Compared to a pitcher's opponents batting average, a pitcher's H/9 benefits from sacrifice bunts, double plays, runners caught stealing, and outfield assists, but it is hurt by some errors. Consider the following hypothetical innings, which demonstrate the difference:
Inning 1: Batter 1 hits a double. Batter 2 receives an intentional walk. Batter 1 caught stealing at 3rd base. Batter 2 advances on attempted double steal. Batter 3 reaches base via either walk (baseball) or hit by pitch. Batter 4 hits into double play. During this inning, the opponent batting average was .500, while the hits per nine innings was 9.00. In a more typical inning a .500 batting average would imply 3 hits and 3 outs, and 27.00 hits per nine innings.
Inning 2: Batter 1 hits a triple. Batter 2 walks. Batter 3 hits a sacrifice fly. Batter 2 advances to 2nd base. Batter 4 hits safely with a base hit, but batter 2 is out at home. Batter 5 hits into a fielder's choice. During this inning the 2 hits imply 18 hits per nine innings, and the pitcher endured an opponent batting average of .500. Again, however, the .500 batting average might have implied 3 hits and 3 outs.
In both situations, the pitcher was involved in outs recorded against runners not at bat. Thus, he was able to lower his hits per nine innings after the runner reached base. The two measures differ in their implications when pitchers (or their fielders) induce outs that are not related to official at bats.