OK let me try this. The closer position is overrated, not because it isn't important, but because it isn't that much more important than the guys who pitch the 7th and the 8th. To win games in the modern era you need to have a good 'late inning unit' of 3 pitchers (4 if you're really stacked). Starting pitchers average 6 innings, so bullpens are pitching roughly one third of the innings.
A late inning unit of 3 guys will total 180 to 200 innings over the course of the season. But in general these will be very crucial innings, because they will typically only be used when the team is ahead after 6 innings, or tied - games that the team has a high probability of winning if the unit puts up 3 zeroes, or maybe 1 run.