The Theory of Soccer

| Educational level: this is a non-formal education resource.

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| Educational level: this is a research resource.

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## The Theory's Focus and Benefit

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Soccer is twofold: it is both sport and game. As a sport, soccer requires various  individual technical skills that the players implement, such as dribbling, passing and shooting. As a game, soccer is based on some basic principles of ordered movement. Because the technical skills are the difficult part of soccer, everybody concentrates on them and disregards the simple ordering fundamentals of the game. In the Theory of Soccer, these fundamentals are explained and the historical and cultural evolution of soccer as a game is analysed.

In the Theory, a soccer game is considered in which both teams are equally talented. Under this assumption, the hypothesis is that soccer relies on a very simple best strategy. If only one team follows this strategy, it always will win. If both teams follow this strategy, the matches are well-ordered; they are enjoyable to play and to be watched. Complicated tactics become superfluous.

Understanding and believing in the Theory of Soccer, the players easily know at every time what to do and where to position themselves optimally and the spectators can enjoy the match from a superior point of view.

## How to Play the Game?

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### The Basic Need to Collaborate

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Let's consider a one on one duel, where a player takes the ball and an opponent other than the goalkeeper faces him. Basically, the ball’s possessor can try two things in order to score:

* He may try to score himself, by shooting immediately or after dribbling.
* He may pass the ball, directly or indirectly, to a team-mate in the best position to score.

The first possibility may be successful under certain circumstances. But when the players' quality is similar in both teams, mostly the opponent in front of him or subsequently other opponents won't let the ball's possessor finish without major disruption. The second possibility means that team-mates must collaborate in the attack. In a match where all players are equally talented in physical and technical skills, the team with the best internal collaboration will win.

### The Common Soccer Strategy

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In the last section, we have noticed that there is a basic need for team collaboration to pass the ball to the team-mate who is in the best position to score, let's call him the finisher. A very good opportunity to score is when the finisher is in a free position. In such a position, he wouldn’t be met by an opponent except the goalkeeper on his way to score. The defending team must prevent any opponent from getting into a free position and receiving the ball to finish successfully. It must subtly avoid the advance of any attacking player that has no ball at his feet. This defence challenge is called coverage.

Look at the diagram below. It shows the strategic states \- circles in the diagram - of a soccer team that order the game. When a team has lost ball possession, it has to cover every opponent. When a team controls the ball, it tries to get one of its players into a free position to score. When this is achieved, the team tries to pass him the ball. During the game, the transitions – arrows in the diagram – from one state to another are often quick and dynamic. This is the Common Soccer Strategy.

We conclude that the essential strategical questions of the soccer game are:

* How can the team in possession get one of its players in free position and pass him the ball?
* How can the opposing team avoid it?

### The Evolution of Soccer Strategy

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There are basically two ways to implement the suitable strategy for a game: by thought and collaboration and by refining some laws of the game. Let's talk about how these two possibilities combined historically.

Historically, soccer strategy is tightly related to the ruling offside law. The original offside rule was regulated to a game law in 1863, but it was in practice long before. It was substantially changed in 1866 and finally in 1925. This leaves the offside law still effective today.

According to the Theory of Soccer, there are three stable strategic systems in the evolution of soccer: the Ancient, the Classic and the Modern system. They correspond to the three successive offside laws. Each system is consistent with The Common Soccer Strategy explained above. In a stable strategic system, every player knows in theory where to position himself and what to do at every moment. Defence and attack are well ordered.

However, soccer is a cultural phenomenon, in which things evolve by experience. The crystallisation of a stable system is not straight forward. It is preceded by lengthy transitional periods. A stable system is influenced in practice by many remnants of previous times.

## Past Soccer Times

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### From Primitive Soccer to the Ancient System

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In its primitive origins, soccer had only vague rules. It was more rude sport than game. Each participant disputed the ball possession selfishly. There was no sense of collaboration or game ordering. We can observe the same thing when children play soccer for the first time without instruction.

Gradually leaving primitive soccer, soccer participants began to decide before starting the game which rules (number of players, pitch measures, duration, fouls,...) would be applied. Among the rules, there was one, called the offside rule, that restricted the advance of attacking players. It was an offence to pass the ball to a player at the time he was in a offside position. The rule stated:

Ancient Offside Rule
An attacking player is in offside position if he is more advanced than the ball.

Obeying the offside rule, which became official law in 1863, each team was obliged to stay behind the ball, as illustrated above. The attacking players without the ball couldn’t advance freely in order to receive a forward pass. They were all covered.

This kind of coverage is very efficient but overly inhibits the game. In order to get rid of the coverage, the ball possessor, that couldn’t advance through the cloud of opponents, used to throw the ball backwards to a non crowded zone, where a team-mate would kick the ball long and high. This gave the attackers time and opportunity to run forward. They hoped that a free player could control the ball and score.

Look at the diagram above. The player with the ball has an opportunity to kick high. To avoid offside, the team-mate must stay behind the ball. It will be difficult for him to control the ball, since he can start to run only after the kick, and the opponents are in general nearer to the landing point than he is. However, there was no better strategy to counter ancient soccer’s defence.

Now we have seen why the offside rule, born from experience, became very important: It implemented completely for both teams an automatic defence strategy to cover every opponent. A corresponding attack strategy could evolve based on it. With this rule, everybody enjoyed soccer more than without it. It led from primitive soccer, in which there was no order, to the ancient soccer system, which had a full stable game strategy, in which every player knew what to do at every time.

### The End of the Ancient System

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The offside law in ancient soccer restricted the attacking team collaboration greatly. To alleviate this, a new offside law was invented in 1866:

Classic Offside Rule
An attacking player is in offside position if he is more advanced than both the ball and the antepenultimate opponent.

After the advent of the new offside law, some Scottish teams realized first that the attackers were able to position behind the defender's back and receive a forward pass. This baffled the teams whose players continued to play by habit according to the ancient system. It took time until a new efficient defence strategy was generally adopted, leading to the Classical System.

### The Classical System

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The new offside law definition led gradually to the classic soccer system, where a remarkable phenomenon appeared: Only two defenders, besides the goalkeeper, were sufficient to control the advance of any number of attackers. One defender always opposed the attacker that had the ball and determined, by his position, the offside zone. The other defender was situated more backward, in the offside zone, being able to intercept any attacker that could enter the offside zone legally with the ball.

How to counter this coverage? Look at the following diagram. A wing attacker has succeeded in almost reaching the goal line with the ball. Since there is no offside behind the ball, some team-mate in the middle may receive a backward pass and score. In order to play this way through the wings and centre, five forwards turned out to be optimal.

Given two defenders and five attackers, three players are left in-between. The task of these midfielders was to transmit the ball quickly from defence to attack. This 2-3-5 scheme was called pyramidal formation. Games played by both teams in this formation were very attractive both to play and to watch. The ball, which is faster than the quickest player, could move easily on the ground forward and every player could stay in his assigned zone.

The spectators and players of this classical system are quickly dying out. It would be interesting to recreate games played in this system before their input becomes unavailable to us.

## Modern Soccer Times

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### The End of the Classical System

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Although the classical system offered beautiful soccer for a long time, a crisis exploded in the English Professional League. The number of goals and spectators decreased continuously. This was due to some defenders like Billy McCracken of Newcastle United who provoked countless offside whistles with an offside trap. In 1925, officials decided to diminish the power of the law and redefined it as follows:

Current Offside Rule
An attacking player is in offside position if he is more advanced than both the ball and the penultimate opponent.

This law definition is, with minor modifications, still in force.

Look at the diagram above. In the classic model, the defender who determined the offside line could stop the advance of all opponents, since another defender was behind him. But with the new rule, there is no defender in the offside zone. The player with the ball can pass it to a team-mate in free position to score.

A slight word modification – penultimate instead of antepenultimate – had an enormous impact: In its modern version, the offside law has ceased to be a sufficient, automatic defence strategy.

### The WM Formation

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With the new offside law of 1925, two players were insufficient to defend. The classic 2-3-5 formation became obsolete, a period of disconcert began. There were several trial and error attempts to reinforce the defence. Finally, the idea of an English coach, Chapman, prevailed. He decided to shift a midfielder back to defence. The resulting player's arrangement was called the WM formation because it brings these two letters to mind. Like the classic system, every player stayed in his own zone. It was the ball that circulated quickly.

There is something remarkable about the WM formation that was not conciously intended: Opposing teams arranged in this 3-2-2-3 scheme overlapped. One team's front half coincides with the other's team back half. Therefore, in every zone there are two paired opponents.

The WM formation dominated the game for a long time, but it was not a stable strategic system. On the one hand, it allowed a way to defend in that each player covered the opponent in his zone. On the other hand, no strategic solution could crystallise in attack due to the tight pair coverage in the zone. Thus, it became more and more difficult to place a player in free position to score.

### Trying to Leave the Zone

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In the last section, we have noticed that the the rigid WM formation made it impossible to fulfil the Common Soccer Strategy. Staying in his zone, each attacker was always covered by an opponent. Why did each player actually stay in his zone? The reason is historical. In the classic system, it was strategically sound that each player had an assigned zone. This was kept in the WM formation by habit. But gradually, the attacking player got the urge to separate from his opponent and even to leave the zone.

There were two ways to leave your own zone: horizontally or vertically. Horizontally, two attackers at the same level would swap. This caused the defence a bit of confusion, but every player remained covered. Vertically, some player of the back region would advance into the forward region while his team possessed the ball. It was the vertical way that threw the WM formation off balance: It was no longer sufficient for the players of the defending team to stay in their zone and wait because there was necessarily a single defender somewhere who would have to meet more than one opponent. The greatest example of abandoning the zone vertically was exhibited by the Brazilian Team that won the World Championship 1958.

When the phenomenon of leaving the zone began, defenders thought that coverage consisted in shadowing the opponent all the time and attackers believed that getting into free position meant moving to somewhere with no opponents around. All this induced an augmentation of non strategic runs, both tiring and unnecessary, that do not comply with the Common Soccer Strategy. The right way to abandon the zone was not found, and so zonal concepts like arbitrary formations (4-4-2, 4-3-3, 5-3-2, ...) and fixed positions (sweeper, centre forward, flat back four, ...) were rehashed and persist today.

## Towards the Modern System

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### Let's Keep It Simple

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In ancient and classical times, soccer strategy was simple. The ruling offside law implemented an automatic defence strategy, from which an attack strategy could evolve. In modern times, the offside law is insufficient as a defence. So we have to think about how to defend. Unfortunately, there are complications in that. By trial and error, habits from the past, like formations and offside are used that don't belong to modern times.

We know that the current offside law is not sufficient as a defence. Is it necessary? It may in some circumstances be useful but mostly it is counterproductive. In order to preserve a big offside zone, the defenders don't often position themselves backward enough to cover opponents effectively. A lot of goals are conceded for this reason. In the Soccer Theory, the belief is that sooner or later, convinced by experience or research, the teams will absolutely ignore the offside law as a defence method. It will become obsolete. It is interesting to note that in small sided soccer, played for example indoor five against five, there is no offside law.

A further trap is rigid formations. Every rigid formation will be cracked a soon as the opposing team abandons the zone vertically, as it happened in the WM formation. Let's face it: formations are just respected before kickoff.

Let's look for a modern system that implements the Common Soccer Strategy in the only way that is possible in modern times: with no zone bindings and no offside aid.

### Modern Defense

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To fulfil the Common Soccer Strategy, the defending team must be sure that no opponent is ever free. If an opponent is free and gets the ball, he can advance without hindrance: The defence is unstable. The solution in modern soccer is to assign an opponent permanently to each player of the defending team. Each player orients his position towards his opponent in order to guarantee that, if his opponent gets the ball, he can hinder him before he can either score or destabilise the defence.

In the diagram above, we see that each defender is responsible for an opponent. Note that it is unnecessary to shadow the opponent all the time. Opponents far from the defended goal may be covered from a distance. It is important that every defending player concentrates on this “opponent oriented coverage” without being distracted by zone assignments, by the offside rule or by the ball's position.

### Modern Attack

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To counter the pair coverage, the attacking team aims to force a superior number of attackers than defenders into the active zone. The active zone is defined as the zone between the ball and the goal. Look at the following example. When Player 1 has the ball, the active zone goes from line A to the goal line. Because the defender that should have covered Player 1 got temporarily behind him, there are now four attackers against three defenders – the goalkeeper doesn’t matter – in the active zone. The defence is unstable.

If Player 1 passes the ball to Player 2, the new active zone goes from line B to the goal line. Now there are three defenders against three attackers in the active zone; the attacker’s numerical superiority vanishes, and the defence becomes stable. That’s the reason that it is not always clever to pass forward. If Player 1 advances with the ball instead of passing it, sooner or later one of the defenders must abandon his opponent to fight for the ball. This opponent then becomes free near the goal, and would be able to score if he received the ball.

The other way round: Sometimes it is clever to pass the ball backward. In our example, a pass from player 2 to player 1 creates a numerical superiority by shifting the active zone from B to A.

## Comparing Soccer Times

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### Time Table

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In the following coarse time table, the main soccer epochs from the strategical point of view are represented with their most relevant periods and dates.

Epoch  | Offside  | Period  | Years

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Primitive Epoch  | No offside  | Primitive Soccer  | Middle Age
Ancient Epoch  | Offside rule habit  | Ancient System  | 18?? - 1866
Offside Law 1863
Classic Epoch  | Offside Law 1866  | Forward pass and combination game (with antic remnants)  | 1870
Most brilliant zone oriented Classical System  | 1920
Offside trap (Billy McCracken)
Modern Epoch  | Offside Law 1925  | WM formation and variants of the Classical System  |
Trying to leave the zone  | 1958 (World Champion Brazil)
Back to remnants (zonal formations, offside trap)  | 1970 - 20??
Transition to the Modern System
Abolishment of the offside law?  | Modern System  | 20??

In the table, we see that primitive soccer surged in the Middle Ages. In the 19th Century, the offside rule spread and finally became law, leading to the Ancient System.

With the new offside law dated 1866, the Classic Epoch began. After the initial confusion, the combination game surged thanks to the new possibility of passing forward. However, ancient remnants were often observed, like crowding around the ball or kicking high. It was only some decades after the end of the Antic System that the Classic System crystallised and became mainstream.

The Modern Epoch began when the current offside law was introduced 1925 as an answer to the offside trap. In the next decades, no new strategic system was anticipated. The games were played in zonal systems like the WM formation or variants of the Classical System. Such games were mostly attractive but in the long term strategically unstable. Finally the players tried to liberate themselves from the zone binding, which was a remnant of the Classical Epoch. This attempt to leave the zone failed, probably because it was not supported by theory. Soccer fell back into remnants of the classical system such as zonal formations and even the offside trap. In the years around 2000, some new habits are observed that could announce the transition to the Modern System. It is a guess that the offside law will eventually become obsolete and the Modern System reality.

### Verifying the Common Soccer Strategy

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The Ancient, the Classic and the Modern System are concrete implementations of the Common Soccer Strategy, giving answer to the two fundamental strategic questions:

* How can the team in possession get one of its players in free position and pass him the ball?
* How can the adversary team avoid it? (How to cover?)

Let's verify this in the following brief outlines.

System  | Coverage  | Freeing and passing

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Ancient  | Every player must stay behind the ball. Thus, the ball “covered” all attacking players!  | To run forward while the ball is very high in the air.
Classic  | The antepenultimate player covered all opponents!  | To play over the wings and to center back to the finisher.
Modern  | Each player relates his position to his fixed opponent.  | To establish numerical superiority in the active zone and to create lapses in coverage as defence shifts among attackers.

In past times, the coverage was entirely supported by the former offside laws. But the current offside law doesn’t guarantee the coverage. Remember that coverage means to avoid with no physical contact the advance of the attacking players that don't have the ball at their feet. A covered player won't advance until he perceives a propitious situation that might cause him or a team-mate to become uncovered.

### Kinds of Collaboration

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While practising a team sport, the players can feel the joy of collaborating inside the team. This is especially encouraged in the soccer game. It is not by accident that soccer is officially called Association Football.

The most trivial collaboration is just the fact of belonging to the same team. If the team scores or even wins, there is a collective joy; the exact value of every single contribution is secondary. This kind of collaboration was always present.

Beyond that, an important collaboration task is to move the ball. In primitive and ancient soccer, the ball's advance was only driven by individual effort. By replacing the first offside law dated 1863, the forward pass and the combination game became possible. Since then, the players move the ball in soccer mainly by collaboration, passing it to each other.

What about the coverage, the great defence challenge in the Common Soccer Strategy? The following table is an overview of collaboration quality for defence in important soccer periods.

Soccer Period  | Defence Method  | Collaboration quality

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Primitive Soccer  | none  | accidental
Ancient System  | All players stayed behind the ball. This way, they could hinder any advancing opponent.  | Unconscious collaboration forced by the offside law dated 1863.
Classic System  | The antepenultimate player defined the offside zone, the penultimate player hindered any intrusion in it. These two players were sufficient to cover all opponents.  | The two back defenders collaborated together. The rest of their team wasn’t needed to cover.
WM Formation  | In each zone, there were two opponents that covered each other.  | Unstable “collaboration” between both teams thanks to the habit of staying in a zone.
Modern System  | Each player covers a fixed opponent.  | Every player is needed to cover. If a player fails to cover, the whole defence fails.

Finally, let's look at the collaboration quality for the attacking challenge in the Common Soccer Strategy: freeing the finisher and passing him the ball. The following table is an overview of collaboration quality in the attack method of each stable soccer system.

Soccer System  | Attack Method  | Collaboration quality

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Ancient System  | The ball was kicked back and then long and high; the possible finishers ran while the ball was in the air.  | Sporadic, cumbersome collaboration, made difficult by the powerful offside law.
Classic System  | The two defenders and the three midfielders passed the ball quickly to the front. The five forwards played together through the wings and passed back to the finisher.  | The attack was orchestrated by the whole team. However, the more advanced the player's zone was, the more important was his role and involvement.
Modern System  | The team tries to establish a numerical superiority in the active zone and to pass the ball to the free player.  | Every player must collaborate with subtle synchronized movements to the right place at the right time. A most challenging collaboration of the whole team is required!

## More About the Theory

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### The Theory's Origin

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The Theory of Soccer, as explained here, was first discussed by Ricardo Olivós Arroyo (1910-2003). Don Ricardo came from Huelva in the Southwest of Spain. He played soccer semi-professionally at the University of Seville. When he finished his studies and became a lawyer, he abandoned soccer practice. Some years later, he noticed, while watching games, some strange changes in the way of playing since his active days and decided to research them. He didn’t find any documents on soccer theory, so he started writing a first booklet on this matter. In the nineteen seventies, this booklet was distributed by the Spanish Sports Administration to all major soccer clubs in Spain. Don Ricardo and his theory were lauded by a famous soccer coach and attained a certain attention from the mass media. Encouraged by this success, Don Ricardo wrote a more exhaustive book[1]. But unfortunately, the theory fell into oblivion. In a further book[2] he refined the theory but it didn’t achieve the expected distribution. Nevertheless, his work is referenced in a few research papers about soccer. In his last years, Don Ricardo dreamed of a book about his theory written in a more popular style.

### Research Directions

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Don Ricardo himself was aware that the research on “The Theory of Soccer” is not completed and must go on in order to deliver detailed knowledge and definitive proofs. This is mainly true for the modern system. Can we describe more soundly and accurately the “opponent based coverage” and the movements to achieve numerical superiority? A model should be defined to be tested in simulations as well as with real game data. Don Ricardo's and other's[3][4] highly controversial hypothesis is that the current offside law is completely superfluous. An interesting approach to prove or discard this belief would be to investigate first small sided soccer, in which no offside law exists, and then verify the attained model on bigger teams, increasing the size one by one until eleven. Is there a critical team size at which the offside law becomes indispensable?

Finally, the possibility should be considered of organising a soccer league without offside law and seeing what strategies the teams develop. It would of course be important to carry it out during a very long period to permit the players to abandon habits induced by the offside law and to find out by trial and error the suitable strategic methods of attack and defence. It wouldn't be necessary to involve professional players, convinced amateurs would be very satisfactory.

### Software Applications

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There are two software applications dedicated to the Theory of Soccer. Both are available at Github.

* The application named DRIOLAR is written in the programming language  Java. Its development is discontinued. It offers a stand-alone installation to be downloaded for  Windows.
* The application named SoTheBo is written in the programming language  Pharo. It is partially ported from DRIOLAR for further development.

## Appendices

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### Glossary

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Term  | Definition

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Active zone  | Rectangle with the following boundaries: both side lines, the defending team's goal line and a line at ball's level in parallel to the goal lines.
Attacker  | Every player belonging to the team that possesses the ball. When any player of a team possesses the ball, every player of that team becomes an attacker.
Basic formation | Starting team formation before kickoff. Excepting the ancient and the classic formation, basic formations are strategically arbitrary because the are not based on a system.
Combination Game | A style of soccer that favoured the passing of the ball between players instead of individual dribbling skills.
Culture  | Knowledge that members of a human group have acquired by experience. Through this knowledge, the group satisfies its material and spiritual needs, orders itself and organises itself as a group.
Defence  | What is opposing the attackers that don't have the ball. In the ancient system, it was the ball. In the classic system, it was the penultimate field player. In the modern system, every player of the team not possessing the ball.
Defence zone  | Rectangle that can be entered by the attacker taking the ball but not by the rest of attackers. Boundaries: both side lines, the defending team's goal line and the offside line.
Defender  | The player that hinders the attacker with the ball.
Finisher  | The attacker that tries to score as soon as he receives the ball.
Last defender  | With the offside law dated 1866, the last defender was in the offside zone. He opposed any attacker entering in it.
Move  | A sequence of executed game movements.
Penultimate defender  | With the offside law dated 1866, the penultimate defender marked the beginning of the offside zone.
Research  | Studying a culture. Discovering the reasons causing a culture's phenomenon.
Sport  | Activity that requires mainly physical strength or agility to win.
Strategy  | Fundamental decisions taken before kickoff about choice and order of the moves. Thanks to strategy, favourable situations arise during the game that can be tactically exploited.
Sweeper/libero  | During a period of Modern Times, defenders have had a last defender called the sweeper/libero behind them. In contrast to the Classic System's last defender, the sweeper/libero didn't get established.
System  | Ordering based on some rules that rely on a fundamental principle.
Tactics  | Decisions taken during the game's dynamic. Tactics take advantage of conditions created by the strategy.
Theory  | Rational explanation of related phenomenons. Ideas abstracted from facts.
To attack  | To order the game aiming to score.
To cover  | To subtly prevent the attacking team from bringing one of its players into a free position to score or passing him the ball. To reduce a collective attack to the attack of the single player having the ball.
To play  | To order moves aiming to win.
Uncultivated  | Belonging to a group that has not yet developed its culture.

### References and Notes

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1. ↑ Olivós Arroyo, Ricardo (1992). Teoría del fútbol (in Spanish) (2nd ed.). Sevilla: Wanceulen Editorial Deportiva S.L.. ISBN 84-604-3705-1.
2. ↑ Olivós Arroyo, Ricardo (1997). Fútbol: Análisis del Juego (in Spanish) (1st ed.). Sevilla: Wanceulen Editorial Deportiva S.L.. ISBN 84-87520-42-1.
3. ↑ Another well-known soccer scientist, Ken Bray, has also predicted the abolishment of the offside rule in his book “Bray,K. (1998). How to Score: Science and the Beautiful Game. London,UK: Granta. ISBN 9781862079885 (Chapter 8)”.
4. ↑ Marco van Basten, FIFA technical director, suggests to abolish offside: http://thesefootballtimes.co/2017/02/01/marco-van-basten-abolishing-the-offside-rule-and-why-we-need-to-talk-about-it/