  This paper applies the major computational tool from Topological Data
Analysis (TDA), persistent homology, to discover patterns in the data related
to professional sports teams. I will use official game data from the
North-American National Hockey League (NHL) 2013-2014 season to discover the
correlation between the composition of NHL teams with the currently preferred
offensive performance markers. Specifically, I develop and use the program
TeamPlex (based on the JavaPlex software library) to generate the persistence
bar-codes. TeamPlex is applied to players as data points in a multidimensional
(up to 12-D) data space where each coordinate corresponds to a selected
performance marker.
  The conclusion is that team's offensive performance (measured by the popular
characteristic used in NHL called the Corsi number) correlates with two
bar-code characteristics: greater \textit{sparsity} reflected in the longer
bars in dimension 0 and lower \textit{tunneling} reflected in the low
number/length of the 1-dimensional classes. The methodology can be used by team
managers in identifying deficiencies in the present composition of the team and
analyzing player trades and acquisitions. We give an example of a proposed
trade which should improve the Corsi number of the team.
