Yes, I'm writing a fanpost about the bullpen, not because I want to call it "teh pen", not because I want to talk about Joba, and not because I want to talk about some of the recent meltdowns. I've been writing/thinking about this for a few days, so please don't take my ideas of change in the pen as reactionary or doomsday. Now that all of the disclaimers are aside, let's talk about using the bullpen in the best possible way.
After the league expanded and free agency struck, the most watered-down talent area has always been in middle relief. With very few exceptions, MLB teams have three, maybe four, relievers that they're comfortable with, and everyone else is an implosion waiting to happen, a journeyman, a prospect, or a washout. With that said, and the fact that the even the best relievers can't be effective every day (Mariano's career high is 74 appearances, so less than half of the regular season games), you can only expect to get two innings from your top relievers on any given night.
My claim of two innings of quality relief per game is something of an oversimplification, but let's assume that it's true (In fact, for the Yankees last year, the combo of Rivera / Hughes[pen only] / Aceves[pen only] / Robertson logged 241 1/3 innings last season, or just a shade under 1.5 innings over 162 games, but D-Rob spent some time in AAA and Hughes/Ace in the rotation). So on any given game, you can only expect 6 quality outs from the bullpen before you're in Brian Bruney, Boone Logan, Chad Gaudin, and Jose Veras territory.
With that said, that average figure doesn't really speak to the way the bullpen is used. In a close game, all of your best pitchers might be used, and in a blowout, all of your best pitchers may be rested, but quality bullpen outs are certainly a finite quantity, and the way that they are currently used across MLB isn't even close to optimal.
When dealing with a limited quantity of good pitchers/innings in the bullpen, the only logical way to negotiate the end of a game is to use your best pitcher in the highest leverage situation, regardless of inning, and use your worst pitcher, regardless of inning, in the lowest leverage situation. How many times have we seen the game slipping away in the 7th or 8th inning, with the heart of the lineup due up, and our best arms (Hughes in '09, Joba in '10, Mariano) stay in the pen, while a lesser pitcher (lookin' at you and your 5 blown saves last year Phil Coke) gives away the lead?
The Yankees bull pen was very solid last year, allowing the fewest blown saves (15) in the AL East (Sox: 18, Rays: 22, Jays: 16, O's: 22), and when you consider how many games they had the lead in, that's a pretty impressive achievement. However, Phil Coke also had 1/3 of the teams blown saves. And the problem isn't necessarily with Phil Coke, he's a pretty mediocre pitcher who was put into the game far too often in high leverage situations because he throws with the wrong hand (never trust a lefty).
To truly optimize a bullpen, the closer, 8th inning, 7th inning, system would be scrapped, to be replaced by a simple pecking order. Mariano, in all of his glory, would obviously be at the top of this group. Then when we play the Twins and we're up 3-1 in the 8th inning with 2 on and Mauer and Morneau due up, we don't have to suffer through a Damaso Marte appearance (cuz.....he's a lefty). If we get through that 8th inning with Mariano, and are up 3-1 going into the 9th inning with the bottom of the order due up, there's something like a 95% chance that we win, and a lesser pitcher can be used.
Unfortunately, everything that I just said will fall upon deaf ears at the MLB level. Tony LaRussa made Dennis Eckersley his 9th inning man (if I'm not mistaken) and the closer was born. The closer gets paid the most, and needs the ego boost and the familiarity of only pitching in the 9th inning. And also, could you imagine the media flogging that Girardi would take if he used Mariano in the 8th inning, or God forbit the 7th, and some other pitcher blows the game later. He would be murdered on the spot.
In today's game, it's easier and acceptable to be conventionally wrong than unconventionally right.