How the Rapport de Forces Evolves

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Revista de Psicologa del De porte Universitt de les Ules Balears2011.Vol. 20 , nm . 2, pp. 747-765 Universitt Autno ma de BarcelonaISSN: 1132-239X

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

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

HOW'THE '-RAPPORTDE FORCES ElX)LIT-S IN A SOCCER MATCH: THE D'i'NAMICS OF COLLECTIVEDECISIONSINA COMPLEX SYSTEMKF.\'V('ORDS: Soccer, Com plex system, Modeling, Tactics, Moves.ABSTRACT: This article discusses thecontribution ofdynamicsto thestudyof complex systems with regardsto performance analysis in soccer. Evaluation toolsarepresented to better understand how the rapport deforcesevolves with perturbations ofplay, contraction / expansion phasesofgame play,andpossession of the ball.It ishypothesized that applicationof these toolsandmodels may enable researchersandtrainers to efficiently analyzeconfigurations ofplayandidentify th ose that appear to becritical forsuccess.Allthings considered, nothing maybefundamentally understood about team sportsifone d oes not shift fromaspatialto temporal reference system.Itmakesitpossible tobring tolight thesystem's evolving tren ds. Th is way,it is possible to understand howplayers produc efunctional behaviors or answerstomomentary' configurations of play, whatever their complexity'.

Correspondencia: Jean-Francis Grhaigne, Ph.D. TUFM de Franche-Comt. Fort Griffon. 25042 Besanon Cedex. France.E-mail: jean-francis.grehaigneifi^univ-fcomte.fr

* G RIAP S, U niversit'ofFranche-Comt, France.** l^val Universit}', Quebec city, Canada.


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Complex systems analysis is a sciendficfield which studies the common properdes ofsys tems cons idered complex in nature ,society and science. The key problems ofsuch systems are difficuldes with their formalmodel ing and s imulat ion . From suchperspecdve, complex systems are defined onthe basis of their different attributes. Thestudy of complex systems brings new vitaUtyto many areas of science where a moretypical reducdonist approach has faUen short.Complex systems analysis is therefore oftenused as a broad term encompass ing aresearch approach to problems in manydiverse areas such as team ball sports. From asystemic analysis point ofview,key concepts,such as self-organization, t ime andconstraints, can be used to help explainingstability, variability and transitions amongconfiguradons of play (Grhaigne, 1989).

The central nodon of opposidon 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 tradidonally) 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 ins tance(Garganta, 1997; Grhaigne, 1992).We are tempted to say that it is asimportant, and maybe more important, to getplayers to optimally manage disorder(Grhaigne, 1989; Grhaigne Godbout, 1995;ViUepreux, 1987). A game rarely rests upon thesimple applicadon of tacdcal combinadonslearned previously dudng training. Thus, mostof the time dudng the game, one can foresee

BalanceImbalance

Breaking Continu ity

Delay Advance

RiskSecurity


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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 r isks 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(Grhaigne, 2009). All things considered,nothing may be fundamentally understoodabout team sports if one does n ot shift froma spatial to a temporal reference system. Thesynchronous properties of a system relate tothe relationships between several of itscharactedstics at a given time. The diachronicproperties relate to the relationships of those

bring to l ight the system's evolutionarytrends.

Team ball sports in general, and soccer inparticular, can be considered as complexsys tems composed of many in ter -acting components (Arajo, Davids, Bennett,Button y Chapman, 2004; Grhaigne, 1989;Grhaigne, 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-r ized by ord er-d isord er t rans i t ion s(Grhaigne, 1989) , where indiv idual orcollective actions may destabil ize 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 m atch organi-zational level, the set made ofthe confronta t ion 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 t ime related processes such asexchanges, regulations and re-organization ofthe e lements . Funct ional ly-wise , one isdealing with the evolution in time of theopposing relationship between the two teams(advance, delay; breaking, continuity). These


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shape of play repre sentin g the partialforefront organizational level . At anyspecific moment, according to the evoludonof play, this reciprocity reladonship offers,for example, a specific problem to attackersbut, at the same time, contains pertinentsolu t ions for conduct ing the act ion(Grhaigne, 1992).

Grhaigne et al. (1997) argued thatchanges in the momentary' configuradon ofgame play have to be examined in Ught ofthe previous configuradons, an example ofthe concept of conditional coupling incomplex systems theory (Davids, Arajoand Shuttleworth, 2005; Davids, Button andBe nne t t , 2008) . They concluded that choice s are made based on p os i t io n ,movement and the speed of one ' steamm ates and op po ne nts (p. 148). W iththe oppos i t ion re la t ionship , order anddisorder can emerge from the play at anymom ent. This way, the energy and choicesof the players serve to create the condidonsfor transitions between configurations ofplay and transform the play (p. 148). Thesetransidons 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 theor)' with regards to performanceanalysis, using football for illustrations.Evaluation tools are presented to betterunderstand how the rapp ort de forces(Grhaigne, Go db out y Bouthier , 1999)evolves with perturbations of play,contracdon / expansion phases ofg meplay,and possession of the ball. It is hjpothesizedthat applicadon of these tools and models

configuradons of play and idendfy those thatappear to be cridcal for success.

Ad opting 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 locadon and displacement.To this end, we tested the concepts of effecdveplay-spaces in expansion and / or contracdonto experiment different analysis of the rap por t de forces between two teams.Transidons and transition game play oftenrefer to configurations where one hassufficient dme 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 configuradons change shape and aremost often in expansion. For its part, the incom pression model appears in a stabilizedgame play with a high density' ofplayers.

This succession of momentary configu-radons 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 contracdon; Ball stopped at the periphery of thecontracdon;Moving baU towards the contracdon;Ball stopped in an expansion phase;Ball moving in an expansion phase; Moving the ball at the periphery ofeither the contracdon or the expansion.One must, of course, consider both the

paths and trajectories of the ball in order toobtain a more accurate assessment of thesituadon and a better idea of the rapp ort de


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Observation of game-playTo better understand the contribudon of

a com plex sys tem ap proach to theconception of team-sport learning, we usethe nodon of effecdve (occupied) play-space(EP-S) as a tool to extract data on theevoludon of game-play.Effective play-spaceIf one considers a given configuradon ofplay (see Figure 1), one can summarize itusing the nodon of effecdve play-space, asillustrated in Figure 2 (Grhaigne, 1989;Grhaigne, Richard and Grif f in , 2005;Mrand, 1977). Th e effecdve play-space (EP-S) may be defined as the polygonal area thatone obtains by drawing a line that links allinvolved players located at the peripherj' ofthe play at a given instant.

This conception of effecdve play-spacepostulates that between the elements ofbo th t eams in compet i t ive oppos i t ionsetdngs, a structuring of cooperation andoppos i t ion r e la t ionsh ip t akes p lace .Considering the locadon of the EP-S on thefield and the direction of the attack, theposidon of players of both teams and theposidon of the ball constitute a particularconfiguradon of play at instant T. In thesecondidons, the defined shape of a pardcularconfiguradon and its possible evoludon mayprovide significant information on the valueand the limits of a player's adaptation, thatis to say on what his/her behavior expressesin t e rms o f innova t ion , inven t ion , o runlikely regre ssion when confro nted toopponents.

Dt fBCUon^ofatta i r

Figure 2 A given configuration of play insoccer Th eball is at the rear of the configuration

F i g u r e 3 . T h e e f f e c t iv e p l a y - s p a c e E P - S ) o f e i s c o r t g u r a t i o n .

Offensive and defensive effective play-spaces OEP-S and DE P-S)Considering the respecdve posidoning ofat tackers and defenders , one may a lsodetermine an offensive effecdve play-space(OEP-S) and a defensive effecdve play-space(DEP-S). Then, two more or less interpene-trated polygonal surfaces are obtained (seeFigures 4 and 5 where polygonal areas are

ship between these two opposing areas andtheir respective evolutions in t ime mayenlighten us on changes in the balance of theoppos i t ion re la t ionship dur ing matches .Pardcularly, the locadon of the ball or of theball holder in the offensive effective play-space, according to the attack phases, pro-vides good indicadons depend ing if the ball isat the rear, within, at the periphery or at the


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Directionof attack


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Grhaigne,J. F. Godbout, P . y Zerai, Z. How the rappo rt de forces evolves in a soccer ...

om plexion of playDuring a match, a unit of play evolves

from a state to a state 2 and so on to a staten. As in a photo, the configuradon of play isdefined by the position of all players at am o m e n t A Through the analysis of thedifferent baU-bolders' tacdcal choices prior toa goal, one may better understand how goalsare scored. To that end, Gthaigne et al.(1997) have devised some diagrams represen-dng the few seconds preceding a goal. Foreach player, one can note a) the player'sposit ion, 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 (Grhaigne et al., 1997) the nodonof sector of play for the attackers and thatof sector of intervendon for the defenders.Those sectors spatially define the limits ofpossible acdons for the different players.

within one second, considering the threeparameters mendoned above. With referenceto concepts used by Plank (1941) in physics,we shall name such a distribution a com plexion of system . In short , thepurpose is to descdbe the dynamic states ofplayers who pardcipate in the attack and thoseof thei r opponents . Whereas a s ta t icconfiguradon ofplayis iUustrated in Figure 10,dynamic pictures of the transidon betweentwo configuradons 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 stadc spadal distribudon of theplayers on the field or court, a dynamicanalysis of the play actually indicates a moregeneral homogeneit)' with respect to players'moves. Whereas the stadc spadal distribudonof players (Figure 10) suggests severalpossible tacdcal decisions on the part of theattackers (grey circles), the two successive

Direction of attack


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dynamic configuradons of play (Figures 11and 12) sugg est a relatively bala nce d

confronta t ion between a t tackers anddefenders.

Figure 1 1. Dyn am ic conf igurat ion o f p lay a tM l sec tors o f p lay in gray and sec tors o f in t ervention in b lack) .


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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(Grhaigne and Godbout, 1995).

Part of the receivers ' sectors of play(Grhaigne 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 'posit ions 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. bservation and system

The stable state of 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. bservation and intention

To be more precise, let us consider twodifferent observers of a system composed of'n ' players on the field. A first ob serv erconsiders 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 com plexions , but by

Considering that the second observer canonly take into consideration the different com plexio ns 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 probabilit}' of occurrence. Heis able to define as a stable dynamic statethe 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 precis ion. Inherently, our twoobservers have done the same kind of workto characterize the elem ents, to classifythem, but each using different scale:

The first observer has characterized the'n' players according to static criteria (onecriterion being the fact that players are partof one oftwosets, 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 -hom ogen eou s dis tr i-bution of theirenergystate. A certain kind ofhomogeneous scattering characterizes theequilibrium state toward which invasive teamsport systems always evolve. It corresponds,therefore, to a homogeneous distribution of


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The degree of homogeneit)' of the dynamicconfiguradons of play can also he explainedby a distribution of the probabiUdes of thepresence of the players in certain parts of thefiel

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 dialecdcbalance / unbalance of game play operates.On the one hand, very stable structures makeone think of a crystalUne structure... definedas dgid and with few chances of evoludon, asfor example in set-plays. On the other hand,the dynamical configurations of play havewithin themselves a num ber of transfor-mations limited according to the differentpossibiUdes of the condnuous evolution ofthe game but nevertheless important if onechooses a break in modifj'ing the movementin process. n elastic system

Chow, Davids, Button, Shuttleworth,Renshaw and Arajo (2007) have exploredthe potential of a nonlinear pedagogicalf ramework, based on dynamic sys temstheory, as a suitable explanadon for tacdcalapproach in team spor ts in phys icaleducation. Nonlinear pedagogy involvesmanipuladng key task constraints on learnersto facilitate the emergence of qualitativeinformadon on game-play, funcdonal move-ment pat terns and decis ion-makingbehaviors . So , to bet ter unders tand theevolution of configurations of play, it ispossible to study shapes and distordons of

main d is tor t ions are the respect ivecontracdons or expansions of the offensiveor defensive effective p lay-s pac e. Acontraction of game play i l lustrates thepresence of several players on a smallsurface; for its part, an expansion representsthe distribudon of several players over a largearea. For us, an elastic system is made of aseries of contractions and expansions. Forplayers, it is necessary to fmd the stablesolution of the system within a few secondswhUe a tension is appUed to the system. Tounderstand how an elasdc system works, onemust first understand how configuradons ofplay work, ln 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 modon at different velocides. This couldconsdtute a first approach of a definidon ofdisorder in team sports.

On a quick restart of the game or on aball recover)' and swift counterattack by thegrey team, the type of configurationschemadzed in Figure 13 is very common. Ifthe ball holder is a good thrower, the OEP-Slengthens, with a verj' significant expansionwhile the DE P-S is sd in contracdon.

In team sports, the nodon of density ofthe players' distribution would refer to ara ther qual i ta t ive approach to theobservation of game play, whereas theconcentration / dispersion construct seemsmore related to a quandtadve approach interms of number of players. Nodons of com-pression / extension for the movement andof contracdon / expansion about successivestatic s tates (or discontinuous temporalaspects) appear to work in close harmony todescr ibe and ant ic ipate the moves in


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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 ofdistance to be covered and speed of theplayer are, in our view, key concepts.

Direction of attack

Figure 13 Contraction of the black / expansion of the grey within theel sticsystem

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

With beginners (Grhaigne 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 sedes 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.


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irection of attack

1) c

Figure 14 A su ession of contraction / expansion

rganizational levelDifferent organizational levels can beidentified. In fact, during the game, theglobal opposition reladonship that we call ma tch organizational level breaks downinto pardal opposidon reladonships. Theseopposidon setdngs that momentarily involvesome of the players generate a particularshape of p lay repre sent in g the par t ia lforefront organiz ational level (see Figure

15).At any moment of the match, this partialforefront contains a 3rd-level opposidon unitthat links the ball holder and his / her directop pon en t. This is called primary organi-zadonal level .Figure 15 iUustrates these organizadonallevels, whereas the drawing of the fieldwould represent the organizational level

ma tch . Thus the r app or t de fo rce(Grhaigne et al., 1999) may be looked at as

The condnuity of opposidon influences theopponents' moves not only at the one-to-onelevel, but at the pardal forefront level and atthe match level as well. These simultaneousinterlocked opposidon setdngs consdtute thecontext of play (Bouthier, 1988; Deleplace,1979). They evolve in reciprocal rapport inresponse to the evoludon of any part of thesystem.Towards a dynamic conceptual modelingofgam e play in soccer

VC'e ha ve seen in t his p ap er th at th econfiguradons of play occur in varied partsof the field depending upon team strategiesof offensive or defensive tactical decisions,the opposition relationship, the score at agiven dme, etc. Configuradons of play mayalso be considered from a dual point of view,taking both attackers and defenders into


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Grhaigne,J. F. Godbou t, P. y Zerai, Z. w the rapport de forces evolves in a soccer .

CaptionDefenderAttsdMr

O Ball

MatchPartialor ront

- o / ;Primary level x

igure 15 .Match partialforefrontand primary organisationa l level.

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, contracdon 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 bdng it in the scoring zoneand effectively score: penetrating, goingaround or over play. Cooperadon betweendefensive players rests on two forms: man toman or zone defense. Defensive players mayuse one of two tacdcs: playing at the front of

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. Th e 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 somedmescreates 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 aforemendoned skills thengoals wl be conceded freely.


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of our model. For the level match system ,each team is characterized by 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

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 ver)' largevariety of concrete game situations inconnection with the notion of oppositionrelationship.

Contraction

ooper ting for defenseMan toMan logicZone logic

against the target t>ack at the ball front

nse ^ W1 \

Goingbackward

In closed space: the field court)BallPaths and ortrajectoriesof the ball

Goingforward

Advance / DelayBlock Pursuit

Coope rating far attackPenetratingGoing aroundOver play

ExpansionFigure 16. A dynamic rystem model for invasive team sports. The efense is in block black tircles).

ConclusionThe task of a team sport player lies indetecting, during game-play, incipient

appropriate successive actions, for bothoffensive and defensive purposes, givenpossible game situations that can develop onthe playing surface at any moment. The relative


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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 ofplay and are related tothe purpose ofthegame and to the acdon 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.

Th e shape of a particu lar-gam e playconfiguradon, like the odentadon of offensiveor defensive acdon, makes sense according tothe characterisdcs of evolving acdons from theopposing team. Understanding these reciprocalreladonships between the state of movementof the two dimensions of opposidon (offensevs.defense), and knowing how they operate inreal game-play, constitutes, by definition,tacdcal intelUgence with regards to opposidon.

So, it is almost impossible to re-create ausuch situadons during pracdce sessions, but ifone considers their charactedsdcs, they can becategodzed into a smaUer number of patternsin a coherent model. Essential to the leamingprocess is the need for players to be providedwith opportunides to learn and to perceive keyspecifying information sources within aconstrained environment (Grhaigne, Godbouty Bouthier, 2001). As a result, players should beable to produce functional behaviors oranswers to momentary configuradons of playwhatever their complexity.

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

COMO EVOLUCIONA EL RAPPORT DE FORCES DURANTE UN PARTIDO DE FTBOL- LA DINMICADE LA TOMA DE DEOSIONES COLECTIVA EN UN SISTEMA COMPLEJOPALABRAS CL AVE; F tbol, Sistemas comp lejos. Modelos, TcticaRESUMEN: Este artculo pretende contribuir al estudio de la dinmica de sistemas complejos, en relacin con el anlisisdel rendim iento en el ftbol. Se presentan herramientas de evaluacin para comp rende r mejor cm o la relacin defuerzas evoluciona en funcin de las diferentes variaciones del juego, la contraccin/a mpliacin de las fases del juego, y laposesin de baln. La aplicacin de estas herramientas y modelos permitir a los investigadores y entrenadores analizarms eficientemente la estructura del juego y poder identificar posibles obstculos para el xito. En general, no se puedeentender la dinmica de los deportes de equipo, si no es desde una perspecdva espacio-temporal. Fsto permite vislumbrartendencias cambiantes del sistema. De esta manera, ser posible entender cules son las conductas funcionales de losjugadores y sus respuestas a las configuraciones especficas del juego, sea cual sea la complejidad de ste.O OEQUE O RAPPORTDE FORCES EVOLUINUMJOGO DE FUTEBOL: A DIN-WICA DAS DECISOESCOLECTIVAS NUM SISTEMA COMPLEXOPALAVRAS-CHAVE; Futebol, Sistemas complexos. Modelos, TticaRESUMO: Este ardgo discute a contribuio da dinmica para o estudo de sistemas complexos, no que respeita anliseda performance em futebol. Sao apresentados instrumen tos de avaliao para melhor compreender com o que o rappo rtde forces (jogo de foras) evolui com as perturbaes as jogadas, as contraes/ex pans es das fases do jogo, e a posseda bola. E hipotetizado que a aplicao destes instrumentos e modelos permite aos investigadores e aos treinadoresanalisarem eficientemente configuraes do jogo e identificar aquelas que parecem ser crticas para o sucesso. No geral,nada pode ser fundamentalmente compreendido sobre os desportos de equipa se nao se mudar de um sistema dereferencia espacial para um temporal. Este torna possvel iluminar as tendencias evolutivas do sistema. Dcsta forma, possvel compreender como os jogadores produzem comportamentos funcitinais ou respostas a configuraces


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