated before the game starts (or during the half-time brake), specif ing the tactical moves the team will follow during the match, depending upon various circumstances. For instance, the basic elements of a team’s tactics are/ which pla ers will pla the game, which tasks the will perform, where the will be positioned and how the team will be formed and reformed in the pitch. Similarl , a team’s strategies might be to pla a short passing game with a high ball possession, attacking with the ball moving 1uickl and pressing high up its competitors, while another team’s strateg might be to defend with a -onal or a man-to-man s stem, and using the speed of its fullbacks to attack, or pla ing long passes and crosses as a counter attacking (see http/CCwww.talkfootball.co.ukCguidesCfootball_tactics.html). Conse1uentl , both managers need somehow to guess correctl how the opponents will pla in order to be successful. 0eedless to sa , all decisions made b humans are vulnerable to an cognitive biases and are not perfect when the tr to make true predictions. 0ot onl the number of tactics and strategies in a football match is large, their measures are ver hard indeed. Eow can one define and measure correctl Fcounter attacksG, Fhigh pressureG, Fattacking gameG, Flong passesG, FrunsG etcH The e,isting data on match-statistics cover relativel Feas G variables, like/ Fball possessionG, Fshots on targetG, Ffouls committedG, FcornersG, FoffsideG and F ellowG or Fred cardsG, (see for instance UEFA’s official site http/CCwww.uefa.comCuefachampionsleagueCseasonI2012CstatisticsCinde,.html). 2 If one wants to measure the appropriate teams’ strategies or tactics, one has to collect such measures, which is obviousl an e,tremel time-consuming task, especiall if a Fstatisticall G large sample of matches, where the same teams are involved, is re1uired. In this case-stud , I have collected detailed statistics from just one match, a UEFA Champions League group match, between AC Milan (ACM) and FC Barcelona (FCB), held in Milan on 0ovember 23, 2011, where FCB defeated ACM b 3-2. 2espite the fact that both teams were practicall 1ualified before the game, the game had more a prestigious character and would determine to a large e,tent, which team would be the winner of the group. Given the fact that I have concentrated on si, strategies per team, four offensives and two defensive, and that FCB wins over ACM in more strateg pairs, the aim of this paper is indeed to e,amine to what e,tent the optimal game strategies derived from some deterministic, possibilistic and fu-- LP models would improve the pa off of ACM. Obviousl , there are two shortages with the use of such match statistics. First, we can’t blame the teams or their managers for not using their optimal pure or mi,ed strategies, if the pa offs from the selected strategies were not known in advance, but were observed when the game was being pla ed. Second, it is unfair to blame the manager of ACM (the looser), if his pla ers did not follow the correct strategies suggested b him. It is also unfair to give credits to the manager of FCB (the winner), if his pla ers did not follow the (possibl ) incorrect strategies suggested b him. Thus, we modif the purpose and tr to find out the optimal strategies, assuming that the pa offs were anticipated b the managers and the pla ers did what the have been asked to do. On the other hand, the merits of this case-stud are to treat a football match not as a trivial -ero-sum game, but as a non-constant sum game, or a bi-matri, game, with man strategies. It is not the goal scored itself that is anal -ed, but merel under which mi,ed offensive and defensive strategies the teams (and especiall ACM) could have done better and collected more pa offs. As is known, in such games, it is rather difficult to find a solution that is simultaneousl optimal for both teams, unless one assumes that both teams will have 0ash beliefs about each other. Given the uncertaint in measures of some or all selected strategies, possibilistic and fu-- formulations are also presented. The structure of the paper consists of five sections/ In section 2 we discuss the selected strategies and how we measured them. In section 3, using the pa offs from section 2, we formulate the following models/ (i) classical optimi-ation7 (ii) ma,imum of minimum pa offs7 (iii) LP with complementar constraints7 (iv) 0ash7 (v) Chance Constrained LP7 (vi) Possibilistic LP7 (vii) Fu-- LP. In section 4 we present and comment on the results from all models and section 5 concludes the paper. 3 2. Selected strategies and Data FCB and ACM are two world-wide teams who pla a ver attractive football. The use almost similar team formations, the 4-3-3 s stem (four defenders, three midfielders and three attackers). All football fans know that FCB’s standard strateg is to pla an e,cellent passing game, with high ball possession, and 1uick movements when it attacks. According to official match statistics, FCB had 60L ball possession, even if a large part of the ball was kept awa from ACM’s defensive area. All managers who face FCB e,pect that to happen, and knowing that FCB has the world’s best pla er, Messi, the must decide in advance some defensive tactics to neutrali-e him. Since the official match statistics are not appropriate for our selected strategies1, I recorded the game and pla ed it back several times in order to measure all interesting pairs of pa offs. Both teams are assumed to pla the following si, strategies/ (i) shots on goal, (ii) counter-attacks, (iii) attacking passes, (iv) dribbles, (v) tackling and (vi) zone marking. The first four reflect offensive strategies and the last two defensive strategies. 0eedless to sa that most of these variables are hard to observe (and measure). It is assumed that the pa offs from all these strategies are e1uall worth. One can of course put different weights. (i) shots on goal ( G) Teams with man G, are e,pected to score more goals. In a previous stud (Papahristodoulou, 2008), based on 814 UEFA CL matches, it was estimated that teams need, on average, about 4 G to score a goal. In this paper all G count, irrespectivel if the saved b the goalkeeper or the defenders, as long as the are directed towards the target, and irrespectivel of the distance, the power of the shot and the angle the were kicked2. G from fouls, corners and head-nicks are also included. According to the official match statistics, FCB had 6 G and 3 corners. According to m own definition, FCB had 14 G. The defenders of ACM blocked 13 of them (including the 4 savings b the goal-keeper). One of the shots was turned into goal, b Mavi. On the other hand, the other two goals scored do not count as G, because the first was b penalt (Messi) and the other b own goal (van Bommel). Similarl , according to the official match statistics, ACM had 3 G and 4 corners, while in m 1 Since a game theoretic terminolog is applied, we use the term Fstrateg G in the entire paper, even if we refer to tactics.