Building on Jeff's graphical analysis of the Royals' bullpen usage, I put together a color-coded table of what optimal usage would have looked like (using my 20/20 hindsight glasses.)

With seven colors, I picked out the 1/7 highest LI bullpen appearances (in different games, obviously), the next 1/7 highest, etc., until I had seven groups of nine appearances each. The average LI's of those seven bullpen roles are here:

green: 2.87
orange: 2.25
purple: 1.75
blue: 1.28
pink: 0.71
grey: 0.28
white: 0.06

Obviously, there are some overly optimistic assumptions with thinking Joakim Soria could have a 2.87 pLI so far this year instead of his 2.17. Trey Hillman would have to be clairvoyant, for one. And Soria would have had to pitch on four of the first five days of the season. But this is a move in the right direction, at least.

(Also, I'd rather use gmLI -- the LI when a reliever enters the game -- or innLI -- the LI at the beginning of each inning a reliever pitches -- because worse relievers will create more LI for themselves by allowing runners on base. But laziness trumped perfection this time.)