The stat hasn't changed since 1969, when it was created.
10.19 Saves For Relief Pitchers
A save is a statistic credited to a relief pitcher, as set forth in this Rule 10.19.
The official scorer shall credit a pitcher with a save when such pitcher meets all four of the following conditions:
(a) He is the finishing pitcher in a game won by his team;
(b) He is not the winning pitcher;
(c) He is credited with at least a third of an inning pitched; and
(d) He satisfies one of the following conditions:
(1) He enters the game with a lead of no more than three runs and pitches for at least one inning;
(2) He enters the game, regardless of the count, with the potential tying run either on base, or at bat or on deck (that is, the potential tying run is either already on base or is one of the first two batters he faces); or
(3) He pitches for at least three innings.