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Connections throughout Basketball History (a small world)

A network of professional basketball players throughout history follows the small world phenomenon as well as any other instance. We can discuss the, perhaps, surprising links between every basketball player from past to present. Like the 6 degrees of Kevin Bacon or Erdős number, the same concept can be applied to the NBA and all its current and former athletes.
As discussed in class, the concept behind the 6 degrees of Kevin Bacon or Erdős number is that it does not take a long connection to tie two people of the same profession or the same field (in Erdős’s case) together. The way it works is that the person of focus has a connection of zero because Bacon and Erdős are themselves. Then, from there, each fellow actor or mathematician that is directly connected to Bacon or Erdős through a movie or as a collaborator is assigned a connection of one. From them, each actor or collaborator they worked with has a connection of their connection to the original people plus one, and so forth. This very same concept can be applied to the National Basketball Association’s pool of former and current players.
In the NBA version of this concept, players are tied together through teams. For example, Kobe Bryant of the Los Angeles Lakers was at one point a teammate with player Jannero Pargo. Pargo also played with point guard Chris Paul on the New Orleans Hornet. Therefore, Kobe Bryant’s degree number to Chris Paul is two and vice versa. According to the source (and as of earlier this year), the highest number that was found was eight, linking relatively new player Blake Griffin of the Los Angeles Clippers to Charlie Parsley of the 1949-1950 Philadelphia Warriors. However, if any two players were selected to be tested by this procedure, it is found that on average, only 3.37 connections are necessary to tie them together. The center of the NBA universe is James Edwards, who only has a 2.46 degree average. On the other hand, Bill Roberts, who played for the 1949-1950 St.Louis Bombers, has an average of 5.63, the largest for all former and current NBA players. As you can see, the NBA world is indeed quite a small place, with many players able to be linked together through a pretty small amount of connections.
It might seem strange that so many players are tied together so nicely through teammates. However, it makes sense once you take into account the large amount of players, the difficulty it takes to make it into a professional sport and the fact that players are constantly traded. At first, it is surprising that even rookies and players who come into the league for only a very short amount of time are easily connected to so many other players. But, the truth is that it only takes just one teammate who has been on several teams over his career to suddenly give a player the connections boost he needs. Also, there are players who play a long time, with Hall of Famer Robert Parish playing an astounding 21 seasons. With all those years under his belt, it would make sense that he had many different teammates to branch out from. Like in any other network, being connected to just one person who has the ability to branch out to an enormous amount is enough to give a person a small degree of separation. This phenomenon seems to transcend many boundaries, from mathematicians to actors to athletes.
Try out the device yourself (you might have to click “GO” twice to get it to work sometimes):
https://www.hcs.harvard.edu/pallas/
http://harvardsportsanalysis.wordpress.com/2011/03/04/six-degrees-of-nba-separation/

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