Remember those complex math calculations from the movie A Beautiful Mind? Here's some of the same stuff applied to our beautiful game.
Ah left out de formulas and variables and kept the general info. Iz an excerpt of recent research by German economists.
They call it
'The Penalty-Duel and Institutional Design: Is There a Neeskens-Effect?' ... ah know men like Observer and others know 'bout Neeskens the player.
I. Introduction: Penalty taking and game theoryIn soccer, penalty kicks and shootouts are taken from twelve yards (= 10, 9728 meters) out from goal, with only the goalkeeper between the penalty taker and the goal.
Penalty kicks were first introduced in Ireland in the 1891-92 season in order to punish a foul within the penalty area. Penalty shootouts were introduced in 1970 to determine who progresses after a tied match. Since then, penalty taking determined the outcome of numerous soccer games and tournaments, including, for instance, the FIFA World Cup finals 1994 between Brazil and Italy, and 2006 between Italy and France.
In this paper, we ask what strategies in penaltytaking can be considered ‘clever’ or ‘rational.’ We focus in particular on strategies that involve shooting to the middle of the goal.Game theory analyzes and predicts behavior when people interact with each other. Taking the framework of the interaction – the game – as given, game theory offers solutions. A game includes the rules of interaction, the strategies available to the “players,” and the payoffs (or ‘utilities’) each player assigns to all possible outcomes of the game.
... game theory focusses on behavior arising from a given set of institutional rules and asks how institutions affect behavior. The answer, as we will argue, may depend on the shared perceptions of the interactive decision situation by the players.
Regarding penalty taking, the institutional rules are pretty clear, even though they may change over time. The strategies available to the players are, however, less obvious, and in fact we will discuss the impact of different possible sets of strategies – and hence different game forms – on behavior in this paper. We will also argue that the payoffs assigned to the outcomes of penalty taking, goal or no goal, are more subtle than has previously been assumed. Players may not only want to maximize respectively minimize the probability of a goal, but there are also indications that players have preferences over the strategies that can be chosen.
II. A (too) simple game theoretic modelLet us begin with the simplest possible game theoretic modelling of what might be called the “penalty-duel.”
A penalty-duel involves two players, the kicker and the goalkeeper. The interests of the players are perfectly opposing; success of the kicker implies failure of the goalkeeper, and the other way round. More precisely, the conflict structure is such that the goalkeeper wants to coordinate his action with the one of the kicker, while the kicker aims at discoordination of actions. We also assume that the two players must move simultaneously,
implying that players are not able to react to the movements of the opponent. Indeed, many observers argue that neither does the speed of the ball allow goalkeepers to react to the ball’s course (e.g., Palacios-Huerta 2003) nor does a goalkeeper wish to move early in order to avoid signalling to the kicker about his intentions. Furthermore, Chiappori et al. (2002), among others, provide empirical evidence suggesting that moves of the players in penalty taking are simultaneous ones. Summing up, from a simple game theoretic perspective, a penalty-duel can be seen as a simultaneous, two-person game with strictly opposing preferences.
A simple model assumes that the kicker (K) has only two strategies; he can either choose to kick to the left side (L) or to the right side (R); the option of shooting to the middle is ignored here for the moment. Accordingly, the goalkeeper (G) can either jump to the left or to the right side. (Here and in the following, left and right is defined from the kicker’s perspective.) If both players choose the same side (the top left or the bottom right corner of the table), the goalkeeper succeeded in coordination and manages to save the penalty. In this case, the kicker’s payoff is zero and the goalkeeper’s payoff is normalized to one. In the cases, when the goalkeeper fails to jump to the side chosen by the kicker, who succeeded in discoordinating actions, there is a goal and the goalkeeper’s payoff is zero while the kicker’s payoff is normalized to one.
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We finally note that, mainly because of this random element in the strategies,
penalty shootouts have been criticized as an unsatisfactory way to decide a soccer game. However, later in this paper, we will develop a more realistic model, in which the players’ skills affect the probability of success, so that the outcome is still influenced but not entirely determined by randomness.
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We credit Johan Neeskens, a Dutch midfielder playing for Ajax Amsterdam and FC Barcelona in the 1970s, with this clever innovation, which gradually changed the perception of the essence of the penalty game by kicker and goalkeeper from a 2x2 to a 3x3 game. E.g., the German site of Wikipedia mentions that ever since the 1974 World Cup Final, Neeskens is credited by soccer commentaries as the inventor of the Neeskens-variant (“Neeskens-Variante”) of taking a penalty: shooting straight to the middle, while the goalkeeper dives for a corner (http://de.wikipedia.org/wiki/Johan_Neeskens).
In this game the referee awarded a penalty to the Netherlands against Germany in the second minute of the game, which Neeskens had the nerve to take in precisely this way – while Sepp Maier, the German goalkeeper, opted for his right corner. As mentioned by wikipedia the double prominence of the occasion, a penalty in the second minute of World Cup Final, propelled the Neeskens-variant to international prominence and recognition as a valid and serious option for taking a penalty.It is not known to us, whether there ever was a penalty at a similarly important or internationally prominent occasion, which was (intentionally?) taken this way before. However, there was another – and now in Germany equally historical – penalty taken this way at an almost equally important and prominent occasion two years later: the last penalty of the penalty shoot-out that decided the Final of the European Championships in 1976 between Germany and Tchechoslovakia. It was taken by Antonin Panenka, who delicately chipped the ball right into the middle of the goal mouth – while Sepp Maier opted for his left corner. Panenka undoubtedly did so intentionally. He later said: “I knew long before that I would take the penalty this way.” His own goalkeeper warned him the night before the final, that – if the occasion should arise – doing so would be “too arrogant.” Panenka himself was aware of the risk: “If Maier would have stayed put, they would have sent me to the factories for the next 25 years. The communists would have accused me of ridiculing their system” (Martens, 2003). Alas, it went well to the fame of Panenka (and the Neeskens-variant).[/color]These observations lead us to the following claim: before 1974 (and the Neeskens penalty) the “institution” penalty-duel was a standard of behavior, according to which kickers chose L or R and goalkeepers did likewise. That is, a 2x2-game form gives an adequate description of the penalty situation. After 1976 (and the Panenka-penalty) the “institution” penalty-duel was perceived as a 3x3 game form constrained by certain behavioral rules.
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IV. Opting for alternative M: Why is the middle relatively unattractive to players?While there is anecdotic evidence, there is no statistically unambiguous evidence in our data that Neeskens’ innovation significantly changed the way penalty kicks were executed. Several statistical tests applied to our limited data from the Bundesliga could not reveal a structural break in the mid-seventies.
Part of the reason might be that the middle is a less attractive strategy than the corners to both, kicker and goalkeeper: Based on data from 459 penalties from French and Italian League 1997 – 2000, Chiappori et al. (2002) found that
• the kicker chooses middle less often than either corner,
• the goalkeeper chooses middle less often than either corner, and
• the goalkeeper chooses middle less often than kicker (in fact, goalkeepers almost
never stay in the middle).
As a consequence, kicking to the middle on average has the highest probability of scoring
(81.0% as compared to 70.1% for the right corner and 76.7% for the left corner; see Table 4 in
Chiappori et al. 2002).
Obviously, these observations are not in line with our simple model of Game II, which suggests that the middle should be as attractive as each of the corners. They also appear inconsistent with the Fundamental Lemma described above: in equilibrium, the expected payoff to every action to which a player’s strategy assigns positive probability should be the same.
Chiappori et al. (2002) explain some of these effects with heterogeneity with respect to the players’ capabilities to score when choosing one of the three strategies, left, right and middle.
For instance, it is typically easier for a kicker to score when kicking to the converse side of his strong foot. This heterogeneity can explain why certain strategies are more often chosen than others by certain kickers. But it cannot explain the superior average scoring rate for the middle strategy. So we suspect that heterogeneity is only part of the explanation.
In order to find out more about why the middle seems a rather unattractive strategy despite the strategic advantage of using it, we asked Harald “Toni” Schumacher and Hans Jörg Butt about their strategies in penalties. Toni Schumacher is considered one of the world’s best goalkeepers during the 1980s and was capped 76 times for Germany. Hans-Jörg Butt is an active goalkeeper playing in the Bundesliga for Bayer Leverkusen. He is most remarkable – and unique – among German goal keepers, because he is not only considered a penalty killer` - Wikipedia notes that he on average saves 7 out of 10 penalties -, but at the same time one of the most successful penalty takers. He currently (November 2006) has 26 goals from the penalty spot to his credit, more than any other goalkeeper ever in the Bundesliga. So, if anyone knows how to put himself into the opponent`s shoes, it is him. Both goalkeepers confirm that there is heterogeneity among kickers, though the classifications they use are quite different. Toni Schumacher mentioned that there are 4 types of kickers distinguishable according to whether they shoot with the left or right foot, and whether the shot is powerful or more technically demanding.A powerful shot from a rightfooter, for instance, would most likely go to the left corner.
Hans-Jörg Butt, on the other hand, classifies kickers according to whether they try to react to goalkeepers, or whether they
choose the corner independent of the movements of the goalkeeper. So, there is heterogeneity – implying that we should not observe equal probabilities for choosing the actions right, middle and left. At the same time, however, both goalkeepers suggested that the unattractiveness of the middle-strategy is also driven by an asymmetric payoff structure, which has not been considered in earlier work. Toni Schumacher, for instance, noted that he never just stayed in the middle. Asked why, he responded that this would be “against my honour.” When we remarked that, knowing this, a kicker’s best response would be to shoot in the middle, he answered that a kicker, who shoots in the middle, “does not deserve to kick a penalty against me,” and that this would be “a different game” (sic!). While Hans-Jörg Butt also pointed out that there are technical difficulties with shooting to the middle (“schippen”), he reasoned that it is a larger “disaster” for the kicker when a shot to the middle is saved (recall Panenka`s statement!), than it is a disaster for the goalkeeper when he does not save a shot to the middle. A kicker, who gets caught with middle is a “fool” (“Depp”). Both views indicate that the payoffs associated with corner and middle actions need to be treated differently.
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ConclusionNeeskens and Panenka demonstrated that going beyond shared perceptions of how to play the game (i.e. fulfill the roles of the institution), and devising new, innovative strategies may yield a competitive edge. They possibly changed the way penalty-kicks are perceived in a permanent way. Their innovation accounts for and answers to the growing competitiveness of professional sports – and in particular soccer – due to increased commercialization. While game theory may capture the consequences of institutional change created by innovators such as Neeskens and Panenka, it cannot as easily portray creativity in institutional design, because that would have to start with a description of all conceivably available strategies.
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We demonstrate how a number of empirical observations and statements by goalkeepers (and a kicker) about the attractiveness of the middle option in penalty taking can be accounted for by an equilibrium analysis of the penalty duel with modified payoffs.
Kickers and goalkeepers do not only have preferences on the outcome of the game, goal or not goal, but also on the way the kick is taken or saved, which has to do with the perception of their roles.Although new behavior in a role may become legitimate, it need not be perceived as acceptable as the
traditional one. More specifically,
our study strongly suggests that a shot or even goal to the middle is evaluated differently than a shot or goal to a corner by both, goalkeepers and kickers. We show for the first time, that this observation has great explanatory power for actual behavior.http://papers.ssrn.com/sol3/papers.cfm?abstract_id=988698#PaperDownload