A team of Northwestern and Columbia university researchers analyzed more than 700,000 (pitches) thrown during the 2008 and 2009 seasons. They found that umpires called about 14 percent of nonswinging pitches wrong. And umps were least (accurate) when the game was on the line in the ninth inning and when calling a strike would end an at-bat. They also tended to favor All-Star pitchers, especially those with a (reputation) for good control.

Of course, there’s no way to know how (challenging) a handful of the hundreds of pitches thrown in any given game would affect the outcome. And you might create a different umpire bias—against managers who demand too many replays.