No, the answer is not Andrew McCutchen, even though he won the National League batting title and was an All Star in 2012.
The reason is that he was already very good in 2011.
Put another way, he couldn't win the improvement sweepstakes because he was starting off a high base. His OPS (the sum of on-base and slugging percentage, the measure we're using) of .953 in 2012 is a lesser improvement off his .820 OPS in 2011 than some others discussed below.
We can immediately rule out a few more players: Clint Barmes, Rod Barajas, Gaby Sanchez and Travis Snider weren't Pirates in 2011 and are ineligible for this competition because there is no basis for comparison.
In the next category of elimination are players who declined in 2012 and, therefore, cannot be said to have "improved." These include Alex Presley, Jose Tabata and Josh Harrison.
Garrett Jones and Neil Walker are worthy of consideration. Both of them improved somewhat in 2012.
An increased slugging rate was primarily responsible for the rise in Garrett Jones' OPS from .753 to .832 in the past year. Neil Walker's OPS climbed to .768 this year from .742 last year, with modest improvements in his batting average and slugging rate.
Two players improved a lot in 2012, which makes for an interesting comparison. They are Pedro Alvarez and Michael McKenry.
Alvarez's batting average was just below the Mendoza line in 2011 and an unprepossessing .244 in 2012.
But he finally lived up to his reputation as a "slugger" this year.
He hit 30 home runs this year, just behind Andrew McCutchen's 31, raising his slugging percentage from an anemic .289 to .467.
Like Alvarez, McKenry's most impressive gain came in slugging percentage, from .322 to .442. The gain in McKenry's batting average was less than Alvarez's, but the two players' gains in on-base percentage (OBP) were similar because McKenry walked more than he did last year.
Alvarez's 2012 OPS was .784, compared to McKenry's .762. In terms of actual 2012 performance, the two were actually quite close.
Then the remaining question is, who had the lower base in 2011?
Alvarez started from an atrocious OPS of .561. McKenry's 2011 OPS base was a somewhat higher .598. This, together with Alvarez's higher 2012 OPS, makes Alvarez the most improved player.
This was somewhat to my surprise (because I've been a big McKenry fan).