A few years ago the most commonly-used possession metric was Corsi or Fenwick close. Corsi and Fenwick are slightly different methods of measuring shot ratios, while "close" meant that we were only including shot attempts while the score was tied or the teams were only one goal apart (with one exception, which is that in the 3rd period only score-tied shot attempts were included).
The idea behind these "close" stats was that teams will typically alter their strategies when the score is further apart, so by only including data from when games were at their most competitive we were getting a better idea of the true talent level of teams.