We construct player-based complex network models of Australian football teams for the 2014 Australian Football League season; modelling the passes between players as weighted, directed edges. We show that analysis of these measures can give an insight into the underlying structure and strategy of Australian football teams, quantitatively distinguishing different playing styles. The relationships observed between network properties and match outcomes suggest that successful teams exhibit well-connected passing networks with the passes distributed between all 22 players as evenly as possible. Linear regression models of team scores and match margins show significant improvements in R2 and Bayesian information criterion when network measures are added to models that use conventional measures, demonstrating that network analysis measures contain useful, extra information. Several measures, particularly the mean betweenness centrality, are shown to be useful in predicting the outcomes of future matches, suggesting they measure some aspect of the intrinsic strength of teams. In addition, several local centrality measures are shown to be useful in analysing individual players' differing contributions to the team's structure.