Maximize lefty batter advantage: get a lefty batting catcher.

It would be stupid not to take advantage of a stupid rule: lefty batters are allowed to stand closer to the bases than righty batters.

So load up on lefty batters.  The catching position, which should be eliminated, is the best place to do it because catchers:

1. get injured more
2. need more rest so that they do not get injured or wear down.

From 2000 through 2012 for batters who played at least 90% of their games at catcher, only 96 batter seasons qualified for leading in batting average (BA) and of those 96 only 14 batter seasons had at least 600 plate appearances (PA).  Jason Kendall had the top four seasons in PA 6 of the top 13.  Russell Martin had positions 5 ad 11.  Joe Mauer placed 6th with 633 PA in 2008 when he led the American Conference (AC) in BA for the second of three times.  Buster Posey, National Conference (NC) 2012 Most Valuable Player (MVP) did not have a season among those 96.  Posey had his career high in PA in 2012 with 610 but did not meet the 90% criteria.

Click link to view data.

Mauer:
Born: April 19, 1983
Positions: Catcher and First Baseman
Bats: Left, Throws: Right
Height: 6' 5", Weight: 230 lb.

Posey:
Born: March 27, 1987
Positions: Catcher and First Baseman
Bats: Right, Throws: Right
Height: 6' 1", Weight: 220 lb.

Mauer bats left.  Posey bats right.  Neither makes his living based on being a fast runner.

Mauer was age 26 in 2009 when he was AC MVP and led the AC in BA for the third and final time as well as achieving his personal high in home runs (HR) with 28.  Mauer hit 13 HR in 2005 and 10 in 2012 his only other seasons in double figures.

Posey was 25 in 2012 and he was credited by some with having the highest NC BA.  Posey hit 24 HR.  In his only other season with at least 100 games played (108) Posey hit 18 HR in 2010 in 406 at bats (AB).

So, two modern MVP catchers who led in BA, and had a personal best in HR.

Mauer had 63% of his 606 PA against righty pitchers.  Righty/lefty splits:
OPS: 1.103/.910
AB/HR: 15.5/28.1 (lower is better)

Posey had 70% of his 610 PA against righty pitchers.  Righty/lefty splits:
OPS: .822/1.262
AB/HR: 33.3/12.6 (lower is better)

So, when you need to rest one of these catchers, what will you do?  Lefty batting Mauer hits better against righty pitchers.  Looks like you'd rest Mauer against lefty pitchers who throw about 30% of innings.

Posey hits worse against righty pitchers than Mauer does against lefty pitchers and Posey hits much worse against righty pitchers than he does against lefty pitchers, so resting Posey is more problematic.  Since only about 30% of Posey's PA would be against lefty pitchers, you have much less latitude.

Best bet is get a good hitting lefty catcher but not one who is among your best batters because you'll be tempted and/or coerced into over paying him as Minnesota did with Mauer whose best value is as a really good hitting catcher who unfortunately gets injured and/or needs rest.

Yes, I know about Johnny Bench and Mike Piazza but generally better a good hitting lefty catcher than a righty.

Update 2/26/13:
             
wOBA  % over MLB:
0.428 30.12%    Mauer    2009
0.402 27.54% Posey    2012

OPS % over MLB:
37.28%    Mauer    2009
32.18%    Posey    2012

wOBA: Weighted On Base Average based on linear weights