Saves, like every stat, don't tell the whole story. But they are still a good indicator of if a closer is getting the job done. To get the whole story you obviously need to check other stats and watch game video.
RRA (Relief Run Average), IRS% (Inherited Runners scored % or Inherited runners stranded %, which is basically the same as IRA-Inherited Runs Allowed), and then you can go as deep as a whether the pitcher is a ground ball pitcher a fly ball type guy (as well as what hand they are) to see what fits your needs.
Relief Run Average
A pitching statistic used in baseball that measures a relief pitcher's ability to keep inherited runners from scoring once they enter the game. Any runner already on base when a relief pitcher enters is considered an inherited runner, and R.R.A. takes into account how many outs there are and where the runners are located.
IRS% is a stat in OOTP games. Very useful, but again, doesn't tell the whole story.
LOB% includes runners the pitcher put on.
Who cares if a relief pitcher gives up a walk every time he comes out if he inherits two other runners and never gives up a run. His LOB% is going to be 3 players, while IRS% will only be 2 players (or 0% if you're using it as scored instead of stranded which I've seen done before).
EDIT: Just saw someone else explained that. My bad.