Figure 1 identifies some concepts which come into focus when one points out .... be respected in a dynamical configuration of play for a goal to be scored. Figure ...
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Dynamic-system Analysis of opponent relationships in collective actions in soccer.
Jean-Francis Gréhaigne* ; Daniel Bouthier** ; Bernard David**.
* Institut Universitaire de Formation des Maîtres ; Université de Franche-Comté. Fort Griffon. 25042 Besançon cedex, France. ** C.E.D.A.P.S. ; Université Paris-Sud. 91405 Orsay cedex, France.
Running title : Dynamic configuration of play.
Mailing address : Jean-Francis GREHAIGNE. Institut Universitaire de Formation des Maîtres. Fort Griffon. 25000 Besançon. France. (PHONE) (33) 81 65 71 01 FAX) (33) 81 82 02 55
Key-words : Soccer ; Systemic approach ; Space ; Tactics ; Configuration of play ; Goals.
Journal of Sports Sciences. Abstract :
The purpose of this paper is to examine the contribution of the systemic approach to the analysis of play in team sports. A first part focuses on the theory of dynamical systems which attempts to consider the interactions between the main variables of the different components of systems and sub-systems in soccer. In team sports, these variables represent fluctuating conditions which momentarily constrain the organisation of action for the players. Thus, the changing of the momentary configuration of the game has to be examined in light of previous configurations, the outline of the defensive device and the tactical choices involved. To start studying this problem, the present study analyses the antecedents of goal in soccer. A procedure is proposed which analyses transitions between configurations of play in order to take time into consideration when studying the evolution of the match. In order to illustrate the use and interest of the analytical procedure, two goals are described in terms of dynamic configurations of play and opportunity of choices made by the attackers.
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Journal of Sports Sciences. Over the last 10 years, there has been a growing interest in match-analysis of football. Generally, notational analysis uses numerical data to study and assess the quality of a match. But concerning the analysis of the tactical aspects of the game, there is a dearth of published research with regards to their theoretical bases. To that end, the purpose of this paper is to examine the contribution of a dynamic systems approach to the analysis of play in team sports and especially in soccer. The systems perspective has been developed as a reaction to the reductionist approach that dominated science for centuries. The main challenge in team sport is that in an opposition relationship (Deleplace, 1979), the team must coordinate its actions in order to recapture, conserve and move the ball so as to bring it within the scoring zone and effectively score. Brackenbridge (1979, cited in Thorpe et al., 1986) suggests as a definition of the game : "a struggle for a territorial dominance within a set of rules which includes significant strategic and technical aspects and in which coincidence anticipation is paramount. The struggle for territorial dominance is decided by a system of scoring which symbolises the extent of victory. The code of rules identifies the problem and ensures that both teams or individuals meet on an equal basis". Gréhaigne (1991) indicates "that this way of viewing team sports brings in three main categories of problems". i) Problems related to space and time In an attack situation, one must find solutions to problems of individual and collective handling of the ball in order to overtake, use and/or avoid varying mobile obstacles. In defence, one must bring forward obstacles in order to slow down or stop the movement of the ball and of the opponents in view of an eventual recapture of the ball. ii) Problems related to information
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Players must also deal with problems related to the production of uncertainty1 for the opponents and of certainty for their partners in a situation which remains fundamentally reversible. The reduction of uncertainty for the team in possession of the ball is a function of the quality of the communication codes and the choice of explicit tactics, thus allowing appropriate choices, understood by all partners, according to momentary configurations of play. iii) Problems related to organisation Players must accept the move from an individual to a collective project. The player must truly merge the collective project with his personal actions while giving the best of himself to the group. To better understand the principles at work in soccer, a pertinent approach could be to model the interactions between the players and the environment as a complex system. The systems perspective attempts to reduce the phenomena in the interactions between the main variables of the different components in order to study them. In team sport, these variables represent fluctuating conditions which momentarily constrain the organisation of action for the players. (e.g. Ali and Farraly, 1990 ; Bouthier, 1988 ; Davids et al., 1994 ; Gréhaigne, 1988 ; Gréhaigne and Godbout, 1995 ; Walliser, 1977). According to the space available, the choices of the player in possession of the ball should be related to the success of an attack. In order to better understand such choices, this paper examines, in its first part, the systemic nature of soccer. The second part presents a descriptive research procedure which makes it possible to study transition between configurations of play.
1. The systemic nature of soccer. 1.1. Theory of dynamical systems. Systemic analysis was born in the last 30 years as a result of the junction of various disciplines such a biology, information theory, cybernetics, and theory of 1
Uncertainty and certainty are related to the quantity and quality of available information. Uncertainty is the information that we do not possess about the state of the system (e.g. Atlan, 1979).
Journal of Sports Sciences. systems. According to Atlan (1979), it should not be considered as a science, a theory or a discipline but rather as a new process allowing for the gathering and the organisation of knowledge in view of more efficient action. The systemic approach aims to find answers to three essential concerns (Walliser, 1977). 1. The will to come back (as a reaction to ultra-analytic tendencies of some sciences) to a more synthetic approach which would recognise properties of dynamic interactions between elements of a whole, giving it a totality character. 2. The need, in order to conceive and control large and complex wholes, to put together a method which would make it possible to summon and organise knowledge so as to better relate means and objectives. 3. The necessity, in face of fragmentation and dispersal of knowledge (analytical approach to promote a utilitarian language which could support the articulation and integration of theoretical models and methodological precepts scattered in various disciplines. 1.1.1. General properties of systems. The analytical approach tries to break a system down to its most simple constituent elements. Then, modifying one variable at a time, it tries to deduct general laws which make it possible to predict the properties of the system in different conditions. For such predictions to be feasible, additive laws of elementary properties must come into play. However, in the case of highly complex systems (such as a soccer match), these additive laws do not work. Therefore, such systems must be approached with new methods such as those gathered under the systemic approach. Studying the system's behaviour over time leads to the determination of action rules which are used to influence or modify the state of the system. To achieve this, systemic approach relies on the notion of system or a whole made up of interacting elements, that is : 1. A whole in reciprocal rapport with an environment, such exchanges providing it with some autonomy;
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Journal of Sports Sciences. 2. A whole composed of interacting sub-systems, such interdependence ensuring a certain coherence; 3. A whole submitted to more or less important modifications over time while maintaining a certain permanence. Often, in a classical approach, the only explanation of phenomena relies on linear causality : it is an explanatory mode based on a logical chain of causes and effects. With the systemic approach, movement replaces permanence, flexibility and adaptability take over inflexibility and stability. Notions of flow and flow balance join those of forces and force balance. In a word, by integrating time, systemic approach reveals the interdependence of phenomena and their gradual change. Causality has become circular and a regulation loop (see Bertalanffy, 1972 ; Caverni et al., 1988 ; Morin, 1986 ; Rosnay, 1975). Two main categories of system are defined : closed systems and open systems. A closed system exchanges neither energy nor matter with its environment; it is selfsufficient. On the other hand, an open system relates constantly with its environment. It exchanges energy, matter and information useful for maintaining its organisation. Its complexity takes into account variety and interaction between elements. Some liaisons may be studied from a causal point of view (balance, stability, etc. or from an end product point of view (adaptation, learning). 1.1.2. Systems and sub-systems. A system is said to be quasi-decomposable if it can be decomposed into quasiisolated sub-systems, with some interaction between them and with the environment (Walliser, 1997). With reference to a given system, one may consider : 1. Microsystems - obtained by retaining only a few sub-systems with all their interactions (e.g., confrontation between two force lines at a given time). 2. Infrasystems - obtained by retaining only a few sub-systems with some of their interactions (1 vs. 1 or 2 vs. 2 at some point in the match). As was the case for general characteristics of systems, interactions between subsystems are energy-based or information-based. These sub-systems may organise
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Journal of Sports Sciences. themselves into various types of networks either superimposed upon or merged inside the system. Each sub-system can generally be in turn decomposed into other sub-systems according to an interlocking order which reflects hierarchies or multiple level sets of combinations. Relationships between elements of a given level differ, in terms of nature and intensity, from those between elements of sub-systems pertaining to different levels (one may not switch from 5 vs. 5 soccer to 11 vs. 11 mode without reorganising one's knowledge and one's capacities). This is so even though relatively homogeneous sub-systems may sometimes show up (e.g., 3 player configurations of play at the periphery of the field (pitch) between a defender, a midfield player and the involved wing). 1.1.3. Systems and time. The temporal dimension is important in studying systems because it is the medium through which they operate and evolve. All things considered, nothing may be fundamentally understood about soccer if one does not shift from a spatial to a temporal reference system while processing information. The synchronous properties of a system relate to the relationships between various of its characteristics at a given time. The diachronic properties relate to the relationships of those same characteristics through many successive moments in time. They make it possible to bring to light the system's evolutionary trends. In a quasidecomposable system, one may differentiate between modifications mainly related to its structure, its functioning, its evolution, or to relationships between these three phenomena. The system's structure, in a strict sense, rests upon the whole set of its most unvarying characteristics; thus, the system's structure ensures its very existence and its permanence. In a larger sense, the structure is formed by all the system's characteristics at a given point in time, thus reflecting the state of the system at that moment. The system's functioning relates on the one hand to each sub-system's transformations and, on the other hand, to flows passing through linking channels between sub-systems and between the system and its environment. The system's evolution is brought about, on the one hand, by a change in the sub-systems'
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Journal of Sports Sciences. transformation laws and, on the other hand, by changes in the way the system organises itself into sub-systems and changes in the linking channels between the system and the environment. For instance, in soccer, the structural dimension is characterised by : 1. A boundary which establishes the frontiers of the system (the stadium and the play area). 2. Elements which may be counted and grouped into categories (the players [attackers or defenders], the ball…); 3. "Containers" in which energy or information is stocked (line forces, the goalkeeper, players' energy potential); 4. A communication network which allows energy and information exchanges (the rules, the code play, a common frame of reference in order to read and interpret plays in the same way…). The functional dimension is characterised by : 1. Flows of energy, information, or elements moving about (players, the ball, replacements, state of fatigue; 2. Gates controlling the rate of various flows (the play leader, players' momentary tactical choices, the referee…); 3. Delays resulting from flows moving at different speeds, or from the gate response time (creating open space, gaining an interval, restoring a defensive block…); 4. Regulation loops, either proactive or retroactive, which play a large part in the system's behaviour by managing all parameters (taking information in order to adjust the game plan, setting a defensive reserve, modifying the system of play). 1.1.4. Regulation : general principle. The information process uses an information collecting mechanism and makes use of information in order to modify the system. To characterise it, one may consider five types of activity which intervene, in a cyclic way, in its functioning (see Malho,
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1974). Information activity : translating into a conceptual form observed real phenomena (perception). Prospecting activity : constructing probable, possible or desirable schemes about the future (planning). Decision activity : translating intents and aspirations into actions on reality (programming and management). Execution activity : transforming the system through voluntary and co-ordinated actions (execution). Control activity : collecting information about the results of actions with view to pursuing or transforming the current action or the upcoming one (regulation). 1.2. Soccer : contribution of systemic analysis. To obtain more information about the structure and the functioning of play, the authors will use a systemic approach to discuss the modelling of team sports. 1.2.1. Some concepts. In a soccer match, structures and configurations of play should be considered as a whole, rather than examined piece by piece. Systems with many dynamically interacting elements are capable of rich and varied patterns of behaviour which are clearly different from the behaviour of each component considered separately. The influence of general systems theory is now clearly evident and one must analyse the performances of the players as a system in synergy with the environment. Indeed, in a match, the opposition generates the unexpected and a constant necessity to adapt to constraints brought about by the confrontation. A match rarely relies upon the simple application of schema of play learned previously during training. Thus, most often, during the game, one can foresee only probabilities of evolution for the attack and defence configurations, hence the importance of heuristics in order to quickly solve the problems inherent in specific interactions between two teams. In a classic learning approach one tries before anything else to teach students technical skills and to maintain order on the playing field by, for example, use of formal groupings. However, it could be argued to say that it is as important, and even maybe more, to get the players to optimally manage disorder (Villepreux, 1987; Gréhaigne, 1989 ; 1992a). This type of approach, which puts forward
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"opposition" and "disorder management" as a base for any progress, brings to light new concepts which appear fundamental for a renewal of team sport teaching. Figure 1 identifies some concepts which come into focus when one points out opposition as a fundamental element of the modelling process in team sports.
Insert Figure 1 about here The central notion of opposition leads us to consider the two teams as interacting organised systems. The structural characteristics of these systems consist in a program that can be modified according to acquired experience; their main functional property is learning. The operational conditions of such systems in team sports require that one manage disorder, before anything else, while preserving a certain order and thus allowing decisions in a not completely a priori foreseeable environment. For instance, let us analyse the organisational level "match"2 looking at its structural and functional characteristics. By structural, one means the spatial organisation of the constituent elements of the system (synchronic and topological property), while the functional aspect refers to the various time related processes such as exchanges, regulations and reorganisation of the elements (diachronic and kinetic property). For the level "match", structurally-wise, the elements of the system are represented by the two opposing teams and the communication network between the two is defined by the rules of the sport. At this level, the idea is to characterise, from a space standpoint, the opposition rapport and to analyse essentially the relationships between the strong points of the attack system on the one hand, and those of the defensive system on the other hand. Notions at stake here are "in block", "in pursuit", centre of gravity, circulation of the ball, etc. (e. g. Winkler, 1984 ; Gréhaigne, 1992 b ; Bouthier et al., 1994 ; Gréhaigne et al., 1994). Functionallywise, one is dealing with the evolution in time of the opposing relationship between
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Set made of the confrontation of two teams.
Journal of Sports Sciences. the two teams (advance, delay ; breaking, continuity …). In this case, each match provides a phenomenal datum, that is something original and unique, thus reducing the efficiency of ready-made motor or strategic solutions. 1.2.2. What are the consequences ? A match constitutes a complex system. Analysis of part of the game reveals the existence of a large number of interacting variables. On the field, a non homogenous distribution of the players brings about a non homogeneous distribution of the energy state of the players. A certain kind of homogeneous scattering characterises the equilibrium state toward which soccer systems always evolve. It corresponds, therefore, to an homogeneity of the players' distribution on the different energetic states. The degree of homogeneity of the configurations of play can also be explained by a distribution of the probabilities of the presence of the players at certain parts of the pitch. Another way to show this consists in defining the micro-states of the system of attack / defence. Each micro-state is defined by a distribution of the players on the pitch's area according to their positions, orientations and their speeds. One can call this kind of distribution a dynamical configuration of play. The apparent disorder indicates then a homogeneity more general than the simple spatial distribution of the players on the ground because the latter distribution influences only two energetical levels (Potential and Speed). In those situations of opposition, the kinetic interactions lead to the stabilisation of the spatially non homogeneous states by other non homogeneous distributions which appear homogenous if one looks for certain energetic states. It means that those states would seem to be more homogeneous for an observer who would be able to recognise the different kinetic states. Conversely, to this, a classic observation would stress the heterogeneous aspects by dealing only with positions and geometric shapes. That is how, according to us, the dialectic equilibrium / desequilibrium of the game operates. On the one hand, very stable structures make one think of a crystalline structure… defined as rigid and with few chances of evolution, as for example in set-plays. On the other hand, the dynamical
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configurations of play have within themselves a number of transformations limited according to the different possibilities of the continuous evolution of the game but nevertheless important if one chooses a break in modifying the movement in process. This group of elements form a foundation for our framework of analysis. Dynamical systems are able to attain multiple patterns of stability in achieving a state of coordination with the opposition. A theoretical framework which focuses on the achievement of coordination within a dynamical system may be appropriate for the study of configurations of play.
2. A procedure to analyse transitions between configurations of play. During a soccer match, the player with the ball faces some problems dealing with the choices that have to be made. In a preliminary approach to this problem the authors tried to model those aspects of the game by considering the possibilities of the attackers' exchange of ball . From the notion of a hypothetical sphere of operations (the area of play in attack which is composed of free space + interacting space + surfaces hidden by the defenders), we tried to determine the available area for the attackers (movement + available space) to obtain the probabilities of passes. Some important difficulties with the previous approach in the precise determination of the different areas led us to search for a new option for analysis. 2.1. Purpose and underlying assumptions. During the game a unit of play evolves from a state 1 to a state 2 and so on to a state n. As in a photograph, the configuration of play is defined by the positions of the players at a moment M . Through analysis of the tactical choices of the different ball-holders in a collective movement preceding a goal, one may better understand how the goals are scored (Gréhaigne and Bouthier, 1994). In short, the aim is to describe the "dynamic states" of the players who participate in the attack and those of their opponents. To that end, the authors have devised some diagrams representing the few seconds preceding a goal. For each player, one can note a) the
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player's position, b) the direction of movement and c) the speed of movement; these parameters define the potential turning angle and the amount of ground that can be covered. To represent those kinetic data in a plane, we propose the notion of "sector of play" for the attackers and that of "sector of intervention" for the defenders. Those sectors spatially define the limits of possible actions for the different players, within one second, considering the three variables mentioned above. These three variables and the parameters discussed hereafter have been selected on the basis of the following assumption : a collective offensive movement leads to a goal when the ball-holders respect the offensive parameters imposed by the situation of play and especially pass the ball into an open space. What are these parameters ?
Insert Figure 2 ; 3 ; 4 ; 5 about here Based on field experience, the authors think that a number of parameters must be respected in a dynamical configuration of play for a goal to be scored. Figure 2 shows three cases : 1) For a ball that can be intercepted (- 2m), there must not be any sector of intervention to act as a block between two sectors of play where the players exchange the ball ; 2) The ball must not cross a sector of intervention ; 3) the player in possession is ahead of the defender and has a sector free or nearly free. Figure 3 shows that if an interceptable ball crosses (entering and going out of) a sector of intervention, the time taken by the ball between the kick and the clearing of the sectors must be less than to the time taken by the defender to cut the trajectory of the ball. It must arrive in a free sector of play or a partially free one in the case of an exchange of ball. Figure 4 shows that an accurate ball must leave a free or partly free sector of play and reach another sector of play, free or partially free as well. In the case of a successful shot on target, only the sector of play of the striker need be free or partly free. Figure 5 shows that when a player decides to dribble the ball, that sector of play must be free or partly free. The difference of speed is important as well. 2.2. Tools used for analysis.
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To analyse configurations of play, we noted the position, the type of move and the speed of the players, with a video recorder. Since the recording gave twenty five frames per second it was easy to collect a precise diagram of the action. The different lines on the ground were used to estimate the position of the players. These positions were then marked on an index card depicting a standardised half pitch. International match pitches are 112 meters by 70 meters. The data collection diagram represents proportionally half a pitch and is covered with a squared pattern (Figure 6). Each square stands for two square meters3 on the ground for greater accuracy in plotting the players' positions. When the pitch sizes were different, the grid was adjusted to the dimensions given by the FIFA in its World Cup presentation book.
Insert Figure 6 about here The video recorder was used to obtain the positions, the movements and the speeds of the players. Second by second the positions taken up by all the players who participated in the attack or the defence during the pre-goal phase were noted. Successful attacks which culminated in a goal, generated four to ten topographic diagrams of the precise spots occupied by the players and the ball. For each diagram the calculated speed was the average speed. by using the diagram with the grid, the distance covered by a player can be determined. Similarly, the video recorder, can be used to obtain the time between two configurations of play. It is then easy to find the speed of the player. Looking for a procedure which would make it possible to pattern the potential sphere of operation of a given player and accordingly draw the player's sector of play, the authors tested 20 P.E. students registered on a soccer course at the University of Burgundy (see Figure 7).
3
Sometimes, for a precise location we used a square pattern of 1 meter.
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Insert Figure 7 about here Each player ran, without a ball, from marker A to marker B. Upon reaching B, he tried to turn to his right as sharply as he could. This task was realised with the speed effectively found in a soccer match (Dufour, 1989 ; Lacour 1983 ; Reilly and Thomas, 1976). The speed was monitored by photoelectric eyes at marker B and the references used were : stop : [ 0 m/s] ; walk : ] 0 m/s to 2] ; Jog : ] 2 m/s to 4] ; cruise : ] 4 m/s to 6] ; sprint : ] 6 m/s to 8 or more ]. Table I shows the average of the angles found in our experiment for the 20 players according to their speeds.
Insert Table 1 about here During the test, the players diverted their run to only one side. Assuming similar angles for a turn to the other side, the following angles for the sector of play were obtained by doubling the results of our test: stop : 180 x 2 = 360°
Values obtained
360°
Walk : 120 x 2 = 240°
Values obtained
240°
jog : 51 x 2 = 102°
Values obtained
100°
cruise : 41 x 2 = 82°
Values obtained
80°
sprint : 21 x 2 = 42°
Values obtained
40°
Knowing the speed of a player, and consequently the distance he can cover in one second, the depth of his potential sphere of action can be can determined (table III) and his sector of play or sector of intervention drawn (Figure 8).
Insert Table 2 about here
Insert Figure 8 about here 2.3. An illustration.
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To illustrate the results of this type of observation, one will analyse the Jean-Pierre Papin's goal, scored at 59 min of the France-Sweden match in the European soccer championship in Sweden, 1992.
Insert Figures 9 a to 9 g about here Figure 9 a : M -8s ; M -7s (8 and 7 seconds before the goal). PE recovers the ball on the left side of the French half. He has many options : executing a lateral pass, a set back pass for AM or keeping the ball. He chooses the third solution. His choice respects the fourth parameter : his sector of play is partly free in spite of the intervention of the defender d3. He maintains an option on the left and on the right. PE decides to dribble past defender d3 on the right-hand side (sense of the attack) ; his choice can be realised. One can see on the drawing that he has just the necessary space to dribble the ball (respect of the fourth parameter, Figure 5). Figure 9 b : M -6s. PE has dribbled past d3. His sector is now free, he has a lot of space in which to manoeuvre. Three possibilities are offered to him : keeping the ball, giving the ball to CA by virtue of a low pass between d1 and d2 or giving the ball to CA but with a high pass over d1 and d2. He decides to carry on dribbling the ball. His choice respects once more the fourth parameter. Figure 9 c :M -5s ; M -4s. PE chooses to dribble his opponent in a one to one; considering defender d2's moves, he has some opportunities to manoeuvre. His sector of play is partly free since he is using a body screen ; the fourth parameter is respected. Figure 9 d : M -3s. PE has few opportunities to manoeuvre. He has two possibilities : making an accurate pass to CA (who would be in a very uncomfortable position against d4 and d5, d6 representing another important defensive obstacle), or giving the ball to PA who is close to the off-side limit and has a free sector of play. PE chooses the second solution. This choice respects the third parameter (Figure 4). Figure 9 e : M -2s. PA receives the ball with his head and redirects it in the direction of his movement. He has only one possibility ; he must keep the ball and go for the
Journal of Sports Sciences. Swedish target. Indeed, a pass to CA is not feasible because of the position of defenders d5 and d6. Defender d4 is also in front of CA. The choice of PA respects the fourth parameter. Figure 9 f : M -1s. PA's choice is the consequence of CA's position in Figure 9 e. PA being ahead of his closest opponent has only one possibility : he keeps the ball and carries on going towards the target. His choice is a good one since his sector of play is partially free (ahead of d5). The fourth parameter is respected once more. Figure 9 g : M -0. PA who is ahead of d5's movement decides to shot on goal. The trajectory of the ball crosses the sector of play of the Swedish goalkeeper GK. But the time between the shoot and the moment the ball enters the target lasts half a second ; consequently the last defender cannot change the trajectory of the ball because the time he needs to cut the trajectory inside his sector of play is longer than the time between PA's shot and the crossing of his sector (respect of the second parameter, Figure 3). As a consequence, the goal is scored.
3. Discussion. The analysis of collective movements shows that, generally the different ball owners respect the parameters of success. Those choices are made according to the position, the way of moving and the speed of the partner and the opponents. A preliminary analysis on 110 dynamical configurations of play, shows that 102 have respected the principle to pass the ball in an open space. One can think that this principle is a constant of the system (Gréhaigne and Bouthier, 1994). Nevertheless, at the end of the collective movements to which they belong, eight goals were scored although they did not respect the principle. If one makes a closer analysis of those 8 configurations, one can see that the ball owners made a bad choice (no respect of the parameters). The defender should have intercepted the ball but because of clumsiness they did not manage this and the ball was caught again by the attacker which carried on his action of play.
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For example, during Sweden versus Denmark, the collective movement which caused a goal at the 58 th minute shows a mistake at M-1 (Figure 10). A1 has elected to pass the ball to A2 (M -2). The ball is interceptable and reaches defender 1 ; d1 tries to get the ball but fails in his attempt and sends the into A2's sector of play. A2, possessing a location advantage over d2, seizes the opportunity and scores.
Insert Figure 10 about here The contexts in which actions occur in soccer are so varied that, in most instances, the concepts of principle of play and constant of the system are useful in order to understand how the player treats information. Our results show that the position and the movement of the players are reliable and faithful parameters for the analysis of play. The models of the sectors of play and the sectors of intervention can be used to pattern the attacks and obtain more information about the functioning of the system. Beyond the matter of reliability, the analysis shows that a goal has to be constructed and tactical choices of the players optimised. A goal can only be scored if the principles of play are met ; if they are not, the only way to score is by virtue of a mistake on the part of the defence. This type of analysis can be considered as a starting point because, from a methodological point of view, it is a first step to obtain tools which allow simulation of movement in soccer and the production of a model with good predictive power. Moreover, this model materialises and objectifies abstract parameters like the assessment of relative speed and orientation of opponent players. The organisational level "match" or "system match" (a group of players playing together as a whole) seems to be an interesting way to analyse soccer. With the opposition relationship, order and disorder can emerge from the play, at any moment. In this way, energy and choices of the players serve to create the conditions for transitions between configurations of play and thus transform the play. However, in soccer, the different states of the system operate fundamentally according to states
Journal of Sports Sciences. of equilibrium. If a goal is scored, it means that the organisational level "defence" has not found the response to the existing conditions of play imposed by the attack. The implications of such a model for the analysis of team sports seem to be a viable and pertinent basis for explaining the system capabilities underlying persistence and change during a match.
Acknowledgements. The authors wish to thank Paul Godbout and Lew Hardy for their help, suggestions and feedback throughout this project.
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Journal of Sports Sciences. References.
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21
Figures caption.
Figure 1. Concepts related to the notion of opposition Figure 2. Configurations where the exchange of ball is free (the shapes of sectors of play or intervention are in accordance with the players' speed. The trajectory of the ball is noted in function of the height of the ball). Figure 3. Configurations where the defenders have not the time to cut the trajectory of the ball. Figure 4. Configurations where the sectors of play of the attackers are partly free. Figure 5. Configurations where the players dribble the ball. Figure 6. Example of a diagram with grid (square of 2 x 2 m in reality). Figure 7. Experimental set-up to calculate the angles according to the speed. Figure 8. Sectors of play or intervention according to the speed. Figure 9 a. M -8s ; M -7s Figure 9 b. M -6s Figure 9 c. M -5s ; M -4 s Figure 9 d. M -3s Figure 9 e. M -2s Figure 9 f. M -1s Figure 9 g. M o Figure 10. Sweden-Denmark from M-2s to M -1s then M 0.
22
Table I. The angles according to the speed. Speed of players Mean Range S-D
Stop
Walk
Jog
Cruise
Sprint
180° 180° 180° 0
120° 105° 140° 9.5
51° 40° - 60° 6.7
42° 30° - 60° 6.9
21° 10° - 30° 6.9
23
Table II. The potential sphere of action according to the speed Speed of the player 0 1 2 3 4 5 6 7 8 or more
Angle in degree 360 240 240 100 100 80 80 40 40
Depth of the angle in cm 0,35 0,7 1 1,4 1,7 2,1 2,45 2,8
24
Breaking / continuity
Imbalance / balance
Opposition Disorder / order
Delay / Advance
Risk / security
25
Sector of play of attackers Sector of intervention of defenders Ball interceptable (! 2 m).
26
Sector of play of attackers Ball interceptable (! 2 m).
Sector of intervention of defenders
27
28
Sector of play of attackers Sector of intervention of defenders
29
30
A
B 0° 15° 30° 45°
135° 60°
120° 105°
90°
75°
31
1 m/s
Stop
3 m/s
2 m/s
4 m/s
5 m/s
6 m/s
7 m/s
8 m/s
32
France Sweden Ball
Sense of the attack
AM FE
PE
d1
d3 d2
33
France Sweden Ball
Sense of the attack
AM FE
PE
d1
CA
d3 d2
34
France Sweden Ball
Sense of the attack
PE d2 d3
d1 CA
35
PE
France Sweden Ball
d3
Sense of the attack
CA
PA
d4
d5
d6
36
France Sweden Ball
Sense of the attack
CA d3 d6 d4 d5 PA
37
France Sweden Ball
Sense of the attack
d3 d6 d5
CA d4
PA
38
France Sweden Ball
Sense of the attack
CA
d5
d4
d6 PA
GK
0,5 second
39
Sweden Denmark Ball
Movement of the ball M -2
A1
d1 M -1 d2
A2
GdB
M0
