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Depending on who you talk to, the importance of a team's batting order varies. More old-school fans will reiterate what we've heard for years, "Put a speed guy first, a contact hitter second, your best overall hitter third, your best power hitter fourth, and your worst guys at the bottom."
However, with the sabermetric revolution, a new way of thinking has emerged. They say your leadoff hitter should be a guy with a high OBP so he can get on base and set the table. Trying to alternate lefties and righties has also become more prominent. However, more people insist that the order of a lineup isn't of the utmost importance and doesn't have a huge impact; after all, your "leadoff" hitter is only guaranteed to actually lead off once a game.
I fall somewhere in the middle of the two schools of thought. I don't think the lineup matters all that much in terms of "Your x hitter HAS to be able to do this." However, I do think that there's value in having a fluid lineup that fits together nicely, and it's more important who's hitting before/after a guy, not what spot they're in. For instance, it doesn't matter much if Alex Rodriguez hits third or fourth, but I do think it's important that the person hitting behind him can protect him, so someone like Mark Teixeira makes more sense than say, Didi Gregorius.
So if the Yankees make the smart, albeit bold, decision to let me make the lineups this season, I'd go with this.
Against RHP
1. Jacoby Ellsbury
2. Brett Gardner
As much as they drive fans crazy, they're still the best options at the top of the order. Both are coming off subpar seasons, but they did battle with injuries. If both are healthy, they each provide the ability to get on base, and then cause havoc on the base paths. Gardner has a career .346 OBP, while Ellsbury's at .343, both above average marks. They've also both had multiple 40 stolen base seasons, and although they don't run as frequently anymore, they're still very capable base stealers. Overall, despite recent struggles, they're still two of the Yanks' best all-around players and are built for the top of the order. This does come with a caveat, though. Given their streakiness, I wouldn't hesitate to drop one to the bottom of the order if he's in a funk, and put Chase Headley or Starlin Castro in the two hole.
3. Carlos Beltran
A case can also probably be made for A-Rod or Mark Teixeira, but Beltran makes the most sense here. If you abide by the "best hitter third" theory, then Beltran is likely their best overall hitter. More importantly, though, he makes sense here because his K% is lower than both Rodriguez's and Teixeira's, and Beltran is such a professional hitter that he usually finds a way to keep the line moving, or at least make a productive out with runners on.
4. Alex Rodriguez
5. Mark Teixeira
You can go either way here, but at this stage of his career, A-Rod really benefits from being protected by the hitter behind him. McCann is no slouch, but when healthy, Teixeira is the better hitter and provides more power. Also, hitting Teixeira behind A-Rod was effective last season, so there's no reason to mess with a good thing. Either way, these are the Yankees' two best run producers, and the season largely hinges on their health.
6. Brian McCann
If all goes well, the Yankees' will have runners on in this spot, so it makes sense to go with your next best hitter. McCann really struggled in the second half last season, but he's still talented and one of the best home run hitters on the Yankees.
7. Chase Headley
8. Didi Gregorius
9. Starlin Castro
This should be one of the better bottom of the orders in baseball, as all three are capable hitters. Headley is probably the best of the three, and he has the most pop in his bat, so it makes sense to put him first. Gregorius and Castro are pretty similar offensively, but putting Sir Didi ahead of Castro assures that they don't have three lefties in a row at 9-1-2.
Against LHP
1. Jacoby Ellsbury/ Brett Gardner
2. Starlin Castro
Aaron Hicks figures to fill the Chris Young role this season, meaning either Ellsbury or Gardner will be sitting against lefties. Given that both are less productive against left-handers, it's a good opportunity to get one a day off and (hopefully) keep them healthy. Sit Ellsbury against one lefty, then Gardner against the next, or vice versa. That leaves the second spot open, and I think that Castro is the best option here. Headley's bat is better suited for when there should be more people on base; and while Hicks has hit lefties well in his career, Castro has too and is considered to be the better overall hitter.
3. Carlos Beltran
4. Alex Rodriguez
5. Mark Teixeira
No reason to switch this up
6. Chase Headley
7. Aaron Hicks
8. Didi Gregorius
9. Gary Sanchez
The notable difference here is Sanchez starting for McCann, but I think it's something the Yankees should consider. McCann's second half struggles could have been a result of fatigue, so I think it's important the Yankees get him more rest this season, maybe even a 102/60 split or so if Sanchez is as good as advertised. Sanchez has a promising righty bat, so playing him against all lefties, and in other situations where McCann is resting, is a good way to get his bat in the lineup, while also keeping McCann fresh for late in the season.
So, while the exact lineup order doesn't matter nearly as much as how the hitters are actually performing, it does have some impact. To me, using these lineups would give the Yankees their best shot at bringing a championship back to the Bronx.