HOW IMPORTANT ARE UMPIRE ERRORS ON BALLS AND STRIKES?

HOW IMPORTANT ARE UMPIRE ERRORS ON BALLS AND STRIKES? In his article, Todd Lindbergh cites studies by sabermatricians that estimate the average value of turning a single ball into a strike at 0.13 runs. I posted here about a study that showed error rates by individual major league umpires from 2008 to 20013. The percentage of errors was about 12.5% (or one eighth). Taking into account that about half of the pitches in an inning don’t need to be called by an umpire, and assuming 16 pitches per half inning, gives one umpire error per half inning. Over the course of a game, that would be equivalent to 16 times 0.13 runs per game or about two runs a game. If the mistakes split evenly, there is a only a small problem. If the split is roughly 9 to 7, the mistakes would amount to 0.25 runs a game.