Gréhaigne, J.F. (1992b). A weighted model to analyse the conditions of scoring in soccer. Paper presented to the 1 First A WEIGHTED MODEL TO ANALYSE THE CONDITIONS OF SCORING IN SOCCER Jean Francis Gréhaigne. IUFM, Universty of Franche-Comte, France The main problem in soccer when you want to analyse part of the game is the existence of a large number of interacting variables. The aim of this paper is to explain a new method of analysis of how goals are scored. It is important to give players and coaches some idea of how the attack / defense's system is working and more importantly how to adapt the game to score more goals. METHODS. Source of data : Data has been collected from the World soccer championship of in France, 1998.We have analysed the goals (except the goals on set-play) from the second round in a five-round knock-out competition up to and including the final. Data collecting and recording : To study this problem, we have used a video recorder. We have noted second by second the positions taken up by all the players who participated in the attack or the defense during the pregoal phase. Depending on the available pictures of a successful attack which has culminated in a goal, we have from four to eight topographic diagrams of the precise spot occupied by players and the ball. To obtain precision diagrams,we have used an index card depicting a standardized half pitch. International match pitches are 112 meters by 70 meters. Our data collection diagram represents half a pitch to scale to which we have added a squared pattern. Each square stands for two square meters on the ground for greater accuracy in plotting the players' positions. Figure 1 Exemple of a topographic diagram with grid. The figure 1 presents an example of a topogragraphic diagram. The ball is on the left side of the pitch, the defense seems in a good position. Despite this, a goal will be scored in four seconds. Now,we are going to explain our method of analysing these situations in order to better understand
Gréhaigne, J.F. (1992b). A weighted model to analyse the conditions of scoring in soccer. Paper presented to the 2 First the mechanics of how goals are scored. We obtain a cloud of points on each diagram which has to be analysed. But, any given cloud of points can be characterized by its center of gravity and its principal axis (PCA). This type of analysis is particularly useful in our research because the reciprocal positions of the centers of gravity appear to constitute an important indication in characterizing the notion of "in block" or "in pursuit " for the defense. The principal axis of inertia serve to sum up the dimensions and the surface of a cloud of points of the attack or of the defense. So to help process those configurations of the game that occur prior to a goal, we have decided to sum up the characteristics of the cloud of points of the attack and of the defense by three criterions : - The center of gravity is defined as the barycenter of the different players' positions who take part in the attack and / or the defense. - The principal axis is a measure, obtained by the application of the weighted sum of the distances' squared,which gives the main direction of the cloud of points. - The scattering axis, orthogonal to the principal axis is used to evaluate the range of the cloud of points. This process gives us the position of the subsystem of attack or defense on the field, its largest dimension and its degree of spreading which we shall be able to compare with the two main dimensions of the pitch : the width and the depth (in soccer the length is often designated by the depth). We have created a programme for an APPLE - MACINTOSH which permits automatic numeric calculations. To transcribe the precise spot of a player onto the computer's screen, you just have to click, his position onto the field diagram, with the mouse. Once, the data is entered and the calculations made, we obtain a graphic representation of the diagram. The principal axes of the attack are represented by a full line and those of the defense by a dashed line and they intersect at the center of gravity. INSERT FIGURE 2 Figure 2. Example of a processed diagram With this process, we can analyse this action sequence thus : the defense is spread widthwise and it is thin in the scattering axis. The center of gravity of the defense is situated "in block" between the target and the center of gravity of the attack. The ball is at the periphery on the left side of the field. The attack is spread diagonally. The defense's weak dimension is the depth and the attack is going
Gréhaigne, J.F. (1992b). A weighted model to analyse the conditions of scoring in soccer. Paper presented to the 3 First to play on it. Let us clarify the different parameters, we use to understand how a goal is scored. - The ball. With regard to the position which the ball can take in relation to the effective space game, we shall put the location of the ball into one of five categories. As a convention : B1 is a ball that is in a central position (in the corridor defined by the attacked goal and the defensed goal), ahead of the effective space game summed up by the principal axis. B2 is a ball that is in a central position, in the middle of the effective space game. B3 is a ball that is in a central position, in the rear of the effective space game B4 is a ball that is in a flank position (on the left or right periphery of the pitch), ahead of the effective space game. B5 is a ball that is in a flank position, in the rear of the effective space game. The centers of gravity. Their locations on the ground, their movements in the continuity of the game and the relationship with the position of the ball seems to be the most interesting data to analyse. According to the different configurations obtained, we shall study in depth the distance between the attacks'centers of gravity and those of the defense as well as their reciprocal positions on the pitch. For example, the fact that the attack's center of gravity is ahead of the defense is an indicator that proves that the attack is in advance temporarily of the repositioning of the defense. In this particular case we can consider that the attack has acquired a positional avantage and that an imbalance has been brought about in attack / defense ratio. Axis' configuration. The axes will be studied according to their lengths and their principal directions in relation to the dimensions of the field, that is the width or the depth. But we calculate the equibarycenter of the cloud of points. Consequently, the players have all the same weightings and this might be a cause of errors. To improve our model, we have developed another model which takes care of different weightings for the players. For this purpose, we note the angle between the player and the goal-posts of the target. We test if there is a defender in the triangle constituted by the player and the penalty-area. If the computer finds a defender in this area we multiply the weighting of the player by 0.2. We note the distance between the player and the center of the goal. The weighting of the player with the ball is multiplied by two because this player has the initiative in the game. The final model can be summed up in the following : Striker Weighting = a / d (*0,2 if "in block) Player with the ball Weighting = 2 * a / d (*0,2 if "in block) Defender Weighting = a / d RESULTS. Results for one configuration of play. We are going to analyse a formal configuration of play to show the use of our model. We have a configuration of play with the player with the ball ahead of the effective spave game. He has two partners on both side. The danger that a goal could be scored for the defense is real. But two others partners of the attackers near the center of the pitch in the rear of the efective space game have the same weighting. Consequently the equibarycenter of the defense is between the equibarycenter of the attack and the target (Figure 4 a)
Gréhaigne, J.F. (1992b). A weighted model to analyse the conditions of scoring in soccer. Paper presented to the 4 First Figure 4 a. A formal configuration with the simple model. With our weighted model (figure 4 b), we can obtain a result which is the nearest from the reality of the game. The center of gravity of the attack is ahead of the effective space game and the defense's one is for the moment out of position. Figure 4 b. A formal configuration with the weighted model. Results for one goal. INSERT FIGURES 5.
Gréhaigne, J.F. (1992b). A weighted model to analyse the conditions of scoring in soccer. Paper presented to the 5 First Choisir un but de la coupe d u monde en France For instance, we are going to describe the first goal of the Cameroon versus Colombia match in the last eight of the World Championship in Italy. On the left side of the figure, the weightings of the players are noted. Normally, this goal should be described in this way : Miller after a pass from Omam-Biyik makes a long run with the ball, enters the penalty area, shoots on the left of the target and scores. With our method, we can analyse this goal in the following way : Figure 5 a. Cameroon versus Colombia Moment M -7. Figure 5 a. Cameroon versus Colombia Moment M -6 In this first diagram at M -7, on seven players in defense, 4 are depthwise in the rear of the effective space game (E.S.G.) The attack is widewise. So, this makes the configuration [A1-D1]. The ball is in the middle of the E.S.G. in a central position. We can sum it up as follows : A1-D1, B2. The position of the center of gravity of the defense is between the attack and the target but the situation can be considered out of balance because the defender in front of the player The aim of the attack is to try and pass the ball ahead of the effective space game. At M -6 the defense is trying to restore the balance by changing configuration. The ball is always in the middle of the E.S.G. Figure 5 a. Cameroon versus Colombia Moment M -5 Figure 5 a. Cameroon versus Colombia Moment M -4 A pass from Djonkep (Cam) to Omam-biyik on the flank of the attack involves a change in the configuration of the attack because an attacker has moved in the depth and is temporarely off-side (A3-D1). Figure 5 a. Cameroon versus Colombia Moment M -3 Figure 5 a. Cameroon versus Colombia Moment M -2 At this moment, the attackers begin a movement depthwise with a pass and support between Omam-Biyik and Miller. The ball is progresively coming forward of the axes while the defense and the attack centers of gravity are superimposed. A beginning of imbalance really appears at this moment. The defense has not made up lost time (A1_D1, B1) and the player with the ball has space before him. Figure 5 a. Cameroon versus Colombia Moment M -1. Taking advantage of this space, Miller continues playing depthwise. In a dangerous position, the defense begins a manœuvre "in pursuit". The pursuit manœuvre is not well executed, the Cameroon center of gravity is getting more and more late. At (M -1) The player with the ball, still ahead of the E.S.G. is approaching the target [A1-D3, B1]. Figure 5 a. Cameroon versus Colombia Moment M 0 M 0 : the goal is scored. The attacker in a favourable position has succeeded in shooting and the goalkeeper has not been able to stop it. DISCUSSION. This sequential analysis seems to show that there is crucial moment in an attack. We can identify three points as follow : - when, from the rear, the ball is passing ahead of the effective space game ; - when the centers of gravity are superimposed, because it is the precise instant when the attack can take advantage and exploit the time gained. We have called this, the breaking point of the balanced state. - when the player with ball penetrates into the penalty area ahead of the E.S.G. So the player has to pull off his shot to score. The breaking point of the state.equilibrium can be defined when the centers of gravity are superimposed. Here, either the attack takes the lead over the replacing of the defense or looses the ball. Finally to score a goal, more often, the attack : must take the lead conserved this lead and score.
Gréhaigne, J.F. (1992b). A weighted model to analyse the conditions of scoring in soccer. Paper presented to the 6 First Another important thing which should be noted from our data collection of goals is that the time between the breaking point of the state.equilibrium and the goal itself is never more than four seconds and the number of passes is rarely greater than 3 or 4. If the attack takes the lead over the replacing of the defense, the next step is to exploit that advance. If the players persist in playing the ball back or squaring across the field, the opportunities to exploit this advantage will be lost soon. Having created a configuration which can permit a goal to be scored, players must now think in terms of exploiting it and making rapid progress toward shooting at the opponent's goal. Time is precious in soccer at such moments. The point we would like to emphasize is that we do not consider the goalkeeper'position. Statistically, they stop a third of the shots But with our model, the goalkeeper sums up, in his own position, the center of gravity of the defense (figure 6). Figure 6. The goalkeeper and our weighted model. CONCLUSION The main purpose of our research was to identify - with the aid of a new method of analysis - the crucial points in an attack. This analysis can be considered as a beginning because the study is only based on a small number of goals and we have only analysed the attacks which culminate in a goal. The second point is that we can analyse formal configurations of play in order to find promising configuration or successfull patterns of play to score a goal Finally, using these tools and currently available models, research should be pursued to try and identify the principles at work in the game of soccer REFERENCES
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First world congress on notational analysis of sport. Barton Manor. November 22nd-25th 1992. 8 Cameroon Colombia Player with the ball Figure 5 a. Cameroon versus Colombia Moment M -7. Figure 5 b. Cameroon versus Colombia Moment M -6.
First world congress on notational analysis of sport. Barton Manor. November 22nd-25th 1992. 9 Figure 5 c. Cameroon versus Colombia Moment M -5. Figure 5 d. Cameroon versus Colombia Moment M -4.
First world congress on notational analysis of sport. Barton Manor. November 22nd-25th 1992. 10 Figure 5 e. Cameroon versus Colombia Moment M -3. Figure 5 f. Cameroon versus Colombia Moment M -2.
First world congress on notational analysis of sport. Barton Manor. November 22nd-25th 1992. 11 Figure 5 g. Cameroon versus Colombia Moment M -1. Figure 5 h. Cameroon versus Colombia Moment M 0.