Well, here is some research done on win expectancy given a situation http://www.hardballtimes.com/thtstats/other/wpa_inquirer.php that can say some things about closers and what is a key situation:
If you take the numbers based on how average teams do - basically you take a 1 run lead into the 9th inning without baserunners - the Win Probability is 88.03% basically need to cash in 9 out 10 of these sorts of games to be doing your job as a closer. A 2-run lead, the probabilty goes to 95.27% - in other words, you'd want your closer to be able to nail down 19 of 20 of these. (note the win prob goes down if you are the road team as there is no chance to come back from a blown lead). A 3-run lead, the probability goes to 98.07%, basically 49 out of 50 save chances. If a closer has an equal number of those sorts of games, you are looking at 94% being sort of the required number, a bit less than 19/20 in save chances to be doing a "good job". Obviously the percentages go up based on outs as well, if you have one out to get with the bases empty and a 1 run lead, it becomes 97.34% (basically 30 of 31 chances).
What is interesting is the four out save ... if a reliever comes in with a 1 run lead with 2 gone in the 8th, here are some win probs:
runner at 1st: 84.93%
runner at 2nd: 82.12%
runner at 3rd: 81.23%
1st and 2nd: 80.12%
1st and 3rd: 78.57%
2nd and 3rd: 75.02%
bases loaded: 72.40%
2nd and 3rd in a tie game?: 47.20%
When you get to a late situation - something like 2nd and 3rd and 2 out ... that final out protecting a 1 run lead is worth almost a 16% increase in the expected win% - more crucial than any of the 9th inning situations during that game. It is mystifying how many managers are squeamish about using your best pitcher then.