Get rid of the save statistic now. Teams just refuse to use their closer in the highest leverage situations. I don't get why a manager doesn't use their best reliever in the 8th inning with people on base and the heart of the lineup batting. I can understand why some relievers are on limited innings do to previous injuries (i.e. Soria, Wood), but the best person should be used when the game is on the line.
The following are excuses I hear when I bring up this argument.
Excuse #1 - "He can't go two innings."
I agree, let someone else pitch the ninth inning.
Excuse #2 - "He won't get the save."
So the player is not that much of a team player that he won't do his job when it is needed.
Excuse #3 - If a team doesn't allow the top closer to get saves, the team won't be able to get top relievers to play for them.
I hope this is not the main reason driving these game time decisions, the illusion that players won't play for a team for multi-millions of dollars because some of their stats won't get padded to their liking.
My solution would be to get rid of saves entirely and make only holds count. The holds could eventually be weighted someway with innings pitched or leverage index. First, let us start with baby steps and get rid of saves. Everyone that helps keep a lead get the same credit and maybe some of the stupid manager decisions based on saves will be eliminated.