Starting in the 90s, a trend has developed to use left handed pitchers in critical, high leverage situations to neutralize left handed batters. Sometimes called a LOOGY (Lefty One Out GuY), left handed specialists are noted both for their ability to get left handers out due to platoon splits and for pitching less than one inning per appearance. Given the quality of players we have to choose from for "The Greatest Possible Baseball Team", I doubt I would use my choice less than one inning per appearance, but I did pick him due to his ability to get left handers out. And please note that, strictly speaking, the left handed specialist doesn't really need to be left handed -- Roger Clemens and Roy Halladay both have had excellent results against lefty batters (going back to Fangraph's beginning of platoon split data, 2002).
Selection: Randy Johnson
Originally, I had Sabathia here. I disqualified pitchers that didn't make the 162 innings per season limit necessitated by the ERA title qualifier and apparently those years he didn't qualify since 2002 make the difference for Johnson. Just looking at the 2002-2009 data, Johnson has the lowest Fielding Independent Pitching of any pitcher versus left handed batters, at 2.40. That excludes about two thirds of his peak, so I wouldn't be surprised if peak Randy Johnson were even better than that against lefties.
I don't think I need to really explain why Johnson is a good fit here. And frankly, I'd just as likely use him in a starting role. But for now, he occupies my LOOGY slot. But back to Johnson's greatness: not only was the Large Unit amazing againt left handed batters, he's was phenomenal against everyone. Career 3.29/3.19/76/73 (ERA/FIP/ERA-/FIP-) pitcher with an average of 10.6 K/9. That's 4875 strikeouts. His peak season was probably 2001 with the Diamondbacks (memorable year, for sure): 2.49/2.13/55/46.
Retired since the 2009 season, Johnson seems to spend a signficant amount of his time making commericals where he throws baseballs and Pepsi bottles through things like jackets, garages and trash can lids. I can't wait to see him through through a tank. Of course, the commercials should really show off his legendary slider, maybe have it out turn a Sidewinder in a dogfight.
Oh, one more thing, Randy Johnson is maybe the second greatest baseball player of all time to bat right handed and throw left handed.
Simply put, Sabathia has the lowest FIP of any qualified for ERA title (162 innings pitched per year) pitcher versus left handed batters since such splits have been recorded, coming in at 2.85. His career numbers, 3.52/3.52/80/81 and durability have combined to set him on a potential Hall of Fame track, as well. His peak season, 2008, he posted 2.70/2.91/63/68.
One of the cases where picking the reliever for the relief slot doesn't really hurt you. Wagner actually has the nearly the lowest FIP versus left handed batters among relievers since 2002 at 1.73. While Wagner received a boost by pitching mostly in relief, his career numbers aren't anything to sneeze at: 2.31/2.73/54/63 with almost 12 Ks per 9 innings.
After Mariano Rivera, I don't think there's actually a full time reliever better than Billy Wagner,As such, I think a strong case can be made to put Wagner in the Hall of Fame, but the gate keepers of that Hall aren't the sort who'd likely listen to me, by and large.
Any great left handed pitcher
Lefty Grove, Warren Spahn, Steve Carlton, hell, Babe Ruth if you want. You might bring up Jamie Moyer, but I prefer 20th century and later players.