Tom Ruane posted three separate items and I combined them all into one site which you can read at Do Batters Learn During Their Career? The basic question is how batters do against pitchers the more they face them.
Below is an excerpt from the first post Tom did in 1999 and then a list of some issues he dealt with in the next two posts.
"Back in 1996, Dave Smith, the president and founder of Retrosheet, did a study showing that batters tended to improve against a pitcher as a game went on. His paper was entitled "Do Batters Learn During a Game?" and, rather than attempt to summarize his methods and findings, I recommend that you read his work for yourself. A copy of the paper can be found at:
This got me to wondering if a batter showed a similar increase in performance as his career progressed. Was a batter or a pitcher at a disadvantage the first time they ever faced each other? How did their performance change as they got more familiar? In order to attempt to answer these questions, I looked at all batter-pitcher matchups from 1980 to 1998. I only considered matchups where the batter and pitcher faced each other at least 20 times over the course of their careers and examined how they did in each of their first 20 confrontations. (Note: since my data started in mid-career for all players active prior to 1980, I did not include any match-ups where both pitcher and batter were active in the 1970s.)
[Editor's note: Tom has a very detailed table here so click on the link I provided to see it]
So Batters seem to be at a noticeable disadvantage when facing an unfamiliar pitcher. The field seems to level off after the third time they see each other, but the batter still seems to get slightly better the more he sees a pitcher. Here's the breakdown in groups of five plate appearances:
1- 5 .727
Five of the top six slugging percentages and four of the top five on-base percentages occurred in PAs 16 through 20."
Now some issues that Tom addressed in the second two posts:
Someone wondered if requiring twenty or more plate appearances was biasing the sample by eliminating the batters who fail to learn (and so leave the big leagues before facing any one pitcher enough to meet my criteria).
Someone else argued that what we're really seeing here are within-game effects, that the first appearance is earlier in a game than the second, which is probably earlier in a game than the third.
Someone else wondered if the later plate appearances came in higher run scoring years.
There was also some question at the time about how much of this effect was really due to batter learning during a game.