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The Inherent Connection Between Mathematics and Football- The Diagonal System Of Control

Sudipto Das Jan 28, 2019

The Diagonal System of Control or the DSC was created purely for the benefit of football referees.

The system allows 3 officials working together to manage a football match effectively and with maximum control. It’s completely based on mathematics providing the officials with the best possible view of the match in action.


The DSC System - In a nutshell

The DSC provides refs with a clear idea of positioning.

They should follow the system in a pattern so that s/he occupies the best position on the pitch to view various game attributes like on-the-ball or off-the-ball tackles, offsides, handballs etc.

We are not saying that this system is flawless and the ref following this system won’t be making mistakes during the game. Nevertheless, this system will still provide you with the maximum possible accuracy of flawless management. But that is where it ends.

The final decision ultimately rests on a human and all humans make errors. After all the refs do have a split-second time for making a decision. So, you should not consider a wrong ref decision as the result of a wrong application of DSC. DSC was implemented by Sir Stanley Rous, a former referee who had also been the FIFA president from 1961 to 1974.


Sir Stanley Rous as the ref

DSC System’s Main Motto

DSC System

The assistant refs should try to maintain a consistent view of all the actions on and off the ball in their halves and make decisions accordingly.

The on-field ref monitors players on the opposite side of the respective assistant ref in that specific half of the field and makes decisions appropriately. This is mainly done to split the responsibilities effectively between the on-field ref and the assistant refs on the sidelines.

The DSC system enables the ref to avoid getting into the view of the assistant ref, thereby ensuring a smooth and effective passage of play.

What’s the System?

The ref has to control the game based on a certain position along a diagonal line like this one shown in the picture below.


(AR= Assistant referee  R=Referee)

This pattern is an effective way through which the officials can get their maximum control over the game in progress.

The ref may choose to cross the specified diagonal line shown above when the ball in play gets close to an assistant ref sp that he can observe the penalty box clearly. This allows the ref to conduct the game smoothly without the need of turning his back to action.

To sum it up, we can say that the DSC prevents the ref from stopping and taking a sharp turn to turn his/her attention to a specific play and waste valuable seconds in the meantime because the assistant ref is there for that specific job behind his/her back.


The benefit of the DSC is that when it’s utilized properly it can be said that there are always 2 pairs of eyes supervising each and every move on field from the opposite sides.

The selection of the diagonal angle is based on the situation of the play and the field movements that revolve around that play. To sum it up, the Diagonal System of Control enables the refs to see the things that they “should” see including the off-the-ball confrontations between players, possible rule violations, fouls, hand-balls, offsides and so on. The implementation of DSC reduces uncertainty and mistakes among the refs.


According to the diagram above, it’s pretty clear that the entire concept is based on the simple concept of geometry.

The diagonal is the shortest distance between two corners of a rectangle. Shortest way of achieving the maximum. The ref follows this specific line so that he/she can maintain an effective control over the entire game from one part of the field to another. It can be concluded that this is certainly the best way through which a ref can cover the entire ground effectively and manage the game in the same manner. The application of mathematics makes this game more splendid and more attractive.

Mathematics is not enclosed within the boundaries of text books and is implemented in almost all fields of daily life including sports, games, marketing etc.

It’s necessary for students to develop a strong base on mathematics and understand the basic principles so that they are not troubled in higher classes when they face more advanced problem sums. The best way to develop such knowledge is by citing the application of mathematics in various real-life fields.

Then only, they would see the true meaning of this abstract subject and develop an affinity to the same. Certain after-school online mathematics tutorials can also benefit them in the long run. After all, seeing is believing and we believe that the same principle needs to be applied in the field of teaching as well. That makes the learning experience more interesting and gratifying.


  • Author:

    Sudipto Das.

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    Content Head

  • Bio:

    Sudipto writes educational content periodically and backs it up with extensive research and relevant examples. He's an avid reader and a tech enthusiast at the same time with a little bit of “Arsenal Football Club” thrown in as well. He's got more than 5 years of experience in digital marketing, SEO and graphic designing.

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