Also, starting with this post I'm going to make a conscious effort to switch from using OPS as my default batting stat to wOBA. wOBA, which is on the same scale as on-base percentage, is basically a version of OPS that uses more accurate weightings for events.
On average, in 2012, the first time pitchers saw a batter they allowed a wOBA of about 0.338. The second time they saw those batters, the wOBA jumped to about 0.350, for a difference in wOBA of about 0.011. I'm going to name this statistic--wOBA for second plate appearances minus wOBA for fist--w-diff.
So the league average w-diff in 2012 was about 0.011. But different pitchers had different w-diffs.
Look, for instance, at R.A. Dickey. Dickey is a knuckleballer, and so one would expect hitters to be unusually bad the first time they see him--they have no practice hitting a knuckle-ball--but to get much better the second time, meaning one would expect him to have an unusually large w-diff. And, in fact, he does have a large w-diff over his career if you ignore all of the seasons in which he didn't have a large w-diff, which is a thing that makes a lot of sense to do if you have a personal vendetta against the year 2011.
In fact, there is something slightly surprising about w-diff. I calculated w-diff for all pitchers who met an innings threshold* in both 2011 and 2012. 68 pitchers met this definition, and the correlation between w-diff in 2011 and 2012 for those pitchers was 0.0508. It seems that there is almost no correlation between w-diff for a pitcher between years (though w-diff across the league seems relatively stable: it was 0.0107 in 2011 and 0.0113 in 2012). So while it seems like pitchers in general do better the first time they see a hitter, there don't seem to be many pitchers who consistently over or under perform the league w-diff.
For those who like graphs, here's a graph of w-diff in 2011 on the x-axis and w-diff in 2012 on the y-axis for those 68 pitchers:
So, without further ado, I present you a list that I just said is meaningless: the pitchers with the top ten w-diff scores from 2012. Do you see any patterns in these pitchers? I don't. (Remember that league-average w-diff is 0.011.)
10: Yu Darvish
2012 w-diff: 0.083. 2011 w-diff: N/A.
9: Rich Porcello
2012 w-diff: 0.083. 2011 w-diff: 0.129.
8: Ivan Nova
2012 w-diff: 0.084. 2011 w-diff: 0.088.
7: Bartolo Colon
2012 w-diff: 0.089. 2011 w-diff: -0.052.
6: C.J. Wilson
2012 w-diff: 0.096. 2011 w-diff: 0.037.
5: Mat Latos
2012 w-diff: 0.101. 2011 w-diff: 0.041.
4: Vance Worley
2012 w-diff: 0.102. 2011 w-diff: -0.093.
3: Joe Saunders
2012 w-diff: 0.103. 2011 w-diff: -0.038.
2: Jon Lester
2012 w-diff: 0.119. 2011 w-diff: -0.043.
And, highest w-diff from the 2012 season belongs to:
1: Tommy Hunter
2012 w-diff: 0.170. 2011 w-diff: 0.177.
Tommy Hunter was a not very good starting pitcher for the Baltimore Orioles last season; his ERA was 5.45. But Tommy Hunter was an especially not very good starting pitcher the second time he saw a batter. I ran a basim simulation on his 2012 statistics the first and second times he saw batters. Basim predicted that the first time through the lineup, he would have a 3.06 ERA; the second time through his ERA would be 7.65. I guess the moral of the story is: friends don't let Tommy Hunter pitch past the second inning.
* technically, the (arbitrary) threshold that used was that they had to face at least 150 batters at lest twice in a game during the season, which is roughly equivalent to making at least 17 starts.