The Six Degrees of Football Separation
- essentialbrentford
- Jul 23, 2015
- 3 min read
The six degrees of separation is the theory that everyone and everything is six or fewer steps away, by way of introduction, from any other person in the world, so that a chain of "a friend of a friend" statements can be made to connect any two people in a maximum of six steps.
The phrase "six degrees of separation" is often used as a synonym for the idea of the "small world" phenomenon.
Over the years multiple studies have been conducted to explore the theorem and to determine whether the idea is valid. These studies have been accelerated by the advancement of social media, as Twitter and Facebook can now determine the average number of steps linking one person to another.
This is all very interesting, but how can it be applied to football?
One could intepret it by looking at the Player Separation Number (PSN) of one footballer to another. This is the number of links between any two professional football players.
A link is determined through having played in the same squad as another, or been part of the same team at the same time. The players needn't have played on the field at the same time, but have to have been on the books of the same club at the same time. Thus Josh McEachran and David Button is a plausible link to make, even though they haven't played in a competitive match together.
Each player has a PSN which relates to another player. For example, Andre Gray has a "Ronaldo number", just as Cristiano Ronaldo has the same "Gray number".
This may seem complicated, but is really quite simple. Allow us to demonstrate using the examples of Andre Gray and Cristiano Ronaldo:
Link 1 - Andre Gray has played in the same squad as Kevin O'Connor (Brentford)
Link 2 - O'Connor has played in the same squad as Wojciech Szczesny (Brentford)
Link 3 - Szczesny has played in the same squad as Mesut Ozil (Arsenal)
Link 4 - Ozil has played in the same squad as Cristiano Ronaldo (Real Madrid)
Therefore, Andre Gray's "Ronaldo Number" is PSN(4). Equally, Ronaldo's "Gray Number" is PSN(4).
We'll give you one more example, this time using James Tarkowski and Adebayo Akinfenwa:
Link 1 - James Tarkowski has played in the same sqaud as Jake Reeves (Brentford)
Link 2 - Jake Reeves has played in the same squad as Adebayo Akinfenwa (AFC Wimbledon)
Therefore Tarkowski's "Akinfenwa Number" is PSN(2), and equally Akinfenwa's "Tarkowski Number" is PSN(2).
Thus, it is clear that every professional footballer is linked to every other professional footballer by a certain number of links. The question is whether two players can be found whereby their PSN in relation to each other is less than six (or PSN(6)).
This would disprove the theory that is "The Six Degrees of Football Separation"; the theory that all players who have played in the four divisions of English football are bound to one another by six or less links.
Mathematically speaking, this seems pretty plausible. If you think about it, how many players has the average footballer played in the same squad as (ie. how many players does the average footballer have a PSN(1) with)? Well that depends on how many clubs he has played at, how long he has been playing football, and other varying factors. We would suggest the average is about 60 or so.
This means that each player's "reach" (i.e. the number of players that he has six links with, or a PSN(6) with) is 60 x 60 x 60 x 60 x 60 x 60. This means that the reach of the average footballer is 46,656,000,000, or 46.7 billion other players.
The population of the Earth is only 7.13 billion currently. With the average footballer having a reach of that many footballers after six links shows that it is highly likely that the Six Degrees of Football Separation is a valid theory, as long as you stick to players who have played within the English football league system.
It is doubtful that some obscure Japanese team members have six links with a South American team that has been under a transfer embargo for five years. Therefore, one must remain within players who have played in England.
If anyone would like to try and invalidate our theory and can find two players with a PSN of more than six then feel free to post them to our Twitter.
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