Baseball purists might decry the game's increased reliance on relief pitching, but it's a trend that's unlikely to reverse itself any time soon. While much of the recent talk around pitch counts and early exits centers around injury prevention, there's also the simple fact that starting pitchers become less and less successful as the game wears on. Part of this decline is simply due to waning velocity (more on this later), but some of it can be attributed to familiarity -- hitters become increasingly comfortable when seeing the same pitcher for the second, third or even fourth time on the same day. We all know this, and batting averages on second and third times through lineups confirm it.
There do exist glimpses of hope for the purists, however. Not all pitchers lose velocity during the game and some, like Justin Verlander, actually throw harder and maintain their effectiveness as the game wears on. And Verlander isn't on a performance island.
To get an accurate picture of how a starting pitcher's effectiveness changes throughout games, we need to control for the quality of the pitchers (better starters go deeper into games) as well as the quality of opposing batters (starters might only see the top of the batting order in their final time through the lineup and are unlikely to face an opposing pitcher late in the game). When we do this we see that pitchers are, on average, half a run worse in ERA by the time they face the 25th batter of the game and are almost 20 percent less likely to get a strikeout. You can see the effects of both familiarity and diminished velo. Young pitchers (under 25 years of age) lose velocity and value most rapidly, whereas older pitchers (33 and older), as a group, lose almost no velocity (perhaps because they're smarter about not over-throwing early). But even older pitchers become less effective as hitters adjust to their offerings.