Fig. 1. Offside
In order to detect an offside in real time, without possibility of physiological or technological error, the current text of the Offside Rule demands the active participation some Physical Laws and all the present knowledge on Ocular Neurophysiology.
Physical Laws and offside rule.
The offside rule is directly related to some physical concepts: speed, space, time and acceleration. The human eye needs time to carry out the eye movements; players run at a different speed and they cover different spaces in the playing field as the eye tries to locate the exact position that those players had in the field "in the precise moment when the player who has the ball passes it". The acceleration in each players' race allows them to run a specific space in the pitch in some second tenths.
Ocular Neurophysiology and offside rule.
The peripheral retina gathers information that the brain uses to program the eye movements, basically from the parafoveal area(5,6,7).
In a football match the saccadic eye movements are those used between two players, to look at each other. In the offside, saccades are used when the ball has already been passed, to locate all the players that take part in a game (if they are all within the visual field).
A saccadic movement needs time that depends on the latency(8) (duration 80-135 miliseconds) and duration of the saccadic movement(9,10) - between 30 and 100 msec: A 40º saccade(9) requires 110 msec, 40 msec for 7'5º and 30 msec for 2º saccade(11) -.
The cognitive process to acquire and to process all the visual information of the object in the visual field and to decide which is the following object of interest is performed during ocular fixation(12). The duration of ocular fixation can be extremely brief(13): about 40 or even 30 msec.
Eye accommodation is the capacity that the eye has to focus. Within the visual field, when we want to change the fixation point from a far object to another one located at less than 6 metres from us, the crystalline changes its convexity(14). Normal latency as well as duration appear to have a large interindividual variability(15). The normal response latency is of 394 ms (± 46 SD). In order to change the focus from a far to a close object, 640msec. are needed, and viceversa (from a close to a far object), it takes 560ms(16,17).
In an Offside game, if there are players located further than 6 meters away from the Referee or the AR and other players located at less than 6 metres, they have to carry out the Eye Accommodation.
When the eye moves, several anatomical structures of the human brain(18,19) take part. The function of these structures is to process at the same time(13,20) all the information gathered during the fixations(12), store it(21) and integrate it, as well as to program the following eye movements(22). The combined presentation of auditive and visual stimuli reduces saccadic latency(23).
Fig. 2. Visual sequence.
In order to carry out this saccadic sequence, all the players must be within the visual field. If any of the players is not within it, it would be necessary to move the head to locate the players. And that would mean that the amount of time to detect the players would obviously be higher.
To have a wider visual and graphical knowledge about saccades, fixations and smooth pursuit eye movements, it is advisable to read the web page from the University of Western Ontario(26), Canada.
If in an offside position there are two players located more than 6 metres away or more than 6 metres close to the Referee and the Asistant Referee, their eyes have to accomodate. This situation would require more than 1 second to locate all the players who take part in a game.
2. Which distance in centimeters can a football player run in 200 milliseconds?
The problem arises when we apply Physical laws to the Offside and to the Occular Neurophysiology: speed, space, time and acceleration are incompatible with this rule application.
In order to obtain these data, I have used the results of the final race of the 100 metres flat race of the 1997 World Championship in Track and Field, which took place in Athens (27), Greece. I compare the average results of the eight finalist athletes with the results of a football player who would have run 100 metres in 14 seconds, quite a slow speed for a professional player (Table 1). The distance ran by the football player in the first 10 metres is the addition of the reaction time plus the time needed to run those 10 metres.
Table 1. Distance run by a football player (cm/200msec) if he covers 100 metres in 14 seconds.
From the results in Table 1 we can deduce that the eyes of the Referee and of the AR need 230msec to detect the player who the ball was passed and the second last defender (28). Both of them may have changed their position in the field from the moment when the ball was passed. This distance will be of 76.05cm in 200msec if they started from a static position, depending on how the players speed up, or of 165.29cm if the players were already running.
These data have an added value if we take into account that, generally, the forward player runs to the opposite field, and the defender to the center of the pitch, to try to play an offside position on the forward player. In position A, Fig.3, we see a player who is not in an offside position exactly in the moment when the ball is passed from one of his team mate, because he is 1 metre away from the second last defender. However, if both players run in opposite directions, 200msec later, in position B the forward player is located 52cm before the defender (they start the race from a static position); and in position C he is located 2.30m before the defender (both of them are running). In situation B and C the player starts from a correct position, but, 30msec later, when the Referee or the AR would finish the saccadic sequence, they would say that there is an offside, when it is not true.
Fig. 3. Relative change in the players' locations in an offside position.AR´s try to solve the problems of this rule appliance with two mistaken techniques.
- Some AR´s try to run next to the most advanced player who is playing the ball. However the AR has to carry out saccades continuously to detect the moment when the ball is passed and the geographical location of the most advanced player. In the precise moment when the ball is being passed, the AR has to look again to that player, but during the period of the sequence fixation-saccade-fixation the player has the opportunity to change his position in the pitch.
- The rest of the AR´s are just looking at the first player (most advanced player) and they try to listen to the sound of the kick to the ball in the moment when the ball is going to be passed. But this means an additional problem, because the speed of sound is slower than the speed of light and during that time difference (during the time that takes the ear in perceiving the sound of the ball), the first player may have changed his position.
3. Which probabilities have referees and AR´s of detecting an offside?
Reckoning the probabilities that Referees and AR's have of "getting right" an offside can be quite a difficult job, because they depend on a series of too wide and maybe infinite variables. From these variables, we can underline: the attention on the game, the floodlighting, the luminosity or the colour of the players' t-shirts, the stripes on the grass, how the Refere and the AR (4) are located during the game, the insertion of other players in the game... However, in the last analysis, and despite all the variables, a player can be in an offside position or not. For the referee it is "heads or tails" and, as he is not capable of spotting it, he has to make a decision with just two possibilities. That means that Referees and AR's always have 50% of probabilities to "get an offside right", but also 50% of errors.
Table 2. Minimum distance which separes both players to be able to see and judge an offside position avoiding visual errors.
As we can see in Table 2, the minimum distance that separates these two players to detect an offside has to be bigger than 87.46cm (position 5). In this position the forward player runs to the opposite goal, speeding up from a static position and the second last defender is static, with no movement.
4. Which criteria should the technological media follow to detect an offside?
As it happens with the human eye, the technological media have to detect all the players who take part in this game "in the precise moment when the ball is being passed". That is why physics play such an important role evaluating the media. The most important premise is time and any technological media cannot consume time to detect the players, because they can move within the pitch and they wouldn't be in the initial position (when the ball was passed). So a media which does not consume time should be used. Nowadays there is not such media, because the electrical, electronical, radiofrequency or laser signal transmission needs time.
Currently there is just a way to know if a player was or not in an offside position, without any visual error. We can only affirm that there was an offside or not repeating and freezing the image on television, in the precise moment when the ball is being passed. In that case, it would be necessary to stop the match to confirm the offside, time which could be used for advertisements.
The key factor in this rule application is that the player must be in the offside position exactly in the moment when the ball is passed from one of his team mates, not when he receives the ball or when the ball is en route between the players (1,29). In order to achieve this axiom, it is necessary to stop time (30) and to locate all the players who take part in that game in zero milliseconds. If some time passes, although it is just 1msec, the players can change their position in the pitch.
In an offside, the Referee and the Assistant Referee may have within their visual field five objects (24): two attacking players, the last two players of the defending team and the ball. The Referee and the AR's need time to detect an offside position, and this time is mainly defined by the saccades (latency and duration) and the eye fixations (28,31). This is incompatible with the philosophy of football and with physics, because the players have speed and acceleration to change their position within the pitch in a specific amount of time, so that they cannot be located in the original position, exactly when the ball was passed (28).
When an offside is misjudged, human mistakes are always mentioned. However, that is not correct. To make a mistake means to carry out incorrectly an action that we are qualified to do, and that we can carry out correctly. The Referee and the AR's are physiologically incapable of detecting an offside (28,31). That is why they can just "get right" some of the offsides, because they have 50% of possibilities of judging correctly an offside (32).
The Referee, the Assistant Referees, the public at the stadium and the viewers at home have to perform saccadic movements and fixations (28,30,31).
A Referee and an AR may find three different physiological situations in an offside game:
- If all the players who take part in an offside are not within their visual field, they would never know if there is or not an offside.
- When all the players are located within the visual field, at least 230msec are needed to locate the two main players in that game (the player who the ball was passed and the second last defender).
- If there are players who are located more than 6 metres away or more than 6 metres closer to the Referee or the AR, the eye needs to accommodate (21), and this physiological situation needs more than 1 second.
Which is the problem of the offside rule that makes it impossible for the human eye and technological media (33) to detect it?
The problem is a notion error, because when it was created, nobody took into account the time needed to locate the different players who take part in the game. That time is fantastically used by the players to change their position in the pitch, so that they cannot be detected exactly in the precise moment when the ball is being passed.
The offside rule in football was introduced (34) in 1866 (19th century). Since then, such a simple concept has gone unnoticed. Sometimes, the mankind has needed centuries to understand very simple concepts and to accept them. We are living in the 21st century, the century of technology and it is impossible to detect and judge an offside in real time, not even using technological media.
- Nowadays, in real time, nobody can spot and judge an offside, not even using technological media.
- The keypoint of the offside in football is to do it "in the precise moment when the ball is played".
- In that moment, the Referee and the Assistant Referees eye should have within their visual field five objects: the ball, two players of the attacking team and two players of the defending team.
- The human eye needs to perform saccadic and fixational movements in order to detect those players. Time is necessary to do that, but players make profit and change their position meanwhile.
- The offside is also incompatible with physical laws related to speed, space, time and acceleration.
- Conceptually, the offside requires stopping time to be applied correctly. But this is something impossible, even with technical media. An offside can be just seen freezing images on television in the precise moment when the ball is played.
- A Referee does not make an error when he misjudges an offside: He is physiologically unable to judge it.
THANKS TO: Nuria Navarro Zaragoza for translating the article into English. To Joaquín Zaragoza Celdrán for designing the figures.
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