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You be the manager: where do you play these infielders?

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I received this question in an e-mail today.

I manage and play on a men’s adult baseball team, basically a bunch of professors and grad students, so it’s not elite competition or anything.

We have two starting pitchers, one is a strikeout machine, very hard thrower, and when they make contact on him, it’s usually a fly ball (he’s fastball-change-curve). The other pitcher is a contact pitcher, throws five different pitches and variations on them (fastball-change-curve-splitfinger-knuckleball), and gets a large number of ground balls. The first essentially has an ERA roughly equal to his runs allowed, or what one would say is normal. The second pitcher, while having a lower ERA, gives up an inordinate number of unearned runs (he also doesn’t hold runners very well)—he puts more balls in play, and therefore there are a lot more chances for errors. The goal here is to cut down on unearned runs, if such a thing is possible.

The infield is composed (at present):

1B: poor range on ground balls and positioning, decent arm, excellent receiver of thrown balls at 1st (he’s very athletic, just doesn’t move or position well on batted balls, particularly grounders)

2B: weaker (though not terrible) arm, not as much range as the SS and 3B. He’s also the oldest guy on the team, very athletic for his age, but he is in his 40’s. He gets to balls, just takes a long route to do so and often can’t do much with them when he does get there.

SS: good arm, good range, probably one of the best SS in the league.

3B: rocket arm, strongest on the team, lightning quick reflexes, good range, and probably it would be a push between him and the regular SS – he plays 3B because he joined the team after the SS (this is old-men baseball!, seniority comes into play)

If you were managing this team, would you shift the players in that infield according to the pitcher on the mound (with our strikeout pitcher, I think I’d keep things as they are)? Is there a greater benefit with a ground ball pitcher on the mound to having the best two defenders (the current SS and 3B) up the middle, and moving the current 2B to 3B? We would lose the sure-fire out on any ground ball at 3B, as well as the line drive outs that would go for extra bases otherwise with our current 3B’s arm and glove, but gain a more rangy defender up the middle who is the equivalent of a SS at 2B.

Ladies and gentleman, that's your question.  What are your answers?  

I'll post my response (for whatever they're worth) later today in the comments.