'Game Score' is a metric devised by baseball historian and stat guru Bill James to reflect how good a pitcher's performance was beyond just runs allowed.
Per Baseball Reference, Game Score is calculated like so:
Start with 50 points. Add 1 point for each out recorded, (or 3 points per inning). Add 2 points for each inning completed after the 4th. Add 1 point for each strikeout. Subtract 2 points for each hit allowed. Subtract 4 points for each earned run allowed. Subtract 2 points for each unearned run allowed. Subtract 1 point for each walk.