# Arthur: The new best way to measure plate discipline

From SABR member Robert Arthur at Baseball Prospectus on November 7, 2014:

In the sortables section of Baseball Prospectus, there is a report called Batter Plate Discipline. If you’re trying to get a handle on how good hitters are at reacting to balls and strikes, this section contains measurements on such things as swing and contact rates. A natural way to divide such rates is based on the strike zone: A swing at a pitch inside the zone is a different event than at one outside the zone. A whiff on a pitch middle-middle is a disparate event from a whiff on a pitch way outside, so it makes sense to tabulate them in different columns. There is a problem with this dichotomy, however: There is no strike zone.

In the words of Michael Lopez (who borrowed in turn from Bobby Ojeda), the strike zone is a unicorn. By this I mean not that the strike zone does not exist at all, but rather that it does not exist in the way that Major League Baseball defines it. The rulebook definition is a rectangular solid hanging in space, with infinitesimally thin boundaries which, once touched, trigger strike calls.

The actual strike zone is a shifting, nebulous cloud of probability density. It moves up and down with the whims of the umpire and the policy changes of MLB. It shrinks and expands as the count becomes favorable or unfavorable. It grows when an experienced pitcher throws and contracts when bad pitch framers snatch pitches with exaggerated body movements. It’s not a static thing, fixed for every hitter of every height; instead, it is constantly dynamic, flowing with the previous pitches and at-bats in a game. I render here no judgment as to whether the strike zone ought to be this way. I’m only noting that according to all available evidence, it is this way.

As a first pass approximation, it’s okay to think of the zone as that imaginary rectangular solid, i.e. in its unicorn form. But with the greater granularity afforded us by PITCHf/x data, we can do better. We ought to reckon strike calls in terms of their probabilities. In so doing, we can get a more accurate and authentic picture of a hitter’s plate discipline. The decision to swing is indefensible on a pitch four feet off the edge of the plate, but perfectly understandable on a pitch painting the black.