Network theory and football? I was reading the latest post on Azimuth, Network Theory in Turin, and I watched many of the lectures Baez posted on his site here. This might be a crazy question to ask considering it's not necessarily a scientific field like Biology, Physics or Ecology, but has anyone considered applying the mathematics of network theory or related to plays in football?
I was just at the Western Reserve Historical Society's museum (which is in Cleveland, OH) and I happened to walk past an exhibit dedicated to the Cleveland Browns. Behind the glass were notebooks filled with football plays, and oddly enough the first thing that came to mind was networks and diagrams. Although they're not necessarily cyclic it seems (I know little to nothing about football) I can't help but wonder what may have been done in sports of this kind. Also whether someone could apply the mathematics Baez talks about to diagrams such as these.
Hopefully I don't get down-voted too much with this question but I don't have anyone to bounce ideas off of.
 A: In 2012, Javier Lopez Pena and Hugo Touchette published a paper (http://arxiv.org/pdf/1206.6904v1.pdf) describing the application of network theory to the analysis of football team strategies. Using passing data recorded during the 2010 FIFA World Cup, they constructed networks and calculated centralities to "identify play pattern, determine hot-spots on the play, and localize potential weaknesses" of Spanish and Dutch teams.  
I can imagine that a similar analysis of the Cleveland Browns match data could provide and interesting insight into their team structural dynamics. Additionally, by comparing the passing strategies recorded in the Western Reserve Historical Society's play notebooks with actual passing data of competitive games, you could quantify how well individual players contribute to particular strategies, the scoring success of certain play strategies, or even how lucky particular coaches are over the course of their career (i.e. whether their planned strategies match their players' actual plays, versus the ending game score).
A: Advanced "analytics" are progressing slower in (American) football than in basketball and especially baseball, perhaps because the interactions are more complex.  In baseball, practically all tangible interactions are mediated by the baseball itself.  The sorts of ancillary actions represented by picks in basketball and by blocks in football are much reduced in baseball, so reducing baseball plays to a series of exchanges doesn't lose as much information as it would in other sports.  There is no analogue to a "6-4-3" double play in football, where that shorthand tells you more or less how that defensive play went.
What's more, though, is that American football, unlike soccer, is predominantly a one-exchange offense.  That is to say, the vast majority of handoffs involve just the QB handing it off to a RB, and the vast majority of passes involve just the QB passing it to a receiver, without any further exchange.  "Trick" plays like the flea-flicker work mostly because they are infrequent; otherwise, they would be inefficient because they take time to execute, and seconds are worth their weight in gold in football, so to speak.  This tends to limit the applicability and utility of network analysis in football, even in comparison with games like basketball, which are otherwise like football in their complexity vis à vis baseball.
