  We formulate the head-to-head matchups between Major League Baseball pitchers
and batters from 1954 to 2008 as a bipartite network of mutually-antagonistic
interactions. We consider both the full network and single-season networks,
which exhibit interesting structural changes over time. We find interesting
structure in the network and examine their sensitivity to baseball's rule
changes. We then study a biased random walk on the matchup networks as a simple
and transparent way to compare the performance of players who competed under
different conditions and to include information about which particular players
a given player has faced. We find that a player's position in the network does
not correlate with his success in the random walker ranking but instead has a
substantial effect on its sensitivity to changes in his own aggregate
performance.
