I just did some really basic 'back of napkin' research on closer usage patters. I looked at data for three of the top closer - Joe Nathan, Mariano Rivera, and Francisco Rodriguez. Altogether there were 197 games where they had pitched the previous day. Out of those 197 games, they were used in a total of 51 games, and picked up 42 wins or saves. There were 289 games where they had not pitched the previous day. Out of those 289 games, they were used in a total of 145 games. So in games where they pitched the previous day they picked up a win or save 21% of the time, while in games where they did not pitch the previous day, they picked up a win or save 31% of the time. And they actually appeared in games almost twice as often following a day off. Note that the results would have been even more extreme if I had eliminated games where a player missed time for an injury, since these periods obviously consisted only of days off, followed by games where they did not pitch.
Why does this matter? Well, in many leagues, it doesn't. But in leagues where there's a possibility of rotating closers...for example a salary cap league with daily transactions, this is huge. Closers are going to be AT LEAST 50% more valuable in games where they didn't pitch the previous day.