# NFL Graph Theory

So far this year:

New England beat Tennessee; Tennessee beat Detroit; Detroit beat Philadelphia, Philadelphia beat the NY Giants; the Giants beat Carolina; Carolina beat New Orleans; New Orleans beat San Diego; San Diego beat Oakland; Oakland beat Pittsburgh; Pittsburgh beat the NY Jets beat Indianapolis; Indianapolis beat Minnesota; Minnesota beat San Francisco; SAn Francisco beat Green Bay; Green Bay beat Chicago; Chicago beat St. Louis; and St. Louis beat Arizona; who beat the Patriots.

Here’s a directed graph of the entire NFL so far this year with the cycle I described about highlighted in think black edges.  Node size is proportional to the number of team wins, and the colored groups are the divisions.

Cheers.

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Posted on October 16, 2012, in Football, NFL, Sports. Bookmark the permalink. 1 Comment.

• ### Comments 1

1. Question – What is the stochastic component of a football outcome? I.e. if two teams played again, what is the chance that the team that won the first time would also win the second time?

Second question – Given that stochastic component to football scores, what is the probability that the play offs and super bowl are actually won by the best team?

In baseball, multi game league and world series formats reduce the impact of stochastic fluctuations and increase the probability that the team with the highest probability of winning will be crowned champion. Not so confident about football.

Note: there is a competing explanation for the presence of cycles. Think “rock, paper, scissors”. Maybe the particular skills of A insure victory over B, and B’s skill set guarantees victory of C. It is still possible that the strengths of C and how they match up against the weaknesses of A will lead to victory of C over A.