First, I will just say that looking at a few starts doesn't tell much of anything.

Secondly, it is tough to discuss your example given that you don't cite who you looked at or when you looked at it.

However, I did a little research. What I did was go to Fangraphs and look at every 10th pitcher on their leaderboard (of 88, including #88 Ervin Santana) as well as every Red starter from last year. I looked at their entire career splits for what they did the first, second and third time through the order. I left out the 4th time since most guys had very small sample sizes for the 4th time through the lineup. I looked at BB%, K% (both calculated as stat/PA) and OPS against. There were 13 pitchers in total. Here is the chart:

**Strikeout Rate**
It is worth noting that every single pitcher tested had a lower strikeout rate from the first time through to the second and from the second to the third. Every time. That certainly works against my side of things.

**Walk Rate**
Four of the 13 pitchers improved their walk rate from the first to second time through the lineup. Nine of 13 pitchers improved their walk rate from the second to third time through the lineup.

**OPS Against**
Four of the 13 pitchers improved their OPS against from the first to second time through the lineup. Six of the 13 pitchers improved their OPS against from the second to third time through the lineup.

What does this tell us? Well, I would certainly agree that with this random sample, hitters are quite likely improving their ability to put the bat on the ball with seeing the pitcher on a given day more. Something I contended shouldn't happen. The walk rates being lower could be a by product of more contact being made, but more guys showed improvement the final time through, so maybe it is more than just the lowered contact rate since everyone had a lower K rate each time through. OPS Against though is interesting. We are a little more split there. I would actually like to see more done with all of this.