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How the “rapport de forces” evolves in asoccer match: the dynamics of collective

decisions in a complex systemJean-Francis Gréhaigne*, Paul Godbout** y Zeineb Zerai***

HOW THE “RAPPORT DE FORCES” EVOLVES IN A SOCCER MATCH: THE DYNAMICS OF COLLECTIVE

DECISIONS IN A COMPLEX SYSTEM

KEYWORDS: Soccer, Complex system, Modeling, Tactics, Moves.ABSTRACT: This article discusses the contribution of dynamics to the study of complex systems with regardsto performance analysis in soccer. Evaluation tools are presented to better understand how the “rapport de forces”evolves with perturbations of play, contraction / expansion phases of game play, and possession of the ball. It ishypothesized that application of these tools and models may enable researchers and trainers to efficiently analyzeconfigurations of play and identify those that appear to be critical for success. All things considered, nothing may befundamentally understood about team sports if one does not shift from a spatial to temporal reference system. It makes itpossible to bring to light the system’s evolving trends. This way, it is possible to understand how players producefunctional behaviors or answers to momentary configurations of play, whatever their complexity.

Correspondencia: Jean-Francis Gréhaigne, Ph.D. IUFM de Franche-Comté. Fort Griffon. 25042 Besançon Cedex. France.E-mail: jean-francis.grehaigne@univ-fcomte.fr

* GRIAPS, University of Franche-Comté, France.** Laval University, Quebec city, Canada.*** ISSEP de Tunis and GRIAPS, University of Franche-Comté, France.— Artículo invitado con revisión

Revista de Psicología del Deporte2011. Vol. 20, núm. 2, pp. 747-765ISSN: 1132-239X

Universitat de les Illes BalearsUniversitat Autònoma de Barcelona

Greihaigne:1. Reverter 28/06/11 12:55 Página 747

Complex systems analysis is a scientificfield which studies the common properties ofsystems considered complex in nature,society and science. The key problems ofsuch systems are difficulties with their formalmodeling and simulation. From suchperspective, complex systems are defined onthe basis of their different attributes. Thestudy of complex systems brings new vitalityto many areas of science where a moretypical reductionist approach has fallen short.Complex systems analysis is therefore oftenused as a broad term encompassing aresearch approach to problems in manydiverse areas such as team ball sports. From asystemic analysis point of view, key concepts,such as self-organization, time andconstraints, can be used to help explainingstability, variability and transitions amongconfigurations of play (Gréhaigne, 1989).

Gréhaigne, J. F. Godbout, P. y Zerai, Z. How the “rapport de forces” evolves in a soccer ...

Revista de Psicología del Deporte. 2011. Vol. 20, núm. 2, pp. 747-765 748

The central notion of opposition leads usto consider the two teams involved in amatch as interacting organized systems. Asystemic view of team sports may then beseen as fundamental to the emergence of anew understanding of the game. In a morecommonly (and traditionally) used learningapproach, one tries first to teach students thetechnical skills of the game and second tomaintain order on the playing field, by theuse of formal groupings, for instance(Garganta, 1997; Gréhaigne, 1992).

We are tempted to say that it is asimportant, and maybe more important, to getplayers to optimally manage disorder(Gréhaigne, 1989; Gréhaigne y Godbout, 1995;Villepreux, 1987). A game rarely rests upon thesimple application of tactical combinationslearned previously during training. Thus, mostof the time during the game, one can foresee

Figure 1. Concepts related to the notion of opposition (Translation from Gréhaigne, 1992).


only probabilities of evolution for the attackand defense configurations, hence theimportance of player’s tactical knowledge torapidly and efficiently solve game playproblems (Figure 1).

The concept of opposition, between twoteams, helps in highlighting the notion ofpressure on a particular point in the gameplay, in order to break the balance of forcesin momentary configurations of play. Such apressure creates a favorable imbalance inorder to score a goal. Finally, two aspects arecontradictory to manage in the attack:

Taking risks in order to create anadvantage (thus creating an imbalance in theopponents), but at the expense of main -taining an adequate defensive coverage;

Putting emphasis on security, temporarilypreserving some stability in the exchange ofball, but without really putting the opponentin trouble.

From the defense point of view, playersmay favor security by maintaining tempo -rarily one’s defensive stability (in order toavoid being late or in pursuit), but in sodoing, the initiative of the game is left to theopponents.

Moreover, the temporal dimension isimportant in studying these systems becauseit is the medium through which they operateand evolve (Davis and Broadhead, 2007).One of the most important performanceparameters is the speed of the play(Gréhaigne, 2009). All things considered,nothing may be fundamentally understoodabout team sports if one does not shift froma spatial to a temporal reference system. Thesynchronous properties of a system relate tothe relationships between several of itscharac teristics at a given time. The diachronicproperties relate to the relationships of thosesame characteristics through many successivemoments in time. They make it possible to

bring to light the system’s evolutionarytrends.

Team ball sports in general, and soccer inparticular, can be considered as complexsystems composed of many inter -acting components (Araújo, Davids, Bennett,Button y Chapman, 2004; Gréhaigne, 1989;Gréhaigne, Bouthier and David, 1997;McGarry, Anderson, Wallace, Hughes andFranks, 2002). The theory of open complexsystems seeks to explain how regula -rity emerges within a given system. Thisimplies the consideration of the concept ofequilibrium / non-equilibrium phase transi -tions in the study of systems and models(Walliser, 1977).

For us, the heart of this theory ishow configurations of play are formed andtransformed as complex systems with smallchanges in the opposition relationship. Fromthis viewpoint, game play can be characte -rized by order-disorder transitions(Gréhaigne, 1989), where individual orcollective actions may destabilize or(re)stabilize the system of play. These ideasfit well with tactical considerations in teamsports since, at one level of analysis, thegame can be described as a series of sub-phases. For instance, at the “match” organi -zational level, the set made ofthe confrontation of two teams, hasstructural and functional characteristics. Bystructural, one means the spatial organizationof the constituent elements of the system,while the functional aspect refers to thevarious time related processes such asexchanges, regulations and re-organization ofthe elements. Functionally-wise, one isdealing with the evolution in time of theopposing relationship between the two teams(advance, delay; breaking, continuity). Theseopposition settings that momentarily involvesome of the players generate a particular




shape of play representing the “partialforefront organizational level”. At anyspecific moment, according to the evolutionof play, this reciprocity relationship offers,for example, a specific problem to attackersbut, at the same time, contains pertinentsolutions for conducting the action(Gréhaigne, 1992).

Gréhaigne et al. (1997) argued thatchanges in the momentary configuration ofgame play have to be examined in light ofthe previous configurations, an example ofthe concept of conditional coupling incomplex systems theory (Davids, Araújoand Shuttleworth, 2005; Davids, Button andBennett, 2008). They concluded that“choices are made based on position,movement and the speed of one’steammates and opponents” (p. 148). Withthe opposition relationship, order anddisorder can emerge from the play at anymoment. “This way, the energy and choicesof the players serve to create the conditionsfor transitions between configurations ofplay and transform the play” (p. 148). Thesetransitions may best be understood in termsof the interactions of multiple localfactors (location of the players and of theball, their speed, player’s cognitions andresources, etc.).

Next, we discuss the use of complexsystems theory with regards to performanceanalysis, using football for illustrations.Evaluation tools are presented to betterunderstand how the “rapport de forces”(Gréhaigne, Godbout y Bouthier, 1999)evolves with perturbations of play,contraction / expansion phases of game play,and possession of the ball. It is hypothesizedthat application of these tools and modelsmay enable researchers to efficiently analyze



configurations of play and identify those thatappear to be critical for success.

Adopting a vocabulary focused ondynamics implies a clear understanding of theterms used. We shall therefore consider, in thispaper, the different terms used when onewants to talk about location and displa cement.To this end, we tested the concepts of effectiveplay-spaces in expansion and / or contractionto experiment different analysis of the“rapport de forces” between two teams.Transitions and transition game play oftenrefer to configurations where one hassufficient time to act because the density of theplayers is less important: the attack must stayahead of the effective play-space and thedefense must go back or stay in block. The useof long-ball plays changes rapidly configu -rations. Once players perform the long-ballplay the configurations change shape and aremost often in expansion. For its part, the “incompression” model appears in a stabilizedgame play with a high density of players.

This succession of momentary configu -rations of play between regaining possessionof the ball and the loss of the ball is asequence of play. Main actions on thecirculation of the ball and players may becategorized as follows:

– Ball stopped in the contraction;– Ball stopped at the periphery of thecontraction;– Moving ball towards the contraction;– Ball stopped in an expansion phase;– Ball moving in an expansion phase;– Moving the ball at the periphery ofeither the contraction or the expansion.One must, of course, consider both the

paths and trajectories of the ball in order toobtain a more accurate assessment of thesituation and a better idea of the “rapport deforces” between attack and defense.


Observation of game-play

To better understand the contribution ofa complex system approach to theconception of team-sport learning, we usethe notion of effective (occupied) play-space(EP-S) as a tool to extract data on theevolution of game-play.

Effective play-space

If one considers a given configuration ofplay (see Figure 1), one can summarize itusing the notion of effective play-space, asillustrated in Figure 2 (Gréhaigne, 1989;Gréhaigne, Richard and Griffin, 2005;Mérand, 1977). The effective play-space (EP-S) may be defined as the polygonal area thatone obtains by drawing a line that links allinvolved players located at the periphery ofthe play at a given instant.

This conception of effective play-spacepostulates that between the elements ofboth teams in competitive oppositionsettings, a structuring of cooperation andopposition relationship takes place.Considering the location of the EP-S on thefield and the direction of the attack, theposition of players of both teams and theposition of the ball constitute a particularconfiguration of play at instant T. In theseconditions, the defined shape of a particularconfiguration and its possible evolution mayprovide significant information on the valueand the limits of a player’s adaptation, thatis to say on what his/her behavior expressesin terms of innovation, invention, orunlikely “regression” when confronted toopponents.



Figure 2. A given configuration of play in soccer. The

ball is at the rear of the configuration.

Figure 3. The effective play-space (EP-S) of this configuration.

Offensive and defensive effective play-

spaces (OEP-S and DEP-S)

Considering the respective positioning ofattackers and defenders, one may alsodetermine an offensive effective play-space(OEP-S) and a defensive effective play-space(DEP-S). Then, two more or less interpene -trated polygonal surfaces are obtained (seeFigures 4 and 5 where polygonal areas areschematized in triangular form). The relation -

ship between these two opposing areas andtheir respective evolutions in time mayenlighten us on changes in the balance of theopposition relationship during matches.Particularly, the location of the ball or of theball holder in the offensive effective play-space, according to the attack phases, pro -vides good indications depending if the ball isat the rear, within, at the periphery or at thefront of the offensive effective play-space.


Modeling of OEP-S and DEP-S

A given cloud of points, as in aconfiguration of play, can be characterized byits “center of gravity” and its two principalaxes (Gréhaigne, 1989). This type of analysisis particularly useful in research because thereciprocal positions of the centers of gravityappear to constitute an important indicationin characterizing the notion of “in block”(Figure 6) or “in pursuit” for the defense(Figure 7). We shall consider that the defenseis in “block” when it is generally positionedbetween the ball holder, the attackers and itsown goal. We shall consider that the defense

is in “pursuit” when it is generally positionedbehind the ball holder, the attackers and itsgoal (Gréhaigne, 1990).

A defense in pursuit is a defensemomentarily out-of-position which seeks toreposition itself as quickly as possiblebetween the ball and goal; in this case theattack is in advance on the defensivereplacement (Caty, Meunier and Gréhaigne,2007).

So, we can sum up the dimensions andthe surface of a cloud of points representingthe attack or the defense. The maindimensions can be studied according to their



Figure 4. OEP-S and DEP-S. Figure 5. Modeling of OEP-S and DEP-S.

Figure 6. Defense (black circles) in block and ball at

the rear of the EP-S for the grey squares. Figure 7. Defense (black circles) in pursuit and ball

at the front of the EP-S for the grey squares.


length or their width and their prevalentdirection in relation to the dimensions of thefield, meaning its width or its depth. In ourexample (Figure 8), we studied differentshapes of EP-S based on this idea.

A preliminary analysis of the differentpositions and shapes of the effective play-spaces led us to suggest a theoretical typologyof the configurations that can be obtainedwhen defense is in block. We shall call:

A1: an attack configuration where themain dimension of OEP-S is widthwise. Thesame shape for the defense will be called D1;

A2: an attack configuration where thelength of OEP-S is nearly equal to its width.The same shape for the defense will be calledD2;

A3: an attack configuration where themain dimension of OEP-S is lengthwise. Thesame shape for the defense will be called D3.



Figure 8. Modeling of OEP-S (grey) and DEP-S (black) with defense in block.


– Location of ball recovery withreference to the field: high-ball recovery(in the opponents’ side of the field);recovery in the middle area of the field;low recovery (in one’s own side of thefield); recovery at the periphery.– Location of recovery with reference tothe effective (occupied) play-space (EP-S):recovery at the front of the E P-S; recoveryat the rear or the middle area of the E P-S.Figure 9 illustrates different effective

play-spaces (high, middle and low); areas ofball recovery are analyzed with respect to“defense in block” plays or “in pursuit”plays, with the ball at the rear or at the frontof EP-S.



From a formal point of view, if wecombine these different configurations oneby one we obtain a theoretical matrix of ninepossible cases. If the defense is not in block,there are other reciprocal rapports betweenthe two EP-Ss. For an inventory of thesedifferent configurations, see Gréhaigne, Catyand Marle (2004, 2007). For ball moves inrelation to effective play-space, seeGréhaigne et al. (2005).

Location of EP-S

One other important information relatesto the location of the EP-S on the field. Toinsure reliable observations, data are basedon two criteria (see Figure 8):

Figure 9. Different areas of ball recovery analyzed with respect to “defense in block” plays (1) or “in pursuit” plays

(2).


755Revista de Psicología del Deporte. 2011. Vol. 20, núm. 2, pp. 747-765


Complexion of play

During a match, a unit of play evolvesfrom a state 1 to a state 2 and so on to a staten. As in a photo, the configuration of play isdefined by the position of all players at amoment M. Through the analysis of thedifferent ball-holders’ tactical choices prior toa goal, one may better understand how goalsare scored. To that end, Gréhaigne et al.(1997) have devised some diagrams represen -ting the few seconds preceding a goal. Foreach player, one can note a) the player’sposition, b) the direction of his/hermovement and c) the speed of his/hermovement. These parameters define thepotential turning angle and the amount ofground that can be covered. To representthose kinetic data on a plane, we haveproposed (Gréhaigne et al., 1997) the notionof “sector of play” for the attackers and thatof “sector of intervention” for the defenders.Those sectors spatially define the limits ofpossible actions for the different players,

within one second, considering the threeparameters mentioned above. With referenceto concepts used by Plank (1941) in physics,we shall name such a distribution a“complexion of system”. In short, thepurpose is to describe the “dynamic states” ofplayers who participate in the attack and thoseof their opponents. Whereas a staticconfiguration of play is illustrated in Figure 10,dynamic pictures of the transition betweentwo configurations of play are illustrated inFigures 11 (between moment 0 and moment1, one second) and in Figure 12 (betweenmoment 0 and moment 2, two seconds).

Despite an apparent disorder suggestedby the simple static spatial distribution of theplayers on the field or court, a dynamicanalysis of the play actually indicates a moregeneral homogeneity with respect to players’moves. Whereas the static spatial distributionof players (Figure 10) suggests severalpossible tactical decisions on the part of theattackers (grey circles), the two successive

Figure 10. Static spatial distribution at M 0.


dynamic configurations of play (Figures 11and 12) suggest a relatively balanced

confrontation between attackers anddefenders.



Figure 11. Dynamic configuration of play at M1 (sectors of play in gray and sectors of intervention in black).

Figure 12. Dynamic configuration of play at M2 (sectors of play in gray and sectors of intervention in black).


In a complex system like a soccer match,all players affect each other in an intricateway. Focusing on each player individuallydisrupts the observer’s perception of players’usual interactions. It is, therefore, inappro -priate to study a configuration of play apartfrom its environment, the match system(Gréhaigne and Godbout, 1995).

Part of the receivers’ sectors of play(Gréhaigne et al., 1997) is always free inorder for them to exchange the ball or toshoot on goal according to their position.When a team is attacking, the idea is to createor keep available time and, consequently,available space. The ball should be passed tothe player who is in the best position topenetrate defense: that player is not neces -sarily the one with the largest space available.

Such results show that the receivers’positions and their way of moving areimportant information for the ball holder.Concepts of sector of play and sector ofintervention can be used to provide infor -mation both for attack and defense.

Observation and system

The stable state of a system is the one forwhich chances of occurrence are the greatest.In other words, it is the one that can bereached or realized in most different ways. Infact, this definition of stability depends onthe observer’s intention.

Observation and intention

To be more precise, let us consider twodifferent observers of a system composed of‘n’ players on the field. A first observerconsiders each of the ‘n’ players as distinctindividuals, whereas the second one considersthe elements as equivalent to a dynamicconfiguration of play. The first observer isnot interested by the “complexions”, but bythe “static repartition modes” of the players.

Considering that the second observer canonly take into consideration the different“complexions” of the system, it is obviousthat the first observer has more work to dofor describing the system (having moredifferent states to consider).

The work of our second observer is evenmade easier due to the fact that for him orher, the different states of the system do nothave the same probability of occurrence. Heis able to define as a “stable dynamic state”the one where all players are distributedequally on the field. In this case, one acceptsnot to detail, not to differentiate; when oneagrees to let the perception of details growpoorer, one improves his/her understandingof the whole system. However, the differencebetween the two observers is only due to thefact their observations do not have the samelevel of precision. Inherently, our twoobservers have done the same kind of workto characterize the elements, to “classify”them, but each using a different scale:

The first observer has characterized the‘n’ players according to static criteria (onecriterion being the fact that players are partof one of two sets, the two teams);

The second one had only to classifyplayers depending upon their dynamicdistribution on the field.

This passage from one level of analysis tothe other has structured the observers’ visionof the system and has provided a frame ofreference, consciously or not. A matchconstitutes a complex system. On the field, anon-homogenous distribution of the playersbrings about a non-homogeneous distri -bution of their energy state. A certain kind ofhomogeneous scattering characterizes theequilibrium state toward which invasive teamsport systems always evolve. It corresponds,therefore, to a homogeneous distribution ofthe players on the different energetic states.




The degree of homogeneity of the dynamicconfigurations of play can also be explainedby a distribution of the probabilities of thepresence of the players in certain parts of thefield.

It means that those states would seem tobe more homogeneous for an observer whowould be able to recognize the differentkinetic states, as is the case for the secondobserver. Conversely, a classic observationwould stress the heterogeneous aspects bydealing only with positions and geometricshapes. That is how, we think, the dialecticbalance / unbalance of game play operates.On the one hand, very stable structures makeone think of a crystalline structure… definedas rigid and with few chances of evolution, asfor example in set-plays. On the other hand,the dynamical configurations of play havewithin themselves a number of transfor -mations limited according to the differentpossibilities of the continuous evolution ofthe game but nevertheless important if onechooses a break in modifying the movementin process.

An elastic system

Chow, Davids, Button, Shuttleworth,Renshaw and Araújo (2007) have exploredthe potential of a nonlinear pedagogicalframework, based on dynamic systemstheory, as a suitable explanation for tacticalapproach in team sports in physicaleducation. Nonlinear pedagogy involvesmanipulating key task constraints on learnersto facilitate the emergence of qualitativeinformation on game-play, functional move -ment patterns and decision-makingbehaviors. So, to better understand theevolution of configurations of play, it ispossible to study shapes and distortions ofoffensive effective play-spaces (OEP-S) anddefensive effective play-spaces (DEP-S). The

main distortions are the respectivecontractions or expansions of the offensiveor defensive effective play-space. Acontraction of game play illustrates thepresence of several players on a smallsurface; for its part, an expansion representsthe distribution of several players over a largearea. For us, an elastic system is made of aseries of contractions and expansions. Forplayers, it is necessary to find the stablesolution of the system within a few secondswhile a tension is applied to the system. Tounderstand how an elastic system works, onemust first understand how configurations ofplay work. In soccer, the dimensions of thefield limit the elasticity of the system,widthwise and lengthwise. When the systemis in large expansion, there are considerableperturbations and vibrations, and players arein motion at different velocities. This couldconstitute a first approach of a definition ofdisorder in team sports.

On a quick restart of the game or on aball recovery and swift counterattack by thegrey team, the type of configurationschematized in Figure 13 is very common. Ifthe ball holder is a good thrower, the OEP-Slengthens, with a very significant expansionwhile the DEP-S is still in contraction.

In team sports, the notion of density ofthe players’ distribution would refer to arather qualitative approach to theobservation of game play, whereas theconcentration / dispersion construct seemsmore related to a quantitative approach interms of number of players. Notions of com -pression / extension for the movement andof contraction / expansion about successivestatic states (or discontinuous temporalaspects) appear to work in close harmony todescribe and anticipate the moves ingame play and make appropriate decisions.This could be a way to explain the organic




links between the concepts of time andspace. The notion of open space is a dynamicdatum constantly changing; it is created or itdisappears depending upon player’s runs andmoves. We can then define the existence and



size of an open space from the time it takesfor a given player to cover it (go through it)and this, at a given speed. This idea of distance to be covered and speed of theplayer are, in our view, key concepts.

Figure 13. Contraction of the black / expansion of the grey within the elastic system.

During game play, the paths of the ballcause a succession of temporary contractionsand expansions. Whenever the ball holderstops, the EP-S is reformed, often, incontraction in front of him/her and so onsince every new pass induces changes in theconfiguration of game play.

With beginners (Gréhaigne et al., 2004),the succession of effective play-spaces arevery reduced and concentrated. One can notethat most often the ball circulates on the sideor at the front of the EP-S followingsuccessive passes intended to go forward.The ball stops when it is thrown in the

middle of the group of players. As is oftenthe case, for a game level under ten hours oflearning time, one can see, in this phase ofball circulation, a series of indirect plays withpauses that cause temporary contractions. Atthe end, if the ball reaches the key, one canobserve a contraction game-play on a stablespace (Figure 14, on the right hand side).

A succession of pauses by different ballholders often is the essential reason for thistype of game-play. In that case, the EP-Susually reshapes itself in contraction in frontof the player with the ball and so on. Now,let us consider another tool to analyze theopposition relationship.


Organizational level

Different organizational levels can beidentified. In fact, during the game, theglobal opposition relationship that we call“match organizational level” breaks downinto partial opposition relationships. Theseopposition settings that momentarily involvesome of the players generate a particularshape of play representing the “partialforefront organizational level” (see Figure15). At any moment of the match, this partialforefront contains a 3rd-level opposition unitthat links the ball holder and his / her directopponent. This is called “primary organi -zational level”.

Figure 15 illustrates these organizationallevels, whereas the drawing of the fieldwould represent the “organizational levelmatch“. Thus the “rapport de force”(Gréhaigne et al., 1999) may be looked at asinvolving two teams, two sub-groups ofplayers, or eventually two specific players.



The continuity of opposition influences theopponents’ moves not only at the one-to-onelevel, but at the partial forefront level and atthe match level as well. These simultaneousinterlocked opposition settings constitute thecontext of play (Bouthier, 1988; Deleplace,1979). They evolve in reciprocal rapport inresponse to the evolution of any part of thesystem.

Towards a dynamic conceptual modeling

of game play in soccer

We have seen in this paper that theconfigurations of play occur in varied partsof the field depending upon team strategiesof offensive or defensive tactical decisions,the opposition relationship, the score at agiven time, etc. Configurations of play mayalso be considered from a dual point of view,taking both attackers and defenders intoconsideration, either in the match system orin partial confrontation.

Figure 14. A succession of contraction / expansion.


The model presented in Figure 16 is anattempt to illustrate the use of complexsystem theory in team sports. In a closedspace (the field or the court), four mainevolutions of game-play (going forward,going backward, contraction and expansionof the effective play-space) are combinedwith paths and trajectories of the ball. Oneshould note that this complex systemoperates in a closed space, the pitch or thecourt, which restricts the scope of expansion.Cooperation between offensive players isbased on specific tactics intended to movethe ball so as to bring it in the scoring zoneand effectively score: penetrating, goingaround or over play. Cooperation betweendefensive players rests on two forms: man toman or zone defense. Defensive players mayuse one of two tactics: playing at the front ofthe ball or playing against the target line.



Some teams use forward defending,aggressively challenging the ball when on thedefensive in any part of the field. Others relyon a “collapsing” style, that falls back deepinto its own half when the opponent is inpossession of the ball. The “forward” policycan put immense physical and psychologicalpressure on opponents. It has more physicaldemands however, and may spread adefensive formation more thinly. The“collapsing” approach is more economical inphysical demand, and provides a packed backzone to thwart attacks. However it sometimescreates large gaps in midfield, and invites theopposing team to dribble forward and to takeshots from long range; if the opposing teamis good at the two aforementioned skills thengoals will be conceded freely.

Moves, contractions and expansions of theeffective (occupied) play-space are at the heart

Figure 15. Match, partial forefront and primary organizational level.


of our model. For the level “match system”,each team is characterized by a level of disorder/ order that shows the extent of organizationor un-organization of the group of players.Perception of this level of disorder / order isuseful to appreciate the collective functioning,but disorder must remain within an acceptablerange to ensure the continuity of game play.Too much order in the attack leads to a simpleand easy recovery tactical maneuver for theopponents. Too much disorder may induce

762 Revista de Psicología del Deporte. 2011. Vol. 20, núm. 2, pp. 747-765


confusion for the partners. Uncertainty is animportant element strongly linked to time. Agood information process and quick decision-making are key elements to reduce uncertainty.So, the objective for each team is to reduceuncertainty for itself and, at the same time, toincrease uncertainty for the opposite team. Thereality of evolving game play offers a very largevariety of concrete game situations inconnection with the notion of oppositionrelationship.

Figure 16. A dynamic system model for invasive team sports. The defense is in block (black circles).

Conclusion

The task of a team sport player lies indetecting, during game-play, incipientevolutions in the opposition relationship. Theplayer must infer or deduct the choices of

appropriate successive actions, for bothoffensive and defensive purposes, givenpossible game situations that can develop onthe playing surface at any moment. The relativepositioning of defenders to one another, theirlocation on the field and their proximity or not




to the target area (e.g. basket) have been shownto be important environmental constraints inthe behaviors of attackers in team sports. Taskconstraints are specific to the task at hand(given configuration of play) and are related tothe purpose of the game and to the action rulesthat govern the sequence of play (cf. Glazier,2010). Scoring goals (or points) or defending alead are key task constraints in sport. In thiscase, instructions, strategy and tactics helpplayers and must be considered as major in themanagement of game-play.

The shape of a particular-game playconfiguration, like the orientation of offensiveor defensive action, makes sense according tothe characteristics of evolving actions from theopposing team. Understanding these reciprocalrelationships between the state of movementof the two dimensions of opposition (offensevs. defense), and knowing how they operate inreal game-play, constitutes, by definition,tactical intelligence with regards to opposition.

So, it is almost impossible to re-create allsuch situations during practice sessions, but ifone considers their characteristics, they can becategorized into a smaller number of patternsin a coherent model. Essential to the learningprocess is the need for players to be providedwith opportunities to learn and to perceive keyspecifying information sources within aconstrained environment (Gréhaigne, Godbouty Bouthier, 2001). As a result, players should beable to produce functional behaviors oranswers to momentary configurations of playwhatever their complexity.

Finally, dynamic modeling of game-play insoccer can bring about a better understandingof best playing practices. This kind of modelingand the observational tools also provideknowledge and coaches can gain deeper insightfrom players’ training. This allows a coach totry out new strategies and to obtain feedbackon how these strategies work in the team.

COMO EVOLUCIONA EL “RAPPORT DE FORCES” DURANTE UN PARTIDO DE FUTBOL: LA DINAMICA

DE LA TOMA DE DECISIONES COLECTIVA EN UN SISTEMA COMPLEJO

PALABRAS CLAVE: Fútbol, Sistemas complejos, Modelos, TácticaRESUMEN: Este artículo pretende contribuir al estudio de la dinámica de sistemas complejos, en relación con el análisisdel rendimiento en el fútbol. Se presentan herramientas de evaluación para comprender mejor cómo la “relación defuerzas” evoluciona en función de las diferentes variaciones del juego, la contracción/ampliación de las fases del juego, y laposesión de balón. La aplicación de estas herramientas y modelos permitirá a los investigadores y entrenadores analizarmás eficientemente la estructura del juego y poder identificar posibles obstáculos para el éxito. En general, no se puedeentender la dinámica de los deportes de equipo, si no es desde una perspectiva espacio-temporal. Esto permite vislumbrartendencias cambiantes del sistema. De esta manera, será posible entender cuáles son las conductas funcionales de losjugadores y sus respuestas a las configuraciones específicas del juego, sea cual sea la complejidad de éste.

COMO E QUE O “RAPPORT DE FORCES” EVOLUI NUM JOGO DE FUTEBOL: A DINAMICA DAS DECISOES

COLECTIVAS NUM SISTEMA COMPLEXO

PALAVRAS-CHAVE: Futebol, Sistemas complexos, Modelos, TáticaRESUMO: Este artigo discute a contribuição da dinâmica para o estudo de sistemas complexos, no que respeita à análiseda performance em futebol. São apresentados instrumentos de avaliação para melhor compreender como é que o “rapportde forces” (jogo de forças) evolui com as perturbações nas jogadas, as contrações/expansões das fases do jogo, e a posseda bola. É hipotetizado que a aplicação destes instrumentos e modelos permite aos investigadores e aos treinadoresanalisarem eficientemente configurações do jogo e identificar aquelas que parecem ser críticas para o sucesso. No geral,nada pode ser fundamentalmente compreendido sobre os desportos de equipa se não se mudar de um sistema dereferência espacial para um temporal. Este torna possível iluminar as tendências evolutivas do sistema. Desta forma, épossível compreender como os jogadores produzem comportamentos funcionais ou respostas a configuraçõesmomentâneas do jogo, qualquer que seja a sua complexidade.


764 Revista de Psicología del Deporte. 2011. Vol. 20, núm. 2, pp. 747-765


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