Proposed Stat: Incomplete Plate Appearance

I've thought of a new statistic that could prove some use for baseball. I'll call it the "Incomplete Plate Appearance." Baseball has a stat called the "At Bat" which consists of all hits, outs and fielder's errors combined. An expanded stat called the "Plate Appearance" (is this the "AP" for "Appearance at the Plate"?) includes "At Bats" but adds walks, hit by pitch, sacrifices and sac flies." This is commonly viewed as the number of times a batter appears at the plate. But it is not.

Another incident in baseball that has no official accounting anywhere is the time when a batter comes to the plate, sees pitches, but the third out of the inning is made on the bases before his at bat concludes. This has no category. Because the third out is made during the at bat, he leads off the next inning, and that plate appearance is counted. But I'm wondering if his "appearance" the previous inning isn't counted anywhere because he doesn't decide the out. This unaccounted for "thing" may actually have a large effect on the game. It could eat up the pitcher's pitch count.

Say a batter comes up with a runner on and two out. He works the count to 2-2, fouls off five pitches, and the next pitch sees the runner caught stealing for the third out. He just ate up 10 pitches. If the pitcher has a 100 pitch limit, that one "thing" that isn't counted for is responsible for 10% of the opposing pitcher's time out there. And if he leads off the next inning with a five pitch "real" accounted for plate appearance, he could chew up 15% of the other pitcher's value, get him yanked an inning early, setting up a bullpen meltdown, resulting in a victory. The most valuable plate "appearance" could go unnoticed in the stats. The pitches he uses up are counted against the pitcher's pitch count, but the plate appearance isn't.

Better yet, let's say this player is a pinch hitter who doesn't stay in the field for the next half inning. He could prove to be the most valuable player of the game, but shows up nowhere in the stats. Let's account for this by creating the "Incomplete Plate Appearance."